Earth-to-air Heat Exchanger Research Articles

Improving sustainability: Exergy, energy analysis and CO2 mitigation of greenhouse integrated with thin-film photovoltaic and earth-to-air heat exchanger

Adopting passive cooling systems has become especially vital due to the high energy consumption and adverse impacts of conventional air conditioning systems on the environment. Sustainable green energy structure development includes a periodic thermal model of a greenhouse integrated with thin-film photovoltaics (GiTPV) and the earth-to-air heat exchanger (EAHE). The system can provide plants in the greenhouse with air from extreme weather conditions: 5 °C in the winter and 45 °C in the summer, corresponding to thermal comfort standards in structures. According to the results, at 0.5 kg/s air mass flow rates of EAHE, the air temperature in the greenhouse room rises by 5 °C in the winter and falls by 17 °C in the summer. The greenhouse can save 9864 kWh/year before and 41,587 kWh/year after integrating EAHE. The seasonal energy efficiency ratio (SEER) for EAHE varies between 1 and 3. The yearly carbon credit of a greenhouse is expected to be 3166 US dollars, and EAHE reduces CO2 emissions by around 65.68 tons per year. Finally, the Quonset GiTPV system generates 29.22 kWh and 17.6 kWh of electrical energy per day on extremely hot and cold days respectively, making the system self-sustainable.

Experimental and numerical research on the thermal performance of a vertical earth-to-air heat exchanger system

The Earth-to-Air Heat Exchanger (EAHE) system is an efficient and clean geothermal application technology that can be used for pre-cooling in summer and heating in winter. This paper proposes a novel Vertical Earth-to-Air Heat Exchanger (VEAHE) system that uses baffles to divide the vertical duct into two ventilation tunnels with a hollow area at the bottom for air circulation. This system occupies a small land area and has a relatively high geothermal energy utilization efficiency. This study evaluates the thermal performance of the system through experimental tests under various operating conditions. Additionally, a numerical model of the system was established to explore the influence of baffles length, thickness, and duct depth on its thermal performance. The experimental results show that the 2.5-meter deep VEAHE system achieves an average air pre-cooling temperature reduction of 5.42 °C, with a maximum temperature reduction of up to 7.58 °C. Below the 1.2-meter mark of the system, the cooling capacity of the descending pipe is 1.52 times that of the ascending pipe. The simulation showed a Maximum Absolute Relative Error (MARE) of 3.15 % compared to the experimental results. As the length and thickness of the baffles, duct length, and soil thermal conductivity increase, the average outlet air temperature gradually decreases, while the system's heat exchange capacity significantly improves, in contrast to the duct diameter. Among the influencing factors, the duct length has the greatest impact on the system. Under the recommended configuration, the system's maximum pre-cooling potential is 915.90 W, with the outlet air temperature ranging from 12.05 °C to 14.79 °C.

Techno-Economic Feasibility Study of Earth Air Heat Exchangers for Gas Turbine Inlet Air Cooling

In response to pressing energy crises and environmental concerns, enhancing the performance of existing energy conversion systems, such as gas turbines, and tapping into renewable resources have become critical imperatives. Escalating ambient temperatures poses a notable challenge, hampering the efficiency of gas turbines. This study rigorously explores the feasibility of earth-to-air heat exchangers (EAHEs) as a pragmatic solution to cool gas turbine inlet air. The primary objective is an exhaustive techno-economic analysis evaluating the long-term operational viability of EAHE systems. Employing the Taguchi method, the study optimizes the system geometry and pipe arrangement, focusing on four key control factors: pipe diameter, spacing, length, and depth. The pivotal optimization criterion is the levelized cost of energy (LCOE), encompassing thermal performance and economic viability. The net present value (NPV) and Discounted Payback Period provide supplementary insights into the economic prospects. Integral to the study is a novel and intricate hybrid analytical-numerical model that simulates the long-term transient operation of EAHE. Findings from a detailed case study unveil an optimized scenario yielding an LCOE amounting to 0.071 $/kWh, accompanied by a substantial NPV of 4.5 million dollars.

Theoretical modelling and experimental evaluation of thermal performance of a combined earth-to-air heat exchanger and return air hybrid system

To both alleviate thermal saturation in surrounding soil and avoid indoor air pollution caused by closed-loop earth-to-air heat exchanger (EAHE) systems, this study proposes a hybrid mode that combines EAHE and return air (RA), i.e., the EAHE-RA system. A theoretical model was proposed to predict the thermal performance of EAHE-RA systems considering both sensible and latent heat transfer inside the EAHE. Full-scale experiments on both open-loop EAHE system and EAHE-RA system were carried out. The results indicated that the average cooling capacity of EAHE in EAHE-RA system was decreased by 1202.8 W (43.82 %) in summer compared to open-loop EAHE system, while the average cooling capacity recovery of return air was 645.4 W. In winter, the average heating capacity of the EAHE of EAHE-RA system was decreased by 394.1 W (48.91 %), while the average heating capacity recovery of the return air was 1021.7 W. Theoretical predictions of EAHE outlet and indoor air temperature agree well with the measured ones in both summer and winter. Theoretical results indicated that the EAHE-RA system has lower/higher pipe wall temperatures in summer/winter than the open-loop EAHE does, indicating a lower thermal interference on surrounding soils and thus better durability.

EVALUACIÓN DEL POTENCIAL DE UN SISTEMA HÍBRIDO INTERCAMBIADOR TIERRA-AIRE Y ENFRIAMIENTO EVAPORATIVO

These days, everyone is concerned with conserving energy. Among the existing heating and cooling technologies to reduce energy consumption in buildings are the Earth-to-Air Heat Exchangers (EAHE). These systems can be combined with evaporative cooling, either direct or indirect, to improve the global performance. In the literature, hybrid solutions with direct evaporative cooling systems at the exit of EAHEs are proposed for indoor cooling. Due to limitations of indoor RH, most applications focus on greenhouses. Moreover, existing works target hot and arid climates. This work targets both indirect evaporative cooling (IEC) and direct evaporative cooling (DEC) to be combined with an EAHE installed at a near Zero Energy Building. The supplied relative humidity is analyzed to evaluate its feasibility for occupied spaces. The performance and energy savings achievable are studied through simulation using TRNSYS software.

A Study on Optimization of Grid-Layout Earth-to-Air Heat Exchangers (EAHEs) at Constant Total Heat Transfer Surface by using Taguchi Method

A Study on Optimization of Grid-Layout Earth-to-Air Heat Exchangers (EAHEs) at Constant Total Heat Transfer Surface by using Taguchi Method

Efficient operation of earth–air heat exchanger system for air cooling in a hot climate based on a new control strategy

The present research contributes to filling a gap not covered in the previous studies on shallow geothermal applications using earth-to-air heat exchanger (EAHE) systems. The authors think that operating the EAHE continuously for long periods, as presented in many of the previous studies, is not efficient, and this is due to the following reasons:- At specific periods, especially during the night and early morning, the difference between the ambient air temperature (Tamb) and the undisturbed ground temperature (UGT) is small and even negative, meaning the ambient air is colder than the ground.- The continuous operation of the EAHE for a long time leads to the ground saturation with heat, which means that the ground cannot absorb more heat from the EAHE inlet air.So, the present study investigates performance improvement by applying a control strategy to the EAHE system according to two different modes: mode 1 and mode 2. These two operational modes depend on the difference between the ambient air temperature and the UGT value. In mode 1, the ambient air flows inside the EAHE and supplies fresh air to the building. This mode is applied when the temperature difference (Tamb-UGT) exceeds 1.5 οC. When the condition of mode 1 is not satisfied, mode 2 is used, where the ambient air bypasses the EAHE and is supplied directly to the ventilated space. To carry out the present investigation, a numerical model of the EAHE system is developed, and its results are validated against published data from the literature.The simulation of EAHE in Madinah City, KSA, presenting a hot climate region, has been carried out. The study's results confirmed that the control strategy is an efficient solution for the continuous operation of the EAHE. The applied control strategy guarantees that the air supplied to the building is the coldest among the ambient air and the EAHE outlet air. Also, it has been shown that when the control is applied (mode 2), the temperature of the air supplied to the building is 1.5 °C lower than that of the case related to mode 1. Finally, the results showed that the ground can be recovered thermally when the air bypasses the EAHE (mode 2). The ground temperature recovers almost to its undisturbed value during specific periods, which enhances the potential for subsequent heat absorption.

Performance measurement and configuration optimization based on orthogonal simulation method of earth-to-air heat exchange system in cold-arid climate

The earth-to-air heat exchanger (EAHE) is a remarkable technology that taps into the Earth’s subsurface heat to either heat or cool the air circulating within buried underground pipes, which can effectively reduce building energy consumption. In cold-arid regions of northwest China, outdoor climate parameters vary considerably throughout the year, and shallow soil temperatures also fluctuate dramatically. This dynamic thermal environment significantly impacts the practical application of the EAHE system. Furthermore, the operation efficiency of the EAHE system can be influenced by the configuration of system parameters. Therefore, this paper takes an EAHE project in Lanzhou as the research object to investigate the operation performance, energy consumption and economy of EAHE in the cold-arid regions of Northwest China. The research results show that heat exchange potential is high in summer and winter, and the outlet temperature varies more gently in winter. During the summer, the cooling capacity of the system is sufficient to the cooling demands of the building, without using auxiliary equipment for cooling; compared to an air-cooled unit with a COP of 3.2, the system reduces cooling energy consumption by 2063.4 kWh. Moreover, we determined the influence degree and optimal scheme of each factor under different evaluation indexes through orthogonal simulation. The specific parameters of the optimal scheme are as follows: pipe length 20 m, pipe diameter 100 mm, buried depth 4 m, and airflow velocity 7 m/s. Compared with the original scheme, the heat transfer efficiency and heat transfer power of this scheme are increased by 37.91 % and 17.6 %, respectively, and the cost per unit heat transfer power is 11,700 CNY/kW, which is 8000 CNY/kW lower than the original scheme.

DESIGN OF A LOW COST HOUSE USING LOCAL MATERIAL COUPLED TO MECHANICAL -EARTH TUBE VENTILATION SYSTEM

The building sector accounts for 50% of the total worldwide energy consumption. This percentage is expected to increase with the population growth and climate change compounding the problem of dwindling in energy resources. One means of mitigating the increase in energy consumption is by relying on natural ventilation systems for thermal comfort purposes and on the applications of natural (as compared to processed and manufactured) and recycled materials in building construction. Nonetheless, the use of natural ventilation systems with energy efficient construction materials and building envelope cannot always ensure thermal comfort conditions throughout the whole year. Additional systems are sometimes necessary to aid in providing continuous thermal comfort, year round. One such system, the Earth to Air Heat Exchanger (EAHE), has been found to have the potential of providing indoor comfort at reduced energy cost. In this paper, different scenarios for natural building materials coupled with an earth tube heat exchanger are investigated with the aim of reducing the operational energy of a typical house in Lebanon. It is found that use of an optimal wall configuration when coupled with the EAHE results in 76.7% energy savings compared to reference case

Unlocking geothermal energy for sustainable greenhouse farming in arid regions: a remote-sensed assessment in Egypt’s New Delta

This study introduces a novel approach for assessing geothermal potential in arid regions, specifically Egypt’s New Delta Agriculture Mega Project area. The challenge of limited sub-soil temperature profile data was addressed by integrating Global Land Data Assimilation System (GLDAS) weather data. Using the Earth-to-Air Heat Exchanger (EAHE) model, the extracted air and sub-soil temperature profiles the potential for geothermal energy production was estimated. We modeled the annual sinusoidal soil surface periodic heating pattern by utilizing GLDAS ambient air temperature (AAT) and land surface temperature (LST). Using either AAT or LST yielded a Root-Mean-Square Error (RSME) of 0.2°C. The generated sub-soil profiles for the New Delta region showed a temperature variation of no more than 1.5°C at a 4-m depth, making it an optimal depth for EAHE installation. One-pipe EAHE demonstrated a cooling/heating capacity ranging from 400 W (cooling) to −300 W (heating). The study highlights the New Delta region’s strong geothermal potential for greenhouse cooling and heating, underlining its suitability as a sustainable energy source in arid areas. It also offers a practical guide for the EAHE application and it emphasizes the global potential for geothermal energy exploration, using innovative GLDAS data to expand sub-soil temperature profile accessibility.

Experimental and Hybrid Numerical Analytical Approach of an Earth-to-Air Heat Exchanger

Abstract The primary goal of this paper is to assess the thermal behaviour of Earth-to-Air Heat Exchanger (EAHE) under continuous operation mode during the cooling period in warm climatic conditions. An experimental setup was conducted in Biskra University (Algeria) to test the ability to use EAHE as an alternative solution to conventional air conditioning systems. Besides, a transient numerical approach for the flowing air within the EAHE was developed using energy balance equations, discretised by the implicit finite differences method and solved by Thomas method. Furthermore, the transient temperature profile of the soil around the EAHE was investigated in order to determine the adiabatic radius of the soil as a function of the duration of operation. In this context, a transient semi-analytical model was integrated to the air model to estimate the transient EAHE’s performance deterioration. This deterioration is produced by the thermal saturation of the soil, which is influenced by the heat released from the air inside the pipe. Results showed that continuous operation for a duration of four days has minimal impact on the outlet air temperatures due to the implementation of night purging. Furthermore, the design and thermal efficiency of the EAHE are impacted by factors such as higher air velocity and reduced soil thermal conductivity.

Improvement of earth-to-air heat exchanger performance by adding cost-efficient soil

Geothermal research advances earth-to-air heat exchanger (EAHE) technology, offering promising air conditioning solutions for all buildings. Our study targets improved energy efficiency for the EAHE system, focusing on cost-effective approaches to enhance its technical, economic, and environmental performance. The thermal performance and economic viability of the EAHE system hinge on the thermal characteristics of the surrounding soil. The EAHE model features a single pipe with dimensions of 0.5 meters in diameter, 1 centimeter in thickness, and 10 meters in length. These pipes are strategically placed at depths of 1 meter, 2 meters, 3 meters, and 4 meters below the ground's surface. To optimize heat exchange efficiency while minimizing pipe length, we propose using a secondary soil material with high thermal conductivity as a lining for the EAHE pipes. Our innovative approach carefully considers the economic and environmental aspects of various lining materials, resulting in optimal performance at a minimal cost. Extensive simulations and data analysis lead us to identify an ideal lining material, naturally available, environmentally friendly, and cost-effective, ensuring peak efficiency. Our investigation assesses the EAHE system's thermal performance for both summer cooling and winter heating, demonstrating its effectiveness across seasons. This research underscores the case for utilizing EAHE systems during winter and autumn for heating and during spring and summer for cooling. Our findings are supported by robust performance indicators, confirming the effectiveness of our approach.

Daily, monthly and seasonal energy performances and economic assessment on the coupling of an earth to air heat exchanger to an already existing HVAC system: A case study for Italian cities

The main aim of the investigation introduced in this paper is to analyze and identify the energy saving and the economic return deriving from the investment of placing an Earth to Air Heat eXchanger (EAHX) as pretreatment unit of a HVAC system serving buildings of a company operating in the industrial sector in Italy. This hybrid system is aimed to take advantage of the heat capacity of the soil surrounding some buried pipes for passively preheating and/or precooling the air before it is ventilated into the building. The buried pipes can then provide preheated and/or precooled air to improve the energy performance of the HVAC system, and ultimately to ensure indoor thermal comfort conditions.The company has various offices in Italy and so a the hourly, daily, monthly, yearly performances of the EAHX, the energy saving of the hypnotized solution with respect to the base HVAC configuration, as well as the economic impact of the investment in terms of payback time and net present value have been investigated and a comparison among different climatic zones of Italy is reported. To perform the above-mentioned objectives a two-dimensional numerical model of a dominium including the soil, the surface and the buried tubes of the EAHX is introduced. The model, experimentally validated and solved through the Finite Element Method, is forced with dynamic boundary conditions on the intensity of the solar radiation and on temperature and relative humidity of the external air entering the tubes, for many Italian localities.The employment of the EAHX in the HVAC reduces the energy consumptions in the various considered Italian climatic zones from: −30 % to −45 % in heating mode; from −23 % up to −43 % in cooling mode. From an economic point of view, the investment at the end of lifetime (25 years) is always positive and it has a discrete return in all the cases investigated.

Analysis of a Hybrid System Solar Chimney-Air Soil Heat Exchanger for Natural Ventilation

The current study looks at a hybrid passive cooling system that combines a solar chimney with an earth-to-air heat exchanger (EAHE) usually called Canadian Well. Numerous experimental and numerical examinations with various applied radiation heat fluxes were carried out to evaluate its ability to cool a room. Glass temperature, wall temperature, air flow mean temperature, hourly rate of air exchange (ACH), outlet airflow velocity, and rate of air mass flow were determined experimentally and numerically, and validated against previously published experimental and analytical works. It was found that the chimney's operation is dependent on the radiation intensity. The EAHE has reduced the room's temperature by improving exchanges with the solar chimney. The comparison of experimental and numerical data for different radiation intensities reveals that the best diameter of the tube of the underground heat exchanger for the proper operation of our system is d = 0.04m. The efficiency of our system increases as the radiation increases, causing an increase in the temperature of the absorber, which influences the air temperature in the chimney.

Refurbishment of a Social Interest Building in Mexico Using Earth-to-Air Heat Exchangers

The refurbishment of a social interest building using Earth-to-Air Heat Exchanger (EAHE) was studied in representative dry climatic conditions of Mexico (dry, very dry, temperate, and sub-temperate). A simulation method that uses both computational fluid dynamics (CFD) and building energy simulation (BES) was used to analyze the influence of the EAHE on the indoor conditions of a room. First, CFD simulations of the EAHE were performed using climatic data and soil properties of the four representative cities, and then the results were loaded into the TRNSYS software to estimate the indoor air temperature and the building room’s thermal loads. When connected to a building room on a warm day, the EAHE reduced the indoor air temperature by a factor ranging between 1.7 and 3.2 °C, while on a cold day, the EAHE increased the indoor air temperature of the room by between 1.0 and 1.9 °C. On the other hand, the EAHE reduced the daily cooling load of the room by a factor between 2% and 6%. The EAHE also reduced the daily heating load by between 0.3% and 11%. Thus, EAHE as a refurbishment technology can benefit social interest buildings in Mexico.

Investigation of earth air heat exchangers functioning in arid locations using Matlab/Simulink

This study presents a MATLAB/Simulink model to predict the distribution of soil temperatures and design Earth-to-Air Heat Exchangers (EAHEs) efficiently. It compares four EAHE configurations, including single-pipe, multi-pipe, multiple-single pipes (MS-pipes), and twisted-single pipes (TS-pipes) systems. The presented model is validated with reliable results and allows for easy modifications to obtain the final design. Results show that MS-pipe EAHE is the better in terms of pressure losses and good in terms cooling potential. The study proves that the installation of the EAHEs in Kufa, Iraq, is highly efficient, achieving cooling potential of 1626 W in August and 129.8 W in March. Additionally, the study highlights the influence of the geometric configuration of EAHEs on both their flow behavior and thermal efficiency, presenting an equation for comparing pipe lengths at different soil depths. This study fills the knowledge gap in the use of MATLAB simulation for designing EAHEs and estimating soil temperatures distribution and it compares four EAHEs configurations.

Optimizing indoor thermal comfort with wind towers and earth to air heat exchangers: a sustainable solution for energy-efficient housing

Abstract The conditioning of living and working spaces in the building sector consumes a significant amount of energy. Among the natural ventilation techniques that rely on renewable energy sources such as geothermal and wind, wind towers and earth to air heat exchangers (EAHEs) hold prominence. This research paper presents a series of experiments conducted in the arid region of Bechar, Algeria, to investigate the effectiveness of combined natural ventilation systems employing wind towers and EAHEs. The test chamber, constructed from plywood, and the tower, along with the buried polyvinyl chloride (PVC) pipe EAHE at a depth of 150 cm in sandy-loam soil, constitute a completely natural system with zero energy consumption. Two scenarios were examined: one with closed windows and the other with open windows measuring 40 × 40 cm2. The results indicate a noteworthy improvement in thermal comfort within the chamber, with an increase from 18.75% for the closed window system to 50% when the window is open. By employing a completely natural system without energy consumption, it becomes possible to fulfill 50% of the thermal comfort requirements during both summer and winter seasons. Consequently, this approach reduces at least half of the energy demands in a region that experiences six months of discomfort.

Evaluating the Thermal Performance and Environmental Impact of Agricultural Greenhouses Using Earth-to-Air Heat Exchanger: An Experimental Study

The thermal performance and environmental impact of agricultural greenhouses (GH) connected to earth-to-air heat exchanger (EAHE) systems depend on the ambient temperature, soil temperature, EAHE system, and greenhouse specifications. The impact of an EAHE system on the temperature and humidity of a GH microclimate, as well as its effects on CO2 emissions and heating energy consumption, are determined experimentally. Two scaled-down models of agricultural GHs (2 × 1.4 × 1.4 m3) were developed. Each GH was equipped with a heater. A spiral EAHE system was integrated into only one of the GHs. The temperature differences in the microclimate range from 3.5 °C to 7.5 °C, with the microclimates of GH + EAHE and GH being quite similar. In summary, the EAHE system helped to reduce the hourly energy consumption of the heating system by more than 40%. It also reduced emissions to the environment by more than 100 g (CO2)/hour. The EAHE coefficient of performance (COP) for the cooling mode has a higher average value than that for the heating mode. The closed-loop performed better in cooling mode, while the open-loop performed better in heating mode. When the difference between the set temperature in the heater and the air outlet temperature of the EAHE system is smaller, the heater performs better in reducing energy consumption and CO2 emissions of the heater. The COPheating range is between 0 and 3.4 and the COPcooling range is between 0.5 and 7.3. The energy consumption ranges between 0 and 1.41 kWh and the CO2 emissions are between 0 and 359.55 g. Thus, using EAHE in agricultural greenhouses improves thermal performance and reduces environmental impact, providing an overall benefit in terms of energy consumption and environmental sustainability.

Earth-to-air Heat Exchanger for Cooling Applications in a Hot and Dry Climate: Numerical and Experimental Study

Shallow geothermal energy, by an earth-to-air heat exchanger (EAHE), is utilized to cool buildings with minimal energy usage. Significant parameters affecting the heat exchanger's performance must be investigated to obtain a suitable design. Shallow geothermal energy, by an earth-to-air heat exchanger (EAHE), is utilized to cool buildings with minimal energy usage. Significant parameters affecting the heat exchanger's performance must be investigated to obtain a suitable design. This article numerically and experimentally investigates the effect of pipe diameter, pipe length, inlet air temperature, soil temperature, airflow velocity, and soil thermal conductivity on the performance of the heat exchanger under hot and dry climate conditions. The soil temperature distribution was measured from the surface to a depth of 7 m in the city of Karbala (center of Iraq) in the summer season. The experimental test for EAHE was carried out in water-saturated soil and ambient air temperatures of 41 ºC, 45 ºC, and 49.5 ºC at four different velocities. The percentage drop in the EAHE outlet air temperature at 9 m/s was 28.3%, 25.5%, and 19.5%, respectively. Also, the three-dimensional model was created, and the simulation results were compared with the experimental results, which were in good agreement. An equation for the outlet air temperature was found as a function of pipe diameter and length, ambient air temperature, soil temperature around the pipe, and soil thermal conductivity. The resulted equation were compared with the current experimental results and experimental results of reported data inliterature. As a result, a very good agreement was observed. The results showed that the parameter L (length of the pipe) causes the strongest nonlinear behavior in the equation. For the cases considered, at diameters 75 and 100 mm, an approximate linear behavior for the length required to achieve a specific outlet temperature was observed. It can be concluded from the results that changing the soil type from dry one (k=0.5 W/m K) to saturated one (case of Karbala city, k=1.5 W/m K) resulted about 25% reduction in the length of the pipe. Also, the results showed that at an air velocity of 7m/s, the length required to obtain 26 ºC at the outlet of EAHE is 62.1 m which is 55% higher than the case of 29 ºC (39.9m).

Thermal design of Earth-to-Air Heat Exchanger: Performance analysis of new transient semi-analytical model for short period of continuous operation

This paper concerns the thermal design of Earth-to-Air Heat Exchanger (EAHE). The paper presents new transient semi-analytical models to estimate i) the disturbed soil thermal resistance of EAHE pipe as a function of duration of operation and ii) thermal performance of EAHE operating under transient conditions. The main aim of this study is to evaluate the parameter choices of this new model for short period of continuous operation of the system (less than 70 h). The results show that time discretization steps of 15 min and 1 h present and lead to appreciable results compared to the experiments. Therefore, the variation of the layer length step of the buried pipe does not alter simulation results. In terms of precision of the soil temperature profile, refined solutions were obtained by the decreasing of the disturbed soil radius and the increasing the number of roots of Bessel's functions. Furthermore, the effect of the variation of surrounding soil radius is discussed for short period of continuous operation of the system. The time step of 1 h and the interval of the surrounding soil radius of 0.4 m–1.1 m are found accurate for good results with a reasonable computational time.