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MODELING OF STANDING COLUMN WELLS IN GROUND SOURCE HEAT PUMP SYSTEMS By ZHENG DENG Bachelor of Science Shenyang Architectural and Civil Engineering Institute Shenyang, P. R. China 1996 Master of Science Tongji University Shanghai, P. R. China 2000 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY December, 2004 ii MODELING OF STANDING COLUMN WELLS IN GROUND SOURCE HEAT PUMP SYSTEMS Thesis Approved: Dr. Jeffrey Spitler Thesis Adviser Dr. Daniel Fisher Dr. David Lilley Dr. James Bose Dr. Gordon Emslie Dean of the Graduate College iii ACKNOWLEDGEMENTS I owe a lot to my advisor, Dr. Jeffrey Spitler, who first introduced me to the fascinating areas of geothermal technology and building energy simulation, which I have enjoyed greatly ever since. Dr. Spitler taught me how to do research: how to understand a problem from a fundamental level, how to spell out the core idea of a solution, and how to strike a good balance between being intuitive and being rigorous. An excellent speaker himself, he also taught me how to give good talks, which I found extremely useful. I thank him for his constructive guidance, constant support, patience, direction, and inspiration throughout my graduate study. Without his timely encouragement and support, this work would not have been done. I would like to extend my sincere gratitude and appreciation to Dr. Simon Rees who served as coadvisor along the course of the research before he returned to the U.K. His expertise in computational methods was quite valuable in helping me to achieve the project goals. My appreciation also extends to the members of my doctoral committee, Dr. Daniel Fisher, Dr. David Lilley, and Dr. Jim Bose for their committed service and support, ideas, and suggestions that helped improve my work significantly. iv I wish to deliver special credit to Mr. Carl Orio of the Water and Energy System Corporation for advice on standing column well design and operation and to Mr. Hugh Henderson of the CDH Energy Corporation for his generous assistance in providing experimental data used in validation of the standing column well system model. I would also like to thank my colleagues at the Building and Environmental Thermal Systems Research Group in Oklahoma State University, both present and former, namely, Andrew Chiasson, Xiaobing Liu, Dongyi Xiao, Weixiu Kong, Tracy Xiao, Xiaowei Xu, Haider Khan, and Bereket Nigusse for their ideas and precious help in a direct or indirect way. I am indebted to my parents, twin sister, and my brother who constantly support my every pursuit. Whatever I am today is because of their love, understanding, encouragement, and sacrifices. My infinite thanks go to Rob, absolutely for everything. This work was partially supported by the ASHRAE RP1119, and partially supported by an ASHRAE GrantinAid scholarship. ASHRAE’s support is gratefully acknowledged. v TABLE OF CONTENTS CHAPTER .................................................................................................................PAGE 1. INTRODUCTION.......................................................................................................... 1 1.1. Operation ................................................................................................................. 4 1.2. Application (limitations and benefits) ..................................................................... 6 1.3. Basic physical mechanism in SCWs (heat transfer and mass transfer in porous media) ............................................................................................................................. 9 2. BACKGROUND AND LITERATURE REVIEW...................................................... 14 2.1. Bose et al. (1979) Geothermal well system.......................................................... 14 2.2. Braud and Oliver’s research (1980’s).................................................................... 16 2.3. Tan and Kush’s research (1986) ............................................................................ 19 2.4. Mikler’s research (1995)........................................................................................ 21 2.4.1. Numerical study.............................................................................................. 21 2.4.2. Experimental study ......................................................................................... 25 2.5. Orio’s research....................................................................................................... 28 2.6. Some typical installations of SCW systems .......................................................... 32 2.6.1. Haverhill public library................................................................................... 32 2.6.2. SCW application in China .............................................................................. 33 2.7. “Geohill”open hole coaxial thermal well ............................................................. 35 2.8. Summary of the different research related to SCWs ............................................ 36 2.9. Some related analytical solutions (to ground source heat pump) .......................... 39 2.9.1. Kelvin line source solution ............................................................................. 40 2.9.2. Cylindrical heat source solution...................................................................... 43 2.9.3. Analytical solution considering the movement of groundwater (groundwater gfunction)................................................................................................................. 49 vi CHAPTER .................................................................................................................PAGE 2.10. Related research  aquifer thermal energy storage (ATES) ................................. 51 2.11. Effect of groundwater flow on closedloop groundcoupled heat exchangers .... 55 2.12. Numerical groundwater flow and heat transport models..................................... 57 2.12.1. Numerical model THETA............................................................................. 59 2.12.2. Numerical model SUTRA............................................................................. 61 2.12.3. Other Numerical models ............................................................................... 63 2.13. Summary of the literature .................................................................................... 65 3. DEFINITION OF THE PROBLEM AND OBJECTIVES........................................... 69 4. DETAILED MODEL FOR STANDING COLUMN WELL SYSTEMS.................... 72 4.1. Descriptions of the model ...................................................................................... 73 4.1.1. Hydrological flow in the SCW systems.......................................................... 73 4.1.1.1. Hydrological flow in the aquifer (porous medium) ................................. 74 4.1.1.2. Hydrological flow in borehole ................................................................. 75 4.1.2. Heat transfer mechanism in SCW systems ..................................................... 76 4.1.2.1. Heat transfer in the aquifer (porous medium).......................................... 77 4.1.2.2. Heat transfer in the borehole.................................................................... 82 4.1.2.2.1. Convective heat transfer in the borehole .......................................... 87 4.1.3. Computer algorithm........................................................................................ 92 4.2. Experimental validation....................................................................................... 101 4.2.1. Ideal experiment............................................................................................ 101 4.2.2. Validation with data from SCW system at Pennsylvania State University .. 102 4.2.2.1. Experimental data .................................................................................. 103 4.2.2.2. Methodology for validation ................................................................... 107 4.2.2.3. Validation results and conclusions......................................................... 110 4.2.3. Validation with data from a SCW system in the Haverhill public library.... 114 4.2.3.1. Experimental data .................................................................................. 114 4.2.3.2. Methodology for validation ................................................................... 116 4.2.3.3. Preprocessing the data .......................................................................... 118 vii CHAPTER .................................................................................................................PAGE 4.2.3.4. Validation results and conclusions......................................................... 120 4.3. The base case ....................................................................................................... 122 4.3.1. Building loads ............................................................................................... 123 4.3.2. Base case SCW design.................................................................................. 124 4.3.3. Results for base case ..................................................................................... 126 5. PARAMETRIC STUDY ............................................................................................ 130 5.1. Organization of parametric study ........................................................................ 130 5.2. Methodology of parametric study........................................................................ 131 5.3. Parameter values .................................................................................................. 132 5.4. System energy calculations.................................................................................. 136 5.4.1. System pressure drop without bleed ............................................................. 136 5.4.2. System pressure drop with bleed .................................................................. 138 5.4.3. Heat pump model .......................................................................................... 140 5.4.4. Circulating pump model ............................................................................... 141 5.4.5. Frictional Pressure Losses............................................................................. 141 5.4.6. Electricity costs ............................................................................................. 144 5.5. Parametric study results ....................................................................................... 144 5.5.1. The effect of thermal conductivity................................................................ 149 5.5.2. The effect of specific heat capacity............................................................... 149 5.5.3. The effect of natural geothermal gradients ................................................... 150 5.5.4. The effects of hydraulic conductivity ........................................................... 151 5.5.5. The effect of surface roughness of borehole wall ......................................... 155 5.5.6. The effect of borehole diameter .................................................................... 156 5.5.7. The effect of casing (liners) .......................................................................... 157 5.5.8. The effects of dip tube insulation and diameter............................................ 158 5.5.9. The effect of bleed ........................................................................................ 160 5.5.10. The effect of the depth of borehole............................................................. 161 5.5.11. The effect of varied depth with different bleed rate.................................... 162 viii CHAPTER .................................................................................................................PAGE 5.5.12. The effect of different rock type ................................................................. 163 5.5.13. The effect of bleed control strategy ............................................................ 164 5.5.14. System energy consumption and costs ....................................................... 168 5.5.15. Summary of parametric study..................................................................... 177 6. SIMPLIFIED MODEL FOR STANDING COLUMN WELL SYSTEMS ............... 179 6.1. Simplified onedimensional model...................................................................... 182 6.1.1. Governing energy equation........................................................................... 183 6.1.2. Groundwater velocity.................................................................................... 184 6.1.3. Boundary conditions ..................................................................................... 185 6.1.4. Borehole heat transfer ................................................................................... 187 6.1.5. Shortcircuiting ............................................................................................. 192 6.1.6. Solution of equations .................................................................................... 198 6.1.7. One dimensional numerical model with enhanced thermal conductivity..... 203 6.2. Experimental validation....................................................................................... 212 6.3. Simplified “bypass” approximation ................................................................... 216 7. ECONOMIC PERFORMANCE ANALYSIS............................................................ 222 7.1. HVACSIM+ models ............................................................................................ 222 7.1.1. The standing column well model .................................................................. 224 7.1.2. The heat pump model.................................................................................... 228 7.1.3. The water pump model ................................................................................. 229 7.1.4. The vertical Utube ground loop heat exchanger model............................... 229 7.1.4. Building description and loads calculation ................................................... 231 7.2. Simplified design procedure for standing column well system........................... 232 7.3. Economic analysis ............................................................................................... 236 7.4. Simulation results and discussions ...................................................................... 238 8. CONCLUSIONS AND RECOMMENDATIONS ..................................................... 255 ix CHAPTER .................................................................................................................PAGE 9. REFERENCES ........................................................................................................... 260 APPENDIX A................................................................................................................. 272 Numerical characteristics of the detailed model ..................................... 272 APPENDIX B................................................................................................................. 287 Grid generation input file........................................................................ 287 APPENDIX C................................................................................................................. 290 Preprocessing of flow rate for the experimental validation in Haverhill library...................................................................................................... 290 APPENDIX D................................................................................................................. 294 Calculation of shortcircuiting heat flux by integral method.................. 294 APPENDIX E ................................................................................................................. 299 Correlation for enhanced thermal conductivity ...................................... 299 x LIST OF TABLES TABLE……………………………………………………………………………...PAGE Table 21 Summary of experimental research related to SCWs....................................... 37 Table 22 Summary of the modeling of SCWs................................................................. 38 Table 23 Numerical models for groundwater.................................................................. 58 Table 24 Summary of the different numerical and analytical models............................. 68 Table 41 Hydraulic and thermal properties of the rock (Karst limestone).................... 108 Table 42 Properties of the borehole............................................................................... 108 Table 43 Hydraulic and thermal properties of the Ordovician and Cambrian sedimentary rock ......................................................................................................................... 117 Table 44 Properties of the borehole in Haverhill library............................................... 117 Table 51 Parametric study parameter values................................................................. 133 Table 52 Electric utility monthly average cost per kilowatthour for Massachusetts ... 144 Table 53 Parametric study results – effect of parameter variations on minimum and maximum exiting water temperatures and design length........................................ 147 Table 54 Results for different roughness height cases .................................................. 155 Table 55 Energy calculation results (water table = 5.0 m)............................................ 170 Table 56 Energy calculation results (water table = 30.0 m).......................................... 173 Table 61 Some information for determining building loads ......................................... 207 Table 62 Enhanced thermal conductivity from numerical insitu experiment .............. 209 Table 63 Rock thermal conductivity for different models using Mikler’s data ............ 213 Table 64 Rock thermal conductivity for different models using Haverhill data........... 213 Table 65 Difference between two limiting cases .......................................................... 218 Table 71 Installation costs for different ground heat exchanger system....................... 237 Table 72 Electric utility monthly average cost per kilowatthour for commercial building in different states..................................................................................................... 238 xi TABLE……………………………………………………………………………...PAGE Table 73 Summary of ground heat exchanger design parameters for Boston, MA...... 239 Table 74 Summary of ground heat exchanger simulation results for Boston weather file ................................................................................................................................ 240 Table 75 Annual energy cost breakdowns for SCW system deadband bleed control in Boston, MA............................................................................................................. 244 Table 76 Far field temperatures and building loads for different cities ........................ 245 Table 78 Summary of ground heat exchanger simulation results for Harrisburg, PA .. 247 Table 79 Summary of ground heat exchanger simulation results for Portland, OR...... 248 Table 710 Summary of ground heat exchanger simulation results for Concord, NH... 249 Table 711 Summary of ground heat exchanger simulation results for Birmingham, AL ................................................................................................................................ 250 Table 712 Feet per ton for different ground heat exchangers ....................................... 251 Table 713 Comparisons of capital cost for different cites............................................. 253 Table 714 20year life cycle cost (present values) for different cites ........................... 254 Table E1 Enhancement factor for different cases.......................................................... 302 xii LIST OF FIGURES FIGURE……………………………………………………………………………...PAGE Figure 11 Schematics of different ground source heat pump systems .............................. 3 Figure 12 A schematic drawing showing the borehole arrangement ................................ 5 Figure 13 How Groundwater occurs in rocks.................................................................... 9 Figure 14 A typical schematic of standing column well ................................................. 13 Figure 21 Geothermal well design (Bose et al. 1979).................................................... 15 Figure 22 Concentric well pipes for thermal exchange to earth with liquid source heat pump (Oliver and Braud 1981) ................................................................................. 16 Figure 23 A schematic ‘thermal well’ studied by Yuill and Mikler (1995).................... 21 Figure 24 Schematics of standing column well from description of Orio (Orio 1999) .. 31 Figure 25 Standing column well water temperature trends in Haverhill public library.. 33 Figure 26 The schematic drawing of “single well for supply and return” (HYY 2003) . 34 Figure 27 Open hole coaxial thermal well “Geohill”...................................................... 36 Figure 28 Schematic drawing showing the cylindrical heat source embedded in an infinite medium......................................................................................................... 40 Figure 29 A schematic drawing of a core separated by the insulation from the sheath .. 47 Figure 210 Heat storage in an aquifer ............................................................................. 52 Figure 41 Distribution of the fluid pressure in the ground with respect to the water table .................................................................................................................................. 74 Figure 42 Heat transfer mechanisms in SCW systems.................................................... 77 Figure 43 The relationship between the actual thermal conductivity and the mechanisms that contribute to it .................................................................................................... 78 Figure 44 Control volume for the solidliquid phase ...................................................... 79 Figure 45 The borehole thermal model ........................................................................... 83 Figure 46 A schematic control volume in the borehole .................................................. 84 xiii FIGURE……………………………………………………………………………...PAGE Figure 47 The geometry of a typical cell in the mesh showing the relationship between the face and cell centroids......................................................................................... 94 Figure 48 Flowchart of computer algorithm for the overall SCW systems .................... 97 Figure 49 A 2D cylindrical grid of single standing column well .................................. 100 Figure 410 Cooling modeground load ......................................................................... 104 Figure 411 Cooling modetotal water flow rate ............................................................ 104 Figure 412 Cooling modeentering and return water temperatures............................... 105 Figure 413 Heating modeground load.......................................................................... 106 Figure 414 Heating modetotal water flow rate ............................................................ 106 Figure 415 Heating modeentering and return water temperatures............................... 107 Figure 416 Comparisons of temperatures back to the heat pump for the detailed model and Mikler’s data in cooling mode ......................................................................... 111 Figure 417 Comparisons of temperatures back to the heat pump for the detailed model and Mikler’s data in heating mode.......................................................................... 112 Figure 418 Water temperatures entering and leaving the well in Haverhill.................. 115 Figure 419 System flow rates in Haverhill library ........................................................ 119 Figure 420 Comparison of temperatures back to heat pump for the detailed model and Haverhill data.......................................................................................................... 121 Figure 421 Building load of a building in Boston......................................................... 124 Figure 422 A schematic drawing showing the borehole geometric arrangement for the base case.................................................................................................................. 125 Figure 423 Borehole temperatures when peak heating load occurs .............................. 127 Figure 424 Borehole temperatures when peak cooling load occurs.............................. 127 Figure 425 Borehole suction and discharge temperatures and building loads for the base case.......................................................................................................................... 128 Figure 426 Head contours for the base case.................................................................. 129 Figure 51 Pipe system schematic for cases without bleed ............................................ 136 Figure 52 Pipe system schematic for cases with bleed.................................................. 138 Figure 53 Schematic diagram of the pipe work showing the arrangement of fittings .. 143 xiv FIGURE……………………………………………………………………………...PAGE Figure 54 Relationship between EWT and length of borehole ..................................... 146 Figure 55 The effect of thermal conductivity of rock on the water temperature back to the heat pump.......................................................................................................... 149 Figure 56 The effect of specific heat capacity of rock on the water temperature back to the heat pump.......................................................................................................... 150 Figure 57 The effect of natural geothermal gradients of rock on the water temperature back to the heat pump ............................................................................................. 151 Figure 58 The effect of hydraulic conductivity of rock on the water temperature back to the heat pump.......................................................................................................... 151 Figure 59 Total heat transfer rates along the borehole wall in the different cases of varied hydraulic conductivity ............................................................................................ 152 Figure 510 The effect of roughness height of borehole wall on the water temperature back to the heat pump ............................................................................................. 156 Figure 511 The effect of borehole diameter on the water temperature back to the heat pump ....................................................................................................................... 157 Figure 512 The effect of casing length on the water temperature back to the heat pump ................................................................................................................................ 158 Figure 513 The effect of thermal insulation of the dip tube on the water temperature back to the heat pump ............................................................................................. 159 Figure 514 The effect of diameter of dip tube on the water temperature back to the heat pump ....................................................................................................................... 159 Figure 515 The effect of bleed rate on the water temperature back to the heat pump .. 160 Figure 516 The effect of depth of borehole on the water temperature back to the heat pump ....................................................................................................................... 161 Figure 517 The effect of depth of borehole on the water temperature back to the heat pump ....................................................................................................................... 162 Figure 518 The effect of rock type on the water temperature back to the heat pump... 164 Figure 519 The effect of bleed control strategy on the minimum water temperature back to the heat pump in winter....................................................................................... 166 xv FIGURE……………………………………………………………………………...PAGE Figure 520 Comparison water temperatures back to the heat pump between nonbleed case, constant bleed and deadband bleed control case............................................ 167 Figure 521 Entering and exiting fluid temperature difference during the heating season under temperaturedifference bleed control showing the points at which bleed was activated .................................................................................................................. 168 Figure 522 Comparison of annual energy costs for water table depths of 5 m and 30 m ................................................................................................................................ 176 Figure 61 Two limiting cases for standing column well system................................... 180 Figure 62 Schematic drawing showing 1D model for the SCW system...................... 186 Figure 63 Water temperature variation along borehole depth without bleed................ 188 Figure 64 Water temperature variation along borehole depth with bleed ..................... 188 Figure 65 The simplified thermal borehole model ........................................................ 189 Figure 66 Crosssection of the borehole in SCW system and the corresponding thermal circuit ...................................................................................................................... 192 Figure 67 Thermal resistances of a D circuit .............................................................. 194 Figure 68 Flow chart for the simplified onedimensional model .................................. 199 Figure 69 Sensitivity of borehole wall temperatures to the grid number in FDM........ 201 Figure 610 The flow chart to get actual /enhanced thermal conductivity ..................... 205 Figure 611 Comparison of minimum temperatures back to the heat pump in different models ..................................................................................................................... 209 Figure 612 Comparison of maximum temperatures back to the heat pump in different models ..................................................................................................................... 210 Figure 613 Comparison of the minimum exiting water temperatures from the well in different models with ground temperature gradient................................................ 212 Figure 614 Comparisons of temperatures back to the heat pump for the simplified model (SCW1D), the detailed model, and Mikler’s data in cooling mode........................ 214 Figure 615 Comparisons of temperatures back to the heat pump for the simplified model (SCW1D), detailed model, and Mikler’s data in heating mode.............................. 215 xvi FIGURE……………………………………………………………………………...PAGE Figure 616 Comparisons of temperatures back to the heat pump for the simplified model (SCW1D), the detailed model, and Haverhill data ................................................. 216 Figure 617 Standing column well showing bleed and bypass flows ........................... 217 Figure 618 Comparison of temperatures back to the heat pump in limiting cases........ 219 Figure 619 Comparison of temperatures back to the heat pump in limiting cases (winter) ................................................................................................................................ 219 Figure 620 Comparison of temperatures back to the heat pump in limiting cases (summer) ................................................................................................................. 220 Figure 71 Threecomponent models of a standing column well system in HVACSIM+ ................................................................................................................................ 223 Figure 72 Component configuration of standing column well model........................... 225 Figure 73 Component configuration of vertical ground loop heat exchanger............... 230 Figure 74 A peak of cooling load event in Boston, MA small office building ............. 232 Figure 75 Flow chart for simplified design procedure .................................................. 233 Figure 76 Required total borehole depth for different ground heat exchanger systems in Boston, MA............................................................................................................. 241 Figure 77 20year life cycle cost (present value) in Boston, MA ................................. 241 Figure 78 Annual energy cost for SCW systems for bleed control operation in 5meter and 30meter water table depths with different bleed rates in Boston, MA ........... 244 Figure 79 Feet per ton for different ground heat exchangers for small office building 251 Figure 710 Required total borehole depth for different ground heat exchanger systems in different cities ......................................................................................................... 252 Figure 711 Capital cost for different ground heat exchanger systems in different cities ................................................................................................................................ 253 Figure 712 20year cycle cost (present value) for different ground heat exchanger systems in different cities........................................................................................ 254 Figure A1 The schematics of simulation domain.......................................................... 274 Figure A2 Sensitivity of integral mass flow rate to the domain depth (Domain radius: 200m) ...................................................................................................................... 277 xvii FIGURE……………………………………………………………………………...PAGE Figure A3 Sensitivity of minimum temperature back to the heat pump to the domain depth (Domain radius: 200m) ................................................................................. 277 Figure A4 Sensitivity of temperature back to the heat pump at the 8760th hour to the domain depth (Domain radius: 200m) .................................................................... 278 Figure A5 Sensitivity of integral mass flow rate to the domain radius (Domain depth: 380m) ...................................................................................................................... 279 Figure A6 Sensitivity of minimum temperature back to the heat pump to the domain radius (Domain depth: 380m) ................................................................................. 279 Figure A7 Sensitivity of temperature back to the heat pump at the 8760th hour to the domain radius (Domain radius: 380 m) .................................................................. 280 Figure A8 Sensitivity of integral mass flow rate to grid number in depth direction (Grid number in Rdirection: 200).................................................................................... 281 Figure A9 Sensitivity of minimum temperatures back to the heat pump to the grid number in depth direction (Grid number in Rdirection: 200)................................ 281 Figure A10 Sensitivity of integral mass flow rate to grid number in radial direction (Grid number in depth direction: 160).............................................................................. 282 Figure A11 Sensitivity of minimum temperatures back to the heat pump to the grid number in radial direction (Grid number in depth direction: 160) ......................... 283 Figure A12 Sensitivity of temperatures back to heat pump to the timestep size ......... 286 Figure D1 Illustration of calculation of shortcircuiting flux........................................ 295 Figure E1 Data density plot........................................................................................... 301 Figure E2 Threedimensional relationship among the enhanced factor, hydraulic conductivity and effective thermal conductivity..................................................... 303 xviii NOMENCLATURE a the radius of pipe(m [ft]) bleedrate the normalized bleed rate in the system (%) B the integration variable C the summation of the series ¥ = + ×  1 1 ( !) ( 1) N N N N N y Cp the specific heat of the ground(J/kgK [Btu/lbmºF]) pw C the specific heat of water (J/kgK [Btu/lbmºF]) D the distance in feet to the recharge well (m [ft]) Dborehole the hydraulic diameter of borehole (m [ft]) f the Moody friction factor Fo the Fourier number defined as: 2 0 r Fo =at g the acceleration due to the gravity (m/s2 [ft/s2]) f G the groundwater factor (+ denotes flow into the well;  denotes flow out of the well) h the hydraulic head (m [ft]) hborehole the heat transfer coefficient at the borehole wall (W/m2K [Btu/hrft2ºF]) H the total dynamic head for the water pump (Pa) Ji the Bessel function of order i xix s k the thermal conductivity of the ground (W/mK [Btu/hrftºF]) kwater the thermal conductivity of water (W/mK [Btu/hrftºF]) eff k the effective thermal conductivity (W/mK [Btu/hrftºF]) k the intrinsic permeability (m2 or Darcy [ft2]) K the hydraulic conductivity of ground (m/s [gpd/ft2]) Keff the effective hydraulic conductivity (m/s [ft/s]) L the borehole depth (m [ft]) m w the mass flow rate of water through heat pump system (kg/s [lbm/sec]) m the mass of water in the standing column well (kg [lbm]) n the porosity of rock Nu the local Nusselt number p the pressure (N/m2 [lbf/ft2]) Pr the Prandtl number q the specific discharge (m/s [ft/s]) q'' the heat flux (W/m2 [Btu/hrft2]) q the specific discharge (volume flow rate per unit of crosssectional area) (m/s [gpd/ft2]) qsc the shortcircuiting heat transfer rate (W/m [Btu/fthr]) R the far field radius rb the borehole radius (m [ft]) Rb the thermal resistance of the borehole (K/(W/m) [hrftºF/Btu]) xx Rsc the short circuiting thermal resistance (K/(W/m) [hrftºF/Btu]) Ree the roughness Reynolds number e e / Re / 2 Re D f = S1 the thermal capacity of the cylinder of perfect conductor (J/m3K [Btu/ft3ºF]) t the heat pump run time (hr) Tb the borehole wall temperature (ºC [ºF]) f 1 T the temperature of water in the annulus (ºC [ºF]) f 2 T the temperature of water in the dip tube (ºC [ºF]) Tf the average fluid temperature (ºC [ºF]) Tfo the water temperature leaving the well (ºC [ºF]) Tfi the water temperature returning to the well (ºC [ºF]) Tf _ old the representative water temperature at the previous time step (ºC [ºF]) T q (t) f the average fluid temperature at time t (ºC [ºF]) Tgw the temperature of groundwater entering into the well (ºC [ºF]) Tr the far field temperature (ºC [ºF]) Tu the undisturbed temperature of the ground (ºC [ºF]) Tw the borehole wall temperature (ºC [ºF]) Tfreeze the fluid temperature at freezing point (oC [ºF)]) TExFT the exiting fluid temperature from the heat pump (i.e., the fluid temperature entering the ground heat exchanger) (oC [ºF)]) xxi TEFT the entering fluid temperature to the heat pump (i.e., the fluid temperature leaving the ground heat exchanger) (oC [ºF)]) u the integration variable V the mean velocity in the given pipe(m/s [ft/s]) Vr the average linear groundwater velocity vector (m/s [ft/s]) w the power consumption of the circulating water pump (W) Yi the modified Bessel function of order i z the vertical coordinate (m [ft]) a the thermal diffusivity of the ground (m2/s [ft2/hr]) b the underrelaxation factor l the integration variable g the Euler’s constant, 0.5772157… r the density of the ground (kg/m3[lbm/ft3]) r w the density of the groundwater (kg/m3 [lbm/ft3]) rc the volumetric heat capacity (J/m3K [Btu/ft3ºF]) 2 rv2 the velocity pressure (Pa) rgz the elevation pressure (Pa) n the kinematic fluid viscosity (m2/s [ft2/sec]) e the height of the surface roughness (m [ft]) m the dynamic viscosity of water (Ns/m2 [lbfs/ft]) h the efficiency of the circulating water pump T the fluid temperature change across the heat pump (oC [ºF)]) xxii Dt the time increment(sec [sec]) Dp the total pressure loss (fitting +friction) (Pa) sc DT the temperature difference caused by the short circuiting (ºC [ºF]) 1 1. INTRODUCTION In recent years, ground heat source heat pump systems have become increasingly popular for use in residential and commercial buildings. These systems include several different variations, all of which reject heat and/or extract heat from ground: (1) groundcoupled heat pump (GCHP) systems; (2) surface water heat pump (SWHP) systems; (3) groundwater heat pump (GWHP) systems: a. Standing column well (SCW) systems; b. Open loop groundwater systems. The schematics of these different systems are shown in Figure 11. Considerable research effort has been spent on ground heat source heat pump systems, especially on the single Utube ground heat exchanger, in recent decades. Existing engineering design manuals, such as IGSHPA (1988), ASHRAE (1995), Kavanaugh and Rafferty (1997), cover the first two system types and open loop groundwater systems. However, relatively few design tools and simulation models are available for SCW systems. SCW systems are the focus of this research. SCW systems are also referred to in the literature as “turbulent wells”, “energy wells”, “concentric wells”, “recirculating wells”, “geowells”, “thermal wells”, and “closedloop, openpipe systems”. Rawlings and Sykulski (1999) stated that the first documented suggestion of using the ground as a heat source was in 1912 in Switzerland, and the first ground source heat 2 pump in North America was installed in a house in Indianapolis in 1945. However, commercial use of the ground as a heat source/sink didn’t begin until the first oil crisis in 1973. By the mid 1980’s, advances in heat pump efficiencies and operating ranges, combined with better materials for ground loops, allowed this technology to enter the market. At the same time, commercial type applications started to gain popularity. Geothermal systems have the potential to reduce primary energy consumption and thus significantly reduce the emission of greenhouse gases and other pollutants. The use of SCW was first suggested by local Maine well drillers and hydrogeologists (Orio 1994). In fact, the concept of standing column well systems is about as old as the ground water heat pump systems, but is recently receiving much more attention because of their lower installation cost, lower operating cost, and improved overall performance in the regions with suitable geological conditions. In the mid1970’s, Dr. Bose from Oklahoma State University began to do field tests on standing column well systems. Later, Dr. Braud from Louisiana State University further evaluated this technology. Compared with other ground heat source heat pump systems, shorter boreholes and more stable water temperatures make the SCW system an attractive commercial and industrial design approach. Now, there are approximately 1000 SCW installations in the United States. Most of them are located in the Northeast and Pacific Northwest in addition to parts of Canada in heatingdominated residential and light commercial applications (ASHRAE 1119TRP). These regions have lower mean ground temperature and higher heating loads than other areas, so now most SCW design is focused on heat extraction. 3 Figure 11 Schematics of different ground source heat pump systems (Reprinted by permission from Oak Ridge National Laboratory) (http://www.eren.doe.gov/femp) 4 1.1. Operation The SCW system can be thought of as a cross between closedloop earthcoupled system and openloop groundwater source system. During much of the year, they operate by recirculating water between the well and the heat pump. However, during peak temperature periods, they can “ bleed” some water from the system to induce groundwater flow. Usually, only one well is required; larger projects may have several wells in parallel. In SCW systems, water is recirculated between the well and the building (heat pump). Deep bores are drilled in hard rock, creating a standing column of water from the static water level down to the bottom of the bore. Water is recirculated from one end of the column to the heat pump, and back to the other end of the column (Figure 12). 5 A A AA section Discharge Tube Ground Surface Borehole Wall (Suction Tube) Dip Tube Heat Pump Water Table Dip Tube Discharge Tube Figure 12 A schematic drawing showing the borehole arrangement During peak heat rejection or extraction periods, if the wellwater temperature drops too low or climbs too high, standing column well systems can bleed part of the water rather than returning it all to the well. This causes water to flow to the column from the surrounding formation to make up the flow. This cools the column and surrounding ground during heat rejection in the summer, and heats the column and surrounding ground during heat extraction in the winter, thus restoring the wellwater temperature to the normal operating range and improving the system performance. The bleed water can be diverted to a storm sewer, used for domestic water consumption, or otherwise 6 disposed. Sometimes, SCW systems serve to provide household domestic water, which cause the system to naturally “bleed” the whole year. 1.2. Application (limitations and benefits) SCW systems are used in geologic areas with abundant ground water. This system can provide the necessary water flows as well as shorter heat transfer lengths (depths) and the ability to return water to the same aquifers. The combination of relatively shallow water table and a deep well (sometimes greater than 300 m or 1000 ft) means that the well has a large water volume, about 1800 L per 100 m (150 gal per 100 ft) for a 152.4 mm (6 in) nominal diameter well (Sachs and Dinse 2000). Based on experience by the Water and Energy Systems Corporation, 50 to 60 feet of water column is needed per ton of building load (4.3m/kW to 5.2m/kW). Commercial systems larger than 350 kW (100 tons) have used multiple standing column wells with success (Orio 1994). The application of SCW systems is limited to geologic regions with good ground water quality like other ground water heat pump systems. This enables the ground water to be directly circulated through the heat pump. Applications also exist in areas with poorer water quality. In such situations it is common practice to use an intermediate heat exchanger between the well and the heat pump in order to avoid fouling the heat pump heat exchangers. Sachs and Dinse (2000) suggested that the designer of SCW systems should (1) work with an experienced local hydrologist and (2) avoid any areas with salt bed or other 7 formation that could be dissolved. Also, any water well including standing column wells must be constructed, developed, and operated according to state and local regulations for water wells. It is imperative that designers and installers of SCW systems be aware of the regulations in their locations (DenBraven 2002). Generally speaking, SCW systems have some advantages shared with all the other forms of ground source heat pump systems: · Economy When properly designed, a geothermal heat pump system is one of the lowest cost ways of providing heating/cooling because of high equipment efficiency, annual storage/reuse of energy, and availability. However, geothermal heat pump systems have comparatively high capital costs. A geothermal system often has lower life cycle costs than conventional systems due to its reduced energy and maintenance costs. Because there is no outdoor equipment in the geothermal systems, corrosion, weathering and vandalism are not normal problems. · Environmental benefits The need for electricity (pumps) introduces the only credible source of possible environmental concern for a geothermal system. The geothermal system itself produces zero local pollution. This system causes less carbon dioxide emission and other pollutants than its conventional alternatives, thus reducing global warming and other environmental impacts. 8 · Reduced requirement for mechanical room floor place · Quiet operation · Potential for reducing the peak electrical demand Standing column well systems share the same advantages, in terms of energy efficiency, environmental benefits, low maintenance, etc. with other forms of geothermal heat pump systems. At the same time, the heat exchange rate in a standing column well is enhanced by direct contact and by the pumping action, which promotes ground water flow to and from the borehole. Consequently heat transfer with the surrounding rock takes place by advection in addition to conduction. If a standing column well is considered as a cylinder, the surface area for heat exchange of a 152.4 mm (6 in) borehole with 304 m (1000 ft) long is about 145 m2 (1570 ft2), which allows substantial heat exchange. Put another way, SCW systems have substantially heat exchange rate and the fact that such systems are open loop means that the fluid flowing through the heat pump system is closer to the mean ground temperature compared to systems with closed loop Utube heat exchangers. SCW systems have a lower initial cost because the borehole depths are in the 5060 feet per ton compared to closed loops at 150 or more feet per ton. Thus, the borehole in SCW systems could be onehalf the depth of closed loop earth coupled methods (Orio, 1994). To date, the typical drill rigs in the regions where SCW system are mainly located (Northeast and Pacific Northwest), can be able to reach 560 m (1800 ft) and the deepest standing column wells are in the range of 460 m (1500 ft). The depth of this costeffective geothermal coupled method can be extended with the development of rigs. 9 1.3. Basic physical mechanism in SCWs (heat transfer and mass transfer in porous media) First, some definitions are given for later use. Above the water table lies the unsaturated zone, where voids between rocks are mostly filled with air. Some water is held in the unsaturated zone by molecular attraction, and it will not flow toward or enter a well. In the saturated zone, which lies below the water table, all the openings in the rocks are full of water that may move through the aquifer to streams, springs, or wells from which water is being withdrawn (see Figure 13). This research is mainly focused on the saturated zone. Figure 13 How Groundwater occurs in rocks* (http://capp.water.usgs.gov/GIP/gw_gip/how_occurs.html) * Public resource provided by USGS website 10 The energy transport in the ground outside of the standing column well is through a porous media (aquifer). An “aquifer” is defined by Driscoll (1986) as formation, group of formations, or part of a formation that contains sufficient saturated permeable material to yield economical quantities of water to wells and springs. The word aquifer comes from the two Latin words, aqua, or water, and ferre, to bear or carry. An aquifer literally carries water underground. We can consider an aquifer as a porous medium that consists of a solid phase and an interconnected void space totally filled with groundwater. Transport of groundwater occurs in the interconnected voids. Heat is transported both in the solid matrix and in the void system, forming a coupled heat transfer process with heat diffusion (conduction) and heat advection by moving groundwater. The governing steady state, onedimensional equations for heat and fluid flow are given by Fourier’s law and Darcy’s law, which are identical in the form: Fourier’s law: dx dT q''= k (1.1) Where q''is heat flux (W/m2 [Btu/hrft2]); k is the thermal conductivity of the ground (W/mK [Btu/hftºF]); Darcy’s law: dx dh q = K (1.2) Where q is the specific discharge (volume flow rate per unit of crosssectional area) (m/s [gpd/ft2]); K is the hydraulic conductivity of ground (m/s [gpd/ft2]); h is the hydraulic head (m [ft]). 11 The specific discharge q is related to average linear ground water velocity v by: n q v = (1.3) Where n is the porosity, which, for a given crosssection of a porous medium, is the ratio of the pore area to the crosssectional area (Fetter 1988). The uncased borehole in SCW systems allows the heat exchange fluid to be in direct contact with the earth and allows ground water infiltration over the entire length of the borehole. This direct contact eliminates the conductive resistances of plastic pipe and grout associated with a typical earthcoupled Utube system. The presence of ground water enhances the usability of the ground as a heat source/sink. The larger heat capacity of the watersaturated soil/rock dampens the temperature changes in the ground compared with unsaturated soil/rock. Furthermore, the movement of ground water enhances the heat transfer. In addition, the rough borehole wall can induce turbulence; so higher heat transfer coefficients can be obtained. The moisture content of soil has a significant effect on its thermal properties. When water replaces the air between particles it reduces the contact resistance. The thermal conductivity can vary from 0.25 W/mK for dry soil to 2.5 W/mK for wet soil (Rawlings and Sykulski 1999). When heat is extracted/rejected, there will be migration of moisture by diffusion, thus the effective thermal conductivity will be increased. As mentioned above, ground water movement will have a significant impact on heat transfer through the ground because heat is transferred by convection due to moving 12 groundwater as well as conduction. In the presence of groundwater, buoyancy flows generated by the temperature differences also affect the temperature distribution in the ground. The presence of groundwater flow in SCW systems changes the heat transfer problem from pure heat conduction to a coupled flow and advectivediffusive heat transfer problem. Accordingly, heat transfer in the ground surrounding SCW systems is much more complicated and much more difficult to simulate. Also, the heat exchange fluid (water) in SCW systems is affected by the transient building thermal loads in addition to the heat transfer in the porous medium (aquifer) around the borehole of SCW systems. Therefore, this problem is characterized by timevarying boundary conditions. Through this research, we hope to make a more complete and much better understanding of the characteristics of standing column well systems, such as necessary well length per given load, preferred operating strategies (bleed, etc.) The first objective of this work is to analyze and evaluate the currently available research on standing column well systems. The second objective is to develop a detailed numerical model of standing column well systems. The third objective is to use the detailed numerical model to perform a parametric study of the effects and significance of standing column well design parameters. Finally, the fourth objective is to develop a simplified analytical and/or numerical model, which is feasible to be used as a design tool by HVAC engineers. 13 Figure 14 A typical schematic of standing column well (http://www.hvac.okstate.edu/ ) 14 2. BACKGROUND AND LITERATURE REVIEW Although there are numerous SCW systems installations in the United States, very little has been published on the theory of operation and modeling. The literature directly related to the standing column well, is reviewed first. Secondly, related research in the discipline of hydrogeology is reviewed. 2.1. Bose et al. (1979) Geothermal well system The first reported field research on SCW systems is described by Bose et al. (1979). This system was referred to as a “Geothermal well system”. The Geothermal well is somewhat different from the current standing column well (Figure 14). While it has a standing column, ground water cannot enter into the well because it is completely cased. A schematic of the Geothermal well is shown in Figure 21. A 5inch PVC pipe with cap at both ends, pressurized to about 15 psig (at the top of the well), is the most important component in this vertical heat exchanger. The water may be discharged to the top or bottom, and the discharge tube may be insulated. In the experimental well described by Bose et al. the water exiting the heat pump is discharged into the bottom of the 5inch PVC pipe by means of 11/4inch tube (the dip tube) running the length of the well. Regarding the location of the discharge pipe, Bose et al. (1979) did some tests during the summer. From the test results, it was found that the entering water temperature to the heat 15 pump would be lower when the hot water from the heat pump was discharged to the bottom of the well rather than to the top of the well. Also a series of tests have shown an improvement of approximately 20 % in Uvalues (overall heat transfer coefficient) for wells by using insulated dip tubes. MANHOLE AIR VENT SAMPLE VAVLE WELL CAP TO HEAT PUMP FROM HEAT PITLESS ADAPTER CONCRETE PLUG (REQUIRED BY HEALTH DEPT.) 1 PVC PIPE WATER TABLE 5'' PVC WELL CASING END CAP PUMP 1 4 '' Figure 21 Geothermal well design (Bose et al. 1979) 16 Since no exchange of water with the surrounding formation is allowed, this system cannot be expected to perform as well as a modern SCW system. 2.2. Braud and Oliver’s research (1980’s) HEAT PUMP EARTH CONCENTRIC PIPE IN WELL Figure 22 Concentric well pipes for thermal exchange to earth with liquid source heat pump (Oliver and Braud 1981) Analysis of steadystate heat exchange to earth with concentric well pipes and governing equations for fluid temperature distribution in the pipes were given by Oliver and Braud (1981). They derived a closedform analytical solution for the concentric vertical, groundcoupled heat exchanger under steadystate operation by assuming an isothermal 17 ground surface 10 m (3.3 ft) away from the center of the heat exchanger. The temperature difference between fluid in the annular area and the earth is the driving force for the heat transfer to the earth mass, and the temperature difference in the two pipes is the driving force for the crossover heat flow. Oliver and Braud’s analysis assumed steadystate, radial, conduction heat flow only. They didn’t account for the effect of ground water flow. Their analysis is based on the following assumptions: all physical parameters are independent of time, location, pressure and temperature; all heat flow is radial in the heat exchanger; the only mechanism for heat transfer is conduction (this has the effect of modeling a cased system as described by Bose); temperature in the fluid is constant at each cross section (inside pipe). They derived differential equations from the standpoint of conservation of energy for a control volume of fluid and surrounding ground, and solved them analytically. The general solution was given by: { } { } { Z} { Z} Z Z Z Z TR Z 2 2 1 1 2 2 2 1 1 1 1 2 exp exp ( 1) exp ( 1) exp ( ) ( ) ( ) l l l l l l l l l l q q  +  + = = (2.1) Where 1 1 0 q = T T ; 2 2 0 q = T  T ; mC U x Z = 21 ; 18 21 02 U b = U ; x is the coordinate of the position along the axis of the heat exchanger well (m [ft]), ( x = 0 at the bottom of well); 0 T is the earth temperature (ºC [ºF]); 1 T is the temperature of the fluid in the inner return pipe at position x (ºC [ºF]); 2 T is the temperature of the fluid in the annular area at position x (ºC [ºF]); m is the fluid circulation rate (kg/s [lbm/hr]); C is the specific heat of the fluid in the pipe (J/kgK [Btu/lbmºF]); 21 U is the fluid to fluid conductance of the inner pipe(W/mK [Btu/hrftºF]); 02 U is the conductance of the well casing plus earth cylinder (W/mK [Btu/hrftºF]), (includes film coefficient if appropriate); 1 2 l ,l are functions of b (the type of function was not described in this paper). In residential heating and cooling use, the operation of a heat pump is cyclic; the energy exchange to earth is highly transient rather than steady state. The steady state value from Oliver and Braud’s model (1981) underestimates the heat transfer during the whole year cyclic operation. It is therefore unrealistic to design the heat exchanger on the basis of its steady–state operation. Moreover, this model does not take into account the beneficial effect of the ground water flow and bleed. Braud et al. (1983) measured the heat exchange rate of earthcoupled concentric pipe heat exchangers in Louisiana State University. They noted greater conductance values of the 19 concentric pipes over the single Utubes when the concentric heat exchanger consisted of a steel outer casing (rather than PVC) and PVC inner pipes. Some thermal “shortcircuiting” could occur between the inner and outer flow channel, but this can be reduced with use of a low thermal conductivity inner pipe. 2.3. Tan and Kush’s research (1986) A 152 mm (6 in) diameter, 189 m (620 ft) deep standing column well located at Westchester County, NY, was used for this R&D/field test project. An offtheshelf, 5 ton waterto –air heat pump intended for groundwater use was installed in this residential building. Tan and Kush (1986) called the SCW a “semiclosed loop” because of the influx/outflow of ground water at fissures in the rock. While it is the first SCW system described with an uncased borehole, no bleed was utilized. Water was withdrawn at a depth of 12.2 m (40 ft) and the return water from the heat pump was reinjected at a depth of 183 m (600 ft). The fluid water flow rate was 0.6935 kg/s (11 gpm) with a 0.25 kW (1/3 hp) circulating pump at the ground level outside the well. The static water table level was at a depth of 1.52 m (5 ft). Water was discharged to the bottom of the well; thus the water supplied to the heat pump does not pass through the region of discharge. The well, heat pump and system parameters such as water temperature back to the heat pump, and from the heat pump were thoroughly measured and documented for a continuous 22month period in this field test project. Also, the linesource theory was used to approximately calculate the theoretical longterm seasonal temperature change of the earth surrounding the well as a function of radius. It was found that the best 20 agreement between the analytical and the actual ground temperature was obtained when a value of thermal conductivity of 2.6 Btu/fthrºF (an “enhanced” thermal conductivity) was used. This may be compared with the actually averaged one (less than 2.4 Btu/fthr ºF, which was assumed to be the value of granite rock surrounding the well). Tan and Kush (1986) didn’t use any insitu test method to obtain this actually averaged value of thermal conductivity. Presumably, they took the values directly from publicly available handbooks. Tan and Kush (1986) pointed out that SCW systems performed very well as earthcoupled devices in both heating and cooling season. They measured the entering water temperature (EWT) to the heat pump and found it ranged from 6.9 ºC (44.5 ºF) in early January to slightly over 15.6 ºC (60 ºF) in midJuly of the second cooling season. According to their field test, Tan and Kush (1986) concluded that SCW systems could give very stable EWT to the heat pump even in severe winter or summer. In their test, the lower limit for the heat pump operation, which was set as leaving water temperature of 3.3 ºC (38 ºF), was never reached. Regarding the influence of ground water, if the well is uncased, the local hydrology will affect the performance of well. Although in their test, this effect was not quantified, Tan and Kush (1986) pointed out that substantial infiltration/exfiltration can enhance the system performance greatly. No information about bleed was found in Tan and Kush’s research. 21 2.4. Mikler’s research (1995) ground water table EW RW steelcasing PVC pipe submersible water pump borehole wall PVC perforated end section return water loss to the ground ground water gain to the system Figure 23 A schematic ‘thermal well’ studied by Yuill and Mikler (1995) 2.4.1. Numerical study Yuill and Mikler (Mikler 1993; Yuill and Mikler 1995) used a well at Pennsylvania State University to research the performance of standing column well systems. They referred to 22 the standing column well as a “thermal well.” The thermal well serves as a circulation, withdrawal and injection well at the same time. But the well does not bleed; the injection rate always matches the withdrawal rate. They developed a simplified mathematical model to describe the coupled thermohydraulic energy transfer by conduction and convection in an aquifer surrounding a thermal well. A schematic of the well system is shown in Figure 23. To simplify the analysis, Yuill and Mikler (1995) used the following assumptions in their study: homogeneous and isotropic aquifer cylindrical symmetry of the coupled flow around the axis of the borehole no heat or ground water flow in the vertical direction laminar ground water no dispersion (no groundwater diverted to other places) thermal well is in the dynamic hydraulic equilibrium with the surrounding groundwater aquifer natural hydraulic gradients in the aquifer are neglected; hydraulic gradients caused by pumping are dominant. Based on these assumptions and by introduction of a “groundwater factor” ( f G ), which is the ratio of convection to conduction, the governing partial differential equations are derived, simplified, and solved numerically. t T r T r G r T f ¶ = ¶ ¶ ¶ ± + ¶ ¶ a 1 1 2 2 (2.2) 23 Where f G is the groundwater factor (+ denotes flow into the well;  denotes flow out of the well); k dz m C G w pw f × × = 2p ; w m is the groundwater mass flow rate (kg/s [lbm/hr]), (either discharge groundwater or suction groundwater flow); pw C is the specific heat of water (J/kgK [Btu/lbmºF]); k is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the ground (m2/s [ft2/hr]); z is the vertical coordinate (m [ft]). The governing equations are converted into explicit forms of finite difference equations by using central difference approximations. To obtain stable solutions, the stability criterion is set as: ( ) 1/ 2 2 £ D = D r t Fo a (2.3) Where a is the thermal diffusivity (m2/s [ft2/hr]). Also, Yuill and Mikler (1995) used a new term, equivalent thermal conductivity ( eq k ), to account for the improved heat transfer due to the induced groundwater flow in the aquifer. To attain the value of eq k , they let heat transfer rates along the borehole wall for the case of coupled thermohydraulic flow considering the real ground thermal conductivity ( k ) equal the ones for the case of pure heat conduction considering the 24 equivalent thermal conductivity ( eq k ). They suggested this equivalent thermal conductivity could be used in the existing pure heat conduction design models to determine the depth of the thermal well. Regarding hydraulic head distribution in the thermal well, Yuill and Mikler (1995) considered this distribution as time independent and used a steadystate solution approach in the thermal well model. They assumed that the hydraulic gradients caused by pumping were dominant with respect to natural hydraulic gradients in the aquifers. Therefore, during their analysis, they neglected the natural hydraulic gradients. The equilibrium well equation relating the groundwater flow rates to the hydraulic gradients in the well was given by: ln( / ) 2 b w R r K h dz Q =  p × × D × (2.4) Where W Q is the water flow rate (m3/s [gpm]); K is the hydraulic conductivity of the ground (m/s [gpd/ft2]); R is the radius of influence (m [ft]); b r is the borehole radius (m [ft]). But this finite difference model that allowed calculation of the radial heat transfer at a particular depth was not truly twodimensional. Consequently, vertical heat transfer, end effects, and bleed operation could not be considered. 25 2.4.2. Experimental study Mikler (1993) did some experimental studies on transient heat and mass transfer in a “thermal well” system installed at Pennsylvania State University. Well #1 was 0.15 m (6 in) and 325 m (1065 ft) deep and was used in a large commercial system with 70 kW (20 tons) cooling capacity. Another well, #2, with the same diameter but 91 m (300 ft) depth was used to monitor and measure ground temperature changes in the vicinity of well #1. The distance between well #1 and well # 2 was 3.65 m (12 ft). Four 17.6 kW (5 ton) heat pumps were operated at full capacity in parallel in this system during the experimental period. Thermocouples were used to monitor both the water temperature distribution along the thermal well as well as the ground temperature in the vicinity of the operating well (well #1) at different depths. Also, thermocouples were used to monitor the entering and return temperature of the circulating water, the inlet and outlet air temperatures passing through the heat pumps, and the ambient temperatures. A flow sensor was used for monitoring total flow rate of the circulating water. Thermal and hydraulic properties of the aquifer were estimated based on the available measured data, “drilling log”, and basic knowledge about the local geology. The heat pumps were operated at fully capacity in cooling mode for a period of 48 subsequent days from August 4 to September 20, 1992, with a total of 235.73 GJ 26 (223.44 MMBtu) of heat injected into the ground. The temperatures of the water flowing down in the annular space and up inside the PVC pipe were measured continuously at five different depths in the well #1 and two depths in well #2. From his experimental data, Mikler (1993) found that the trend of the temperature change confirmed the well known theoretical analysis presented by Eskilson (1987)“On a time scale, one third of the total temperature drop to steady state conditions occurs during the first day, and two thirds during the first two months”. Also, from Mikler’s experimental observation, it was shown that the water temperature at some lower depth inside the PVC pipe is lower than the temperature at the bottom of the well. Mikler contributed this phenomenon to the fact that some amount of fresh water was being drawn into the system and mixed with the return water. After the cooling mode operation, the system was shut off for a period of six weeks from September 21 to December 10, 1992. Temperatures at all monitored locations finally stabilized at a higher level than the corresponding initial undisturbed aquifer temperatures. Then, the heat pumps were operated at full capacity in heating mode for the period of 71 subsequent days from December 10, 1992, to February 19, 1993, with a total of 114.15 GJ (108.20 MMBtu) of heat absorbed from the ground. Temperatures were measured at the same locations in the cooling mode operation. Mikler (1993) observed the temperature difference at the bottom of the well during the heating mode operation, which was proof of the direct interaction between the circulating water in the thermal well and the groundwater. 27 In their paper, Yuill and Mikler (1995) didn’t give any description of bleed. According to their research, they pointed out that the required drilled depth of a 6in thermal well is about 60% of the depth of the 11/2in, Utube earthcoupled borehole, assuming that both are properly designed and are installed in the same geological formation. The authors attribute the superior performance to the increased roughness at the wall of the well together with the induced interaction between the circulating water and groundwater. They didn’t mention that elimination of grout and pipe resistances contribute to the superior performance. The limitations of thermal wells are also listed in this paper (Yuill and Mikler 1995). If the groundwater quality is bad and impossible or too costly to treat (for example, groundwater with high mineral and bacterial content,) the thermal well is not preferable. In some states, this type of well can’t be installed because the waterwell legislation does not permit the “comingling of aquifers”. Sometimes, drilling problem may be the major obstacle. For example, the borehole may collapse in some geological formations. According to their experimental and theoretical study, Yuill and Mikler (1995) concluded that properly designed and installed “thermal wells” could compete with any of the closedloop systems based on their high system performance with smallest borehole depth and lowest combination of installation and operating costs. 28 2.5. Orio’s research Mr. Carl Orio first designed and employed standing column well systems in 1970’s. Since that time, he has been involved in many standing column well systems of Water & Energy System Corporation. Orio (1994, 1995) used the Kelvin line theorem to analyze the heat transfer in this system. ( ) 2 2 ' _ ' 0 2 I X k Q dB B e k Q T T X s B s p p = =  ¥ (2.5) t r X 2 a = Where T is the soil temperature (ºC [ºF]); 0 T is the initial temperature of the soil (ºC [ºF]); Q' is heat transfer rate (negative for heat extraction and positive for heat rejection) (W/m [Btu/fthr]); r is the radial distance from line (m [ft]); s k is the thermal conductivity of the soil (W/mK [Btu/hrftºF]); a is the thermal diffusivity (m2/s [ft2/hr]); t is the heat pump run time (hr); B is the integration variable. The Kelvin line theorem has provided a good correlation with some practical field experience (Orio 1995). But the Kelvin line theorem, offered as a relatively simple treatment of the problem, is not sufficient for the complicated heat transfer in standing column well systems, including conduction, convection, and advection, especially for 29 systems with ground water bleed. The Kelvin line theorem neglects the advection of heat from the borehole due to groundwater flow. The effect of the ground water flow on performance of SCW systems should be taken into account in a more complete and accurate model. In particular, the process of advection is very important in the modeling of SCW systems with groundwater bleed. Thus, the Kelvin theorem cannot be directly used to correctly calculate the temperature distribution of a “bleed” SCW system. The line source analysis with an “enhanced” thermal conductivity might be used to consider the effect of groundwater (See more discussion about related analytical solutions in section 2.9.). In this literature review, Orio’s papers are the only ones that give some detailed information about bleed. It is reported that in the severity of winter or summer, a relatively small (10%) bleed can reestablish water temperature in the well of SCW system at a rapid rate. According to his observations, Orio (1994, 1995) pointed out that bleed can make the effective thermal conductivity increase by factors of 3 to 5. The homogeneity of the geologic formation, the characteristics of the aquifer, and the density of the fractures affect the performance of SCW systems with bleed. Usually, 8090% of the water is returned to the standing column well and the balance is returned to the earth some distance away or disposed of. In some cases, the bleed water is disposed of in a separate return well. The National Ground Water Association (NGWA) provides the following formula to calculate the optimum return well distance: 30 D = 0.2´Q (2.6) Where D is the distance in feet to the recharge well (ft); Qis the design heat transfer rate (Btu/hr) . In fact, a return well is often not required because of the relatively small amount of bleed water. Instead, the bleed water may be disposed of in storm drains, ponds, streams or other natural routes. In wells that also serve as the household domestic water supply, “bleed” is naturally provided. The “bleed” power of a shower, laundry and other water use makes the average water temperature in the well of the residential SCW systems quite stable (Orio 1995). Orio (1999) discussed the placement of pumps and the depth of the boreholes. The boreholes could be onehalf the depth of the closed loop earth coupling methods. When boreholes get deeper than 152 m (500 ft), there is substantial increase in heating energy because the earth temperature increases with the increasing depth. But placing the pump at the bottom of the borehole has some disadvantages such as installation and service. To eliminate these disadvantages, Orio (1999) proposed that the submersible pump should be placed at the top of the borehole, but a lightweight plastic tube (dip tube or tail pipe) should be inserted to the bottom of the borehole (Figure 24b). Thus, the most stable water temperature is achieved, and shorter pipes and wires are required, so the initial investment can be reduced. Deeper wells (depth >152 m [500 ft]) mostly use dip tubes constructed of 100 mm (4 in) diameter PVC pipes to the bottom of the well. The dip tube has a minimum of 120 oneinch perforations in the lowest 12 m (40 ft). 31 Geothermal Heat Pump Domestic Use Water Emergency Bleed Typically 250500 ft 38 tons/bore Submersible Pump Standing Column Well Small Scale (a) Typically 5001500 ft 3040 tons/bore(Max) Bleed Emergency Geothermal Heat Pump Submersible Pump Tail Pipe Commercial Standing Column Well (b) Figure 24 Schematics of standing column well from description of Orio (Orio 1999) 32 2.6. Some typical installations of SCW systems There are approximately 1000 SCW installations in the United States. Most of them are located in the Northeast and Pacific Northwest in addition to parts of Canada in heatingdominated residential and light commercial applications. Also there are some installations out of North America. 2.6.1. Haverhill public library The Haverhill public library is located in Haverhill, Massachusetts. There are four standing column wells to provide a heat sink/source for watertowater heat pumps (initially two SCWs in 1994 but expansion of the library resulted in two additional SCWs after 1996). Each of the standing column well wells is 457 m (1500 ft) deep. Water is drawn from the bottom of the well, run through the heat pump and discharged at the top of the well. Whenever the well water temperature drops below 4.44 °C (40 °F), a bleed cycle initiates. This automatic bleed diverts approximately 10 % of the flow from returning to the wells. A bleed cycle typically lasts for 30 minutes. It acts to limit the lower well temperatures by drawing in new warmer groundwater from far field. There is no bleed for high temperatures. As Figure 25 shows the well water temperature remained above 2.78 °C (37 ºF) and generally operated in the lower 40s (ºF) during heating mode. The peak loop temperature reached 21.1 ºC (70 ºF) in June. However system operation changed after June 25th when 33 the second well pump became active and the maximum well temperature remained below 18.9 ºC (66 ºF) thereafter. There was also less variation in the temperature after June 25th in both heating and cooling mode. Figure 25 Standing column well water temperature trends in Haverhill public library (http://www.cdhenergy.com/ghp/haverhill/haverhill_main.htm) 2.6.2. SCW application in China From March 2001 to present, Ever Source Science & Technology Development Co. LTD in Beijing, China, has been applying the concept of the standing column well in about two hundred projects, with the name “single well for supply and return.” The schematic drawing of the single well is shown in Figure 26. A heat exchanger is located at the well 34 mouth, where the well water and recycle water circulated in separate loops. Therefore, the groundwater from the well is neither consumed nor polluted. According to their experience, this single well system can solve problems such as moving sands, pollution of groundwater, and collapse, which are all related to multiwell systems. More detailed technical information about this system is not available. Heat exchanger Recycle water Heat flux Water table Energy collector Figure 26 The schematic drawing of “single well for supply and return” (HYY 2003) From December 12, 2003 to March 17, 2004, Ever Source Science & Technology Development Co. LTD measured the energy consumption of eleven different type buildings in Beijing. These buildings use standing column wells as a heat source for heating in winter (Sun 2004). This investigation shows that energy consumptions of seven buildings among the eleven buildings are lower than that of the conventional heating system with a coal boiler. All eleven buildings have lower energy consumptions than other conventional oil/gas/electrical boiler heating system. 35 2.7. “Geohill”open hole coaxial thermal well An open loop concentric well heat exchanger called a “Geohill” has been developed by Geocalor A.G. (Hopkirk and Burkart 1990). The system schematic is shown in Figure 27. The borehole is 250 mm (10 in) in diameter and up to 300 m (1000 ft) deep, and it remains open with the exception of a steel casing in the upper part. A central PVC tube is surrounded by graded gravel filling and contains a downhole pump feeding water via an insulated tube to the heat pump. The fluid return is through the gravelfilled annulus. According to this configuration, the gravel filling can increase friction resistance for the return water flowing down, and therefore more groundwater is sucked into the system, especially if the well were drilled in a highly permeable rock formation. According to Hopkirk and Burkart’s research, the “Geohill” system shows much promise, especially in larger commercial installations requiring both heating and cooling. 36 Insulated delivery tube Return tubes Steel casing through unstaurated soil and sensitive aquifers Gravel filling Downhole pump Filter section Figure 27 Open hole coaxial thermal well “Geohill” (Hopkirk and Burkart 1990) 2.8. Summary of the different research related to SCWs Tables 21 and 22 summarize the research related to SCWs to date. Table 21 Summary of experimental research related to SCWs Researcher and date System name Depth of well Diameter of well Placement of well pump Placement of suction tube System water mixes with groundwater (i.e., openloop) System bleeds some groundwater Heat pump capacity ft/ton Bose et al. (1979) Geothermal well 73 m (240 ft) 127 mm (5 in) Ground level Top of the well No No 2.25 tons 106 Braud and Oliver (1980, 1983) Concentric pipe well 154 m (504 ft) 63.5 mm (2.5 in) Ground level Bottom of the well No No 2 tons 77 Tan and Kush (1986) Semiclosed loop standing column well 189 m (620 ft) 152.4 mm (6 in) Ground level Top of the well Yes No 5 tons 124 Hopkirk and Burkart (1990) Open hole coaxial thermal well “GEOHILL” 305 m (1000 ft) 254 mm (10 in) Bottom of the well Bottom of the well Yes No N/A N/A Mikler (1993) Yuill and Mikler (1995) Thermal well 325 m (1065 ft) 152.4 mm (6 in) Top of the well (under the water table) Bottom of the well Yes No 20 tons 53 Orio (1988,1995, 1999) Standing Column Well 73  457 m (2401500 ft) 152.4 mm (6 in) 1. Top of the well (under the water table) 2. Bottom of the well Bottom of the well Yes Yes 5200 tons 5060 HYY Beijing (2000s) Single well for supply and return 80 m 500 mm (19.68in) N/A N/A Yes No N/A N/A 37 Table 22 Summary of the modeling of SCWs Researcher and date System Name Analytical solution Numerical solution Include the effect of groundwater (advective heat transfer) Include the effect of bleed Comments Braud and Oliver (1980, 1983) Concentric pipe well Yes No No No 1. Steady state solution 2. Only consider heat conduction transfer 3. Cannot simulate cases in bleed operation Tan and Kush (1986) Semiclosed loop standing column well Yes No Yes No 1. Based on linesource theory 2. Use “enhanced” thermal conductivity Mikler (1993) Yuill and Mikler (1995) Thermalwell No Yes Yes No 1. Finite difference method 2. Some inputs in their models are based on their experiments Orio (1988,1995, 1999) Standing column well Yes No Yes Yes 1. Based on linesource theory 2. Use “enhanced” thermal conductivity 38 39 2.9. Some related analytical solutions (to ground source heat pump) Several methods to predict the performance of ground source heat pumps are available, including both analytical (line heat source, cylindrical heat source) and numerical methods. Although numerical solutions are very powerful, they are relatively complex. Much data and computer time are usually required to obtain good results. In contrast, the simplified analytical methods such as the line heat source model and the cylindrical heat source model (first presented by Carslaw and Jaeger [1947] and Ingersoll et al. [1948] and later refined by other researchers [Kavanaugh 1984, Bose et al. 1988]) make it relatively simple to perform annual hourbyhour simulations of groundcoupled heat pump systems. Because these analytical solutions might be further modified to be employed in SCW system after considering the movement of groundwater, they are reviewed below. Figure 28 shows the cylindrical heat source embedded in an infinite medium, e.g. the earth. In the simplest case, the borehole is subjected to a constant heat transfer rate, q , from (or to) the surrounding ground for which the far field temperature is the undisturbed temperature, u T . The object of the analytical solution is to calculate the temperature difference between the undisturbed ground temperature, u T , and the borehole wall temperature, w T . Based on the work of Carslaw and Jaeger (1947), Ingersoll et al. (1948, 1951, 1954) gave an analytical solution to the transient heat transfer from a line (or cylinder) embedded in an infinite homogeneous medium. 40 Figure 28 Schematic drawing showing the cylindrical heat source embedded in an infinite medium * * When the diameter of the cylinder is zero, the cylindrical heat source becomes line heat source 2.9.1. Kelvin line source solution The earliest approach to calculating thermal transport around a heat exchanger in the ground was the Kelvin line source theory (Ingersoll et al. 1948,1954). The temperature distribution around a line source of heat buried in a homogenous, infinite media is given by: ( ) 2 2 2 I X k q dB B e k q T T s l X B s l u p p = =  ¥  (2.7) t r X 2 a = Where T is the soil temperature (ºC [ºF]); u T is the uniform initial temperature of the soil (ºC [ºF]); r Tfi Tfo Tw Tr R : the far field radius Tr : the far field temperature Tr = Tu Tu: the undisturbed temperature of the ground q 41 l q is the heat transfer rate applied to the ground (W/m [Btu/fthr]) (a positive q value implies heating mode); r is the radial distance from the line (m [ft]); s k is the thermal conductivity of the soil (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the soil (m2/s [ft2/hr]); t is the heat pump run time (hr); B is the integration variable. This model is based on approximating the borehole as a line source, assuming end effects are negligible. The soil acts as a heat rejection (absorption) medium that has an assumed uniform and constant initial temperature (Tu ). Let t r y X 4a 2 = 2 = . Thus Equation (2.7) can be changed into ) ( !) ( 1) ...... 2 (2!) 3 (3!) ( ln 4 4 2 3 1 N N y y y y y k q d e k q T T N N s l s y l u × + +  × + ×  = =    ¥  + g p l p l l (2.8) Where l is the integration variable; g is Euler’s constant, 0.5772157… Equation (2.8) can be written as: +   = C r t k q T T s b l u w g a p 2 4 ln 4 (2.9) Where Tw is the borehole wall temperature (ºC [ºF]); 42 rb is the borehole radius (m [ft]); C is the summation of the series ¥ = + ×  1 1 ( !) ( 1) N N N N N y . Actually, the integration of Equation (2.7) is from X to r¥ , where r¥ is equal to 4 at . To find how close u T is to the value of the temperature at r¥ , a formula was given by Hart and Couvillion (1986): [0.0019] 2 s l r u k q T T p  = ¥ (2.10) At typical values of l q and s k , r u T T ¥ varies from approximately 0.00167 ºC (0.003 ºF) to 0.0167 ºC (0.03 ºF) when r¥ is equal to 4 at . Considering this correction, Equation (2.9) can be written as +    = C r t k q T T s b l u w 0.0038 4 ln 4 2 a g p (2.11) Ingersoll et al. (1951) stated that the line source equation (Equation [2.9]) is exact only for a true line source, but that it can also be applied with negligible error for pipes less than 4 inch in diameter and times longer than 24 hours. The error does not exceed about 2% under these conditions. For the case where the time is too short or the pipe diameter is too large (in general when 20 2 < r at ), the use of the line source equation will involve the error greater than 2%. Therefore, the line source cannot effectively and accurately model 43 systems with normal transient operating performance. Deerman and Kavanaugh (1991) stated that the line source method had a 10% error when using onehour intervals. 2.9.2. Cylindrical heat source solution The cylindrical heat source solution was developed using a single isolated pipe surrounded by an infinite solid of constant properties. The following assumptions are used in this solution: · heat transfer only by pure conduction · soil acts as an infinite solid · perfect soil and pipe contact · no groundwater movement There are several cylindrical heat source solutions corresponding to different cases of our interest. These include a cylindrical heat source solution with and without considering the thermal mass in the borehole, and a cylindrical heat source solution, which considers two thermal masses in the borehole separated by a thermal resistance. (a). Cylindrical heat source solution without considering the thermal mass in the borehole The cylindrical heat source solution without considering the thermal mass in the borehole for a constant heat flux is as follows (Ingersoll et al. 1954): G(Fo, p) k q T T s l u  = (2.12) Where T is the soil temperature (ºC [ºF]); 44 u T is the uniform initial temperature of the soil (ºC [ºF]); l q is the heat transfer rate applied to the ground (W/m [Btu/fthr]) (a positive q value implies heating); s k is the thermal conductivity of the soil (W/mK [Btu/hrftºF]); G(Fo, p) is the analytical solution; [ ] ¥   +  = 0 2 2 0 1 1 0 1 2 1 ( ) 2 ( ) ( ) ( ) ( ) ( ) ( ) 1 1 ( , ) 2 b b b b b b b b p b d J p Y J Y p J Y e G Fo p Fo (2.13) p is the ratio of the radius where the temperature is calculated over the borehole radius ( 0 r ) ; Fo is the Fourier number defined as: 2 0 r Fo =at . Values of G are available from Ingersol et al. (1954). For p = 1(i.e., at the cylindrical radius, borehole wall), the following equation is given by Bernier (2001). [ 0.89129 0.36081 log ( ) 0.05508 log ( ) 3.59617 10 log3 ( )] 10 2 3 G(Fo,1) 10  + ´ 10 Fo  ´ 10 Fo + ´ ´ Fo  = (2.14) So, for the temperature at the borehole wall, Tw , Equation (2.12) can be reduced to [ 0.89129 0.36081 log ( ) 0.05508 log ( ) 3.59617 10 log3 ( )] 10 2 3 10 10 Fo 10 Fo Fo s l u w k q T T  + ´  ´ + ´  ´  = (2.15) (b). Cylindrical heat source solution with considering the thermal mass in the borehole 45 If a cylinder of radius r b of a thermal massive perfect conductor is surrounded by an infinite medium (e.g. the ground) and is heated at the rate ql per unit length per unit time for t > 0 , all initial temperature being zero, the temperature of the perfect conductor is given by Carslaw and Jaeger (1959): G(h, 1, ,Fo) k q T s = l a ¥ (2.16) ( ) [ ( )] ( ) du u u u Fo Fo h G ¥ D =   0 1 3 2 3 2 2 2 1 1 2 2 1 exp , , , p a a a a (2.17) Where h = 2pRbks , 1 2 a1 = 2prb rCp / S , a 2 ®¥, Fo is the Fourier number defined as 2 rb t Fo = a ; ( ) [ ( ) ( ) ( ) ] [ ( ) ( ) ( ) ]2 1 2 0 2 1 2 1 2 2 1 2 0 2 1 2 1 1 2 ( ) ( ) u hu Y u hu Y u u u hu J u hu J u +    D = +    + a a a a a a a a (2.18) Ji is the Bessel function of order i ; Yi is the modified Bessel function of order i ; s k is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the ground (m2/s [ft2/hr]); r is the density of the ground (kg/m3[lbm/ft3]); Cp is the specific heat of the ground(J/kgK [Btu/lbmºF]); rb is the radius of the cylindrical conductor (m [ft]); Rb is the thermal resistance between the conductor and the ground (K/(W/m) [hrftºF/Btu]); 46 S1 is the thermal capacity of the cylinder of perfect conductor (J/m3K [Btu/ft3ºF]); u is the integration variable. For large values of Fo ( Fo >> 1) Equation (2.16) can be reduced to: = +   +  + ) 1 ) ( 4 ln( 2 2 2 (4 ) ) 4 2 ln( 4 2 1 1 1 1 C Fo Fo Fo Fo h C Fo h k q T s l o a a a a p (2.19) Where C = 1.7811 = exp(g ) , and g = 0.5772157... is Euler’s constant. All other variables are defined as the same in the equation (2.16). The simplified cylindrical solution (considering the thermal mass) to a given borehole with u T , initial temperature of soil, is given:  +   = +  ) 4 ln( 2 2 2 (4 ) ) 4 2 ln( 4 1 1 1 1 C Fo Fo Fo h C Fo h k q T T s l u w a a a a p (2.20) Where u T is the uniform initial temperature of the soil (ºC [ºF]); Tw is the borehole wall temperature (ºC [ºF]); l q is the heat transfer rate applied to the ground (W/m [Btu/fthr]) (a positive q value implies heating); h = 2pRbks , 1 2 a1 = 2prb rCp / S ; Fo is the Fourier number defined as 2 rb t Fo = a ; s k is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the ground (m2/s [ft2/hr]); 47 r is the density of the ground (kg/m3[lbm/ft3]); Cp is the specific heat of the ground(J/kgK [Btu/lbmºF]); rb is the radius of the borehole (m [ft]); Rb is the thermal resistance of the borehole ( K/(W/m) [hrftºF/Btu]); S1 is the thermal capacity of the materials in the borehole (J/m3K [Btu/ft3ºF]); C = 1.7811 = exp(g ) ; g is is Euler’s constant (g = 0.5772157...). (c). Cylindrical heat source solution to a cylinder of perfect conductor with the sheath surrounded by an infinite medium (soil) Core Insulation Soil Perfect conductor Sheath Perfect conductor Figure 29 A schematic drawing of a core separated by the insulation from the sheath 48 Figure 29 shows a schematic drawing of a cylinder of the core with the sheath surrounded by an infinite medium (soil). The core and the sheath are perfect conductors of thermal capacities S1 and S2 , respectively. They are separated by the insulation, which is regarded as of negligible thermal capacity and thermal resistance, R. The cylinder is also supposed to be buried in the soil of thermal conductivity, s k , thermal diffusivity, a , and specific heat, Cp . If the whole system is initially at zero temperature and heat is supplied at the rate ql per unit length per unit time, the temperature of the cylinder is given by Carslaw and Jaeger (1959): G(h, 1, 2 , Fo) k q T s = l a a (2.21) ( ) [ ( )] ( ) du u u u Fo Fo h G ¥ D =   0 1 3 2 3 2 2 2 1 1 2 2 1 exp , , , p a a a a (2.22) Where h = 2pRbks , 1 2 a1 = 2prb rCp / S , 2 2 a 2 = 2prb rCp / S ; Fo is the Fourier number defined as 2 rb t Fo = a ; ( ) [ ( ) ( ) ( ) ] [ ( ) ( ) ( ) ]2 1 2 0 2 1 2 1 2 2 1 2 0 2 1 2 1 1 2 ( ) ( ) u hu Y u hu Y u u u hu J u hu J u +    D = +    + a a a a a a a a (2.23) Ji is the Bessel function of order i ; Yi is the modified Bessel function of order i ; s k is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the ground (m2/s [ft2/hr]); r is the density of the ground (kg/m3[lbm/ft3]); 49 Cp is the specific heat of the ground(J/kgK [Btu/lbmºF]); rb is the radius of cylindrical conductor (m [ft]); Rb is the thermal resistance between the two perfect conductors (the core and the sheath) (K/(W/m) [hrftºF/Btu]); S1 is the thermal capacity of the cylinder of the core (J/m3K [Btu/ft3ºF]); S2 is the thermal capacity of the sheath (J/m3K [Btu/ft3ºF]); u is the integration variable. 2.9.3. Analytical solution considering the movement of groundwater (groundwater gfunction) Claesson and Hellström (2000) gave a new analytical solution for the influence of regional groundwater flow in the performance of borehole heat exchangers based on the groundwater gfunction. The temperature Tb (t) at the borehole wall, which is needed to sustain the constant heat injection rate Q0 from time t = 0 , is denoted by a corresponding dimensionless gfunction: ( ,....) 2 ( ) 0 g t k q T t total s b = × p H Q q 0 0 = (2.24) The gfunctions depend on time, thermal properties, etc. Groundwater flow will diminish the gfunction. Claesson and Hellström (2000) wrote the total gfunction in the following way: 50 ( ) ( ; 0) ( ) 2 ( ; ) 0 T t g t q g t q k g t q b w gw s total w = = =  p (2.25) Where Tb (t) is the temperature at the borehole wall (ºC [ºF]); qw is the constant regional groundwater flow (m3 of water per m2 and s); ks is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); H is the borehole depth (m [ft]). The first term on the righthand side of Equation (2.25) is the ordinary gfunction for the given borehole without the effect of groundwater ( qw = 0 ) (Claesson and Eskilson 1987). The second term accounts for the effect of the groundwater flow. After some calculation, Claesson and Hellström (2000) gave the groundwater gfunction g gw : e erfm s ds s g h h s gw =  × × (1  ) (1/ ) 2 1 ( , ) 0 2 / 4 t t (2.26) Where × = =   x x x e erf s ds erf x x erfm x 0 2 1 ( ) ( ) 1 ( ) p ; 2 4 H t = at ; s w w w k H c q h 2 r = ; qw is the constant regional groundwater flow ( m3 of water per m2 and s). ks is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); 51 a is the thermal diffusivity of the ground (m2/s [ft2/hr]); r w is the density of the groundwater (kg/m3 [lbm/ft3]); cw is the specific heat of the groundwater(J/kgK [Btu/lbmºF]); H is the borehole depth (m [ft]). For t > 1, the following approximation of groundwater gfunction, which is valid for any h , is given by Claesson and Hellström (2000):   @ 2 1 2 4 1 ( , ) 2 t p t t t h erf h h h ggw h Ein t > 1 (2.27) Where ln( ) 0.577(1 ) 1 ( ) 7 / 4 0 x x x s ds x e e s e Ein x    =  @ + +  Also, for t < 1, h < 1, the following simple expression is used to estimate the effect of groundwater flow within 3% error: @  p t t t 9 4 1 8 ( , ) h2 ggw h t < 1, h < 1 (2.28) 2.10. Related research  aquifer thermal energy storage (ATES) A related type of system, with similar analytical requirements, is the aquifer thermal energy storage (ATES) system. ATES systems utilize aquifers for the storage of lowgrade thermal energy such as solar heat or waste heat during periods of low demand. The lowgrade energy is used to heat or chill water, which is injected into an aquifer for storage. Later, during a period of high demand, the water is withdrawn for space heating or cooling. During a period of heat injection, water is extracted from the cold well, heated 52 Warm well Cold well and reinjected into the warm well. The pump is reversed during a period of heat recovery. Water is then extracted from the warm well, cooled and reinjected into the cold well (see Figure 210). The same type of system may be used to store cold water for cooling purposes in warm climates. Figure 210 Heat storage in an aquifer Hall and Raymond (1992) gave a schematic of a simplified ATES system used for air conditioning (Figure 211). In this system, the cooling tower is used for chilling water drawn from the warm well during the winter. The chilled water is stored in the aquifer by the cold well, and is recovered during the summer and passed through heat exchangers to cool the warm air. 80ºC 40ºC 53 cold well warm well cold air Blower cooling tower water return pump water table warm water cirulation pump cold water circulation pump Warm air Air blower Warm air Figure 211 Simplified aquifer thermal energy storage system used for airconditioning (Hall and Raymond 1992) Numerous studies have been performed concerning the concept of ATES. Hall and Raymond (1992) gave the following three elements, which determine whether the design and operation of an ATES system are successful. the presence of a suitable aquifer for groundwater supply and energy storage; the availability of a source of lowgrade thermal energy; a temporal mismatch between thermal energy availability and thermal energy use. Aquifer characterization is very important to the design of an ATES system. However, unlike other components of the ATES system, the aquifer itself cannot be changed to 54 meet the design specification. Thus, the ATES system must be designed with regard to the aquifer characterization. So, as the first step in any ATES project, site investigation is necessary and should be combined with the user’s specific requirements. Hall and Raymond (1992) also pointed out that the aquifer’s hydraulic conductivity, which is dependent on the size and shape of media pores, is of the firstorder importance in the design and evaluation of ATES systems. Basically, under ATES conditions, the differences in the thermal conductivities and thermal capacities of earth materials are relatively small. So, thermal conductivity and thermal capacity are of secondary importance. There are several descriptions of ATES systems in the literature. Midkiff et al. (1992) presented the results of 6 years of study on the longterm performance of an airconditioning system (a building at University of Alabama) based on ATES. During the cold weather, ambient 18ºC water is pumped from warm wells, chilled to about 6 ºC in a cooling tower, and reinjected into the separated cold storage wells. In warm weather, water is withdrawn from the cold wells and pumped through building heat exchangers for airconditioning (see also Figure 211). This ATES system was operated to provide 100% of the building air conditioning with an annual average COP of about 5.0, about twice that for conventional mechanical airconditioning equipment of the same capacity (Midkiff et al. 1992). Marseille and Wilke (1992) provided an overview of an ATES system integrated with a central heating and cooling plant (MidIsland Postal Facility in Melville, New York). 55 Cold wells are charged with water that is cooled during the winter by heat pump. Water from these cold wells is then used to meet the facility’s cooling load during the summer, before being pumped back into the ground at warm wells. Backup cooling is provided by a heat pump. They described and assessed energy and economic merits of this system. Their studies shown that this ATES system can offer both energy and environmental advantages over more conventional systems. 2.11. Effect of groundwater flow on closedloop groundcoupled heat exchangers Although it has been recognized that the convective heat transport by groundwater flow may be an important factor in reducing the necessary size of closedloop groundcoupled heat exchangers, current design and simulation models for closedloop systems still assume that heat transfer underground occurs by conduction only. Little work has been done to quantify the effects of groundwater flow on closedloop systems. Claesson and Hellström (2000) presented models for the influence of regional groundwater flow based on the assumption that the natural groundwater movement is reasonably homogenously spread over the ground volume. This applies well for homogenous and porous ground materials. The authors used the line source theory to model the groundwater effect on a single vertical borehole (groundwater gfunction, see section 2.9.3.) and concluded that under normal conditions, the influence of regional groundwater flow is negligible. Chiasson (1999) made a preliminary investigation of the effects of groundwater flow on the design and performance of vertical closedloop ground heat exchangers. A two 56 dimensional finite element numerical groundwater flow and heat transport model (AQUA3D) was used to simulate and observe the effects (Chiasson et al. 2000). The relative importance of heat conduction in the ground vs. heat advection by groundwater flow is assessed by using of the dimensionless Peclet number, Pe . Pe = r wcwqL / Keff (2.29) Where r w is the density of the groundwater (kg/m3 [lbm/ft3]); cw is the specific heat of the groundwater (J/kgK [Btu/lbmºF]); Keff is the effective hydraulic conductivity (m/s [ft/s]); q is the specific discharge (m/s [ft/s]); L is the characteristic length (m [ft]). Based on their preliminary work (Chiasson et al. 2000), it is shown that heat advection by groundwater flow is a significant process contributing to heat transfer in geologic formations such as coarsegrained soil and rocks with fractures and solution channels. The value of effective thermal conductivity is greater with a flowing fluid than with a stagnant fluid. The results from this work also show that as groundwater flow velocity increases, the values of the predicted effective thermal conductivity, including the effects of groundwater advection, are significantly different. From their preliminary assessment of the effects of groundwater flow, Chiasson et al. (2000) pointed out that it is difficult to adapt results from current design guidelines and software tools to fully account for the effect of groundwater movement. 57 Theoretical studies dismiss significant effects of groundwater flow for typical conditions in a porous ground (Chiasson et al. 2000; Claesson and Hellström 2000). However, groundwater flow in standing column well systems, especially when bleeding, results in higher flow velocities. The hydraulic pressure difference between the suction point and discharge point may also be potentially important. 2.12. Numerical groundwater flow and heat transport models Ground water flow and thermal energy transport in the porous media have been studied in some detail in the discipline of hydrogeology. Numerical research into groundwater and heat transport has been continuing for more than a decade in North American and Europe. Numerous commercially available and public domain numerical software codes exist. Of these, we focus on the simulation modeling both mass and heat transport in groundwater. Table 23 lists some numerical models for groundwater flow and energy or solute transport in groundwater. These models can all be used to simulate an ATES system. Models THETA and SUTRA are selected for a more detailed review, since the information about these two models is readily obtained in the public literature. In assessing the effect of groundwater flow on closedloop heat exchanger performance, Chiasson (1999) reviewed numerical software code, which can be used to model mass and/or heat transport in groundwater. Finally, Chiasson (1999) selected AQUA3D for his study based on his selection criterion: the type of boundary conditions handled by the code 58 the solution scheme employed by the code verification of the code cost Table 23 Numerical models for groundwater Model Creator Descriptions AQUA3D Vatnaskil Consulting Engineers, Reykjavik, Iceland Threedimensional, finiteelement method; developed mainly for simulation of masstransport problems, but can be adapted to model heat transport without densitydependent groundwater flow. HST3D United States Geological Survey (USGS) Threedimensional, finitedifference method; capable of simulating mass and heat transport in variabledensity groundwater flow system. FEFLOW WASY Institute for Water Resources Planning and Systems Research, Ltd., Berlin, Germany Threedimensional, finiteelement method; capable of simulating both mass and heat transport in densitydependent groundwater flow systems. SUTRA (Saturated Unsaturated Transport) Clifford L. Voss Twodimensional hybrid finiteelement and finitedifference method; simulated fluid movement and the transport of either energy or dissolved substances in the subsurface environment. THETA 3.0 Kangas and Lund Threedimensional, finitedifference method; coupled transport of fluid and energy in porous media. 59 2.12.1. Numerical model THETA THETA was developed at Helsinki University of Technology by Kangas (1996). It can be used to accurately simulate the threedimensional coupled transport of fluid and energy in porous media. Simulations have been performed to evaluate the effect of groundwater on the performance of a ground heat extraction system using vertical wells. Injection flow flow Extraction well screen CONFINING LAYER SATURATED LAYER CONFINING LAYER Figure 212 A ground heat extraction system using vertical wells (Kangas 1996). Kangas (1996) used the porous medium approximation to study the groundwater flow. The specific discharge ( q ) is given by Darcy equation: g K p g k k q r r m m =  (Ñ  ), = (2.30) Where: k is the intrinsic permeability (m2 or Darcy [ft2]) ( k is a function of the size of the openings through which the fluid moves. It depends only on the geological properties of the ground. k = C × d 2 ); C is the shape factor and d is the diameter of the effective grain, they are properties of the porous media (Fetter 1994); 60 K is the hydraulic conductivity of rock (m/s [gpd/ft2]) (It depends not only on the geological properties of the ground, but also on the thermal properties of the flowing medium); p is the pressure (N/m2 [lbf/ft2]); g is the acceleration of gravity (m/s2 [ft/s2]); m is the dynamic viscosity of water (Ns/m2 [lbfs/ft]). In addition, Kangas (1996) assumed that, locally, the groundwater and the surrounding ground are in the thermal equilibrium to derive the transferred energy equation in groundwater from the principle of conservation of energy. The resulting energy equation with an incompressible fluid is: T c q T H t T c s f = Ñ× Ñ  ×Ñ + ¶ ¶ (r ) (l ) (r ) (2.31) Where: rc is the volumetric heat capacity (J/m3K [Btu/ft3ºF]); l is the thermal conductivity (W/mK [Btu/hrftºF]); q is the specific discharge (volume flow rate per unit of crosssectional area) (m/s [gpd/ft2]); H is the heat source or sink (W/m3 [Btu/hrft3]); and subscripts: f is fluid (water); s is fluid saturated soil. The above two governing equations are discretized in THETA using the explicit finite difference method (FDM) and solved numerically. 61 The results from the THETA simulations of Kangas (1996) suggest that an increase in groundwater flow will result in improved system performance, which results from the energy transfer by groundwater; groundwater constantly replenishes the recoverable energy at the site of extraction. The presence of groundwater flow significantly increases the amount of recoverable energy. Similarly, standing column well systems, especially with groundwater bleed, make use of the energy stored in the aquifer. The THETA aquifer simulation model has been incorporated into a computer simulation model AQSYST for simulating energy systems employing ATES (Kangas and Lund 1994). This system simulation showed that energy systems employing heat pumps for storage discharge could obtain high performance for the whole range of natural groundwater flow rates from 10 m/year to 600 m/year. THETA simulates the thermohydraulic flow in the aquifer when either injecting water to the well or extracting water from the well. It cannot model simultaneous injection and extraction to/from a single well. The performance of standing column well systems is characterized by circulating, injecting, and extracting water to and from an aquifer at the same time. Therefore, THETA cannot be applied directly to the standing column well system. 2.12.2. Numerical model SUTRA SUTRA (SaturatedUnsaturated Transport) is a computer program developed by Voss (1984). This numerical model simulates fluid movement and the transport of either 62 energy or dissolved substances in the subsurface environment (aquifer). A twodimensional hybrid finiteelement and finite difference method is used to approximate the governing equations. SUTRA can solve the two interdependent processes: 1. fluid densitydependent saturated or unsaturated groundwater flow, and either 2a. transport of a solute in the groundwater, or 2b. transport of thermal energy in the groundwater and solid matrix of the aquifer. SUTRA was primarily intended to simulate twodimensional flow, and either solute or energy transport in a saturated variable density system. To simulate the groundwater in unconfined aquifers affected by a periodic boundary condition, Ashtiani et al. (1999) modified the SUTRA model in three aspects: 1. the basic flow equation is changed from a pressurebased form to a mixedform; 2. an automatic underrelaxation method is applied for adjustment of pressure after each iteration to handle the nonlinearity of the unsaturated zone equations; 3. the model has been adjusted to handle a seepageface boundary condition. The validation tests of this twodimensional numerical model for densitydependent groundwater flow in unconfined aquifers against experimental data were successful. Like THETA, SUTRA cannot model simultaneous heat/mass injection and extraction to/from a single well. So, SUTRA cannot be applied directly to the standing column well system, either. 63 2.12.3. Other Numerical models A few other models address energy transfer in the aquifer. Here are some brief reviews. Hellström et al. (1986, 1989) developed a model that simulates the thermal process in the aquifer and in the surrounding ground under certain simplifying assumptions concerning the groundwater flow. The basic assumption of the model is that the groundwater flow is essentially radial in the thermally active region around the well. There are other assumptions that must be fulfilled: · negligible regional groundwater flow; · negligible buoyancy flow caused by varying water temperature in the aquifer; · negligible influence of viscosity differences between different flow paths. Convective heat transport and threedimensional heat conduction are accounted for in this model. The combined diffusive and convective heat flow processes in the aquifer and the surrounding layers are solved using the explicit difference method (finite difference method). Molson et al. (1992) simulated the thermal energy storage in an unconfined aquifer with a threedimensional finite element numerical model. In their model, the authors coupled the densitydependent groundwater flow and thermal energy transport. A symmetric matrix time integration scheme with the Galerkin finite element method is employed. Recently, Chevalier and Banton (1999) applied the random walk method to model energy transfer in porous media. The method is based on the concept that cumulative results of 64 repeated trials with an arbitrary probability distribution tend to a Gaussian distribution. They compared their random results with the analytical solution and the numerical finite difference solution. The results are similar in both cases. Because the above three models cannot model simultaneous heat/mass injection and extraction to/from a single well, so they cannot be applied directly to the standing column well system. 65 2.13. Summary of the literature From the review of the literature discussed in the previous sections, it is clear that research into the operation and design of SCW systems has been very limited. To date, no models have been developed that have come into common use in design procedures for SCW systems. Attempts have been made to adapt conduction heat transfer models to include the effects of groundwater flow. However, these models (e.g., Yuill and Mikler 1995) do not allow representation of bleed from the well. As this is common practice and can have a significant impact on the design and cost of the well, there is a clear need to be able to model this effect. Based on the existing published research, the following conclusions can be drawn: 1. Because of the direct interaction between the water in the borehole and the groundwater in SCW systems, none of the pure heat conduction models such as Braud’s (1980) could be directly applied to the SCW system without any modification. 2. Only Yuill and Mikler (1995) have developed an analytical tool that accounts for heat transfer improvement due to the presence of groundwater. The influence of infiltration/exfiltration of groundwater to the overall heat transfer depends on the local geological formation and performance characteristics of the system. However, this finite difference model allowing calculation of the radial heat transfer at a particular depth is not a true twodimensional model. A twodimensional model would be much more appropriate. 66 3. In Tan and Kush’s paper (1986), the effect of groundwater was referenced, but not quantified. Only Yuill and Mikler (1995) discussed this effect in detail by the introduction of the “groundwater factor.” But they didn’t account for the effect of bleed and buoyancy. 4. Little information about “bleed” is available in the literature, except that Orio (1994, 1995, 1999) provided some initial information based on his experiences. Much more work must be done to evaluate the performance enhancement provided by “bleed.” It is essential to predict the safe amount of bleed flow to prevent equipment freezeup during peak heating periods. Also, during the bleed times, the water table may fluctuate in response to draw down in the well. It may be helpful to numerically track the water table position, which has a huge influence on the power consumption of water pump in SCW systems during bleed operation. In real life, it has a significant effect on the flow rates. 5. Although some field test projects related to SCW systems have been published (Bose et al. 1979; Braud et al. 1983; Tan and Kush, 1986), no computer simulations of a SCW system have been developed, which could be used to predict the hourly heat pump entering water temperature at given hourly building loads. Hourly energy analyses can allow us to examine the transient nature of SCW systems, especially during “bleed” times. 6. Currently available simplified analytical/numerical solutions based on pure heat conduction assumptions cannot be directly coupled into SCW system simulations, in which the movement of groundwater has a significant effect on heat transfer, especially in bleed operation. 67 The heat transfer and hydrological boundary conditions in SCW systems vary in both time and space and also depend on the mode of operation of the well (e.g., bleed). The full complexity of the boundary conditions associated with standing column well operations can only be dealt with by a numerical model, which considers both groundwater flow and heat transfer. From the review of the literature discussed in Sections 2.102.12, we can see that sophisticated numerical models of groundwater flow and contaminant transport in both the saturated zones (rock) and unsaturated zones (soil) have been developed over the last two decades. These models have been applied by practicing hydrogeologists to study largescale water supply and contaminant transport problems. Although those models effectively model the pumping process and calculation of groundwater flow, they are not adapted to enable the complex timevarying thermal boundary conditions required to model SCW systems over an extended simulation period. The design parameters such as well diameter, dip tube size, insulation, well surface roughness, etc. cannot be studied without a detailed thermal borehole model of the standing column well. A summary of the different numerical and analytical models of interest is given in Table 24. Table 24 Summary of the different numerical and analytical models Analytical solution Numerical solution Effect of groundwater Effect of bleed Effect of buoyancy Comments Braud and Oliver (1980, 1983) Yes No No No No Steadystate, radial, conduction heat flow only. Mikler (1993) Yuill and Mikler (1995) No Yes Yes No No 1. Introduce “groundwater factor” ( k dz m C G w pw f × × = 2p ) to consider the groundwater effect; 2. Finite difference model that allowed calculation of the radial heat transfer at a particular depth was not twodimensional. The vertical heat transfer, end effects and bleed operation could not be considered Kelvin line source Yes No No No No Exact only for a true line source, assuming end effects are negligible. The soil has an assumed uniform and constant initial temperature. Cylindrical heat source (a) Yes No No No No Without considering the thermal mass in the borehole. Cylindrical heat source (b) Yes No No No No Considering the thermal mass in the borehole. Analytical solution with gfunction Yes No Yes No No 1. Based on superposition of steady state, periodic and extraction step analytical solutions; 2. Introduce the groundwater gfunction ( @  p t t t 9 4 1 8 ( , ) h2 ggw h ) to consider the constant regional groundwater flow. AQUA3D No Yes Yes N/A No 1. Threedimensional, finiteelement method; 2. Developed mainly for simulation of masstransport problems, but can be adapted to model heat transport without densitydependent groundwater flow; 3. Used by Chiasson (1999) to simulate and observe the effects of groundwater flow on the vertical closedloop system. SUTRA No Yes Yes N/A No 1. Twodimensional hybrid finiteelement and finitedifference method; 2. Simulated fluid movement and the transport of either energy or dissolved substances in the subsurface environment. 68 69 3. DEFINITION OF THE PROBLEM AND OBJECTIVES The goals of this research have been briefly discussed in the introduction section. In more detail, the specific objectives of this research into standing column well systems will be subdivided into several major stages: The first stage concerns the review, analysis and evaluation of currently available research related with standing column well systems. The strengths and shortcomings of currently available research are to be analyzed and evaluated. The literature review of this research attempts to provide this. The second stage involves analysis of the mechanism of heat transfer and characteristics of hydrological flow about the standing column well systems. As we know, the heat transfer in standing column well systems is very complicated because of the presence of groundwater. The detailed twodimensional numerical model of the standing column well system will consist of two parts: 1) Borehole sub model (using nodal model) The thermal model for the borehole can be described by a series of resistance network. 2) Porous medium model describing heat transfer and groundwater flow in the rock (using finite volume model). 70 The third stage will deal with computer algorithms. The mathematical and physical model will be converted into computer model. The programming language will be Fortran 90/95. At this stage, some experimental data (Mikler 1993; Henderson 2003) will be used to validate and calibrate the numerical models. The fourth stage is a parametric study and energy consumption analysis based on the detailed model. Using the numerical model, the effect of key parameters and operating strategies (e.g., bleed) will be evaluated. This research will be helpful in the design of standing column well systems by providing: simulation of standing column well systems to predict fluid temperature (entering fluid temperature to the heat pump, exiting fluid temperature from the heat pump, average fluid temperature in the well); determination of the necessary well depth per given load in specified hydrogeological conditions; influence of “bleed”. Anticipating that the detailed model will take extensive computing resources, the last stage of this work is to develop a simplified numerical onedimensional model. This should be feasible for use by engineers in HVAC application areas. This simplified model should be compared with the detailed numerical model and experimental data for accuracy. An economic performance analysis based on this simplified model is the last objective of this research. 71 The validation of the models against the experimental d
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Title  Capillary Isoelectric Focusing of Proteins with Carrier Ampholyte Ph Gradient and Immobilized Ph Gradient 
Date  20041201 
Author  Deng, Min 
Keywords  Analytical chemistry 
Department  Mechanical Engineering 
Document Type  
Full Text Type  Open Access 
Abstract  Capillary isoelectric focusing (CIEF) of proteins, which involves the separation of proteins on the basis of differences in their pI values has been investigated. To achieve efficient protein separations in carrier ampholyte pH gradient, different coating methods were studied to reduce the electroosmotic flow (EOF) and proteins interactions with capillary inner surface. It could be concluded that, Glycidoxypropyltrimethoxysilanehydroxypropyl cellulose (HPC) coated capillary column worked better with pressure mobilization while surfactantHPC coated column yielded superior separations with chemical mobilization. Another alternative to achieve CIEF is by immobilized pH gradient (IpG), which is a relatively new technology and it offers several advantages over carrier ampholyte pH gradient. This part of study involved the design of monolithic capillary columns with reactive functional groups that were required to immobilize the ampholyte pH gradient. On the average, CIEF with IpG monolithic columns provided convenient approach to achieve similar or improved CIEF separation than with carrier ampholyte pH gradient. 
Note  Dissertation 
Rights  © Oklahoma Agricultural and Mechanical Board of Regents 
Transcript  MODELING OF STANDING COLUMN WELLS IN GROUND SOURCE HEAT PUMP SYSTEMS By ZHENG DENG Bachelor of Science Shenyang Architectural and Civil Engineering Institute Shenyang, P. R. China 1996 Master of Science Tongji University Shanghai, P. R. China 2000 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY December, 2004 ii MODELING OF STANDING COLUMN WELLS IN GROUND SOURCE HEAT PUMP SYSTEMS Thesis Approved: Dr. Jeffrey Spitler Thesis Adviser Dr. Daniel Fisher Dr. David Lilley Dr. James Bose Dr. Gordon Emslie Dean of the Graduate College iii ACKNOWLEDGEMENTS I owe a lot to my advisor, Dr. Jeffrey Spitler, who first introduced me to the fascinating areas of geothermal technology and building energy simulation, which I have enjoyed greatly ever since. Dr. Spitler taught me how to do research: how to understand a problem from a fundamental level, how to spell out the core idea of a solution, and how to strike a good balance between being intuitive and being rigorous. An excellent speaker himself, he also taught me how to give good talks, which I found extremely useful. I thank him for his constructive guidance, constant support, patience, direction, and inspiration throughout my graduate study. Without his timely encouragement and support, this work would not have been done. I would like to extend my sincere gratitude and appreciation to Dr. Simon Rees who served as coadvisor along the course of the research before he returned to the U.K. His expertise in computational methods was quite valuable in helping me to achieve the project goals. My appreciation also extends to the members of my doctoral committee, Dr. Daniel Fisher, Dr. David Lilley, and Dr. Jim Bose for their committed service and support, ideas, and suggestions that helped improve my work significantly. iv I wish to deliver special credit to Mr. Carl Orio of the Water and Energy System Corporation for advice on standing column well design and operation and to Mr. Hugh Henderson of the CDH Energy Corporation for his generous assistance in providing experimental data used in validation of the standing column well system model. I would also like to thank my colleagues at the Building and Environmental Thermal Systems Research Group in Oklahoma State University, both present and former, namely, Andrew Chiasson, Xiaobing Liu, Dongyi Xiao, Weixiu Kong, Tracy Xiao, Xiaowei Xu, Haider Khan, and Bereket Nigusse for their ideas and precious help in a direct or indirect way. I am indebted to my parents, twin sister, and my brother who constantly support my every pursuit. Whatever I am today is because of their love, understanding, encouragement, and sacrifices. My infinite thanks go to Rob, absolutely for everything. This work was partially supported by the ASHRAE RP1119, and partially supported by an ASHRAE GrantinAid scholarship. ASHRAE’s support is gratefully acknowledged. v TABLE OF CONTENTS CHAPTER .................................................................................................................PAGE 1. INTRODUCTION.......................................................................................................... 1 1.1. Operation ................................................................................................................. 4 1.2. Application (limitations and benefits) ..................................................................... 6 1.3. Basic physical mechanism in SCWs (heat transfer and mass transfer in porous media) ............................................................................................................................. 9 2. BACKGROUND AND LITERATURE REVIEW...................................................... 14 2.1. Bose et al. (1979) Geothermal well system.......................................................... 14 2.2. Braud and Oliver’s research (1980’s).................................................................... 16 2.3. Tan and Kush’s research (1986) ............................................................................ 19 2.4. Mikler’s research (1995)........................................................................................ 21 2.4.1. Numerical study.............................................................................................. 21 2.4.2. Experimental study ......................................................................................... 25 2.5. Orio’s research....................................................................................................... 28 2.6. Some typical installations of SCW systems .......................................................... 32 2.6.1. Haverhill public library................................................................................... 32 2.6.2. SCW application in China .............................................................................. 33 2.7. “Geohill”open hole coaxial thermal well ............................................................. 35 2.8. Summary of the different research related to SCWs ............................................ 36 2.9. Some related analytical solutions (to ground source heat pump) .......................... 39 2.9.1. Kelvin line source solution ............................................................................. 40 2.9.2. Cylindrical heat source solution...................................................................... 43 2.9.3. Analytical solution considering the movement of groundwater (groundwater gfunction)................................................................................................................. 49 vi CHAPTER .................................................................................................................PAGE 2.10. Related research  aquifer thermal energy storage (ATES) ................................. 51 2.11. Effect of groundwater flow on closedloop groundcoupled heat exchangers .... 55 2.12. Numerical groundwater flow and heat transport models..................................... 57 2.12.1. Numerical model THETA............................................................................. 59 2.12.2. Numerical model SUTRA............................................................................. 61 2.12.3. Other Numerical models ............................................................................... 63 2.13. Summary of the literature .................................................................................... 65 3. DEFINITION OF THE PROBLEM AND OBJECTIVES........................................... 69 4. DETAILED MODEL FOR STANDING COLUMN WELL SYSTEMS.................... 72 4.1. Descriptions of the model ...................................................................................... 73 4.1.1. Hydrological flow in the SCW systems.......................................................... 73 4.1.1.1. Hydrological flow in the aquifer (porous medium) ................................. 74 4.1.1.2. Hydrological flow in borehole ................................................................. 75 4.1.2. Heat transfer mechanism in SCW systems ..................................................... 76 4.1.2.1. Heat transfer in the aquifer (porous medium).......................................... 77 4.1.2.2. Heat transfer in the borehole.................................................................... 82 4.1.2.2.1. Convective heat transfer in the borehole .......................................... 87 4.1.3. Computer algorithm........................................................................................ 92 4.2. Experimental validation....................................................................................... 101 4.2.1. Ideal experiment............................................................................................ 101 4.2.2. Validation with data from SCW system at Pennsylvania State University .. 102 4.2.2.1. Experimental data .................................................................................. 103 4.2.2.2. Methodology for validation ................................................................... 107 4.2.2.3. Validation results and conclusions......................................................... 110 4.2.3. Validation with data from a SCW system in the Haverhill public library.... 114 4.2.3.1. Experimental data .................................................................................. 114 4.2.3.2. Methodology for validation ................................................................... 116 4.2.3.3. Preprocessing the data .......................................................................... 118 vii CHAPTER .................................................................................................................PAGE 4.2.3.4. Validation results and conclusions......................................................... 120 4.3. The base case ....................................................................................................... 122 4.3.1. Building loads ............................................................................................... 123 4.3.2. Base case SCW design.................................................................................. 124 4.3.3. Results for base case ..................................................................................... 126 5. PARAMETRIC STUDY ............................................................................................ 130 5.1. Organization of parametric study ........................................................................ 130 5.2. Methodology of parametric study........................................................................ 131 5.3. Parameter values .................................................................................................. 132 5.4. System energy calculations.................................................................................. 136 5.4.1. System pressure drop without bleed ............................................................. 136 5.4.2. System pressure drop with bleed .................................................................. 138 5.4.3. Heat pump model .......................................................................................... 140 5.4.4. Circulating pump model ............................................................................... 141 5.4.5. Frictional Pressure Losses............................................................................. 141 5.4.6. Electricity costs ............................................................................................. 144 5.5. Parametric study results ....................................................................................... 144 5.5.1. The effect of thermal conductivity................................................................ 149 5.5.2. The effect of specific heat capacity............................................................... 149 5.5.3. The effect of natural geothermal gradients ................................................... 150 5.5.4. The effects of hydraulic conductivity ........................................................... 151 5.5.5. The effect of surface roughness of borehole wall ......................................... 155 5.5.6. The effect of borehole diameter .................................................................... 156 5.5.7. The effect of casing (liners) .......................................................................... 157 5.5.8. The effects of dip tube insulation and diameter............................................ 158 5.5.9. The effect of bleed ........................................................................................ 160 5.5.10. The effect of the depth of borehole............................................................. 161 5.5.11. The effect of varied depth with different bleed rate.................................... 162 viii CHAPTER .................................................................................................................PAGE 5.5.12. The effect of different rock type ................................................................. 163 5.5.13. The effect of bleed control strategy ............................................................ 164 5.5.14. System energy consumption and costs ....................................................... 168 5.5.15. Summary of parametric study..................................................................... 177 6. SIMPLIFIED MODEL FOR STANDING COLUMN WELL SYSTEMS ............... 179 6.1. Simplified onedimensional model...................................................................... 182 6.1.1. Governing energy equation........................................................................... 183 6.1.2. Groundwater velocity.................................................................................... 184 6.1.3. Boundary conditions ..................................................................................... 185 6.1.4. Borehole heat transfer ................................................................................... 187 6.1.5. Shortcircuiting ............................................................................................. 192 6.1.6. Solution of equations .................................................................................... 198 6.1.7. One dimensional numerical model with enhanced thermal conductivity..... 203 6.2. Experimental validation....................................................................................... 212 6.3. Simplified “bypass” approximation ................................................................... 216 7. ECONOMIC PERFORMANCE ANALYSIS............................................................ 222 7.1. HVACSIM+ models ............................................................................................ 222 7.1.1. The standing column well model .................................................................. 224 7.1.2. The heat pump model.................................................................................... 228 7.1.3. The water pump model ................................................................................. 229 7.1.4. The vertical Utube ground loop heat exchanger model............................... 229 7.1.4. Building description and loads calculation ................................................... 231 7.2. Simplified design procedure for standing column well system........................... 232 7.3. Economic analysis ............................................................................................... 236 7.4. Simulation results and discussions ...................................................................... 238 8. CONCLUSIONS AND RECOMMENDATIONS ..................................................... 255 ix CHAPTER .................................................................................................................PAGE 9. REFERENCES ........................................................................................................... 260 APPENDIX A................................................................................................................. 272 Numerical characteristics of the detailed model ..................................... 272 APPENDIX B................................................................................................................. 287 Grid generation input file........................................................................ 287 APPENDIX C................................................................................................................. 290 Preprocessing of flow rate for the experimental validation in Haverhill library...................................................................................................... 290 APPENDIX D................................................................................................................. 294 Calculation of shortcircuiting heat flux by integral method.................. 294 APPENDIX E ................................................................................................................. 299 Correlation for enhanced thermal conductivity ...................................... 299 x LIST OF TABLES TABLE……………………………………………………………………………...PAGE Table 21 Summary of experimental research related to SCWs....................................... 37 Table 22 Summary of the modeling of SCWs................................................................. 38 Table 23 Numerical models for groundwater.................................................................. 58 Table 24 Summary of the different numerical and analytical models............................. 68 Table 41 Hydraulic and thermal properties of the rock (Karst limestone).................... 108 Table 42 Properties of the borehole............................................................................... 108 Table 43 Hydraulic and thermal properties of the Ordovician and Cambrian sedimentary rock ......................................................................................................................... 117 Table 44 Properties of the borehole in Haverhill library............................................... 117 Table 51 Parametric study parameter values................................................................. 133 Table 52 Electric utility monthly average cost per kilowatthour for Massachusetts ... 144 Table 53 Parametric study results – effect of parameter variations on minimum and maximum exiting water temperatures and design length........................................ 147 Table 54 Results for different roughness height cases .................................................. 155 Table 55 Energy calculation results (water table = 5.0 m)............................................ 170 Table 56 Energy calculation results (water table = 30.0 m).......................................... 173 Table 61 Some information for determining building loads ......................................... 207 Table 62 Enhanced thermal conductivity from numerical insitu experiment .............. 209 Table 63 Rock thermal conductivity for different models using Mikler’s data ............ 213 Table 64 Rock thermal conductivity for different models using Haverhill data........... 213 Table 65 Difference between two limiting cases .......................................................... 218 Table 71 Installation costs for different ground heat exchanger system....................... 237 Table 72 Electric utility monthly average cost per kilowatthour for commercial building in different states..................................................................................................... 238 xi TABLE……………………………………………………………………………...PAGE Table 73 Summary of ground heat exchanger design parameters for Boston, MA...... 239 Table 74 Summary of ground heat exchanger simulation results for Boston weather file ................................................................................................................................ 240 Table 75 Annual energy cost breakdowns for SCW system deadband bleed control in Boston, MA............................................................................................................. 244 Table 76 Far field temperatures and building loads for different cities ........................ 245 Table 78 Summary of ground heat exchanger simulation results for Harrisburg, PA .. 247 Table 79 Summary of ground heat exchanger simulation results for Portland, OR...... 248 Table 710 Summary of ground heat exchanger simulation results for Concord, NH... 249 Table 711 Summary of ground heat exchanger simulation results for Birmingham, AL ................................................................................................................................ 250 Table 712 Feet per ton for different ground heat exchangers ....................................... 251 Table 713 Comparisons of capital cost for different cites............................................. 253 Table 714 20year life cycle cost (present values) for different cites ........................... 254 Table E1 Enhancement factor for different cases.......................................................... 302 xii LIST OF FIGURES FIGURE……………………………………………………………………………...PAGE Figure 11 Schematics of different ground source heat pump systems .............................. 3 Figure 12 A schematic drawing showing the borehole arrangement ................................ 5 Figure 13 How Groundwater occurs in rocks.................................................................... 9 Figure 14 A typical schematic of standing column well ................................................. 13 Figure 21 Geothermal well design (Bose et al. 1979).................................................... 15 Figure 22 Concentric well pipes for thermal exchange to earth with liquid source heat pump (Oliver and Braud 1981) ................................................................................. 16 Figure 23 A schematic ‘thermal well’ studied by Yuill and Mikler (1995).................... 21 Figure 24 Schematics of standing column well from description of Orio (Orio 1999) .. 31 Figure 25 Standing column well water temperature trends in Haverhill public library.. 33 Figure 26 The schematic drawing of “single well for supply and return” (HYY 2003) . 34 Figure 27 Open hole coaxial thermal well “Geohill”...................................................... 36 Figure 28 Schematic drawing showing the cylindrical heat source embedded in an infinite medium......................................................................................................... 40 Figure 29 A schematic drawing of a core separated by the insulation from the sheath .. 47 Figure 210 Heat storage in an aquifer ............................................................................. 52 Figure 41 Distribution of the fluid pressure in the ground with respect to the water table .................................................................................................................................. 74 Figure 42 Heat transfer mechanisms in SCW systems.................................................... 77 Figure 43 The relationship between the actual thermal conductivity and the mechanisms that contribute to it .................................................................................................... 78 Figure 44 Control volume for the solidliquid phase ...................................................... 79 Figure 45 The borehole thermal model ........................................................................... 83 Figure 46 A schematic control volume in the borehole .................................................. 84 xiii FIGURE……………………………………………………………………………...PAGE Figure 47 The geometry of a typical cell in the mesh showing the relationship between the face and cell centroids......................................................................................... 94 Figure 48 Flowchart of computer algorithm for the overall SCW systems .................... 97 Figure 49 A 2D cylindrical grid of single standing column well .................................. 100 Figure 410 Cooling modeground load ......................................................................... 104 Figure 411 Cooling modetotal water flow rate ............................................................ 104 Figure 412 Cooling modeentering and return water temperatures............................... 105 Figure 413 Heating modeground load.......................................................................... 106 Figure 414 Heating modetotal water flow rate ............................................................ 106 Figure 415 Heating modeentering and return water temperatures............................... 107 Figure 416 Comparisons of temperatures back to the heat pump for the detailed model and Mikler’s data in cooling mode ......................................................................... 111 Figure 417 Comparisons of temperatures back to the heat pump for the detailed model and Mikler’s data in heating mode.......................................................................... 112 Figure 418 Water temperatures entering and leaving the well in Haverhill.................. 115 Figure 419 System flow rates in Haverhill library ........................................................ 119 Figure 420 Comparison of temperatures back to heat pump for the detailed model and Haverhill data.......................................................................................................... 121 Figure 421 Building load of a building in Boston......................................................... 124 Figure 422 A schematic drawing showing the borehole geometric arrangement for the base case.................................................................................................................. 125 Figure 423 Borehole temperatures when peak heating load occurs .............................. 127 Figure 424 Borehole temperatures when peak cooling load occurs.............................. 127 Figure 425 Borehole suction and discharge temperatures and building loads for the base case.......................................................................................................................... 128 Figure 426 Head contours for the base case.................................................................. 129 Figure 51 Pipe system schematic for cases without bleed ............................................ 136 Figure 52 Pipe system schematic for cases with bleed.................................................. 138 Figure 53 Schematic diagram of the pipe work showing the arrangement of fittings .. 143 xiv FIGURE……………………………………………………………………………...PAGE Figure 54 Relationship between EWT and length of borehole ..................................... 146 Figure 55 The effect of thermal conductivity of rock on the water temperature back to the heat pump.......................................................................................................... 149 Figure 56 The effect of specific heat capacity of rock on the water temperature back to the heat pump.......................................................................................................... 150 Figure 57 The effect of natural geothermal gradients of rock on the water temperature back to the heat pump ............................................................................................. 151 Figure 58 The effect of hydraulic conductivity of rock on the water temperature back to the heat pump.......................................................................................................... 151 Figure 59 Total heat transfer rates along the borehole wall in the different cases of varied hydraulic conductivity ............................................................................................ 152 Figure 510 The effect of roughness height of borehole wall on the water temperature back to the heat pump ............................................................................................. 156 Figure 511 The effect of borehole diameter on the water temperature back to the heat pump ....................................................................................................................... 157 Figure 512 The effect of casing length on the water temperature back to the heat pump ................................................................................................................................ 158 Figure 513 The effect of thermal insulation of the dip tube on the water temperature back to the heat pump ............................................................................................. 159 Figure 514 The effect of diameter of dip tube on the water temperature back to the heat pump ....................................................................................................................... 159 Figure 515 The effect of bleed rate on the water temperature back to the heat pump .. 160 Figure 516 The effect of depth of borehole on the water temperature back to the heat pump ....................................................................................................................... 161 Figure 517 The effect of depth of borehole on the water temperature back to the heat pump ....................................................................................................................... 162 Figure 518 The effect of rock type on the water temperature back to the heat pump... 164 Figure 519 The effect of bleed control strategy on the minimum water temperature back to the heat pump in winter....................................................................................... 166 xv FIGURE……………………………………………………………………………...PAGE Figure 520 Comparison water temperatures back to the heat pump between nonbleed case, constant bleed and deadband bleed control case............................................ 167 Figure 521 Entering and exiting fluid temperature difference during the heating season under temperaturedifference bleed control showing the points at which bleed was activated .................................................................................................................. 168 Figure 522 Comparison of annual energy costs for water table depths of 5 m and 30 m ................................................................................................................................ 176 Figure 61 Two limiting cases for standing column well system................................... 180 Figure 62 Schematic drawing showing 1D model for the SCW system...................... 186 Figure 63 Water temperature variation along borehole depth without bleed................ 188 Figure 64 Water temperature variation along borehole depth with bleed ..................... 188 Figure 65 The simplified thermal borehole model ........................................................ 189 Figure 66 Crosssection of the borehole in SCW system and the corresponding thermal circuit ...................................................................................................................... 192 Figure 67 Thermal resistances of a D circuit .............................................................. 194 Figure 68 Flow chart for the simplified onedimensional model .................................. 199 Figure 69 Sensitivity of borehole wall temperatures to the grid number in FDM........ 201 Figure 610 The flow chart to get actual /enhanced thermal conductivity ..................... 205 Figure 611 Comparison of minimum temperatures back to the heat pump in different models ..................................................................................................................... 209 Figure 612 Comparison of maximum temperatures back to the heat pump in different models ..................................................................................................................... 210 Figure 613 Comparison of the minimum exiting water temperatures from the well in different models with ground temperature gradient................................................ 212 Figure 614 Comparisons of temperatures back to the heat pump for the simplified model (SCW1D), the detailed model, and Mikler’s data in cooling mode........................ 214 Figure 615 Comparisons of temperatures back to the heat pump for the simplified model (SCW1D), detailed model, and Mikler’s data in heating mode.............................. 215 xvi FIGURE……………………………………………………………………………...PAGE Figure 616 Comparisons of temperatures back to the heat pump for the simplified model (SCW1D), the detailed model, and Haverhill data ................................................. 216 Figure 617 Standing column well showing bleed and bypass flows ........................... 217 Figure 618 Comparison of temperatures back to the heat pump in limiting cases........ 219 Figure 619 Comparison of temperatures back to the heat pump in limiting cases (winter) ................................................................................................................................ 219 Figure 620 Comparison of temperatures back to the heat pump in limiting cases (summer) ................................................................................................................. 220 Figure 71 Threecomponent models of a standing column well system in HVACSIM+ ................................................................................................................................ 223 Figure 72 Component configuration of standing column well model........................... 225 Figure 73 Component configuration of vertical ground loop heat exchanger............... 230 Figure 74 A peak of cooling load event in Boston, MA small office building ............. 232 Figure 75 Flow chart for simplified design procedure .................................................. 233 Figure 76 Required total borehole depth for different ground heat exchanger systems in Boston, MA............................................................................................................. 241 Figure 77 20year life cycle cost (present value) in Boston, MA ................................. 241 Figure 78 Annual energy cost for SCW systems for bleed control operation in 5meter and 30meter water table depths with different bleed rates in Boston, MA ........... 244 Figure 79 Feet per ton for different ground heat exchangers for small office building 251 Figure 710 Required total borehole depth for different ground heat exchanger systems in different cities ......................................................................................................... 252 Figure 711 Capital cost for different ground heat exchanger systems in different cities ................................................................................................................................ 253 Figure 712 20year cycle cost (present value) for different ground heat exchanger systems in different cities........................................................................................ 254 Figure A1 The schematics of simulation domain.......................................................... 274 Figure A2 Sensitivity of integral mass flow rate to the domain depth (Domain radius: 200m) ...................................................................................................................... 277 xvii FIGURE……………………………………………………………………………...PAGE Figure A3 Sensitivity of minimum temperature back to the heat pump to the domain depth (Domain radius: 200m) ................................................................................. 277 Figure A4 Sensitivity of temperature back to the heat pump at the 8760th hour to the domain depth (Domain radius: 200m) .................................................................... 278 Figure A5 Sensitivity of integral mass flow rate to the domain radius (Domain depth: 380m) ...................................................................................................................... 279 Figure A6 Sensitivity of minimum temperature back to the heat pump to the domain radius (Domain depth: 380m) ................................................................................. 279 Figure A7 Sensitivity of temperature back to the heat pump at the 8760th hour to the domain radius (Domain radius: 380 m) .................................................................. 280 Figure A8 Sensitivity of integral mass flow rate to grid number in depth direction (Grid number in Rdirection: 200).................................................................................... 281 Figure A9 Sensitivity of minimum temperatures back to the heat pump to the grid number in depth direction (Grid number in Rdirection: 200)................................ 281 Figure A10 Sensitivity of integral mass flow rate to grid number in radial direction (Grid number in depth direction: 160).............................................................................. 282 Figure A11 Sensitivity of minimum temperatures back to the heat pump to the grid number in radial direction (Grid number in depth direction: 160) ......................... 283 Figure A12 Sensitivity of temperatures back to heat pump to the timestep size ......... 286 Figure D1 Illustration of calculation of shortcircuiting flux........................................ 295 Figure E1 Data density plot........................................................................................... 301 Figure E2 Threedimensional relationship among the enhanced factor, hydraulic conductivity and effective thermal conductivity..................................................... 303 xviii NOMENCLATURE a the radius of pipe(m [ft]) bleedrate the normalized bleed rate in the system (%) B the integration variable C the summation of the series ¥ = + ×  1 1 ( !) ( 1) N N N N N y Cp the specific heat of the ground(J/kgK [Btu/lbmºF]) pw C the specific heat of water (J/kgK [Btu/lbmºF]) D the distance in feet to the recharge well (m [ft]) Dborehole the hydraulic diameter of borehole (m [ft]) f the Moody friction factor Fo the Fourier number defined as: 2 0 r Fo =at g the acceleration due to the gravity (m/s2 [ft/s2]) f G the groundwater factor (+ denotes flow into the well;  denotes flow out of the well) h the hydraulic head (m [ft]) hborehole the heat transfer coefficient at the borehole wall (W/m2K [Btu/hrft2ºF]) H the total dynamic head for the water pump (Pa) Ji the Bessel function of order i xix s k the thermal conductivity of the ground (W/mK [Btu/hrftºF]) kwater the thermal conductivity of water (W/mK [Btu/hrftºF]) eff k the effective thermal conductivity (W/mK [Btu/hrftºF]) k the intrinsic permeability (m2 or Darcy [ft2]) K the hydraulic conductivity of ground (m/s [gpd/ft2]) Keff the effective hydraulic conductivity (m/s [ft/s]) L the borehole depth (m [ft]) m w the mass flow rate of water through heat pump system (kg/s [lbm/sec]) m the mass of water in the standing column well (kg [lbm]) n the porosity of rock Nu the local Nusselt number p the pressure (N/m2 [lbf/ft2]) Pr the Prandtl number q the specific discharge (m/s [ft/s]) q'' the heat flux (W/m2 [Btu/hrft2]) q the specific discharge (volume flow rate per unit of crosssectional area) (m/s [gpd/ft2]) qsc the shortcircuiting heat transfer rate (W/m [Btu/fthr]) R the far field radius rb the borehole radius (m [ft]) Rb the thermal resistance of the borehole (K/(W/m) [hrftºF/Btu]) xx Rsc the short circuiting thermal resistance (K/(W/m) [hrftºF/Btu]) Ree the roughness Reynolds number e e / Re / 2 Re D f = S1 the thermal capacity of the cylinder of perfect conductor (J/m3K [Btu/ft3ºF]) t the heat pump run time (hr) Tb the borehole wall temperature (ºC [ºF]) f 1 T the temperature of water in the annulus (ºC [ºF]) f 2 T the temperature of water in the dip tube (ºC [ºF]) Tf the average fluid temperature (ºC [ºF]) Tfo the water temperature leaving the well (ºC [ºF]) Tfi the water temperature returning to the well (ºC [ºF]) Tf _ old the representative water temperature at the previous time step (ºC [ºF]) T q (t) f the average fluid temperature at time t (ºC [ºF]) Tgw the temperature of groundwater entering into the well (ºC [ºF]) Tr the far field temperature (ºC [ºF]) Tu the undisturbed temperature of the ground (ºC [ºF]) Tw the borehole wall temperature (ºC [ºF]) Tfreeze the fluid temperature at freezing point (oC [ºF)]) TExFT the exiting fluid temperature from the heat pump (i.e., the fluid temperature entering the ground heat exchanger) (oC [ºF)]) xxi TEFT the entering fluid temperature to the heat pump (i.e., the fluid temperature leaving the ground heat exchanger) (oC [ºF)]) u the integration variable V the mean velocity in the given pipe(m/s [ft/s]) Vr the average linear groundwater velocity vector (m/s [ft/s]) w the power consumption of the circulating water pump (W) Yi the modified Bessel function of order i z the vertical coordinate (m [ft]) a the thermal diffusivity of the ground (m2/s [ft2/hr]) b the underrelaxation factor l the integration variable g the Euler’s constant, 0.5772157… r the density of the ground (kg/m3[lbm/ft3]) r w the density of the groundwater (kg/m3 [lbm/ft3]) rc the volumetric heat capacity (J/m3K [Btu/ft3ºF]) 2 rv2 the velocity pressure (Pa) rgz the elevation pressure (Pa) n the kinematic fluid viscosity (m2/s [ft2/sec]) e the height of the surface roughness (m [ft]) m the dynamic viscosity of water (Ns/m2 [lbfs/ft]) h the efficiency of the circulating water pump T the fluid temperature change across the heat pump (oC [ºF)]) xxii Dt the time increment(sec [sec]) Dp the total pressure loss (fitting +friction) (Pa) sc DT the temperature difference caused by the short circuiting (ºC [ºF]) 1 1. INTRODUCTION In recent years, ground heat source heat pump systems have become increasingly popular for use in residential and commercial buildings. These systems include several different variations, all of which reject heat and/or extract heat from ground: (1) groundcoupled heat pump (GCHP) systems; (2) surface water heat pump (SWHP) systems; (3) groundwater heat pump (GWHP) systems: a. Standing column well (SCW) systems; b. Open loop groundwater systems. The schematics of these different systems are shown in Figure 11. Considerable research effort has been spent on ground heat source heat pump systems, especially on the single Utube ground heat exchanger, in recent decades. Existing engineering design manuals, such as IGSHPA (1988), ASHRAE (1995), Kavanaugh and Rafferty (1997), cover the first two system types and open loop groundwater systems. However, relatively few design tools and simulation models are available for SCW systems. SCW systems are the focus of this research. SCW systems are also referred to in the literature as “turbulent wells”, “energy wells”, “concentric wells”, “recirculating wells”, “geowells”, “thermal wells”, and “closedloop, openpipe systems”. Rawlings and Sykulski (1999) stated that the first documented suggestion of using the ground as a heat source was in 1912 in Switzerland, and the first ground source heat 2 pump in North America was installed in a house in Indianapolis in 1945. However, commercial use of the ground as a heat source/sink didn’t begin until the first oil crisis in 1973. By the mid 1980’s, advances in heat pump efficiencies and operating ranges, combined with better materials for ground loops, allowed this technology to enter the market. At the same time, commercial type applications started to gain popularity. Geothermal systems have the potential to reduce primary energy consumption and thus significantly reduce the emission of greenhouse gases and other pollutants. The use of SCW was first suggested by local Maine well drillers and hydrogeologists (Orio 1994). In fact, the concept of standing column well systems is about as old as the ground water heat pump systems, but is recently receiving much more attention because of their lower installation cost, lower operating cost, and improved overall performance in the regions with suitable geological conditions. In the mid1970’s, Dr. Bose from Oklahoma State University began to do field tests on standing column well systems. Later, Dr. Braud from Louisiana State University further evaluated this technology. Compared with other ground heat source heat pump systems, shorter boreholes and more stable water temperatures make the SCW system an attractive commercial and industrial design approach. Now, there are approximately 1000 SCW installations in the United States. Most of them are located in the Northeast and Pacific Northwest in addition to parts of Canada in heatingdominated residential and light commercial applications (ASHRAE 1119TRP). These regions have lower mean ground temperature and higher heating loads than other areas, so now most SCW design is focused on heat extraction. 3 Figure 11 Schematics of different ground source heat pump systems (Reprinted by permission from Oak Ridge National Laboratory) (http://www.eren.doe.gov/femp) 4 1.1. Operation The SCW system can be thought of as a cross between closedloop earthcoupled system and openloop groundwater source system. During much of the year, they operate by recirculating water between the well and the heat pump. However, during peak temperature periods, they can “ bleed” some water from the system to induce groundwater flow. Usually, only one well is required; larger projects may have several wells in parallel. In SCW systems, water is recirculated between the well and the building (heat pump). Deep bores are drilled in hard rock, creating a standing column of water from the static water level down to the bottom of the bore. Water is recirculated from one end of the column to the heat pump, and back to the other end of the column (Figure 12). 5 A A AA section Discharge Tube Ground Surface Borehole Wall (Suction Tube) Dip Tube Heat Pump Water Table Dip Tube Discharge Tube Figure 12 A schematic drawing showing the borehole arrangement During peak heat rejection or extraction periods, if the wellwater temperature drops too low or climbs too high, standing column well systems can bleed part of the water rather than returning it all to the well. This causes water to flow to the column from the surrounding formation to make up the flow. This cools the column and surrounding ground during heat rejection in the summer, and heats the column and surrounding ground during heat extraction in the winter, thus restoring the wellwater temperature to the normal operating range and improving the system performance. The bleed water can be diverted to a storm sewer, used for domestic water consumption, or otherwise 6 disposed. Sometimes, SCW systems serve to provide household domestic water, which cause the system to naturally “bleed” the whole year. 1.2. Application (limitations and benefits) SCW systems are used in geologic areas with abundant ground water. This system can provide the necessary water flows as well as shorter heat transfer lengths (depths) and the ability to return water to the same aquifers. The combination of relatively shallow water table and a deep well (sometimes greater than 300 m or 1000 ft) means that the well has a large water volume, about 1800 L per 100 m (150 gal per 100 ft) for a 152.4 mm (6 in) nominal diameter well (Sachs and Dinse 2000). Based on experience by the Water and Energy Systems Corporation, 50 to 60 feet of water column is needed per ton of building load (4.3m/kW to 5.2m/kW). Commercial systems larger than 350 kW (100 tons) have used multiple standing column wells with success (Orio 1994). The application of SCW systems is limited to geologic regions with good ground water quality like other ground water heat pump systems. This enables the ground water to be directly circulated through the heat pump. Applications also exist in areas with poorer water quality. In such situations it is common practice to use an intermediate heat exchanger between the well and the heat pump in order to avoid fouling the heat pump heat exchangers. Sachs and Dinse (2000) suggested that the designer of SCW systems should (1) work with an experienced local hydrologist and (2) avoid any areas with salt bed or other 7 formation that could be dissolved. Also, any water well including standing column wells must be constructed, developed, and operated according to state and local regulations for water wells. It is imperative that designers and installers of SCW systems be aware of the regulations in their locations (DenBraven 2002). Generally speaking, SCW systems have some advantages shared with all the other forms of ground source heat pump systems: · Economy When properly designed, a geothermal heat pump system is one of the lowest cost ways of providing heating/cooling because of high equipment efficiency, annual storage/reuse of energy, and availability. However, geothermal heat pump systems have comparatively high capital costs. A geothermal system often has lower life cycle costs than conventional systems due to its reduced energy and maintenance costs. Because there is no outdoor equipment in the geothermal systems, corrosion, weathering and vandalism are not normal problems. · Environmental benefits The need for electricity (pumps) introduces the only credible source of possible environmental concern for a geothermal system. The geothermal system itself produces zero local pollution. This system causes less carbon dioxide emission and other pollutants than its conventional alternatives, thus reducing global warming and other environmental impacts. 8 · Reduced requirement for mechanical room floor place · Quiet operation · Potential for reducing the peak electrical demand Standing column well systems share the same advantages, in terms of energy efficiency, environmental benefits, low maintenance, etc. with other forms of geothermal heat pump systems. At the same time, the heat exchange rate in a standing column well is enhanced by direct contact and by the pumping action, which promotes ground water flow to and from the borehole. Consequently heat transfer with the surrounding rock takes place by advection in addition to conduction. If a standing column well is considered as a cylinder, the surface area for heat exchange of a 152.4 mm (6 in) borehole with 304 m (1000 ft) long is about 145 m2 (1570 ft2), which allows substantial heat exchange. Put another way, SCW systems have substantially heat exchange rate and the fact that such systems are open loop means that the fluid flowing through the heat pump system is closer to the mean ground temperature compared to systems with closed loop Utube heat exchangers. SCW systems have a lower initial cost because the borehole depths are in the 5060 feet per ton compared to closed loops at 150 or more feet per ton. Thus, the borehole in SCW systems could be onehalf the depth of closed loop earth coupled methods (Orio, 1994). To date, the typical drill rigs in the regions where SCW system are mainly located (Northeast and Pacific Northwest), can be able to reach 560 m (1800 ft) and the deepest standing column wells are in the range of 460 m (1500 ft). The depth of this costeffective geothermal coupled method can be extended with the development of rigs. 9 1.3. Basic physical mechanism in SCWs (heat transfer and mass transfer in porous media) First, some definitions are given for later use. Above the water table lies the unsaturated zone, where voids between rocks are mostly filled with air. Some water is held in the unsaturated zone by molecular attraction, and it will not flow toward or enter a well. In the saturated zone, which lies below the water table, all the openings in the rocks are full of water that may move through the aquifer to streams, springs, or wells from which water is being withdrawn (see Figure 13). This research is mainly focused on the saturated zone. Figure 13 How Groundwater occurs in rocks* (http://capp.water.usgs.gov/GIP/gw_gip/how_occurs.html) * Public resource provided by USGS website 10 The energy transport in the ground outside of the standing column well is through a porous media (aquifer). An “aquifer” is defined by Driscoll (1986) as formation, group of formations, or part of a formation that contains sufficient saturated permeable material to yield economical quantities of water to wells and springs. The word aquifer comes from the two Latin words, aqua, or water, and ferre, to bear or carry. An aquifer literally carries water underground. We can consider an aquifer as a porous medium that consists of a solid phase and an interconnected void space totally filled with groundwater. Transport of groundwater occurs in the interconnected voids. Heat is transported both in the solid matrix and in the void system, forming a coupled heat transfer process with heat diffusion (conduction) and heat advection by moving groundwater. The governing steady state, onedimensional equations for heat and fluid flow are given by Fourier’s law and Darcy’s law, which are identical in the form: Fourier’s law: dx dT q''= k (1.1) Where q''is heat flux (W/m2 [Btu/hrft2]); k is the thermal conductivity of the ground (W/mK [Btu/hftºF]); Darcy’s law: dx dh q = K (1.2) Where q is the specific discharge (volume flow rate per unit of crosssectional area) (m/s [gpd/ft2]); K is the hydraulic conductivity of ground (m/s [gpd/ft2]); h is the hydraulic head (m [ft]). 11 The specific discharge q is related to average linear ground water velocity v by: n q v = (1.3) Where n is the porosity, which, for a given crosssection of a porous medium, is the ratio of the pore area to the crosssectional area (Fetter 1988). The uncased borehole in SCW systems allows the heat exchange fluid to be in direct contact with the earth and allows ground water infiltration over the entire length of the borehole. This direct contact eliminates the conductive resistances of plastic pipe and grout associated with a typical earthcoupled Utube system. The presence of ground water enhances the usability of the ground as a heat source/sink. The larger heat capacity of the watersaturated soil/rock dampens the temperature changes in the ground compared with unsaturated soil/rock. Furthermore, the movement of ground water enhances the heat transfer. In addition, the rough borehole wall can induce turbulence; so higher heat transfer coefficients can be obtained. The moisture content of soil has a significant effect on its thermal properties. When water replaces the air between particles it reduces the contact resistance. The thermal conductivity can vary from 0.25 W/mK for dry soil to 2.5 W/mK for wet soil (Rawlings and Sykulski 1999). When heat is extracted/rejected, there will be migration of moisture by diffusion, thus the effective thermal conductivity will be increased. As mentioned above, ground water movement will have a significant impact on heat transfer through the ground because heat is transferred by convection due to moving 12 groundwater as well as conduction. In the presence of groundwater, buoyancy flows generated by the temperature differences also affect the temperature distribution in the ground. The presence of groundwater flow in SCW systems changes the heat transfer problem from pure heat conduction to a coupled flow and advectivediffusive heat transfer problem. Accordingly, heat transfer in the ground surrounding SCW systems is much more complicated and much more difficult to simulate. Also, the heat exchange fluid (water) in SCW systems is affected by the transient building thermal loads in addition to the heat transfer in the porous medium (aquifer) around the borehole of SCW systems. Therefore, this problem is characterized by timevarying boundary conditions. Through this research, we hope to make a more complete and much better understanding of the characteristics of standing column well systems, such as necessary well length per given load, preferred operating strategies (bleed, etc.) The first objective of this work is to analyze and evaluate the currently available research on standing column well systems. The second objective is to develop a detailed numerical model of standing column well systems. The third objective is to use the detailed numerical model to perform a parametric study of the effects and significance of standing column well design parameters. Finally, the fourth objective is to develop a simplified analytical and/or numerical model, which is feasible to be used as a design tool by HVAC engineers. 13 Figure 14 A typical schematic of standing column well (http://www.hvac.okstate.edu/ ) 14 2. BACKGROUND AND LITERATURE REVIEW Although there are numerous SCW systems installations in the United States, very little has been published on the theory of operation and modeling. The literature directly related to the standing column well, is reviewed first. Secondly, related research in the discipline of hydrogeology is reviewed. 2.1. Bose et al. (1979) Geothermal well system The first reported field research on SCW systems is described by Bose et al. (1979). This system was referred to as a “Geothermal well system”. The Geothermal well is somewhat different from the current standing column well (Figure 14). While it has a standing column, ground water cannot enter into the well because it is completely cased. A schematic of the Geothermal well is shown in Figure 21. A 5inch PVC pipe with cap at both ends, pressurized to about 15 psig (at the top of the well), is the most important component in this vertical heat exchanger. The water may be discharged to the top or bottom, and the discharge tube may be insulated. In the experimental well described by Bose et al. the water exiting the heat pump is discharged into the bottom of the 5inch PVC pipe by means of 11/4inch tube (the dip tube) running the length of the well. Regarding the location of the discharge pipe, Bose et al. (1979) did some tests during the summer. From the test results, it was found that the entering water temperature to the heat 15 pump would be lower when the hot water from the heat pump was discharged to the bottom of the well rather than to the top of the well. Also a series of tests have shown an improvement of approximately 20 % in Uvalues (overall heat transfer coefficient) for wells by using insulated dip tubes. MANHOLE AIR VENT SAMPLE VAVLE WELL CAP TO HEAT PUMP FROM HEAT PITLESS ADAPTER CONCRETE PLUG (REQUIRED BY HEALTH DEPT.) 1 PVC PIPE WATER TABLE 5'' PVC WELL CASING END CAP PUMP 1 4 '' Figure 21 Geothermal well design (Bose et al. 1979) 16 Since no exchange of water with the surrounding formation is allowed, this system cannot be expected to perform as well as a modern SCW system. 2.2. Braud and Oliver’s research (1980’s) HEAT PUMP EARTH CONCENTRIC PIPE IN WELL Figure 22 Concentric well pipes for thermal exchange to earth with liquid source heat pump (Oliver and Braud 1981) Analysis of steadystate heat exchange to earth with concentric well pipes and governing equations for fluid temperature distribution in the pipes were given by Oliver and Braud (1981). They derived a closedform analytical solution for the concentric vertical, groundcoupled heat exchanger under steadystate operation by assuming an isothermal 17 ground surface 10 m (3.3 ft) away from the center of the heat exchanger. The temperature difference between fluid in the annular area and the earth is the driving force for the heat transfer to the earth mass, and the temperature difference in the two pipes is the driving force for the crossover heat flow. Oliver and Braud’s analysis assumed steadystate, radial, conduction heat flow only. They didn’t account for the effect of ground water flow. Their analysis is based on the following assumptions: all physical parameters are independent of time, location, pressure and temperature; all heat flow is radial in the heat exchanger; the only mechanism for heat transfer is conduction (this has the effect of modeling a cased system as described by Bose); temperature in the fluid is constant at each cross section (inside pipe). They derived differential equations from the standpoint of conservation of energy for a control volume of fluid and surrounding ground, and solved them analytically. The general solution was given by: { } { } { Z} { Z} Z Z Z Z TR Z 2 2 1 1 2 2 2 1 1 1 1 2 exp exp ( 1) exp ( 1) exp ( ) ( ) ( ) l l l l l l l l l l q q  +  + = = (2.1) Where 1 1 0 q = T T ; 2 2 0 q = T  T ; mC U x Z = 21 ; 18 21 02 U b = U ; x is the coordinate of the position along the axis of the heat exchanger well (m [ft]), ( x = 0 at the bottom of well); 0 T is the earth temperature (ºC [ºF]); 1 T is the temperature of the fluid in the inner return pipe at position x (ºC [ºF]); 2 T is the temperature of the fluid in the annular area at position x (ºC [ºF]); m is the fluid circulation rate (kg/s [lbm/hr]); C is the specific heat of the fluid in the pipe (J/kgK [Btu/lbmºF]); 21 U is the fluid to fluid conductance of the inner pipe(W/mK [Btu/hrftºF]); 02 U is the conductance of the well casing plus earth cylinder (W/mK [Btu/hrftºF]), (includes film coefficient if appropriate); 1 2 l ,l are functions of b (the type of function was not described in this paper). In residential heating and cooling use, the operation of a heat pump is cyclic; the energy exchange to earth is highly transient rather than steady state. The steady state value from Oliver and Braud’s model (1981) underestimates the heat transfer during the whole year cyclic operation. It is therefore unrealistic to design the heat exchanger on the basis of its steady–state operation. Moreover, this model does not take into account the beneficial effect of the ground water flow and bleed. Braud et al. (1983) measured the heat exchange rate of earthcoupled concentric pipe heat exchangers in Louisiana State University. They noted greater conductance values of the 19 concentric pipes over the single Utubes when the concentric heat exchanger consisted of a steel outer casing (rather than PVC) and PVC inner pipes. Some thermal “shortcircuiting” could occur between the inner and outer flow channel, but this can be reduced with use of a low thermal conductivity inner pipe. 2.3. Tan and Kush’s research (1986) A 152 mm (6 in) diameter, 189 m (620 ft) deep standing column well located at Westchester County, NY, was used for this R&D/field test project. An offtheshelf, 5 ton waterto –air heat pump intended for groundwater use was installed in this residential building. Tan and Kush (1986) called the SCW a “semiclosed loop” because of the influx/outflow of ground water at fissures in the rock. While it is the first SCW system described with an uncased borehole, no bleed was utilized. Water was withdrawn at a depth of 12.2 m (40 ft) and the return water from the heat pump was reinjected at a depth of 183 m (600 ft). The fluid water flow rate was 0.6935 kg/s (11 gpm) with a 0.25 kW (1/3 hp) circulating pump at the ground level outside the well. The static water table level was at a depth of 1.52 m (5 ft). Water was discharged to the bottom of the well; thus the water supplied to the heat pump does not pass through the region of discharge. The well, heat pump and system parameters such as water temperature back to the heat pump, and from the heat pump were thoroughly measured and documented for a continuous 22month period in this field test project. Also, the linesource theory was used to approximately calculate the theoretical longterm seasonal temperature change of the earth surrounding the well as a function of radius. It was found that the best 20 agreement between the analytical and the actual ground temperature was obtained when a value of thermal conductivity of 2.6 Btu/fthrºF (an “enhanced” thermal conductivity) was used. This may be compared with the actually averaged one (less than 2.4 Btu/fthr ºF, which was assumed to be the value of granite rock surrounding the well). Tan and Kush (1986) didn’t use any insitu test method to obtain this actually averaged value of thermal conductivity. Presumably, they took the values directly from publicly available handbooks. Tan and Kush (1986) pointed out that SCW systems performed very well as earthcoupled devices in both heating and cooling season. They measured the entering water temperature (EWT) to the heat pump and found it ranged from 6.9 ºC (44.5 ºF) in early January to slightly over 15.6 ºC (60 ºF) in midJuly of the second cooling season. According to their field test, Tan and Kush (1986) concluded that SCW systems could give very stable EWT to the heat pump even in severe winter or summer. In their test, the lower limit for the heat pump operation, which was set as leaving water temperature of 3.3 ºC (38 ºF), was never reached. Regarding the influence of ground water, if the well is uncased, the local hydrology will affect the performance of well. Although in their test, this effect was not quantified, Tan and Kush (1986) pointed out that substantial infiltration/exfiltration can enhance the system performance greatly. No information about bleed was found in Tan and Kush’s research. 21 2.4. Mikler’s research (1995) ground water table EW RW steelcasing PVC pipe submersible water pump borehole wall PVC perforated end section return water loss to the ground ground water gain to the system Figure 23 A schematic ‘thermal well’ studied by Yuill and Mikler (1995) 2.4.1. Numerical study Yuill and Mikler (Mikler 1993; Yuill and Mikler 1995) used a well at Pennsylvania State University to research the performance of standing column well systems. They referred to 22 the standing column well as a “thermal well.” The thermal well serves as a circulation, withdrawal and injection well at the same time. But the well does not bleed; the injection rate always matches the withdrawal rate. They developed a simplified mathematical model to describe the coupled thermohydraulic energy transfer by conduction and convection in an aquifer surrounding a thermal well. A schematic of the well system is shown in Figure 23. To simplify the analysis, Yuill and Mikler (1995) used the following assumptions in their study: homogeneous and isotropic aquifer cylindrical symmetry of the coupled flow around the axis of the borehole no heat or ground water flow in the vertical direction laminar ground water no dispersion (no groundwater diverted to other places) thermal well is in the dynamic hydraulic equilibrium with the surrounding groundwater aquifer natural hydraulic gradients in the aquifer are neglected; hydraulic gradients caused by pumping are dominant. Based on these assumptions and by introduction of a “groundwater factor” ( f G ), which is the ratio of convection to conduction, the governing partial differential equations are derived, simplified, and solved numerically. t T r T r G r T f ¶ = ¶ ¶ ¶ ± + ¶ ¶ a 1 1 2 2 (2.2) 23 Where f G is the groundwater factor (+ denotes flow into the well;  denotes flow out of the well); k dz m C G w pw f × × = 2p ; w m is the groundwater mass flow rate (kg/s [lbm/hr]), (either discharge groundwater or suction groundwater flow); pw C is the specific heat of water (J/kgK [Btu/lbmºF]); k is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the ground (m2/s [ft2/hr]); z is the vertical coordinate (m [ft]). The governing equations are converted into explicit forms of finite difference equations by using central difference approximations. To obtain stable solutions, the stability criterion is set as: ( ) 1/ 2 2 £ D = D r t Fo a (2.3) Where a is the thermal diffusivity (m2/s [ft2/hr]). Also, Yuill and Mikler (1995) used a new term, equivalent thermal conductivity ( eq k ), to account for the improved heat transfer due to the induced groundwater flow in the aquifer. To attain the value of eq k , they let heat transfer rates along the borehole wall for the case of coupled thermohydraulic flow considering the real ground thermal conductivity ( k ) equal the ones for the case of pure heat conduction considering the 24 equivalent thermal conductivity ( eq k ). They suggested this equivalent thermal conductivity could be used in the existing pure heat conduction design models to determine the depth of the thermal well. Regarding hydraulic head distribution in the thermal well, Yuill and Mikler (1995) considered this distribution as time independent and used a steadystate solution approach in the thermal well model. They assumed that the hydraulic gradients caused by pumping were dominant with respect to natural hydraulic gradients in the aquifers. Therefore, during their analysis, they neglected the natural hydraulic gradients. The equilibrium well equation relating the groundwater flow rates to the hydraulic gradients in the well was given by: ln( / ) 2 b w R r K h dz Q =  p × × D × (2.4) Where W Q is the water flow rate (m3/s [gpm]); K is the hydraulic conductivity of the ground (m/s [gpd/ft2]); R is the radius of influence (m [ft]); b r is the borehole radius (m [ft]). But this finite difference model that allowed calculation of the radial heat transfer at a particular depth was not truly twodimensional. Consequently, vertical heat transfer, end effects, and bleed operation could not be considered. 25 2.4.2. Experimental study Mikler (1993) did some experimental studies on transient heat and mass transfer in a “thermal well” system installed at Pennsylvania State University. Well #1 was 0.15 m (6 in) and 325 m (1065 ft) deep and was used in a large commercial system with 70 kW (20 tons) cooling capacity. Another well, #2, with the same diameter but 91 m (300 ft) depth was used to monitor and measure ground temperature changes in the vicinity of well #1. The distance between well #1 and well # 2 was 3.65 m (12 ft). Four 17.6 kW (5 ton) heat pumps were operated at full capacity in parallel in this system during the experimental period. Thermocouples were used to monitor both the water temperature distribution along the thermal well as well as the ground temperature in the vicinity of the operating well (well #1) at different depths. Also, thermocouples were used to monitor the entering and return temperature of the circulating water, the inlet and outlet air temperatures passing through the heat pumps, and the ambient temperatures. A flow sensor was used for monitoring total flow rate of the circulating water. Thermal and hydraulic properties of the aquifer were estimated based on the available measured data, “drilling log”, and basic knowledge about the local geology. The heat pumps were operated at fully capacity in cooling mode for a period of 48 subsequent days from August 4 to September 20, 1992, with a total of 235.73 GJ 26 (223.44 MMBtu) of heat injected into the ground. The temperatures of the water flowing down in the annular space and up inside the PVC pipe were measured continuously at five different depths in the well #1 and two depths in well #2. From his experimental data, Mikler (1993) found that the trend of the temperature change confirmed the well known theoretical analysis presented by Eskilson (1987)“On a time scale, one third of the total temperature drop to steady state conditions occurs during the first day, and two thirds during the first two months”. Also, from Mikler’s experimental observation, it was shown that the water temperature at some lower depth inside the PVC pipe is lower than the temperature at the bottom of the well. Mikler contributed this phenomenon to the fact that some amount of fresh water was being drawn into the system and mixed with the return water. After the cooling mode operation, the system was shut off for a period of six weeks from September 21 to December 10, 1992. Temperatures at all monitored locations finally stabilized at a higher level than the corresponding initial undisturbed aquifer temperatures. Then, the heat pumps were operated at full capacity in heating mode for the period of 71 subsequent days from December 10, 1992, to February 19, 1993, with a total of 114.15 GJ (108.20 MMBtu) of heat absorbed from the ground. Temperatures were measured at the same locations in the cooling mode operation. Mikler (1993) observed the temperature difference at the bottom of the well during the heating mode operation, which was proof of the direct interaction between the circulating water in the thermal well and the groundwater. 27 In their paper, Yuill and Mikler (1995) didn’t give any description of bleed. According to their research, they pointed out that the required drilled depth of a 6in thermal well is about 60% of the depth of the 11/2in, Utube earthcoupled borehole, assuming that both are properly designed and are installed in the same geological formation. The authors attribute the superior performance to the increased roughness at the wall of the well together with the induced interaction between the circulating water and groundwater. They didn’t mention that elimination of grout and pipe resistances contribute to the superior performance. The limitations of thermal wells are also listed in this paper (Yuill and Mikler 1995). If the groundwater quality is bad and impossible or too costly to treat (for example, groundwater with high mineral and bacterial content,) the thermal well is not preferable. In some states, this type of well can’t be installed because the waterwell legislation does not permit the “comingling of aquifers”. Sometimes, drilling problem may be the major obstacle. For example, the borehole may collapse in some geological formations. According to their experimental and theoretical study, Yuill and Mikler (1995) concluded that properly designed and installed “thermal wells” could compete with any of the closedloop systems based on their high system performance with smallest borehole depth and lowest combination of installation and operating costs. 28 2.5. Orio’s research Mr. Carl Orio first designed and employed standing column well systems in 1970’s. Since that time, he has been involved in many standing column well systems of Water & Energy System Corporation. Orio (1994, 1995) used the Kelvin line theorem to analyze the heat transfer in this system. ( ) 2 2 ' _ ' 0 2 I X k Q dB B e k Q T T X s B s p p = =  ¥ (2.5) t r X 2 a = Where T is the soil temperature (ºC [ºF]); 0 T is the initial temperature of the soil (ºC [ºF]); Q' is heat transfer rate (negative for heat extraction and positive for heat rejection) (W/m [Btu/fthr]); r is the radial distance from line (m [ft]); s k is the thermal conductivity of the soil (W/mK [Btu/hrftºF]); a is the thermal diffusivity (m2/s [ft2/hr]); t is the heat pump run time (hr); B is the integration variable. The Kelvin line theorem has provided a good correlation with some practical field experience (Orio 1995). But the Kelvin line theorem, offered as a relatively simple treatment of the problem, is not sufficient for the complicated heat transfer in standing column well systems, including conduction, convection, and advection, especially for 29 systems with ground water bleed. The Kelvin line theorem neglects the advection of heat from the borehole due to groundwater flow. The effect of the ground water flow on performance of SCW systems should be taken into account in a more complete and accurate model. In particular, the process of advection is very important in the modeling of SCW systems with groundwater bleed. Thus, the Kelvin theorem cannot be directly used to correctly calculate the temperature distribution of a “bleed” SCW system. The line source analysis with an “enhanced” thermal conductivity might be used to consider the effect of groundwater (See more discussion about related analytical solutions in section 2.9.). In this literature review, Orio’s papers are the only ones that give some detailed information about bleed. It is reported that in the severity of winter or summer, a relatively small (10%) bleed can reestablish water temperature in the well of SCW system at a rapid rate. According to his observations, Orio (1994, 1995) pointed out that bleed can make the effective thermal conductivity increase by factors of 3 to 5. The homogeneity of the geologic formation, the characteristics of the aquifer, and the density of the fractures affect the performance of SCW systems with bleed. Usually, 8090% of the water is returned to the standing column well and the balance is returned to the earth some distance away or disposed of. In some cases, the bleed water is disposed of in a separate return well. The National Ground Water Association (NGWA) provides the following formula to calculate the optimum return well distance: 30 D = 0.2´Q (2.6) Where D is the distance in feet to the recharge well (ft); Qis the design heat transfer rate (Btu/hr) . In fact, a return well is often not required because of the relatively small amount of bleed water. Instead, the bleed water may be disposed of in storm drains, ponds, streams or other natural routes. In wells that also serve as the household domestic water supply, “bleed” is naturally provided. The “bleed” power of a shower, laundry and other water use makes the average water temperature in the well of the residential SCW systems quite stable (Orio 1995). Orio (1999) discussed the placement of pumps and the depth of the boreholes. The boreholes could be onehalf the depth of the closed loop earth coupling methods. When boreholes get deeper than 152 m (500 ft), there is substantial increase in heating energy because the earth temperature increases with the increasing depth. But placing the pump at the bottom of the borehole has some disadvantages such as installation and service. To eliminate these disadvantages, Orio (1999) proposed that the submersible pump should be placed at the top of the borehole, but a lightweight plastic tube (dip tube or tail pipe) should be inserted to the bottom of the borehole (Figure 24b). Thus, the most stable water temperature is achieved, and shorter pipes and wires are required, so the initial investment can be reduced. Deeper wells (depth >152 m [500 ft]) mostly use dip tubes constructed of 100 mm (4 in) diameter PVC pipes to the bottom of the well. The dip tube has a minimum of 120 oneinch perforations in the lowest 12 m (40 ft). 31 Geothermal Heat Pump Domestic Use Water Emergency Bleed Typically 250500 ft 38 tons/bore Submersible Pump Standing Column Well Small Scale (a) Typically 5001500 ft 3040 tons/bore(Max) Bleed Emergency Geothermal Heat Pump Submersible Pump Tail Pipe Commercial Standing Column Well (b) Figure 24 Schematics of standing column well from description of Orio (Orio 1999) 32 2.6. Some typical installations of SCW systems There are approximately 1000 SCW installations in the United States. Most of them are located in the Northeast and Pacific Northwest in addition to parts of Canada in heatingdominated residential and light commercial applications. Also there are some installations out of North America. 2.6.1. Haverhill public library The Haverhill public library is located in Haverhill, Massachusetts. There are four standing column wells to provide a heat sink/source for watertowater heat pumps (initially two SCWs in 1994 but expansion of the library resulted in two additional SCWs after 1996). Each of the standing column well wells is 457 m (1500 ft) deep. Water is drawn from the bottom of the well, run through the heat pump and discharged at the top of the well. Whenever the well water temperature drops below 4.44 °C (40 °F), a bleed cycle initiates. This automatic bleed diverts approximately 10 % of the flow from returning to the wells. A bleed cycle typically lasts for 30 minutes. It acts to limit the lower well temperatures by drawing in new warmer groundwater from far field. There is no bleed for high temperatures. As Figure 25 shows the well water temperature remained above 2.78 °C (37 ºF) and generally operated in the lower 40s (ºF) during heating mode. The peak loop temperature reached 21.1 ºC (70 ºF) in June. However system operation changed after June 25th when 33 the second well pump became active and the maximum well temperature remained below 18.9 ºC (66 ºF) thereafter. There was also less variation in the temperature after June 25th in both heating and cooling mode. Figure 25 Standing column well water temperature trends in Haverhill public library (http://www.cdhenergy.com/ghp/haverhill/haverhill_main.htm) 2.6.2. SCW application in China From March 2001 to present, Ever Source Science & Technology Development Co. LTD in Beijing, China, has been applying the concept of the standing column well in about two hundred projects, with the name “single well for supply and return.” The schematic drawing of the single well is shown in Figure 26. A heat exchanger is located at the well 34 mouth, where the well water and recycle water circulated in separate loops. Therefore, the groundwater from the well is neither consumed nor polluted. According to their experience, this single well system can solve problems such as moving sands, pollution of groundwater, and collapse, which are all related to multiwell systems. More detailed technical information about this system is not available. Heat exchanger Recycle water Heat flux Water table Energy collector Figure 26 The schematic drawing of “single well for supply and return” (HYY 2003) From December 12, 2003 to March 17, 2004, Ever Source Science & Technology Development Co. LTD measured the energy consumption of eleven different type buildings in Beijing. These buildings use standing column wells as a heat source for heating in winter (Sun 2004). This investigation shows that energy consumptions of seven buildings among the eleven buildings are lower than that of the conventional heating system with a coal boiler. All eleven buildings have lower energy consumptions than other conventional oil/gas/electrical boiler heating system. 35 2.7. “Geohill”open hole coaxial thermal well An open loop concentric well heat exchanger called a “Geohill” has been developed by Geocalor A.G. (Hopkirk and Burkart 1990). The system schematic is shown in Figure 27. The borehole is 250 mm (10 in) in diameter and up to 300 m (1000 ft) deep, and it remains open with the exception of a steel casing in the upper part. A central PVC tube is surrounded by graded gravel filling and contains a downhole pump feeding water via an insulated tube to the heat pump. The fluid return is through the gravelfilled annulus. According to this configuration, the gravel filling can increase friction resistance for the return water flowing down, and therefore more groundwater is sucked into the system, especially if the well were drilled in a highly permeable rock formation. According to Hopkirk and Burkart’s research, the “Geohill” system shows much promise, especially in larger commercial installations requiring both heating and cooling. 36 Insulated delivery tube Return tubes Steel casing through unstaurated soil and sensitive aquifers Gravel filling Downhole pump Filter section Figure 27 Open hole coaxial thermal well “Geohill” (Hopkirk and Burkart 1990) 2.8. Summary of the different research related to SCWs Tables 21 and 22 summarize the research related to SCWs to date. Table 21 Summary of experimental research related to SCWs Researcher and date System name Depth of well Diameter of well Placement of well pump Placement of suction tube System water mixes with groundwater (i.e., openloop) System bleeds some groundwater Heat pump capacity ft/ton Bose et al. (1979) Geothermal well 73 m (240 ft) 127 mm (5 in) Ground level Top of the well No No 2.25 tons 106 Braud and Oliver (1980, 1983) Concentric pipe well 154 m (504 ft) 63.5 mm (2.5 in) Ground level Bottom of the well No No 2 tons 77 Tan and Kush (1986) Semiclosed loop standing column well 189 m (620 ft) 152.4 mm (6 in) Ground level Top of the well Yes No 5 tons 124 Hopkirk and Burkart (1990) Open hole coaxial thermal well “GEOHILL” 305 m (1000 ft) 254 mm (10 in) Bottom of the well Bottom of the well Yes No N/A N/A Mikler (1993) Yuill and Mikler (1995) Thermal well 325 m (1065 ft) 152.4 mm (6 in) Top of the well (under the water table) Bottom of the well Yes No 20 tons 53 Orio (1988,1995, 1999) Standing Column Well 73  457 m (2401500 ft) 152.4 mm (6 in) 1. Top of the well (under the water table) 2. Bottom of the well Bottom of the well Yes Yes 5200 tons 5060 HYY Beijing (2000s) Single well for supply and return 80 m 500 mm (19.68in) N/A N/A Yes No N/A N/A 37 Table 22 Summary of the modeling of SCWs Researcher and date System Name Analytical solution Numerical solution Include the effect of groundwater (advective heat transfer) Include the effect of bleed Comments Braud and Oliver (1980, 1983) Concentric pipe well Yes No No No 1. Steady state solution 2. Only consider heat conduction transfer 3. Cannot simulate cases in bleed operation Tan and Kush (1986) Semiclosed loop standing column well Yes No Yes No 1. Based on linesource theory 2. Use “enhanced” thermal conductivity Mikler (1993) Yuill and Mikler (1995) Thermalwell No Yes Yes No 1. Finite difference method 2. Some inputs in their models are based on their experiments Orio (1988,1995, 1999) Standing column well Yes No Yes Yes 1. Based on linesource theory 2. Use “enhanced” thermal conductivity 38 39 2.9. Some related analytical solutions (to ground source heat pump) Several methods to predict the performance of ground source heat pumps are available, including both analytical (line heat source, cylindrical heat source) and numerical methods. Although numerical solutions are very powerful, they are relatively complex. Much data and computer time are usually required to obtain good results. In contrast, the simplified analytical methods such as the line heat source model and the cylindrical heat source model (first presented by Carslaw and Jaeger [1947] and Ingersoll et al. [1948] and later refined by other researchers [Kavanaugh 1984, Bose et al. 1988]) make it relatively simple to perform annual hourbyhour simulations of groundcoupled heat pump systems. Because these analytical solutions might be further modified to be employed in SCW system after considering the movement of groundwater, they are reviewed below. Figure 28 shows the cylindrical heat source embedded in an infinite medium, e.g. the earth. In the simplest case, the borehole is subjected to a constant heat transfer rate, q , from (or to) the surrounding ground for which the far field temperature is the undisturbed temperature, u T . The object of the analytical solution is to calculate the temperature difference between the undisturbed ground temperature, u T , and the borehole wall temperature, w T . Based on the work of Carslaw and Jaeger (1947), Ingersoll et al. (1948, 1951, 1954) gave an analytical solution to the transient heat transfer from a line (or cylinder) embedded in an infinite homogeneous medium. 40 Figure 28 Schematic drawing showing the cylindrical heat source embedded in an infinite medium * * When the diameter of the cylinder is zero, the cylindrical heat source becomes line heat source 2.9.1. Kelvin line source solution The earliest approach to calculating thermal transport around a heat exchanger in the ground was the Kelvin line source theory (Ingersoll et al. 1948,1954). The temperature distribution around a line source of heat buried in a homogenous, infinite media is given by: ( ) 2 2 2 I X k q dB B e k q T T s l X B s l u p p = =  ¥  (2.7) t r X 2 a = Where T is the soil temperature (ºC [ºF]); u T is the uniform initial temperature of the soil (ºC [ºF]); r Tfi Tfo Tw Tr R : the far field radius Tr : the far field temperature Tr = Tu Tu: the undisturbed temperature of the ground q 41 l q is the heat transfer rate applied to the ground (W/m [Btu/fthr]) (a positive q value implies heating mode); r is the radial distance from the line (m [ft]); s k is the thermal conductivity of the soil (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the soil (m2/s [ft2/hr]); t is the heat pump run time (hr); B is the integration variable. This model is based on approximating the borehole as a line source, assuming end effects are negligible. The soil acts as a heat rejection (absorption) medium that has an assumed uniform and constant initial temperature (Tu ). Let t r y X 4a 2 = 2 = . Thus Equation (2.7) can be changed into ) ( !) ( 1) ...... 2 (2!) 3 (3!) ( ln 4 4 2 3 1 N N y y y y y k q d e k q T T N N s l s y l u × + +  × + ×  = =    ¥  + g p l p l l (2.8) Where l is the integration variable; g is Euler’s constant, 0.5772157… Equation (2.8) can be written as: +   = C r t k q T T s b l u w g a p 2 4 ln 4 (2.9) Where Tw is the borehole wall temperature (ºC [ºF]); 42 rb is the borehole radius (m [ft]); C is the summation of the series ¥ = + ×  1 1 ( !) ( 1) N N N N N y . Actually, the integration of Equation (2.7) is from X to r¥ , where r¥ is equal to 4 at . To find how close u T is to the value of the temperature at r¥ , a formula was given by Hart and Couvillion (1986): [0.0019] 2 s l r u k q T T p  = ¥ (2.10) At typical values of l q and s k , r u T T ¥ varies from approximately 0.00167 ºC (0.003 ºF) to 0.0167 ºC (0.03 ºF) when r¥ is equal to 4 at . Considering this correction, Equation (2.9) can be written as +    = C r t k q T T s b l u w 0.0038 4 ln 4 2 a g p (2.11) Ingersoll et al. (1951) stated that the line source equation (Equation [2.9]) is exact only for a true line source, but that it can also be applied with negligible error for pipes less than 4 inch in diameter and times longer than 24 hours. The error does not exceed about 2% under these conditions. For the case where the time is too short or the pipe diameter is too large (in general when 20 2 < r at ), the use of the line source equation will involve the error greater than 2%. Therefore, the line source cannot effectively and accurately model 43 systems with normal transient operating performance. Deerman and Kavanaugh (1991) stated that the line source method had a 10% error when using onehour intervals. 2.9.2. Cylindrical heat source solution The cylindrical heat source solution was developed using a single isolated pipe surrounded by an infinite solid of constant properties. The following assumptions are used in this solution: · heat transfer only by pure conduction · soil acts as an infinite solid · perfect soil and pipe contact · no groundwater movement There are several cylindrical heat source solutions corresponding to different cases of our interest. These include a cylindrical heat source solution with and without considering the thermal mass in the borehole, and a cylindrical heat source solution, which considers two thermal masses in the borehole separated by a thermal resistance. (a). Cylindrical heat source solution without considering the thermal mass in the borehole The cylindrical heat source solution without considering the thermal mass in the borehole for a constant heat flux is as follows (Ingersoll et al. 1954): G(Fo, p) k q T T s l u  = (2.12) Where T is the soil temperature (ºC [ºF]); 44 u T is the uniform initial temperature of the soil (ºC [ºF]); l q is the heat transfer rate applied to the ground (W/m [Btu/fthr]) (a positive q value implies heating); s k is the thermal conductivity of the soil (W/mK [Btu/hrftºF]); G(Fo, p) is the analytical solution; [ ] ¥   +  = 0 2 2 0 1 1 0 1 2 1 ( ) 2 ( ) ( ) ( ) ( ) ( ) ( ) 1 1 ( , ) 2 b b b b b b b b p b d J p Y J Y p J Y e G Fo p Fo (2.13) p is the ratio of the radius where the temperature is calculated over the borehole radius ( 0 r ) ; Fo is the Fourier number defined as: 2 0 r Fo =at . Values of G are available from Ingersol et al. (1954). For p = 1(i.e., at the cylindrical radius, borehole wall), the following equation is given by Bernier (2001). [ 0.89129 0.36081 log ( ) 0.05508 log ( ) 3.59617 10 log3 ( )] 10 2 3 G(Fo,1) 10  + ´ 10 Fo  ´ 10 Fo + ´ ´ Fo  = (2.14) So, for the temperature at the borehole wall, Tw , Equation (2.12) can be reduced to [ 0.89129 0.36081 log ( ) 0.05508 log ( ) 3.59617 10 log3 ( )] 10 2 3 10 10 Fo 10 Fo Fo s l u w k q T T  + ´  ´ + ´  ´  = (2.15) (b). Cylindrical heat source solution with considering the thermal mass in the borehole 45 If a cylinder of radius r b of a thermal massive perfect conductor is surrounded by an infinite medium (e.g. the ground) and is heated at the rate ql per unit length per unit time for t > 0 , all initial temperature being zero, the temperature of the perfect conductor is given by Carslaw and Jaeger (1959): G(h, 1, ,Fo) k q T s = l a ¥ (2.16) ( ) [ ( )] ( ) du u u u Fo Fo h G ¥ D =   0 1 3 2 3 2 2 2 1 1 2 2 1 exp , , , p a a a a (2.17) Where h = 2pRbks , 1 2 a1 = 2prb rCp / S , a 2 ®¥, Fo is the Fourier number defined as 2 rb t Fo = a ; ( ) [ ( ) ( ) ( ) ] [ ( ) ( ) ( ) ]2 1 2 0 2 1 2 1 2 2 1 2 0 2 1 2 1 1 2 ( ) ( ) u hu Y u hu Y u u u hu J u hu J u +    D = +    + a a a a a a a a (2.18) Ji is the Bessel function of order i ; Yi is the modified Bessel function of order i ; s k is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the ground (m2/s [ft2/hr]); r is the density of the ground (kg/m3[lbm/ft3]); Cp is the specific heat of the ground(J/kgK [Btu/lbmºF]); rb is the radius of the cylindrical conductor (m [ft]); Rb is the thermal resistance between the conductor and the ground (K/(W/m) [hrftºF/Btu]); 46 S1 is the thermal capacity of the cylinder of perfect conductor (J/m3K [Btu/ft3ºF]); u is the integration variable. For large values of Fo ( Fo >> 1) Equation (2.16) can be reduced to: = +   +  + ) 1 ) ( 4 ln( 2 2 2 (4 ) ) 4 2 ln( 4 2 1 1 1 1 C Fo Fo Fo Fo h C Fo h k q T s l o a a a a p (2.19) Where C = 1.7811 = exp(g ) , and g = 0.5772157... is Euler’s constant. All other variables are defined as the same in the equation (2.16). The simplified cylindrical solution (considering the thermal mass) to a given borehole with u T , initial temperature of soil, is given:  +   = +  ) 4 ln( 2 2 2 (4 ) ) 4 2 ln( 4 1 1 1 1 C Fo Fo Fo h C Fo h k q T T s l u w a a a a p (2.20) Where u T is the uniform initial temperature of the soil (ºC [ºF]); Tw is the borehole wall temperature (ºC [ºF]); l q is the heat transfer rate applied to the ground (W/m [Btu/fthr]) (a positive q value implies heating); h = 2pRbks , 1 2 a1 = 2prb rCp / S ; Fo is the Fourier number defined as 2 rb t Fo = a ; s k is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the ground (m2/s [ft2/hr]); 47 r is the density of the ground (kg/m3[lbm/ft3]); Cp is the specific heat of the ground(J/kgK [Btu/lbmºF]); rb is the radius of the borehole (m [ft]); Rb is the thermal resistance of the borehole ( K/(W/m) [hrftºF/Btu]); S1 is the thermal capacity of the materials in the borehole (J/m3K [Btu/ft3ºF]); C = 1.7811 = exp(g ) ; g is is Euler’s constant (g = 0.5772157...). (c). Cylindrical heat source solution to a cylinder of perfect conductor with the sheath surrounded by an infinite medium (soil) Core Insulation Soil Perfect conductor Sheath Perfect conductor Figure 29 A schematic drawing of a core separated by the insulation from the sheath 48 Figure 29 shows a schematic drawing of a cylinder of the core with the sheath surrounded by an infinite medium (soil). The core and the sheath are perfect conductors of thermal capacities S1 and S2 , respectively. They are separated by the insulation, which is regarded as of negligible thermal capacity and thermal resistance, R. The cylinder is also supposed to be buried in the soil of thermal conductivity, s k , thermal diffusivity, a , and specific heat, Cp . If the whole system is initially at zero temperature and heat is supplied at the rate ql per unit length per unit time, the temperature of the cylinder is given by Carslaw and Jaeger (1959): G(h, 1, 2 , Fo) k q T s = l a a (2.21) ( ) [ ( )] ( ) du u u u Fo Fo h G ¥ D =   0 1 3 2 3 2 2 2 1 1 2 2 1 exp , , , p a a a a (2.22) Where h = 2pRbks , 1 2 a1 = 2prb rCp / S , 2 2 a 2 = 2prb rCp / S ; Fo is the Fourier number defined as 2 rb t Fo = a ; ( ) [ ( ) ( ) ( ) ] [ ( ) ( ) ( ) ]2 1 2 0 2 1 2 1 2 2 1 2 0 2 1 2 1 1 2 ( ) ( ) u hu Y u hu Y u u u hu J u hu J u +    D = +    + a a a a a a a a (2.23) Ji is the Bessel function of order i ; Yi is the modified Bessel function of order i ; s k is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); a is the thermal diffusivity of the ground (m2/s [ft2/hr]); r is the density of the ground (kg/m3[lbm/ft3]); 49 Cp is the specific heat of the ground(J/kgK [Btu/lbmºF]); rb is the radius of cylindrical conductor (m [ft]); Rb is the thermal resistance between the two perfect conductors (the core and the sheath) (K/(W/m) [hrftºF/Btu]); S1 is the thermal capacity of the cylinder of the core (J/m3K [Btu/ft3ºF]); S2 is the thermal capacity of the sheath (J/m3K [Btu/ft3ºF]); u is the integration variable. 2.9.3. Analytical solution considering the movement of groundwater (groundwater gfunction) Claesson and Hellström (2000) gave a new analytical solution for the influence of regional groundwater flow in the performance of borehole heat exchangers based on the groundwater gfunction. The temperature Tb (t) at the borehole wall, which is needed to sustain the constant heat injection rate Q0 from time t = 0 , is denoted by a corresponding dimensionless gfunction: ( ,....) 2 ( ) 0 g t k q T t total s b = × p H Q q 0 0 = (2.24) The gfunctions depend on time, thermal properties, etc. Groundwater flow will diminish the gfunction. Claesson and Hellström (2000) wrote the total gfunction in the following way: 50 ( ) ( ; 0) ( ) 2 ( ; ) 0 T t g t q g t q k g t q b w gw s total w = = =  p (2.25) Where Tb (t) is the temperature at the borehole wall (ºC [ºF]); qw is the constant regional groundwater flow (m3 of water per m2 and s); ks is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); H is the borehole depth (m [ft]). The first term on the righthand side of Equation (2.25) is the ordinary gfunction for the given borehole without the effect of groundwater ( qw = 0 ) (Claesson and Eskilson 1987). The second term accounts for the effect of the groundwater flow. After some calculation, Claesson and Hellström (2000) gave the groundwater gfunction g gw : e erfm s ds s g h h s gw =  × × (1  ) (1/ ) 2 1 ( , ) 0 2 / 4 t t (2.26) Where × = =   x x x e erf s ds erf x x erfm x 0 2 1 ( ) ( ) 1 ( ) p ; 2 4 H t = at ; s w w w k H c q h 2 r = ; qw is the constant regional groundwater flow ( m3 of water per m2 and s). ks is the thermal conductivity of the ground (W/mK [Btu/hrftºF]); 51 a is the thermal diffusivity of the ground (m2/s [ft2/hr]); r w is the density of the groundwater (kg/m3 [lbm/ft3]); cw is the specific heat of the groundwater(J/kgK [Btu/lbmºF]); H is the borehole depth (m [ft]). For t > 1, the following approximation of groundwater gfunction, which is valid for any h , is given by Claesson and Hellström (2000):   @ 2 1 2 4 1 ( , ) 2 t p t t t h erf h h h ggw h Ein t > 1 (2.27) Where ln( ) 0.577(1 ) 1 ( ) 7 / 4 0 x x x s ds x e e s e Ein x    =  @ + +  Also, for t < 1, h < 1, the following simple expression is used to estimate the effect of groundwater flow within 3% error: @  p t t t 9 4 1 8 ( , ) h2 ggw h t < 1, h < 1 (2.28) 2.10. Related research  aquifer thermal energy storage (ATES) A related type of system, with similar analytical requirements, is the aquifer thermal energy storage (ATES) system. ATES systems utilize aquifers for the storage of lowgrade thermal energy such as solar heat or waste heat during periods of low demand. The lowgrade energy is used to heat or chill water, which is injected into an aquifer for storage. Later, during a period of high demand, the water is withdrawn for space heating or cooling. During a period of heat injection, water is extracted from the cold well, heated 52 Warm well Cold well and reinjected into the warm well. The pump is reversed during a period of heat recovery. Water is then extracted from the warm well, cooled and reinjected into the cold well (see Figure 210). The same type of system may be used to store cold water for cooling purposes in warm climates. Figure 210 Heat storage in an aquifer Hall and Raymond (1992) gave a schematic of a simplified ATES system used for air conditioning (Figure 211). In this system, the cooling tower is used for chilling water drawn from the warm well during the winter. The chilled water is stored in the aquifer by the cold well, and is recovered during the summer and passed through heat exchangers to cool the warm air. 80ºC 40ºC 53 cold well warm well cold air Blower cooling tower water return pump water table warm water cirulation pump cold water circulation pump Warm air Air blower Warm air Figure 211 Simplified aquifer thermal energy storage system used for airconditioning (Hall and Raymond 1992) Numerous studies have been performed concerning the concept of ATES. Hall and Raymond (1992) gave the following three elements, which determine whether the design and operation of an ATES system are successful. the presence of a suitable aquifer for groundwater supply and energy storage; the availability of a source of lowgrade thermal energy; a temporal mismatch between thermal energy availability and thermal energy use. Aquifer characterization is very important to the design of an ATES system. However, unlike other components of the ATES system, the aquifer itself cannot be changed to 54 meet the design specification. Thus, the ATES system must be designed with regard to the aquifer characterization. So, as the first step in any ATES project, site investigation is necessary and should be combined with the user’s specific requirements. Hall and Raymond (1992) also pointed out that the aquifer’s hydraulic conductivity, which is dependent on the size and shape of media pores, is of the firstorder importance in the design and evaluation of ATES systems. Basically, under ATES conditions, the differences in the thermal conductivities and thermal capacities of earth materials are relatively small. So, thermal conductivity and thermal capacity are of secondary importance. There are several descriptions of ATES systems in the literature. Midkiff et al. (1992) presented the results of 6 years of study on the longterm performance of an airconditioning system (a building at University of Alabama) based on ATES. During the cold weather, ambient 18ºC water is pumped from warm wells, chilled to about 6 ºC in a cooling tower, and reinjected into the separated cold storage wells. In warm weather, water is withdrawn from the cold wells and pumped through building heat exchangers for airconditioning (see also Figure 211). This ATES system was operated to provide 100% of the building air conditioning with an annual average COP of about 5.0, about twice that for conventional mechanical airconditioning equipment of the same capacity (Midkiff et al. 1992). Marseille and Wilke (1992) provided an overview of an ATES system integrated with a central heating and cooling plant (MidIsland Postal Facility in Melville, New York). 55 Cold wells are charged with water that is cooled during the winter by heat pump. Water from these cold wells is then used to meet the facility’s cooling load during the summer, before being pumped back into the ground at warm wells. Backup cooling is provided by a heat pump. They described and assessed energy and economic merits of this system. Their studies shown that this ATES system can offer both energy and environmental advantages over more conventional systems. 2.11. Effect of groundwater flow on closedloop groundcoupled heat exchangers Although it has been recognized that the convective heat transport by groundwater flow may be an important factor in reducing the necessary size of closedloop groundcoupled heat exchangers, current design and simulation models for closedloop systems still assume that heat transfer underground occurs by conduction only. Little work has been done to quantify the effects of groundwater flow on closedloop systems. Claesson and Hellström (2000) presented models for the influence of regional groundwater flow based on the assumption that the natural groundwater movement is reasonably homogenously spread over the ground volume. This applies well for homogenous and porous ground materials. The authors used the line source theory to model the groundwater effect on a single vertical borehole (groundwater gfunction, see section 2.9.3.) and concluded that under normal conditions, the influence of regional groundwater flow is negligible. Chiasson (1999) made a preliminary investigation of the effects of groundwater flow on the design and performance of vertical closedloop ground heat exchangers. A two 56 dimensional finite element numerical groundwater flow and heat transport model (AQUA3D) was used to simulate and observe the effects (Chiasson et al. 2000). The relative importance of heat conduction in the ground vs. heat advection by groundwater flow is assessed by using of the dimensionless Peclet number, Pe . Pe = r wcwqL / Keff (2.29) Where r w is the density of the groundwater (kg/m3 [lbm/ft3]); cw is the specific heat of the groundwater (J/kgK [Btu/lbmºF]); Keff is the effective hydraulic conductivity (m/s [ft/s]); q is the specific discharge (m/s [ft/s]); L is the characteristic length (m [ft]). Based on their preliminary work (Chiasson et al. 2000), it is shown that heat advection by groundwater flow is a significant process contributing to heat transfer in geologic formations such as coarsegrained soil and rocks with fractures and solution channels. The value of effective thermal conductivity is greater with a flowing fluid than with a stagnant fluid. The results from this work also show that as groundwater flow velocity increases, the values of the predicted effective thermal conductivity, including the effects of groundwater advection, are significantly different. From their preliminary assessment of the effects of groundwater flow, Chiasson et al. (2000) pointed out that it is difficult to adapt results from current design guidelines and software tools to fully account for the effect of groundwater movement. 57 Theoretical studies dismiss significant effects of groundwater flow for typical conditions in a porous ground (Chiasson et al. 2000; Claesson and Hellström 2000). However, groundwater flow in standing column well systems, especially when bleeding, results in higher flow velocities. The hydraulic pressure difference between the suction point and discharge point may also be potentially important. 2.12. Numerical groundwater flow and heat transport models Ground water flow and thermal energy transport in the porous media have been studied in some detail in the discipline of hydrogeology. Numerical research into groundwater and heat transport has been continuing for more than a decade in North American and Europe. Numerous commercially available and public domain numerical software codes exist. Of these, we focus on the simulation modeling both mass and heat transport in groundwater. Table 23 lists some numerical models for groundwater flow and energy or solute transport in groundwater. These models can all be used to simulate an ATES system. Models THETA and SUTRA are selected for a more detailed review, since the information about these two models is readily obtained in the public literature. In assessing the effect of groundwater flow on closedloop heat exchanger performance, Chiasson (1999) reviewed numerical software code, which can be used to model mass and/or heat transport in groundwater. Finally, Chiasson (1999) selected AQUA3D for his study based on his selection criterion: the type of boundary conditions handled by the code 58 the solution scheme employed by the code verification of the code cost Table 23 Numerical models for groundwater Model Creator Descriptions AQUA3D Vatnaskil Consulting Engineers, Reykjavik, Iceland Threedimensional, finiteelement method; developed mainly for simulation of masstransport problems, but can be adapted to model heat transport without densitydependent groundwater flow. HST3D United States Geological Survey (USGS) Threedimensional, finitedifference method; capable of simulating mass and heat transport in variabledensity groundwater flow system. FEFLOW WASY Institute for Water Resources Planning and Systems Research, Ltd., Berlin, Germany Threedimensional, finiteelement method; capable of simulating both mass and heat transport in densitydependent groundwater flow systems. SUTRA (Saturated Unsaturated Transport) Clifford L. Voss Twodimensional hybrid finiteelement and finitedifference method; simulated fluid movement and the transport of either energy or dissolved substances in the subsurface environment. THETA 3.0 Kangas and Lund Threedimensional, finitedifference method; coupled transport of fluid and energy in porous media. 59 2.12.1. Numerical model THETA THETA was developed at Helsinki University of Technology by Kangas (1996). It can be used to accurately simulate the threedimensional coupled transport of fluid and energy in porous media. Simulations have been performed to evaluate the effect of groundwater on the performance of a ground heat extraction system using vertical wells. Injection flow flow Extraction well screen CONFINING LAYER SATURATED LAYER CONFINING LAYER Figure 212 A ground heat extraction system using vertical wells (Kangas 1996). Kangas (1996) used the porous medium approximation to study the groundwater flow. The specific discharge ( q ) is given by Darcy equation: g K p g k k q r r m m =  (Ñ  ), = (2.30) Where: k is the intrinsic permeability (m2 or Darcy [ft2]) ( k is a function of the size of the openings through which the fluid moves. It depends only on the geological properties of the ground. k = C × d 2 ); C is the shape factor and d is the diameter of the effective grain, they are properties of the porous media (Fetter 1994); 60 K is the hydraulic conductivity of rock (m/s [gpd/ft2]) (It depends not only on the geological properties of the ground, but also on the thermal properties of the flowing medium); p is the pressure (N/m2 [lbf/ft2]); g is the acceleration of gravity (m/s2 [ft/s2]); m is the dynamic viscosity of water (Ns/m2 [lbfs/ft]). In addition, Kangas (1996) assumed that, locally, the groundwater and the surrounding ground are in the thermal equilibrium to derive the transferred energy equation in groundwater from the principle of conservation of energy. The resulting energy equation with an incompressible fluid is: T c q T H t T c s f = Ñ× Ñ  ×Ñ + ¶ ¶ (r ) (l ) (r ) (2.31) Where: rc is the volumetric heat capacity (J/m3K [Btu/ft3ºF]); l is the thermal conductivity (W/mK [Btu/hrftºF]); q is the specific discharge (volume flow rate per unit of crosssectional area) (m/s [gpd/ft2]); H is the heat source or sink (W/m3 [Btu/hrft3]); and subscripts: f is fluid (water); s is fluid saturated soil. The above two governing equations are discretized in THETA using the explicit finite difference method (FDM) and solved numerically. 61 The results from the THETA simulations of Kangas (1996) suggest that an increase in groundwater flow will result in improved system performance, which results from the energy transfer by groundwater; groundwater constantly replenishes the recoverable energy at the site of extraction. The presence of groundwater flow significantly increases the amount of recoverable energy. Similarly, standing column well systems, especially with groundwater bleed, make use of the energy stored in the aquifer. The THETA aquifer simulation model has been incorporated into a computer simulation model AQSYST for simulating energy systems employing ATES (Kangas and Lund 1994). This system simulation showed that energy systems employing heat pumps for storage discharge could obtain high performance for the whole range of natural groundwater flow rates from 10 m/year to 600 m/year. THETA simulates the thermohydraulic flow in the aquifer when either injecting water to the well or extracting water from the well. It cannot model simultaneous injection and extraction to/from a single well. The performance of standing column well systems is characterized by circulating, injecting, and extracting water to and from an aquifer at the same time. Therefore, THETA cannot be applied directly to the standing column well system. 2.12.2. Numerical model SUTRA SUTRA (SaturatedUnsaturated Transport) is a computer program developed by Voss (1984). This numerical model simulates fluid movement and the transport of either 62 energy or dissolved substances in the subsurface environment (aquifer). A twodimensional hybrid finiteelement and finite difference method is used to approximate the governing equations. SUTRA can solve the two interdependent processes: 1. fluid densitydependent saturated or unsaturated groundwater flow, and either 2a. transport of a solute in the groundwater, or 2b. transport of thermal energy in the groundwater and solid matrix of the aquifer. SUTRA was primarily intended to simulate twodimensional flow, and either solute or energy transport in a saturated variable density system. To simulate the groundwater in unconfined aquifers affected by a periodic boundary condition, Ashtiani et al. (1999) modified the SUTRA model in three aspects: 1. the basic flow equation is changed from a pressurebased form to a mixedform; 2. an automatic underrelaxation method is applied for adjustment of pressure after each iteration to handle the nonlinearity of the unsaturated zone equations; 3. the model has been adjusted to handle a seepageface boundary condition. The validation tests of this twodimensional numerical model for densitydependent groundwater flow in unconfined aquifers against experimental data were successful. Like THETA, SUTRA cannot model simultaneous heat/mass injection and extraction to/from a single well. So, SUTRA cannot be applied directly to the standing column well system, either. 63 2.12.3. Other Numerical models A few other models address energy transfer in the aquifer. Here are some brief reviews. Hellström et al. (1986, 1989) developed a model that simulates the thermal process in the aquifer and in the surrounding ground under certain simplifying assumptions concerning the groundwater flow. The basic assumption of the model is that the groundwater flow is essentially radial in the thermally active region around the well. There are other assumptions that must be fulfilled: · negligible regional groundwater flow; · negligible buoyancy flow caused by varying water temperature in the aquifer; · negligible influence of viscosity differences between different flow paths. Convective heat transport and threedimensional heat conduction are accounted for in this model. The combined diffusive and convective heat flow processes in the aquifer and the surrounding layers are solved using the explicit difference method (finite difference method). Molson et al. (1992) simulated the thermal energy storage in an unconfined aquifer with a threedimensional finite element numerical model. In their model, the authors coupled the densitydependent groundwater flow and thermal energy transport. A symmetric matrix time integration scheme with the Galerkin finite element method is employed. Recently, Chevalier and Banton (1999) applied the random walk method to model energy transfer in porous media. The method is based on the concept that cumulative results of 64 repeated trials with an arbitrary probability distribution tend to a Gaussian distribution. They compared their random results with the analytical solution and the numerical finite difference solution. The results are similar in both cases. Because the above three models cannot model simultaneous heat/mass injection and extraction to/from a single well, so they cannot be applied directly to the standing column well system. 65 2.13. Summary of the literature From the review of the literature discussed in the previous sections, it is clear that research into the operation and design of SCW systems has been very limited. To date, no models have been developed that have come into common use in design procedures for SCW systems. Attempts have been made to adapt conduction heat transfer models to include the effects of groundwater flow. However, these models (e.g., Yuill and Mikler 1995) do not allow representation of bleed from the well. As this is common practice and can have a significant impact on the design and cost of the well, there is a clear need to be able to model this effect. Based on the existing published research, the following conclusions can be drawn: 1. Because of the direct interaction between the water in the borehole and the groundwater in SCW systems, none of the pure heat conduction models such as Braud’s (1980) could be directly applied to the SCW system without any modification. 2. Only Yuill and Mikler (1995) have developed an analytical tool that accounts for heat transfer improvement due to the presence of groundwater. The influence of infiltration/exfiltration of groundwater to the overall heat transfer depends on the local geological formation and performance characteristics of the system. However, this finite difference model allowing calculation of the radial heat transfer at a particular depth is not a true twodimensional model. A twodimensional model would be much more appropriate. 66 3. In Tan and Kush’s paper (1986), the effect of groundwater was referenced, but not quantified. Only Yuill and Mikler (1995) discussed this effect in detail by the introduction of the “groundwater factor.” But they didn’t account for the effect of bleed and buoyancy. 4. Little information about “bleed” is available in the literature, except that Orio (1994, 1995, 1999) provided some initial information based on his experiences. Much more work must be done to evaluate the performance enhancement provided by “bleed.” It is essential to predict the safe amount of bleed flow to prevent equipment freezeup during peak heating periods. Also, during the bleed times, the water table may fluctuate in response to draw down in the well. It may be helpful to numerically track the water table position, which has a huge influence on the power consumption of water pump in SCW systems during bleed operation. In real life, it has a significant effect on the flow rates. 5. Although some field test projects related to SCW systems have been published (Bose et al. 1979; Braud et al. 1983; Tan and Kush, 1986), no computer simulations of a SCW system have been developed, which could be used to predict the hourly heat pump entering water temperature at given hourly building loads. Hourly energy analyses can allow us to examine the transient nature of SCW systems, especially during “bleed” times. 6. Currently available simplified analytical/numerical solutions based on pure heat conduction assumptions cannot be directly coupled into SCW system simulations, in which the movement of groundwater has a significant effect on heat transfer, especially in bleed operation. 67 The heat transfer and hydrological boundary conditions in SCW systems vary in both time and space and also depend on the mode of operation of the well (e.g., bleed). The full complexity of the boundary conditions associated with standing column well operations can only be dealt with by a numerical model, which considers both groundwater flow and heat transfer. From the review of the literature discussed in Sections 2.102.12, we can see that sophisticated numerical models of groundwater flow and contaminant transport in both the saturated zones (rock) and unsaturated zones (soil) have been developed over the last two decades. These models have been applied by practicing hydrogeologists to study largescale water supply and contaminant transport problems. Although those models effectively model the pumping process and calculation of groundwater flow, they are not adapted to enable the complex timevarying thermal boundary conditions required to model SCW systems over an extended simulation period. The design parameters such as well diameter, dip tube size, insulation, well surface roughness, etc. cannot be studied without a detailed thermal borehole model of the standing column well. A summary of the different numerical and analytical models of interest is given in Table 24. Table 24 Summary of the different numerical and analytical models Analytical solution Numerical solution Effect of groundwater Effect of bleed Effect of buoyancy Comments Braud and Oliver (1980, 1983) Yes No No No No Steadystate, radial, conduction heat flow only. Mikler (1993) Yuill and Mikler (1995) No Yes Yes No No 1. Introduce “groundwater factor” ( k dz m C G w pw f × × = 2p ) to consider the groundwater effect; 2. Finite difference model that allowed calculation of the radial heat transfer at a particular depth was not twodimensional. The vertical heat transfer, end effects and bleed operation could not be considered Kelvin line source Yes No No No No Exact only for a true line source, assuming end effects are negligible. The soil has an assumed uniform and constant initial temperature. Cylindrical heat source (a) Yes No No No No Without considering the thermal mass in the borehole. Cylindrical heat source (b) Yes No No No No Considering the thermal mass in the borehole. Analytical solution with gfunction Yes No Yes No No 1. Based on superposition of steady state, periodic and extraction step analytical solutions; 2. Introduce the groundwater gfunction ( @  p t t t 9 4 1 8 ( , ) h2 ggw h ) to consider the constant regional groundwater flow. AQUA3D No Yes Yes N/A No 1. Threedimensional, finiteelement method; 2. Developed mainly for simulation of masstransport problems, but can be adapted to model heat transport without densitydependent groundwater flow; 3. Used by Chiasson (1999) to simulate and observe the effects of groundwater flow on the vertical closedloop system. SUTRA No Yes Yes N/A No 1. Twodimensional hybrid finiteelement and finitedifference method; 2. Simulated fluid movement and the transport of either energy or dissolved substances in the subsurface environment. 68 69 3. DEFINITION OF THE PROBLEM AND OBJECTIVES The goals of this research have been briefly discussed in the introduction section. In more detail, the specific objectives of this research into standing column well systems will be subdivided into several major stages: The first stage concerns the review, analysis and evaluation of currently available research related with standing column well systems. The strengths and shortcomings of currently available research are to be analyzed and evaluated. The literature review of this research attempts to provide this. The second stage involves analysis of the mechanism of heat transfer and characteristics of hydrological flow about the standing column well systems. As we know, the heat transfer in standing column well systems is very complicated because of the presence of groundwater. The detailed twodimensional numerical model of the standing column well system will consist of two parts: 1) Borehole sub model (using nodal model) The thermal model for the borehole can be described by a series of resistance network. 2) Porous medium model describing heat transfer and groundwater flow in the rock (using finite volume model). 70 The third stage will deal with computer algorithms. The mathematical and physical model will be converted into computer model. The programming language will be Fortran 90/95. At this stage, some experimental data (Mikler 1993; Henderson 2003) will be used to validate and calibrate the numerical models. The fourth stage is a parametric study and energy consumption analysis based on the detailed model. Using the numerical model, the effect of key parameters and operating strategies (e.g., bleed) will be evaluated. This research will be helpful in the design of standing column well systems by providing: simulation of standing column well systems to predict fluid temperature (entering fluid temperature to the heat pump, exiting fluid temperature from the heat pump, average fluid temperature in the well); determination of the necessary well depth per given load in specified hydrogeological conditions; influence of “bleed”. Anticipating that the detailed model will take extensive computing resources, the last stage of this work is to develop a simplified numerical onedimensional model. This should be feasible for use by engineers in HVAC application areas. This simplified model should be compared with the detailed numerical model and experimental data for accuracy. An economic performance analysis based on this simplified model is the last objective of this research. 71 The validation of the models against the experimental d 



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