Development of a numerical model to predict heat exchange rates for a ground-source heat pump system

Energy and Buildings 40 (2008) 2133–2140

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Development of a numerical model to predict heat exchange rates for a ground-source heat pump system Yujin Nam *, Ryozo Ooka, Suckho Hwang Cw403 Institute of Industry Science, The University of Tokyo, Tokyo 153-8505, Japan

A R T I C L E I N F O

A B S T R A C T

Article history: Received 12 October 2007 Received in revised form 28 April 2008 Accepted 2 June 2008

Ground-source heat pump (GSHP) systems can achieve a higher coefficient of performance than conventional air-source heat pump (ASHP) systems. For the design of a GSHP system, it is necessary to accurately predict the heat extraction and injection rates of the heat exchanger. Many models that combine ground heat conduction and heat exchangers have been proposed to predict heat extraction/ injection rates from/into the ground in the research field of heating, ventilation and air-conditioning systems. However, most analysis models are inaccurate in their predictions for long periods because they are based on a thermal conduction model using a cylindrical coordinate model or an equivalent diameter model. In this paper, a numerical model that combines a heat transport model with ground water flow and a heat exchanger model with an exact shape is developed. Furthermore, a method for estimating soil properties based on ground investigations is proposed. Comparison between experimental results and numerical analysis based on the model developed above was conducted under the conditions of an experiment from 2004. The analytical results agreed well with the experimental results. Finally, the proposed model was used to predict the heat exchange rate for an actual office building in Japan. ß 2008 Elsevier B.V. All rights reserved.

Keywords: Ground-source heat pump Ground heat exchanger Numerical simulation

1. Introduction Ground-source (geothermal) heat pump (GSHP) systems can achieve a higher coefficient of performance than conventional airsource heat pump (ASHP) systems by utilizing the relatively stable subterranean temperature. The market for these systems in Japan has grown remarkably over the past few years due to efforts to improve the drilling method and reduce the installation cost of ground heat exchanger (for example, utilizing the building pile as ground heat exchanger, Nagano et al. [1] and Sekine et al. [2]). In order to use these GSHP systems, it is necessary to accurately predict the heat extraction and injection rates of the heat exchanger before its introduction and to design an optimum system based on these results. Many analytical methods to predict the heat exchange rate have been proposed and used since the introduction of ‘cylindrical heat source theory’ by Carslaw and Jaeger [3]. This theory, which was developed for a long isolated pipe surrounded by an infinite solid of constant properties, is relatively simple to program and easy to understand. It has been used for numerical models for vertical ground heat exchangers

* Corresponding author. Tel.: +81 3 5452 6434; fax: +81 3 5452 6432. E-mail addresses: [email protected] (Y. Nam), [email protected] (R. Ooka), [email protected] (S. Hwang). 0378-7788/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2008.06.004

reported by Mei and Emerson [4], Yavuzturk et al. [5], and used for analytical approach by Ochifuji and Kim [6] and Bernier [7]. Cui et al. [8] Nagano et al. [9] have conducted numerical, analytical and experimental data comparisons on simulations of ground heat exchangers. Deerman and Kavanaugh [10] described the application of cylindrical heat source model by comparing simulation results with experimental data from test sites. However, most of these models are based on a heat conduction model with cylindrical coordinates, in which the effect of the ground water flow is incorporated into the effective heat conductivities. There is a possibility that models which are not sufficiently represented are inaccurate in their predictions for long periods. Furthermore, most of the proposed models utilize a cylindrical-shaped heat exchanger under the concept of an equivalent diameter and do not consider the effect of the exact shape of the heat exchanger. These models might induce numerical errors in the prediction. Recently, the effect of groundwater flow on the heat transfer rate for vertical ground heat exchanger has been represented in numerical model by many researchers. A finiteelement numerical groundwater flow and heat transport model was used to simulate and estimate the effects of heat advection by moving groundwater and heat conduction in the ground (Chiasson et al. [11]). Barcenilla et al. [12] have also studied the ‘effective’ thermal conductivity correlation to analyze vertical heat exchangers with groundwater flow. Although, these models estimate the

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vai þ

Nomenclature c kij Pr Qr QT Re vi a V

$ij

specific heat (J/kg K) permeability tensor (m2) Prandtl number mass generation term energy generation term Reynolds number velocity vector (m/s) pffiffiffiffiffiffiffiffiffiffiffi absolute value of the velocity vector ( vai vai ) Kronecker tensor

ea



ma



@ pa  ra g j ¼ 0 @x j

(3)

Here, jaiT is the heat flux and is described as follows: a

@T disp a þ li j a Þ jaiT ¼ jaiT ðea ; ra ; vai ; T a Þ ¼ ðlcond ij @x j " ¼ ea ðl

soil particles) volume ratio of each phase a (0  ea  1) heat conductivity (W/mK) viscosity (kg/ms) density of phase a (kg/m3)

a

vai vaj þ ca ra aT V a Þdi j þ ca ra ðaL  aT Þ a V

#

@T a @x j

(4)

disp

cond

Here, li j a and li j a are conduction and dispersion components, respectively, of the heat diffusivity tensor of phase a. aL and aT are horizontal and lateral heat dispersion rates, respectively. Here, dispersion is one of the diffusion phenomena that are caused by spatial non-uniformity. 2.2. Incorporating a heat exchanger model with a ground surface heat balance model

heat exchange performance for various soil and rock conditions, they can not sufficiently represent complicated geological strata, such as that found in Japan, which has multiple layers with various soil properties and hydraulic conductivities. On the other hand, the fields of hydrology, geology, and geotechnical engineering have developed simulation models of groundwater flow, and mass and heat transfer for complicated soil conditions and properties. However, the purpose of these models has been to analyze macroscopic groundwater flow, mass and heat transfer in the soil; modeling of a ground heat exchanger has not been proposed or considered. In this paper, a numerical model that combines a heat transport model with groundwater flow and a heat exchanger model with an exact shape is developed. Furthermore, the authors also propose a method for estimating soil properties based on ground investigations to obtain accurate simulation results. Moreover, the validity of these methods is confirmed by comparing simulations with experimental results. Finally, the proposed model was used to predict the heat extraction and injection rate for an actual office building in Japan.

To calculate boundary conditions on the surfaces of the heat exchanger and the ground for FEFLOW analysis, the heat exchanger and the ground surface heat balance models are incorporated into a user-subroutine. (1) Ground heat exchanger model Here, paired U-tubes (outer diameter: 38 mm, inner diameter: 28.8 mm) are assumed as the ground heat exchanger, as shown in Fig. 1. The ground heat exchanger model consists of the circulatory water model with a 1-dimensional advection-diffusion equation in the ground heat exchanger, and convective heat transfer between the inner surface of the heat exchanger pipe and the circulatory water. The temperature of the circulatory water is given by the following equation:

@Tw lw @2 Tw @Tw hPw ¼ þ  Uw ðT  Tw Þ @t rw Cw @z2 @z rw Cw Aw 1

Q¼

Ts  Tw;i 1=hA

lw

h ¼ Nu

2.1. Simulation code for heat and water transport in the ground

Nu ¼ 0:023 Re0:8 Prn

In this research, FEFLOW [13] is adopted in order to calculate heat exchange rate between ground heat exchanger and its surrounding ground and to estimate the distribution of subterranean temperature. This is an analysis code using a finiteelement method for the simulation of heat and material transport in the ground, which is widely used for the analysis of groundwater flow or ground pollution. Fujii et al. [14] has used this to study design tools for ground-coupled heat pump systems. FEFLOW is based on the following three preservation equations (mass conservation Eq. (1), momentum conservation Eq. (2), and energy conservation Eq. (3)) for the combination of soil particles, liquid water, and gas: (1)

(5)

The heat transfer between the inner surface of the heat exchanger pipe and the circulation water is

2. Numerical model for heat extraction and injection rates

@ @ ð e ra Þ þ ðe ra vai Þ ¼ ea ra Qra @t a @xi a

(2)

@ @ @ a ðe ra Ea Þ þ ðe ra vai Ea Þ þ ð j Þ ¼ ea ra QTa @t a @xi a @xi iT

Greek letters a each phase (liquid water, water vapor, and solid ea l m ra

kaij

r

(6)

(7) (8)

Here, n is 0.3 and 0.4 for cooling and heating, respectively. (2) Ground surface heat balance model

Fig. 1. Heat flux on the surface of heat exchanger.

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Heat flux Q from the ground surface to ground is given by the following heat balance equation (Fig. 2): Q ¼ Rsol þ Rsky  Rsurf  Hsurf  Lsurf

(9)

(1) Total solar radiation (Rsol) Rsol ¼ ð1  as ÞðJdn  sinðhÞ þ Jsh Þ

(10)

Here, Jdn is the direct solar radiation on the ground surface, sin(h) is solar altitude, Jsh is sky radiation, and as is albedo (reflectivity of solar radiation on the ground). (2) Downward atmospheric radiation (Rsky) qffiffiffiffi Rsky ¼ s ð273:16 þ Ta Þ4 ð0:526 þ 0:076 f Þð1  0:062  cÞ (11) Here, s is the Stephen–Boltzmann constant (5.67  108 (W/m2 K4)), f is the water vapor pressure near the ground surface (mmHg), c is the degree of cloudiness, Ta is air temperature. (3) Upward long wave radiation from the ground surface (Rsurf) 4

Rsurf ¼ s ð273:16 þ Ts Þ ð1  0:062  cÞ

(12)

Here, Ts is the ground surface temperature. (4) Sensible heat flux (Hsurf) Hsurf ¼ ac ðTs  Ta Þ

(13)

Here, the convective heat transfer ratio on the ground surface (ac) is given by the experimental equation of Ju¨rges with respect to wind velocity near the ground surface (v).

ac ¼ 5:8 þ 3:9vðv  5 m=sÞ;

ac ¼ 7:1v0:78 ðv > 5 m=sÞ

Lsurf

3.1. Fundamental soil parameters Soil is composed of three elements: soil particles, water, and air. The fundamental physical properties of soil can be estimated from the relationship between each of their volume, mass, specific heat, thermal conductivity, and thermal capacity. Fundamentally, the soil contents are determined from the results of the ground investigation, and the density, void ratio, and water content ratio of the soil are calculated using the three-phase model for soil (Kasubuchi [17]).

(14)

3.2. Thermal soil parameters

(15)

The heat conductivity and heat capacity of soil are required to calculate heat conduction in soil. Heat conductivity of the solid part of soil is estimated from the following geometric average of each solid component:

(5) Latent heat flux (Lsurf) 133:15 ¼b7 ac ð f sat ðTs Þ  Ta Þ 1000

Fig. 2. Thermal balance on ground surface.

Here, b is moisture availability of the ground surface, and fsat(Ts) is the saturate water vapor flux of Ts.

3. Estimation method for soil properties based on a ground investigation As most numerical models for ground-source heat pump are based on principal heat conduction, it is important to determine the thermal properties of ground such as ground thermal conductivity and volumetric specific heat. Recently, methods have been proposed by Austin et al. [15] and Gehlin et al. [16]. They have described portable testing equipments and the method of determination from in situ field test, called the thermal response test, which is to measure the temperature response of a circulatory fluid in a single U-tube given a constant heat flux. However, introducing the experimental equipment and conducting these field tests is expensive, which may be a burden to introducing the entire system. In Japan, items to be examined in a ground investigation before construction of a building are defined by the Japanese Industrial Standards and Japanese Geotechnical Society Standards: for example, the ground water level, void and saturation ratios of soil, mechanical analysis of soil, etc. If these investigations are conducted in three locations, the underground water gradient can be assumed. A method of assuming the soil physical properties is proposed by using the measurement results of these investigations in this section.

ls ¼ lAm=ðmþnÞ lBn=ðmþnÞ

(16)

Here, lA and lB are heat conductivities (W/mK) of solid components A and B, respectively; m and n are volume ratios of A and B, respectively. Comprehensive heat conductivity lepar and heat capacity C are given by the following parallel models of solid soil, gas, and liquid water. n X V i li

lepar ¼

(17)

i¼1

C¼

n X

ri c i V i

(18)

i¼1

Here, Vi is the volume ratio of each component i, respectively. 3.3. Hydraulic conductivity Hydraulic conductivity (permeability) is a very important parameter, and influences heat transport in the soil. There are several experimental formulations that estimate hydraulic conductivity (k) in saturated soil. Hazen’s formula k ¼ Ch ð0:7 þ 0:03tÞD210

(19)

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Terzaghi’s formula   Ct n  0:13 2 2 ffiffiffiffiffiffiffiffiffiffiffi ffi p k¼ D10 m 31n Zunker’s formula Cz  n 2 2 Dw k¼ m 1n

(20)

gradients were deduced from five underground water levels at five observation wells around the experimental site. The ground investigation and boring tests were conducted at the experimental site. The results of the boring tests and soil properties obtained from the results are shown in Fig. 3.

(21)

4.2. Analysis conditions

Kozeny’s formula k¼

Ck

n3

m ð1  nÞ2

D2w

(22)

Here, t is soil temperature, n is the porosity of soil, m is viscosity, and D10 is a 10% effective diameter in a particle size summation curve, and Dw is the average particle diameter. 4. Comparison between experimental and numerical analyses 4.1. Outline of the experiment In this section, the prediction accuracy of the numerical simulation techniques described above is examined by comparison with the experimental results. The experiment was conducted in the ground-source air-conditioning system laboratory constructed at the Chiba Experimental Station of the University of Tokyo’s Institute of Industrial Science in 2003 and 2004 [2]. Two cast-in-place concrete piles, with a diameter of 1.5 m and a length of 20 m, were installed. Eight pairs of U-tubes (45 mm outer and 35 mm inner diameters) were positioned around the surface of each pile. In this experiment, typical office building conditions were assumed, and heating and cooling were operated from 09:00 to 18:00, Monday to Friday. Heating and cooling were conducted over 3-month periods, from December to February and from June to August, respectively. Heat extraction and injection rates in the cooling and heating periods were calculated by the temperature and flow rate of circulatory water in the ground heat exchangers. In this experiment, soil temperatures at 10-m and 19-m depths at measurement points I and II, as shown in Fig. 3, were measured. Furthermore, underground water

The model for the comparison analysis adopted a variation on the heating and cooling loads, in the same manner as the experimental results. Table 1 shows the values of the physical parameters of the soil for numerical simulation based on Section 3. The groundwater level is at a depth of 12 m. The analysis domain is 26 m  20 m  20 m and is shown in Fig. 4. Two cast-in-place concrete piles (1.5 m in diameter and 20 m in depth) are installed in the analysis domain and eight pairs of meshes which imitate Utubes are positioned around the surface of each pile in the same way as in the experiment. The heat flux, which corresponds to the heat extraction and injection rates in the experiment results, is set at the surface of each mesh modeled as a U-tube. The underground water gradient is deduced to be 2.05  103 (m/m) from observations. This corresponds to a groundwater flow velocity of 13.6 m/year. The direction of the groundwater flow is also shown in Fig. 3. The calculation period was from 1st January to 31st December 2004. Initial and boundary values of the ground temperatures are set to 18.1 8C at a depth of 10 m and 17.3 8C at a depth of 19 m, as measured. The boundary value of the underground water temperature is also assumed to be constant at 16.5 8C from the experimental results. 4.3. Results Fig. 5 shows the annual variations in the ground surface heat flux, and in the outdoor and ground surface temperatures, which are calculated using the ground surface heat balance model. The model has employed standard annual meteorological data for Tokyo in the calculation. This is hourly data for every day, which records the air temperature, air humidity, direct solar radiation, sky solar radiation, wind velocity, wind direction, degree of cloud cover, and nocturnal radiation, as provided by the Society

Fig. 3. Soil properties calculated from boring test results.

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Table 1 Calculation conditions

Fig. 4. Simulation model.

In this section, the proposed model was used to predict the heat extraction and injection rate for an actual office building in

Tokyo, Japan. The building plans to introduce a ground-source heat pump system utilizing 20 cast-in-place piles (Ø1600 mm  35 m) as ground heat exchangers. In this analysis, one span (8.8 m  8.8 m) area, which contains four piles, is considered as the analysis model (Fig. 8). Table 2 shows the ground properties of the analysis conditions estimated from the ground investigation data at the site, which was calculated using samples from the boring tests and the estimation method in Section 3. The initial temperature of the ground and circulatory water is set at 16 8C, initial ground water level is G.L.—1.02 m, and the temperature of the circulatory water at the U-tube inlet (heat pump outlet) is assigned by the temperature difference (DT) from that of the circulatory water at the U-tube outlet (heat pump inlet). The heat extraction and injection rate is calculated by DT and the water flow rate. However, the ground temperature around the ground heat exchanger increases by injecting the heat into the ground during cooling operation, and decreases gradually

Fig. 5. Annual variations of the ground surface heat flux, outdoor and ground surface temperature.

Fig. 6. Distribution of temperature around piles.

of Heating, Air-Conditioning and Sanitary Engineers of Japan. Furthermore, the temperature distribution around the piles at a depth of 12 m at 5:00 p.m. on 18th August is shown in Fig. 6, in which the effect of the groundwater flow is evident. Comparisons of the soil temperatures at a depth of 10 m at measurement points I and II (Fig. 4 references) between the analysis and the experimental results are shown in Fig. 7. The measurement points I and II are 1.25 m and 2.75 m apart, respectively, from the center of pile A. Though the analysis results are slightly higher than the experimental ones – about 1 8C at most – they correspond well with the experimental ones. 5. Application to a real building in Tokyo 5.1. Analysis summary

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Fig. 7. Comparison of ground temperature variations between the numerical analysis and the experiment.

by extracting the heat during heating operation. In these conditions, the coefficient of performance (COP) of the heat pump decreases. Therefore, in this calculation, the temperature of the circulatory water is controlled below 35 8C for cooling

and above 5 8C at least for heating to avoid a decrease in COP. When the temperature exceeds this limit, DT is reduced. In these calculations, the initial DT is input as 4 8C. The analysis period is set at 365 days and heating and cooling were performed in December to February and June to August, respectively, from 09:00 to 18:00, Monday to Friday. In this paper, five calculation scenarios are performed, which are shown in Table 3 and Fig. 9. The base case (Case 2) assumes eight pairs of U-tubes around a pile, Cases 1 and 4 have four pairs, and Cases 3 and 5 have 12 pairs, respectively. In Cases 1, 2 and 3, the heat exchange rate using the same flow rate for circulatory water per pile is considered, while Cases 2, 4 and 5 use the same flow rate per Utube, 3.04 L/min. 5.2. Analysis results

Fig. 8. Analysis model (ground plan, cross-section).

Table 4 presents the analysis results for all calculation conditions. When the flow rate for the circulatory water was the same, Case 3, which had 12 pairs of U-tubes installed, achieved better heat exchange rates per pile, 184.7 W/m in cooling and 180.0 W/m in heating than Cases 1 and 2. This was due to the increase in contact surface between the pipes and the ground. Moreover, the average temperature for the water entering the heat pump in Cases 1 and 2 is lower during cooling and higher during heating than that in Case 3. The temperature of water entering the heat pump (the temperature at the U-tube outlet) is important as the COP of the heat pump significantly depends on this temperature. Fig. 10 shows the performance curve for the heat pump used in this research, which is calculated when the outlet temperature from the heat pump to the room is 7 8C (return temperature 12 8C) in cooling mode and 45 8C (return temperature 40 8C) in heating mode (Shiba et al. [18]). The COP of the heat pump was calculated using these curves and Case 3 showed the highest value, 6.72 for cooling and 4.39 for heating. On the other hand, when the flow rate per U-tube is set the same, Case 4, which had four pairs installed, achieved the highest heat exchange rate per pair of U-tubes, 22.7 W/ m for cooling and 23.0 W/m for heating. The distance between adjacent pipes in Case 5 was less than that of the other cases, 0.41 m, and the results were reduced to 20.8 W/ m due to thermal interference. Among these five cases, Case 5 achieved the highest heat exchange rate per pile, 272.4 W/ m for cooling and 227.7 W/m for heating. However, Cases 3 and 5 are more expensive to install. In particular, Case 5 needs a larger capacity circulation pump and is more expensive to run than the other cases. For the optimum design and operation, it is necessary to consider the heat exchange rate, initial cost and running costs, comprehensively.

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Table 2 Calculation conditions

Fig. 9. Cases of calculation.

6. Conclusions For the optimum design of GSHP system, it is necessary to estimate its performance and economic feasibility before the introduction of the system. In this paper, a numerical model was developed to predict heat extraction and injection rates of a ground heat exchanger.

Fig. 10. Performance curve of heat pump. Table 3 Analysis cases Case

Number of U-tube

Distance from adjacent pipe (M)

Flow rate of circulation water (L/(min pile))

1 2 3 4 5

4 pairs 8 pairs 12 pairs 4 pairs 12 pairs

1.13 0.61 0.41 1.13 0.41

24.32 24.32 24.32 12.16 36.48

 It is based on simulation code for the analysis of underground heat and water movement, in which circulatory water model in the heat exchanger and the ground surface heat flux model are incorporated.  An estimation method for the soil thermal properties based on a ground investigation and theoretical formulas was proposed.  Simulation results using the developed prediction model and the soil heat physical property values estimated here were compared with the experimental results, and the validity of the prediction model developed here was confirmed.  This simulation tool was applied to an office building in Tokyo, Japan, and the optimum design of system was examined as case study. In the future, various other considerations for optimum design and operation system will be conducted by coupling the developed model with a building load model.

Table 4 Analysis results Case

1 2 3 4 5

Heat exchange rate per a U-tube (W/m)

Heat exchange rate per a pile (W/m)

Average outlet temperature (8C)

COP of heat pump

Cooling

Heating

Cooling

Heating

Cooling

Heating

Cooling

Heating

44.8 22.7 15.4 22.7 22.7

32.3 20.9 15.0 23.0 19.0

179.2 181.6 184.7 90.8 272.4

129.2 167.2 180.0 92.0 227.7

25.9 23.1 22.6 22.7 25.3

8.6 9.4 10.5 10.4 9.3

5.90 6.57 6.72 6.70 6.05

4.21 4.29 4.39 4.38 4.27

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