# Recoverable Resource Prediction of Shallow Geothermal Energy in Small Towns Using the Finite Volume Method: Taking the Central Urban Area of Danyang City, Jiangsu Province, as an Example

Authors: Qing Zhang; Weiya Ge; Junyuan Jia; Fujin Tian; Xiaojun Chang; Huaixue Xing; Ting Lei
Journal: Mathematical Problems in Engineering
 (2019)

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## Abstract

The ground-coupled ground-source heat pump (GSHP) system is a common method for shallow geothermal energy exploitation and utilization. GSHP has a great heat exchange rate and wide application range. In order to effectively exploit shallow geothermal energy in the central urban area of Danyang City, Jiangsu Province, based on finite volume method, it is adopted to simulate the amount of recoverable shallow geothermal energy in the study area through ground-coupled heat exchange. The simulation is conducted on the development trend of thermal transport and thermal balance in the study area from early June 2015 to the end of May 2025 to obtain the temperature distribution at different times. Under the presupposed working conditions, with the operation of a ground-coupled GSHP, thermal accumulation occurs in parts of the study area. To mitigate the problem of thermal accumulation, two schemes are proposed:(1) adding auxiliary cooling towers and (2) increasing the amount heated domestic water in spring and autumn. Both schemes mitigate thermal accumulation. For Scheme1, the total heat supply for shallow geothermal energy in the central urban area of Danyang City in winter is 2.91 × 106 kW, and the total heat release in summer is 3.53 × 106 kW. For Scheme2, the total heat release in summer is 3.52 × 106 kW and the total heat supply in winter is 2.90 × 106 kW. A ground-coupled GSHP system has significant applicability in the central urban area of Danyang City, where shallow geothermal energy has good exploitation prospects.


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## Body

## 1. Introduction

Shallow geothermal energy refers to thermal energy reserves in rock, soil, underground water, and surface water within 200 m of the earth’s surface and has the value of exploitation and utilization. Shallow geothermal energy reserves are renewable, widespread, clean, environmentally-friendly, economical, and practical and have great security and availability. Shallow geothermal energy resources in China have great potential and broad exploitation and utilization prospects for new-type urbanization in China [1–3]. To rationally utilize shallow geothermal energy in a city, it is necessary to research and evaluate the shallow geothermal energy resources of a given region [4]. The study of recoverable shallow geothermal energy resources has always been a hot-spot, and many researchers have carried out related research on evaluation indicators and methods of shallow geothermal energy resources.The shallow geothermal energy is only useful for space heating and air conditioning systems and is ideally extracted from wells or boreholes combined with heat pumps [5–7]. Alternatively, the ground may be used as storage medium for waste heat or for cooling purposes. The most common variants of geothermal systems are ground-source heat pumps (GSHPs), where vertical boreholes act as borehole heat exchangers (BHEs) [8–10]. Since the geological, geophysical, and hydrogeological conditions that control the heat transfer processes and extraction efficiency vary, field investigation campaigns are suggested for larger-scale systems to ensure appropriate planning of shallow geothermal installation. The thermal response test (TRT), which is conducted in BHEs before heat mining begins, is an established technique [11, 12]. By monitoring the effect of short-term heating (or cooling), the thermal properties of the ground and the heat transfer efficiency between ground and BHE are interpreted. Robert and Gosselin [13] have even proposed a method based on cost minimization to design a complete GCHP system, where the necessity of a TRT depends on the designed bore-field size. Tian et al. [14] proposed a heat compensation unit with thermosyphon which combines an air-source thermosyphon and an air-source heat pump to transfer heat from ambient air into the ground during the nonheating season as seasonal thermal storage and to recover the soil temperature. Han et al. [15] investigated a solar-assisted GSHP heating system with latent heat energy storage tank, which was demonstrated to play a very important role in operation. Wang et al. [16] presented an experimental study of a solar-assisted GSHP system in Harbin, where solar seasonal thermal storage was conducted throughout the non-heating seasons. In winter, the solar energy was used as a priority, and the building was heated by GSHP and solar collectors alternately. Trillat-Berdal et al. [17] presented an experimental study of a ground-coupled heat pump (GCHP) used in a 180 m2 residence and combined with thermal solar collectors. Shallow geothermal energy resources in Danyang City, Jiangsu Province, have a unique endowment and can be utilized greatly in terms of the construction of newly developed cities, towns, high-efficiency agricultural facilities, and tourism and resort development. In 2016, Nanjing Geological Survey Center of the China Geological Survey carried out an urban geological survey project in Danyang, mainly focusing on investigating shallow geothermal energy resources [18]. With respect to the assessment of shallow geothermal energy resource of Danyang City, Luo Zujiang et al. utilized an analytic hierarchy process to assess the suitability zoning of shallow geothermal energy in Binjiang, a newly developed area of Danyang City, and then adopted the volume method based on Monte Carlo simulations to evaluate the shallow geothermal energy resources [19]. As for the recoverable resource capacity of shallow geothermal energy in the central urban area of Danyang City, a similar assessment has not been conducted.In this paper, based on finite volume method, it is used to conduct a predictive study on the recoverable resource capacity of shallow geothermal energy in the central urban area of Danyang City, Jiangsu Province [20]. First, the thermal transport variation trend and thermal balance during the ten years when shallow geothermal energy exploitation is in operation under the mode of ground-coupled heat exchange are predicted. Next, two schemes are proposed to address the problem of thermal accumulation: (1) adding an auxiliary cooling tower and (2) increasing the heated domestic water amount in spring and autumn. Then the recoverable resource capacity of shallow geothermal energy in the study area is calculated. Forecast evaluation is conducted on the recoverable resource capacity of shallow geothermal energy in the study area in the hope of having significance to the exploitation and utilization of shallow geothermal energy in Danyang City.


## 2. Geothermal Geological Characteristics of the Study Area

Danyang City is located in the southern Jiangsu Province, belonging to a plain city. The whole city presents the terrain of being low in the southeastern part and being high in the northwestern part, with an elevation of approximately 7 m above sea level. The study area is the central urban area of Danyang City, with the northern boundary extending to the administrative boundary of the city, the western and southern boundaries extending to National Highway 312 and the eastern boundary extending to the Beijing-Shanghai high-speed railway, Jingdong Road and Jiuqu River. The study area has a total area of 192.5 square kilometers (Figure1). The central urban area of Danyang City is located in the northwestern municipal administrative area, and the terrain is inclined from northwest to southeast with an elevation of 5.0m-8.0m. The humid climate belongs to the north subtropical monsoon climate zone and has four distinctive seasons, abundant rainfall, and abundant sunlight.Figure 1
Map showing the extent of the study area.Shallow geothermal energy reserves in the study area are closely related to the regional Quaternary structure, lithological characteristics, surface-water conditions, rock and soil thermophysical properties, and shallow geothermal field features. According to borehole exposures, the Quaternary system in this area, from top to bottom, can be divided into Holocene Rudongformation (Qhr), Pleistocene Gehu Lake formation (Qp3g), Kunshan formation (Qp3k), Qidong formation (Qp2q), and Haimen formation (Qp1h). The underlying bedrock is dominated by mud-stone (Figure 2). According to comprehensive analysis of the completed borehole data in the central urban area of Danyang City, the mountain areas close to the southwestern part of Quaternary system in this area have smaller thickness, and early and middle Pleistocene strata are not well developed; only the upper hard plastic clay layers of the middle Pleistocene are present. In this area, influenced by the ancient Yangtze River channel, a sand gravel layer and a thicker medium-coarse sand layer are developed, and the middle Pleistocene strata are washed out and eroded, leaving a thickness of 30 m-60 m which gradually increases in the north-east direction. The flood plain deposit of the Yangtze River is widely distributed, featuring a “thousand-layer cake” with interbedded thin layers of clay and silt. Through the analysis of geothermal monitoring data from borehole surveys (Figures 3–7), the constant temperature zone depth in Danyang City is generally between 10 m and 30 m, with the average temperature being 18.5°C.Figure 2
Geologic cross section constructed from borehole exposures.Figure 3
Geothermal vertical variation diagram for DW1.Figure 4
Geothermal vertical variation diagram for DW2.Figure 5
Geothermal vertical variation diagram for DW3.Figure 6
Geothermal vertical variation diagram for DW4.Figure 7
Geothermal vertical variation diagram for DW6.


## 3. On-Site Thermal Response Experiment

The thermal response test depth is 100-120m and 5 groups of single-U and double-U buried pipes are installed (Figure8). Borehole numbers are defined as DW1-4 and DW6, and the borehole layout is shown in Figure 9. According to the numerical values recommended by International Heat Pump Association, the amount of ground-coupled heat exchange per meter of well depth should be guaranteed to be 40-80W/m. Therefore, in the constant heat flow test in this case, the calculation is conducted using a well depth of 100 m. In this paper, tests are carried out with a constant heat flow being 4.5kW and 7.5kW, respectively, to obtain the outlet and inlet fluid temperatures, fluid flow, and constant thermal power for data storage. Data are processed and interpreted indoors (Figure 10). The detailed experiment parameters for all boreholes are shown in Table 1.Table 1
Borehole experiment parameters.
Test hole number Pipe burying mode Test condition Heating power (kW) Backfill materials DW2 Double-U/SSingle-U Constant heat-flow method 4.5/7.5 Medium-coarsesand DW3 Single-U Constant heat-flow method 4.5/7.5 Medium-coarsesand DW1 Single-U Constant heat-flow method 4.5/7.5 Medium-coarsesand DW6 Single-U Constant heat-flow method 4.5/7.5 Medium-coarsesand DW4 Single-U Constant heat-flow method 4.5/7.5 Medium-coarsesandFigure 8
Thermal response experimental facilities.Figure 9
Map showing the borehole layout.Figure 10
Constant-power steady flow test of boreholes and logarithmic fitting curve.The simplified model frequently used in engineering regards buried pipes as homogeneous lineheat sources. Inside boreholes, the heat transfer process can be expressed by(1)Tf-Tb=qlRbwhereTf denotes the average temperature of fluid inside buried pipes (°C), Tb denotes the temperature of borehole walls (°C), ql denotes the heat flow release per unit length of buried pipes (W/m), and Rb denotes the heat-transfer resistance inside boreholes (m·°C/W).The heat conduction outside boreholes can be expressed by(2)Tf=Tff+qlRswhereRs denotes the heat-transfer resistance of rock-soil body (m•°C/W),Tff denotes the soil temperature at infinity, andTff denotes the soil temperature at infinity (°C).With the heat transfer processes inside and outside boreholes taken into consideration, when the testing time is relatively long, the average circulatory mediator temperature for the line heat source model is(3)Tf=Tff+qlRb+Eidb2ρscs/16λsτ4πλsWhen the heat-transfer time is long enough, (3) can be rewritten as follows:(4)Tf=Tff+qlRb+ln⁡db2ρscs/16λsτγ4πλsDuring constant heat flow experiments,ql is a constant and (4) can be rewritten into a linear equation of logarithmic time.(5)Tfτ=kln⁡τ+bhere,(6)k=ql/4πλs(7)b=ql4πλsln⁡16λsdb2ρscs-γ+qlRb+TffThe variation curve for the average fluid temperature is depicted as the curve for a natural logarithm with respect to time, and the expression of heat conductivity coefficient is(8)λs=ql4πkThe thermal diffusion coefficient of the rock-soil body outside boreholes is determined by the following expression:(9)α=λsρscsThe important parameters of 5 thermal response test holes in the working area are calculated according to the abovementioned line heat source model (Table2). A thermal response experiment is conducted on all test holes with the low and high heating power. By comparing the heat conductivity coefficients and their average value under the two kinds of heating power, it is found that three variation trends are relatively consistent, with the values having little difference. The average heat conductivity coefficient under the two kinds of heating power can reflect the comprehensive heat conductivity coefficient of the test hole.Table 2
Results of thermal response experiment.
Test hole number Bed rock’s burial depth (m) Initial average temperature(°C) Heat conductivityCoefficient(W/m▪K) Thermal diffusion coefficient(10−6m2/s) Thermal capacity(106J/m3▪K) Low heatingpower High heatingpower Averagevalue Averagevalue Average value DW2 52.61 18.90 1.73 1.98 1.84 0.58 1.90 DW3 53.50 17.93 1.70 1.62 1.66 0.58 1.58 DW1 52.58 18.37 1.62 1.81 1.72 0.62 1.66 DW6 48.20 18.75 2.38 2.14 2.26 0.78 1.68 DW4 57.60 18.94 2.04 2.17 2.11 0.79 1.54


## 4. Finite Volume Method

FMV is a kind of discretization solving method and it was applied to solving the radiative transfer equation [21, 22]. The finite volume method (FVM) was first proposed by Patankar and Spalding, then it was named SIMPLE (semi-implicit method for the pressure-linked Equation) method [23, 24]. The well-known conventional numerical methods, such as FVM, finite difference method (FDM), finite element method (FEM), and spectral method (SM), can be applied in modelling unsteady heat transfer in the earth and ground-source heat exchangers in shallow geothermal applications. Compared with FDM, FEM, SM, etc., the physical meaning of FVM is straightforward and easily understood, and it can be used for irregular grid to settle down the complex boundary problems [25]. Generally, the FVM features a high computational efficiency and is widely applied in the field of metal forging, viscous flow field calculation, mud flow value simulation, computational fluid dynamics (CFD), etc. [26, 27].The fundamental principle of the FVM divides the computational domain into grid cells to make nonoverlapping control volume around every grid cell. The governing equation is used to integrate the control volumes and obtain a discretization equation. In this paper, hydrothermal coupling under the mode of ground-coupled heat exchange is primarily simulated, and recoverable shallow geothermal energy reserves within 10 years are estimated. In hydrothermal coupling, the transport equation is adopted to study energy control, and the control volume includes the skeleton and fluid of rock mass, both of which are combined to constitute solid nonisothermal filtration energy equation in the computational process [28, 29]. The energy equation for porous media is as follows:(10)σ∂ts∂τ+u∂ts∂X=α∇2ts+qtρcptwhere(11)ρcpt=φρcpt+1-φρcps,λt=φλf+1-φλs,qt=φλf+1-φqs,ο=ρcptρcpf,αt=λtρcpfIn the equation,σdenotes heat capacity ratio, u denotes groundwater velocity, αdenotes thermal diffusion coefficient (m2/s),ρ denotes density (g/cm3), cpdenotes specific heat capacity (J/(g·K)), φ denotes porosity, λdenotes heat conductivity coefficient (W/(m·K)), σ∂ts/∂τdenotes the internal energy variation of the control volume,α∇2ts denotes the heat conduction item, qt/ρcptdenotes the source item, and q denotes the energy of source item (W/m3); subscriptss,f, andt denote solid item, fluid item, and the comprehensive parameters of two items, respectively [30, 31].Without consideration of internal heat sources, the energy balance equation of micro element is as follows:(12)ΔU+ΔQ=Qi-1,j,k+Qi+1,j,k+Qi,j-1,k+Qi,j+1,k+Qi,j,k-1+Qi,j,k+1whereΔU denotes the internal energy variation of the control volume and ∆Qdenotes the energy variation caused by groundwater flow. The energy introduced through the adjacent nodes of the control volume during unit time equals the sum of both.The FVM is to divide grids and establish discretization equations. In this paper, we assume that the rock-soil body is an isotropic porous media, a constant heat conductivity coefficient and specific heat capacity, and groundwater flow conforms to Darcy law. Moreover, the thermal balance between the soil skeleton and the water flow is achieved instantaneously, and the fluid in the same cross-section around buried pipes has the same temperature and flow velocity [32, 33].


## 5. Analysis of Thermal Balance Development Trend of Shallow Geothermal Energy Exploitation

According to the actual seepage field form, the adopted well spacing pattern is that the natural groundwater flow direction is perpendicular to the trend of pumping-injection well groups. Considering actual natural conditions and climate conditions of Danyang City, we adopt the cooling-heating operation mode typical of Southern China, that is, cooling-heating combination mode. June to September every year is the cooling period (122d). October to November is the cooling stopping period (61d). December to February of the following year is the heating period (90d), and March to May is the heating stopping period (92d). The simulation assumes that the system operates continuously for 10 years, and the heat exchange system operates for 10 hours a day. Before simulation and prediction, according to the working area’s administrative division, lithologic structure, and the thermal response characteristics of rock-soil body, the working area is zoned for calculation (Figure11).Figure 11
Zoning map for heat exchange amount of shallow geothermal energy in the study area.The study area is divided into four layers from top to bottom: the first layer is phreatic aquifer (formation), the second layer is confined aquifer I (formation), the third layer is confined aquifer II (formation), and the fourth layer is confined aquifer III (formation) and part of bedrock fissure water. Confined aquifer II (formation) has a relatively wide distribution, good water yield, and certain exploitation potential. Thus, confined aquifer II (formation) is the target layer in this calculation.According toEngineering technology regulations for ground-source heat pump systemand the working condition that the system is in operation for 122 days in summer and for 90 days in winter, the well spacings between Zone I, Zone II, Zone III, Zone IV, and Zone V are all 5 m. According to the on-site thermal response experiment on the rock-soil body andJiangsu Ground-source heat pump engineering technology regulations, the single-hole heat transfer temperature difference and heat exchange amount in every calculation zone are shown in Table 3. Under the abovementioned working conditions, the variation trend of groundwater seepage and thermal transport during ten years of shallow geothermal energy exploitation is predicted underground-coupled heat exchange. The prediction time is from early June 2015 to the end of May 2025, with a year being divided into 12 stress periods. A stress period has one time step. The initial temperature is speculated and obtained according to the investigation and monitoring results and in combination with the on-site thermal response experiment and influence laws of seasonal variations in formation temperature (Figure 12).Table 3
Statistical table for heat transfer temperature difference and single-hole heat exchange amount in every zone.
Number Heat transfer temperature difference summer/winter (°C) Single-hole heat exchange amount in summer (kW) Single-hole heat exchange amount in winter (kW) Zone I 13.24/11.76 4.75 4.22 Zone II 14.27/10.73 4.62 3.46 Zone III 13.56/11.44 5.84 4.93 Zone IV 13.80/11.20 4.12 3.35 Zone V 13.51/11.49 4.97 4.23Figure 12
Temperature distribution of the model at different times ((a) June 1st, 2015, (b) September 30th, 2015, (c) February 28th, 2016, (d) May 31st, 2016, (e) September 30th, 2024, (f) February 28th, 2025, and (g) May 31st, 2025).
(a) (b) (c) (d) (e) (f) (g)After 10 years of shallow geothermal energy exploitation underground-coupled heat exchange, the increasing amplitude of groundwater temperature is relatively large due to the relatively small spacing between heat exchange holes. Temperature values around the monitoring sites in every zone after 1-year of exploitation and 10 years of exploitation are shown in Table4.Table 4
Temperature variation values for different monitoring sites.
Zone Number of monitoring site Temperature after 1 year/°C Temperature after 10 years/°C Zone I 1 18.99 21.31 2 19.71 29.48  Zone II 3 19.49 30.55 4 18.60 25.94  Zone III 5 19.31 30.26 6 19.51 29.89  Zone IV 7 19.02 23.83 8 19.29 27.82  Zone V 9 19.41 26.81 10 19.16 23.54With shallow geothermal energy being exploited year by year, the formation temperature at the end of each operation cycle increases with each passing year, showing an overall increasing tendency. The problem of thermal accumulation is most serious in Zone III. According to the temperature distribution in different layers of the model at different times, the influence range of shallow geothermal energy exploitation on the temperature in the groundwater environment changes constantly within a year, and the influence range for the same time period extends year by year.Because of shallow geothermal energy exploitation through ground-coupled heat exchange, as the heat exchange hole releases heat in summer and extracts heat in winter, the relative temperature will significantly change, and heat will be accumulated with each passing year, producing a series of effects on the surrounding water environment and causing the heat exchange effect to weaken in the middle and later stages of the first operating season, causing efficiency of the heat exchange system to decrease and even fail. Therefore, it is necessary to take measures to decrease thermal accumulation.


## 6. Planning and Assessment of Recoverable Shallow Geothermal Energy Resources Through Ground-Coupled Heat Exchange

In order to guarantee that shallow geothermal energy can be exploited and utilized sustainably, the established model for planning and assessment of recoverable shallow geothermal energy through ground-coupled heat exchange is used to discuss the adoption of the following two schemes to decrease thermal accumulation: Scheme 1: spacing between the heat exchange holes in every calculation zone is 5 m, and the heat supply amount and heat release amount in a single hole within a year are certain with regard to the issue of thermal accumulation. The thermal accumulation phenomenon is simulated after accounting for the cooling tower auxiliary equipment, and the recoverable amount of shallow geothermal energy in the central urban area of Danyang City is calculated. Scheme 2: spacing between the heat exchange holes in every calculation zone is 5 m, and the heat supply amount and heat release amount in a single hole within a year are certain, and the operating condition is changed appropriately. Thermal accumulation is simulated after the amount of heated domestic water in spring and autumn increases. Then, the recoverable amount of shallow geothermal energy in the central urban area of Danyang City is calculated.


### 6.1. Simulation and Prediction Results of Scheme 1

Under the condition that the spacing between heat exchange holes is 5 m and that the number of cooling towers is equal to that of ground-coupled heat exchange holes, the cooling towers are in operation between June and August, and ground-coupled heat exchangers work for 10 hours simultaneously. Heat loss on the pipelines between heat exchangers and underground buried pipes is ignored. The cooling water temperature for the cooling towers of each zone is shown in Table5. After cooling towers are added, the temperature distribution in the study area at different prediction times is calculated (Figure 13).Table 5
Statistical table for water temperature of buried ground pipes and cooling towers in each.
Zone Number Heat transfer temperature difference summer/winter(°C) Cooling temperature in cooling towers(°C) Zone I 13.24/11.76 4.35 Zone II 14.27/10.73 6.12 Zone III 13.56/11.44 4.87 Zone IV 13.80/11.20 5.29 Zone V 13.51/11.49 4.80Figure 13
Temperature distribution at different times for the model after adding cooling towers (((a) September 30th, 2015, (b) February 28th, 2016, (c) May 31st, 2016, (d) September 30th, 2024, (e) February 28th, 2025, and (f) May 31st, 2025).
(a) (b) (c) (d) (e) (f)Temperature values around monitoring sites in every zone after one-year and 10-year exploitation are shown in Table6. After 10 years of shallow geothermal energy exploitation through ground-coupled heat exchange, the adoption of the mixing heat exchange system of cooling towers and buried pipes guarantees a better temperature recovery time, and groundwater temperature within a year shows almost no increase amplitude.Table 6
Temperature variation values in each monitoring site after adding cooling towers.
Zone Number ofmonitoring sites Temperatureafter 1 year/°C Temperature after 10 years/°C Zone I 1 18.74 18.85 2 18.61 19.01  Zone II 3 18.25 18.37 4 17.79 17.84  Zone III 5 18.12 18.29 6 18.39 18.58  Zone IV 7 18.51 18.61 8 18.37 18.54  Zone V 9 18.62 18.84 10 18.67 18.75From temperature variation in the monitoring sites, with the exploitation and utilization of shallow geothermal energy, soil temperatures show a slowly increasing trend and within 10 years the temperature rise in every site is less than 0.5°C. Thus the problem of thermal accumulation is effectively alleviated. When cooling towers are used to assist heat release, shallow geothermal energy exploitation through ground-coupled heat exchange can be carried out continuously in a long-term effective way.When the spacing between heat exchange holes is 5 m, and the heat transfer temperature differences of Zone I—Zone V in summer/winter are 13.24/11.76°C, 14.27/10.73°C, 13.56/11.44°C, 13.80/11.20°C, and 13.51/11.49°C, respectively, the required cooling temperatures of circulation media through cooling towers in summer are 4.35°C, 6.12°C, 4.87°C, 5.29°C, and 4.80°C, respectively. According to the abovementioned exploitation schemes, the maximum recoverable resource amount of shallow geothermal energy can be obtained. The total heat supply amount of shallow geothermal energy through 100-meter ground-coupled heat exchange in the central urban area of Danyang City in winter is 2.91 × 106 kW, and the total heat release amount in summer is 3.53 × 106 kW.


### 6.2. Simulation and Prediction Results of Scheme 2

The single-hole heat exchange amount for each calculation zone is calculated with considering 5% loss, and domestic water is heated from 15°C to 50°C to obtain the heated domestic water amount in every zone. In order to alleviate the problem of thermal accumulation, the total heat supply amount in spring, autumn, and winter should be slightly smaller than the total heat release amount in summer.Through simulation calculation, under the operation scheme of increasing the heated domestic water amount in spring and autumn by 1447826.19m3/d when the spacing between heat exchange holes is 5 m, the problem of thermal accumulation in geothermal fields is effectively alleviated. Temperature distribution in the study area at different prediction times after increasing the amount heated water is shown in Figure 14.Figure 14
Temperature distribution at different time points for the model after increasing domestic water amount ((a) September 30th, 2015, (b) February 28th, 2016, (c) May 31st, 2016, (d) September 30th, 2024, (e) February 28th, 2025, and (f) May 31st, 2025).
(a) (b) (c) (d) (e) (f)Temperatures around the monitoring sites in every zone after one-year and 10-year exploitation are shown in Table7. After 10 years of shallow geothermal energy exploitation under through ground-coupled heat exchange, groundwater temperature within a year has almost no increase amplitude because of increasing the amount of heated domestic water amount in spring and autumn. From temperature variation in the monitoring sites, with exploitation and utilization of shallow geothermal energy, soil temperatures show a slow trend over 10 years. The temperature rise in every site is less than 0.5°C. Thus, the problem of thermal accumulation is alleviated effectively.Table 7
Temperature variations in each monitoring site after increasing domestic water amount.
Zone Number of monitoring sites Temperature after 1 year/°C Temperature after 10 years/°C Zone I 1 18.74 18.80 2 18.60 19.07  Zone II 3 18.25 18.57 4 17.79 17.96  Zone III 5 18.11 18.47 6 18.33 18.68  Zone IV 7 18.49 18.60 8 18.35 18.57  Zone V 9 18.60 18.87 10 18.66 18.76Long-term exploitation and utilization of shallow geothermal energy though ground-coupled heat exchange causes no thermal balance issues in the underground temperature field when the heated domestic water amount in spring and autumn is increased by 1447826.19m3/d. The total heat release amount of shallow geothermal energy under the mode of 100-meter ground-coupled heat exchange in the central urban area of Danyang City in summer is 3.52 × 10 6 kW, and the total heat supply in winter is 2.90 × 10 6 kW.


### 6.3. Discussion the Two Schemes

Compared with the two suggested solutions, the recoverable amount of shallow geothermal energy is basically the same to conduct the attenuation of the thermal accumulation effect. Under Scheme 1, the total heat supply shallow geothermal energy under the mode of 100-meter ground-coupled heat exchange in the central urban area of Danyang City in winter is 2.91 × 106 kW, and the total heat release in summer is 3.53 × 106 kW. Under Scheme 2, the total heat release in summer is 3.52 × 106 kW, and the total heat supply in winter is 2.90 × 106 kW. Thus, from the perspective of effect, it is difficult to judge which scheme has more advantageous.However, from the perspective of facility budget, Scheme 2 has more advantages. In Scheme 1, cooling towers need to be installed, whereas no additional facilities were needed in Scheme 2 and the increasing the amount of heated domestic water can bring more economic benefits. Moreover, when cooling towers are used to assist heat release, the shallow geothermal energy exploitation through ground-coupled heat exchange should be carried out continuously in a long-term way, indicating a lot of maintenance costs.


## 6.1. Simulation and Prediction Results of Scheme 1

Under the condition that the spacing between heat exchange holes is 5 m and that the number of cooling towers is equal to that of ground-coupled heat exchange holes, the cooling towers are in operation between June and August, and ground-coupled heat exchangers work for 10 hours simultaneously. Heat loss on the pipelines between heat exchangers and underground buried pipes is ignored. The cooling water temperature for the cooling towers of each zone is shown in Table5. After cooling towers are added, the temperature distribution in the study area at different prediction times is calculated (Figure 13).Table 5
Statistical table for water temperature of buried ground pipes and cooling towers in each.
Zone Number Heat transfer temperature difference summer/winter(°C) Cooling temperature in cooling towers(°C) Zone I 13.24/11.76 4.35 Zone II 14.27/10.73 6.12 Zone III 13.56/11.44 4.87 Zone IV 13.80/11.20 5.29 Zone V 13.51/11.49 4.80Figure 13
Temperature distribution at different times for the model after adding cooling towers (((a) September 30th, 2015, (b) February 28th, 2016, (c) May 31st, 2016, (d) September 30th, 2024, (e) February 28th, 2025, and (f) May 31st, 2025).
(a) (b) (c) (d) (e) (f)Temperature values around monitoring sites in every zone after one-year and 10-year exploitation are shown in Table6. After 10 years of shallow geothermal energy exploitation through ground-coupled heat exchange, the adoption of the mixing heat exchange system of cooling towers and buried pipes guarantees a better temperature recovery time, and groundwater temperature within a year shows almost no increase amplitude.Table 6
Temperature variation values in each monitoring site after adding cooling towers.
Zone Number ofmonitoring sites Temperatureafter 1 year/°C Temperature after 10 years/°C Zone I 1 18.74 18.85 2 18.61 19.01  Zone II 3 18.25 18.37 4 17.79 17.84  Zone III 5 18.12 18.29 6 18.39 18.58  Zone IV 7 18.51 18.61 8 18.37 18.54  Zone V 9 18.62 18.84 10 18.67 18.75From temperature variation in the monitoring sites, with the exploitation and utilization of shallow geothermal energy, soil temperatures show a slowly increasing trend and within 10 years the temperature rise in every site is less than 0.5°C. Thus the problem of thermal accumulation is effectively alleviated. When cooling towers are used to assist heat release, shallow geothermal energy exploitation through ground-coupled heat exchange can be carried out continuously in a long-term effective way.When the spacing between heat exchange holes is 5 m, and the heat transfer temperature differences of Zone I—Zone V in summer/winter are 13.24/11.76°C, 14.27/10.73°C, 13.56/11.44°C, 13.80/11.20°C, and 13.51/11.49°C, respectively, the required cooling temperatures of circulation media through cooling towers in summer are 4.35°C, 6.12°C, 4.87°C, 5.29°C, and 4.80°C, respectively. According to the abovementioned exploitation schemes, the maximum recoverable resource amount of shallow geothermal energy can be obtained. The total heat supply amount of shallow geothermal energy through 100-meter ground-coupled heat exchange in the central urban area of Danyang City in winter is 2.91 × 106 kW, and the total heat release amount in summer is 3.53 × 106 kW.


## 6.2. Simulation and Prediction Results of Scheme 2

The single-hole heat exchange amount for each calculation zone is calculated with considering 5% loss, and domestic water is heated from 15°C to 50°C to obtain the heated domestic water amount in every zone. In order to alleviate the problem of thermal accumulation, the total heat supply amount in spring, autumn, and winter should be slightly smaller than the total heat release amount in summer.Through simulation calculation, under the operation scheme of increasing the heated domestic water amount in spring and autumn by 1447826.19m3/d when the spacing between heat exchange holes is 5 m, the problem of thermal accumulation in geothermal fields is effectively alleviated. Temperature distribution in the study area at different prediction times after increasing the amount heated water is shown in Figure 14.Figure 14
Temperature distribution at different time points for the model after increasing domestic water amount ((a) September 30th, 2015, (b) February 28th, 2016, (c) May 31st, 2016, (d) September 30th, 2024, (e) February 28th, 2025, and (f) May 31st, 2025).
(a) (b) (c) (d) (e) (f)Temperatures around the monitoring sites in every zone after one-year and 10-year exploitation are shown in Table7. After 10 years of shallow geothermal energy exploitation under through ground-coupled heat exchange, groundwater temperature within a year has almost no increase amplitude because of increasing the amount of heated domestic water amount in spring and autumn. From temperature variation in the monitoring sites, with exploitation and utilization of shallow geothermal energy, soil temperatures show a slow trend over 10 years. The temperature rise in every site is less than 0.5°C. Thus, the problem of thermal accumulation is alleviated effectively.Table 7
Temperature variations in each monitoring site after increasing domestic water amount.
Zone Number of monitoring sites Temperature after 1 year/°C Temperature after 10 years/°C Zone I 1 18.74 18.80 2 18.60 19.07  Zone II 3 18.25 18.57 4 17.79 17.96  Zone III 5 18.11 18.47 6 18.33 18.68  Zone IV 7 18.49 18.60 8 18.35 18.57  Zone V 9 18.60 18.87 10 18.66 18.76Long-term exploitation and utilization of shallow geothermal energy though ground-coupled heat exchange causes no thermal balance issues in the underground temperature field when the heated domestic water amount in spring and autumn is increased by 1447826.19m3/d. The total heat release amount of shallow geothermal energy under the mode of 100-meter ground-coupled heat exchange in the central urban area of Danyang City in summer is 3.52 × 10 6 kW, and the total heat supply in winter is 2.90 × 10 6 kW.


## 6.3. Discussion the Two Schemes

Compared with the two suggested solutions, the recoverable amount of shallow geothermal energy is basically the same to conduct the attenuation of the thermal accumulation effect. Under Scheme 1, the total heat supply shallow geothermal energy under the mode of 100-meter ground-coupled heat exchange in the central urban area of Danyang City in winter is 2.91 × 106 kW, and the total heat release in summer is 3.53 × 106 kW. Under Scheme 2, the total heat release in summer is 3.52 × 106 kW, and the total heat supply in winter is 2.90 × 106 kW. Thus, from the perspective of effect, it is difficult to judge which scheme has more advantageous.However, from the perspective of facility budget, Scheme 2 has more advantages. In Scheme 1, cooling towers need to be installed, whereas no additional facilities were needed in Scheme 2 and the increasing the amount of heated domestic water can bring more economic benefits. Moreover, when cooling towers are used to assist heat release, the shallow geothermal energy exploitation through ground-coupled heat exchange should be carried out continuously in a long-term way, indicating a lot of maintenance costs.


## 7. Conclusions

( 1 ) Based on the FVM is employed to simulate the amount of recoverable shallow geothermal energy through ground-coupled heat exchange, which has a preferable effect, and the results are objective and reliable.( 2 ) When well spacing is 5 m, the formation temperature at the end of each operation cycle increases with each passing year, showing an overall increasing trend. Thermal accumulation causes the heat exchange effect of the ground-coupled heat exchange system to weaken in the middle and later stages of the first operating season, causing the energy efficiency of heat exchange system to decrease and even the heat exchange system to fail.( 3 ) Two schemes are adopted to alleviate thermal accumulation, Scheme 1: install cooling towers; Scheme 2: increase the heated domestic water amount. The recoverable amount of shallow geothermal energy is basically the same for both schemes. From a cost perspective, Scheme 2 has more advantages, where no equipment and facilities were needed and even more economic benefits could be provided.( 4 ) A ground-coupled GSHP system has good applicability in the central urban area of Danyang City, where the shallow geothermal energy has good exploitation prospects.



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*Source: 4154836-2019-04-09.xml*