1、4666 (RP-1119) A Study of Geothermal Heat Pump and Standing Column Well Performance Simon J. Rees, Ph.D. Jeffrey D. Spitler, Ph.D., P.E. Zheng Deng Member ASHRAE Member ASHRAE Carl D. Orio Member ASHRAE ABSTRACT Standing column wells can be used as highly eficient ground heat exchangers in geotherma
2、l heat pump systems, where hydrological and geological conditions are suitable. A numerical model ofgroundwaterflow and heat transfer in and around standing column wells has been developed. This model has been used in aparametric study to identih the most signif- icant design parameters and their ef
3、fect on well performance. For each case in the study, performance has been evaluated in terms of minimum and maximum annual temperatures and design well depth. Energy consumption and annual costs have also been calculated. Groundwater “bled” from the system is one of the most sign$cantparameters a s
4、ystem designer can use to improve wellperformance for a given load. The efects of bleed rate, well depth, and rock properties on heat transfer and energy consumption are discussed. INTRODUCTION Geothermal heat pump systems that use groundwater drawn from wells as a heat source/sink are commonly know
5、n as standing column well (SCW) systems. The ground heat exchanger in such systems consists of a vertical borehole that is filled with groundwater up to the level ofthe water table (Le., similar construction to a domestic water well). Water is circu- lated from the well through the heat pump in an o
6、pen loop pipe circuit. Standing column wells have been in use in limited numbers since the advent of geothermal heat pump systems and are recently receiving much more attention because of their improved overall performance in the regions with suit- able hydrological and geological conditions (Orio 1
7、994,1998, 1999). Student Member ASHRAE Carl N. Johnson, Ph.D. Member ASHRAE The heat exchange rate in a standing column well is enhanced by the pumping action, which promotes movement of groundwater to and from the borehole and induces advec- tive heat transfer. The fact that in such systems groundw
8、ater is circulated through the heat pump means that the fluid flowing through the heat pump system is closer to the mean ground temperature compared to systems with closed-loop U-tube heat exchangers. Accordingly, heat pump efficiency may be improved over that of other heat pump systems. Most applic
9、ations of SCWs in North America (for geological and hydrological reasons) have been in the North- east and Pacific Northwest of the United States in addition to parts of Canada. These regions have lower mean ground temperatures and higher heating loads than other areas. Consequently, the SCW design
10、has been focused on heat extraction capacity. Under normal operating conditions, all water extracted from the well is circulated through the heat pump system and returned to the well. The well temperature can be returned to one closer to the far-field temperature by “bleeding” off some of the system
11、 flow and discharging this proportion of the flow to some other well or watercourse. This induces further flow of groundwater into the well. This effect can be utilized to reduce the required well depth, protect the well against approaching freezing conditions, or to generally increase the heat exch
12、ange capacity for a given well depth. A model of the groundwater flow and heat transfer both within the well and in the surrounding rock has been devel- oped. This has been used to calculate the performance of standing column well systems over yearly periods of opera- tion. A parametric study has be
13、en performed to establish the most significant design parameters. Performance has been Simon J. Rees is a senior research fellow at the Institute of Energy and Sustainable Development, De Montfort University, Leicester, United Kingdom. Jeffrey D. Spitler is a professor and Zheng Deng is a research a
14、ssistant in the School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, Okla. Carl D. Orio is president and Carl N. Johnson is vice president at Water Energy Distributors, Inc., Atkinson, N.H. 02004 ASHRAE. 3 Convection + , Evaporation + i1 ,.,” Transporation I II I as
15、sessed in terms of heat transfer rates, effective well depth, energy consumption, and costs (Spitler et al. 2002). HEAT TRANSFER IN STANDING COLUMN WELLS Conventional closed-loop heat exchangers in geothermal heat pump applications are often modeled assuming no groundwater flow and that the soillroc
16、k can be considered as a solid. In a standing column well, the fluid flow in the bore- hole due to the pumping induces a recirculating flow in the surrounding rock. The groundwater flow is beneficial to the SCW heat exchange as it introduces a further mode of heat transfer with the surroundings-name
17、ly, advection. The heat transfer processes in and around a standing column well are illustrated in Figure 1. In addition to the conduction of heat through both the rock and the water, convective heat transfer occurs at the surfaces of the pipework and at the borehole wall and casing. As the borehole
18、 wall is porous, fluid is able to flow from the borehole wall into and out of the rocks porous matrix. The magnitude of this flow is dependent on the pressure gradient along the borehole and the relative resistance to flow along the borehole compared to the resistance to flow through the rock. If th
19、e dip tube is arranged to draw fluid from the bottom of the well, groundwater will be induced to flow into the rock in the top part of the borehole and will be drawn into the borehole lower down. At some distance down the borehole, there will be a balance point (no net head gradient) at which there
20、will be no flow either into or out of the rock. The advective heat transfer due to the groundwater flow is always beneficial to the heat exchanger performance- whether the water is withdrawn from the top or the bottom of the well. In the cooling season, warm water is forced to flow into the rock and
21、 cooler groundwater flows back out of the rock near the point of suction. Conversely, during the heating season, cool water flows into the rock and warmer water flows out of the rock near the point of suction. The flow is therefore beneficial in either mode of operation. THE STANDING COLUMN WELL MOD
22、EL Previous models of standing column wells (Mikler 1993; Oliver and Braud 1981; Braud et al. 1983; Yuill and Mikler 1995) have made a number of assumptions about the heat transfer between the different components of the well. Groundwater flow in the lateral direction due to gross water movement ari
23、sing from head gradients induced by adja- cent rivers, local pumping, and changes in topology and geol- ogy on a larger scale have not been considered in this study. Consequently, it can be assumed that the groundwater flow and heat transfer are symmetrical about the centerline of the borehole. To m
24、odel the groundwater flow and heat transfer surrounding the well, a finite volume model that uses a mesh in two dimensions (axial and radial) has been developed. The well borehole is modeled as a nodal network that is discretized over the length of the borehole. Fluid flow in the nodal model of the
25、well borehole is modeled using control volumes that Figure I A diagram showing the different modes of heat transfer in und around a standing column well. coincide with those of the adjacent finite volume mesh. Each model is described in further detail below. THE GROUNDWATER FLOW MODEL In order to mo
26、del heat transfer and groundwater flow around the standing column well, it is necessary to solve two sets of partial differential equations. In this work, saturated flow has been assumed, so Darcys equation is used to model saturated groundwater flow. The equation of flow is written in terms of head
27、 and is given by where K = hydraulic conductivity, ds (fth); h = hydraulic head, m (fi); S, = specific storage; and t = time, s (h). In this type of problem with a radial-axial geometry, the static component of the head can be subtracted out-only differences in head induced by pumping cause groundwa
28、ter flow. Heat transfer in the ground is described by a form of the energy equation. We assume that the solid phase and fluid phase are in thermal equilibrium (at the same temperature at a given point) so that we consider the temperature as an average 4 ASHRAE Transactions: Research temperature of b
29、oth phases. An effective thermal conductivity (k kl = thermal conductivity of fluid, W/m.K (Sthft.F); and k, = thermal conductivity of solid, W/mK (Btu/h.ft.OF). The thermal mass of the rock is similarly given by nplCp,+ (1 -n)psCp, where CpI and Cps are the specific heats of the liquid and solid, r
30、espectively. The energy equation is consequently defined (Bear 1972) for the porous medium as nplCpl+(l-n)p C l-+plCplViVT-V.(k,ffVT) = Q, where 5 = average linear groundwater velocity vector, m/s (ft/ n = porosity; keff = p = density, kg/m3 (lbm/ft3); Cp = specific heat, JkgK (Btu/lbm.“F); Q = sour
31、ce/sink, w/m3 (tuni.ft3); 1 = water; and s = solid (water saturated soil). T .Y ps at (3) min); effective thermal conductivity, W/m.K (Btu/h.ft.OF); _- -,-.- . -. . , ;.- . . :, ,I . - Borehole Heat 8 Fluid flow Sub-model -. _ 1. The second term only contains the thermal mass of the liquid, as heat
32、is only advected by the liquid phase. The energy equation (Equation 3) and the equation for head (Equation 1) are coupled by the fluid velocity. The fluid velocity is obtained from the darcian groundwater flux as follows: K n v = -Vh (4) Hence, the solution to the energy equation depends on the velo
33、city data calculated from Darcy s equation. Consequently, Darcys equation and the energy equation are solved in sequence iteratively. Heat transfer in the well bore is characterized in the radial (r) direction by convection from the pipe walls and borehole wall, plus advection at the borehole surfac
34、e, and in the vertical (z) direction by advection only. The thermal model for the well bore can be described by a series of resistance networks, as shown in Figure 2. The thermal network at a particular vertical position varies depending on the presence of the suction and discharge pipes. The Well B
35、orehole Model An energy balance can be formulated at eachzplane in the well bore corresponding to the z plane in the finite volume model of the rock, 4 I I Ground Heat = volume of water in the annular region, m3 (e); = density of water in the annular region, kgm3 (lbdp); = specific heat of water, J/
36、kg.K (Btu/lbm“F). and Making use of the resistance network, the convective heat where R = thermal resistance, “C/W (“F/fi), and rn = any of the surfaces: suction tube, discharge tube, and rock. The thermal resistance based on the inside area is where A = area, m2 (e); r = radius,m(ft); k = thermal c
37、onductivity, W/mK (Btu/h.ft.“F); i = innersurface; o = outersurface; h = convection coefficient, W/mK (Bnih-ft-OF); Nu k = ed;and Uh Dh = hydraulic diameter, m (fi). The second and third terms of Equation 7 do not apply to convective heat transfer at the borehole wall, The advective heat transfer ra
38、tes in Equation 5 are defined as qadvection,n = “p(n - a,=) 9 (8) where ri2 = mass flow rate of the water, kgs (lbm/h), and n = refers to each rock and the annular fluid at adjacent nodes. For the fluid in each of the dip tubes, the energy balance is given by dTtube,z dt vpcP = qconvection,annulor r
39、egion i- qadvection,fube (9) where all terms are expressed as described above. Now, Equation 5 can be expressed in discrete form to find Ta,z and, likewise, Equation 9 can be expressed in discrete form for each tube, resulting in a system of simultaneous equations that can be solved using the Gauss-
40、Seidel method. Upon convergence of the fluid temperatures, the heat flux to the borehole wall is calculated and passed to the finite volume model and used to set the flux boundary condition; the finite volume model, in turn, is used to calculate new temperatures at the borehole wall. This procedure
41、is repeated at each time step until the borehole wall temperatures and fluxes at each z- level are consistent. PARAMETRIC STUDY This section describes the parametric study that has been used to determine the effect of key parameters on the perfor- mance of SCW systems. To examine the effects of part
42、icular parameters, one year of hourly building loads from a prototype building have been used to provide thermal boundary condi- tions for the SCW model. Simulations have been made using a whole year of load data. This allows the highly transient nature of the SCW system to be examined, especially d
43、uring “bleed“ periods. The parametric study has been organized using a “base case“ and calculating the system performance for this and other cases where a single parameter is varied in each case. (It was shown infeasible to consider all possible parameter combinations due to the intensive nature of
44、each calculation). Variations in the following parameters have been studied: Rock thermal conductivity Rock specific heat capacity Ground thermal gradient Borehole surface roughness Borehole diameter Borehole casing depth Dip tube diameter and conductivity System bleed Bleed control strategy Borehol
45、e depth Borehole flow direction Rock hydraulic conductiviy All of the simulations have been made by using building loads calculated for a small office building in Boston, Mass. The building loads are determined by using building energy simulation software (BLAST 1986), and the construction is based
46、on a real building in Stillwater, Okla. Further details of the building, systems and loads are given in Yavutzturk and Spitler (2000). The design data for the base case well design comes mostly from the well used by Mikler (1993). This well has a dip tube (suction tube) extending to very near the bo
47、ttom of the well and discharge from the heat pump system is near the top. The ground conditions are assumed to be similar to those in the northeastern U.S. The base case thermal and hydraulic properties are taken from the mean values for karst limestone. 6 ASH RAE Transactions: Research Power consum
48、ption and energy costs have been calcu- lated for each case in the study and for water table depths of 5 m (1 6 fi) and 30 m (98 fi). Pumping costs were calculated by considering frictional pipe and fitting pressure losses for a typical piping arrangement. In addition to the frictional losses, the h
49、ead required to achieve the various bleed rates was calcu- lated. A schedule of monthly energy prices was used to find the final annual costs. 2 1 .OE-6 (2.11 8) 4.3 (2.48) 5500 (82.03) 0.018 (0.987) 9.OE-3 (2.95E-2) Parameter Values 3 4 7.OE-10 (0.00148) 1.5 5.0 (0.865) (2.88) In the parametric study, each case has one parameter value changed from those of the base case (except the cases that deal with different rock types). Calculations with differing well depths have been made to enable each parameter variation to be correlated with potential reductiodextensi
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