Measuring and Predicting the In-Ground Temperature Profile for Geothermal Energy Systems in the Desert of Arid Regions

Abstract

Instead of fossil fuels, clean renewable energy resources are being used to meet space heating and cooling needs, to reduce global warming and air pollution worldwide. In the desert of the Arabian Peninsula, extensive solar irradiance and drastic variations in air temperatures (daily and/or seasonally) are common; thus, geothermal energy resources are a promising solution that is nearly independent of weather fluctuations. Due to a lack of information about in-ground temperature profiles in these regions, the use of geothermal energy resources for domestic applications is very limited. Therefore, this study aimed to measure the in-ground temperature (T_g) up to 3.5 m in depth for one year. Due to the difficulty of digging in the ground (i.e., gravelly sand; rocky, dry soil), numerical equations were adopted and used to simulate the in-ground temperature (T_g) for a depth > 3 m. These equations were validated by comparing the measured and simulated values of T_g for depths ≤ 3 m under extreme weather conditions. The validation yielded a mean absolute error (E_MA) of ≤ 1.2 °C and a root mean square error (E_RMS) of ≤ 1.42 °C. The measurements showed that at 3 m depth, the in-ground temperature was 32 °C in summer and 29 °C in winter. The simulation showed that values of T_g increased with depth in winter and decreased in summer and became constant as 30 °C at 13 m depth throughout the year (i.e., the undisturbed ground temperature (UGT)). This temperature would provide considerable heating and cooling capacity if an earth-to-air heat exchanger were implemented in arid regions where ambient temperatures exceed 47 °C on summer days and drop below 10 °C on winter nights. The theoretical prediction of T_g using the proposed equations is a useful tool for designers who use geothermal effects for indoor space cooling and heating in the desert of arid regions.

1. Introduction

Global warming, depletion of fossil fuel, and air pollution have pushed many countries worldwide to look for sustainable and clean energies. Renewable energy resources are being used worldwide as an alternative of fossil fuels, for sustainable development and for solving environmental issues (e.g., reducing global warming and air pollution) [1]. The use of renewable energy resources to meet the space heating/cooling requirements could be significantly improved with the exploitation of geothermal energy [2]. The geothermal energy resource is almost independent of weather fluctuations and presents a greater capacity for cooling/heating than solar or wind [2]. In recent decades, geothermal systems (i.e., geothermal heat pumps or earth-to-air heat exchangers) have received considerable attention as alternative energy sources for several domestic applications. There are numerous advantages for using these systems over solar and wind energy resources, such as: energy conservation, lower operating costs, the ground being thermally a more stable heat exchange medium than air, it being unlimited and being always available [3]. In addition, achieving minimal energy consumption for space cooling and heating of residential buildings, greenhouses, livestock, and poultry houses is a key aim in most countries worldwide and has become a particular challenge in the desert climate of Arabian Peninsula countries [4]. Therefore, looking for low-cost, sustainable energy techniques for space heating and cooling is an essential priority for the sustainability and development of rural areas in arid regions [5]. It is worth mentioning that the geothermal energy resource is available at low and medium enthalpy in the shallow zone that is very useful for domestic heating and cooling applications; however, in many countries, geothermal resources have remained unused due to the lake of in-ground information and the know-how and expertise are not available [6].

Principally, in the desert of the Arabian Peninsula, intensive solar irradiance and a high air temperature are common most months of the year [7]. However, solar energy is only available during the day and its heating and cooling capacity is lower than geothermal energy [2]. In contrast, the earth strongly absorbs solar energy during the day and then stores a considerable amount of thermal energy at different depths. This is mainly attributed to the high levels of absorbed solar radiation and the large heat storage capacity of the soil. Therefore, geothermal energy potential is a promising sustainable resource in the desert of the Arabian Peninsula region. The Kingdom of Saudi Arabia (KSA) is considered one of the most geothermally active countries in the Middle East [8]; however, using geothermal energy resources for domestic applications is very limited. This is because the in-ground temperature profile in the shallow zone (0–8 m) has not yet been established for the KSA desert. Specifically, accurate information about the vertical distribution of in-ground temperatures in the shallow zone is still unclear. Among the literature, we noticed a lack of studies that address the issues of geothermal energy potential and its applications in the KSA [9].

Based on the diurnal variation of solar irradiance and ambient air temperature, the maximum oscillation of the in-ground temperature occurs at the earth’s surface. This oscillation attenuates as the depth increases. The cyclic variation of the in-ground temperature depends mainly on the cyclic variation of meteorological parameters. Several studies have reported an in-ground temperature profile at various depths and found that the oscillation of this temperature attenuates and became constant at a particular depth. For example, in New Delhi, India, the daily average for the in-ground temperature was recorded as 17.84 °C in winter and 32.87 °C in summer at a depth of 0.18 m [10]. In the same location at a depth of 4 m, the annual average temperature was 29 °C when the ground surface was exposed to solar radiation; however, it reduced to 19 °C when the ground surface was wet, and reduced to 17 °C when the ground surface was wet and shaded [9]. Therefore, the in-ground temperature value strongly depends on the soil surface conditions. Moreover, the annual average of the in-ground temperature was measured as 23.45 °C at a depth of 4 m in Las Vegas, USA [11]. In Mexico City, the in-ground temperature was measured as 27–28 °C at a 2.5-m depth [12]; in Brazil, it was 18.7 °C at a 2-m depth and 20 °C at a 4-m depth [13]; in Bhopal, India, it was 25 °C at a 2-m depth [14]; in Tianjin, China, it was 11.5 °C in winter and 17.5 °C in summer at a 2-m depth [15]; and in Shouguang, it was 17.6 °C at a 3.6-m depth [16].

In a typical hot summer in an arid climate (the desert in the south part of Algeria), the in-ground temperature has been measured as 30 °C at a 2-m depth and as 27 °C at a 5-m depth [17]. In a recent study, it was measured in the Riyadh area, Saudi Arabia, to be 29 °C in winter and 32 °C in summer at a 3-m depth [18]. Previous studies, as mentioned above, have reported different values for the in-ground temperatures measured at different depths for different locations worldwide. These values depend on the interaction between the meteorological conditions and the thermo-physical properties of soil at the site of measurement. It is well known that at a certain depth in the ground, the temperature is nearly constant during the day and night, throughout the different seasons, and is not affected by the daily cyclic and/or seasonal variation of meteorological factors (i.e., solar radiation flux, ambient air temperature, wind speed, and local rainfall). This temperature is usually defined as the ground undisturbed temperature (GUT). It depends on the groundwater level, the thermo-physical/chemical properties of soil, and the ground surface conditions. Researchers have reported that the GUT is reasonable for indoor space heating and cooling applications (e.g., residential buildings, poultry houses, livestock houses, greenhouses, etc.) [19,20,21,22,23,24]. For effective use of sustainable and low-cost geothermal energy resources, the depth to achieve the GUT should be obtained by digging. However, the cost of digging to the optimal depth for the GUT in order to avail of free geothermal energy should be considered; this may be too expensive, especially in the desert of arid regions such as in the KSA, due to the nature of the ground soil. In addition to the difficulty and high-cost of digging, further factors such as wearing and corrosion of the buried elements of the geothermal heat exchangers strongly affect the economic analysis; this leads to the use of innovative, low-cost, high resistance plastic materials for heat exchanger design [25]. Even though geothermal energy potential is expected to be promising in the KSA desert [9], research on geothermal energy applications has not yet received any attention. In addition, a survey of the literature revealed that there is a lack of clear information about the in-ground temperature profile in the desert in an arid climate (gravelly sand and rocky soil), such as in the KSA. Without this temperature profile, which is essential information, a geothermal heat pump or heat exchanger cannot be analyzed or designed [14]. Accordingly, this study aimed to (i) experimentally measure the in-ground temperature profile at different levels up to a 3.5-m depth at King Saud University campus, and (ii) adopt, validate, and use a numerical model to predict the in-ground temperature profile for depths greater than 3.5 m. This will prevent the difficulty and high cost of digging and measurements.

2. Materials and Methods

2.1. Description of the Experiment

The experiment was conducted in a free, large, desert space related to the Agriculture Engineering Department, King Saud University (Riyadh, Saudi Arabia, 46″47′ E, longitude and 24″39′ N, latitude). The soil in this location, as it is in most of the arid regions such as in the Arabian Peninsula, is a mixture of dry gravelly sand and rocks up of to 5-m depth or more. Digging is quite difficult and expensive in this kind of soil; therefore, mechanical digging was used to prepare a hole with a surface area of about 1 m² and a depth of 3.5 m only. In order to protect the cables of the temperature sensors from damage in the soil, the cables were gathered to pass through a 5-cm diameter PVC pipe, installed vertically at the center of the hole, and fixed at the bottom of the hole with a concrete block as illustrated in Figure 1. Eight small holes were made vertically in the pipe wall at various levels (0.1 m, 0.5 m, 0.9 m, 1.3 m, 1.7 m, 2.1 m, 2.5 m, and 3 m below the ground surface). These holes allow the cables of the temperature sensors to pass through to the data logger, via the pipe, over the ground surface (Figure 1).

2.2. Measuring Procedure

The in-ground temperature profile was measured at the prescribed depths. We were looking for the location at which the soil temperature become constant (i.e., GUT), and was unaffected by the diurnal and seasonal variations of the climatic parameters. The experiment was conducted for one year (from 1 November 2020 to 31 October 2021), to record the in-ground temperature values at depths of 0.1 m, 0.5 m, 0.9 m, 1.3 m, 1.7 m, 2.1 m, 2.5 m, and 3 m, respectively. In addition, the ambient air temperature was measured at 3 m above the ground surface. The sensors were carefully inserted into the soil 0.8 m away from the vertical pipe. Backfilling of the ground hole was carried out in steps; the first fill was up to 3 m in depth, then the temperature sensor was fixed carefully on the soil surface, after which the second fill was carried out to the level of 2.5 m in depth, then the temperature sensor was inserted, etc. Thermocouple sensors (wzp-035 Pt100/k, Shenzhen More-Suns Electronics Co., Ltd., Shenzhen, China) were used to measure the in-ground temperature at the specified locations. The thermocouple sensor has a precision of ±0.1 °C and a temperature range of 0–85 °C. Measurements were taken every 5 min, averaged at every 15 min, and recorded in a COMBILOG-1022 data logger (32 channels, Theodor Friedrichs & Co., Schenefeld, Germany).

2.3. Predicting the In-Ground Temperature

The ground is considered a semi-infinite homogenous solid in an un-steady state conduction process. One-dimensional conduction as a function of depth (z) and time (t) assuming constant thermal diffusivity of soil (α_s) is given by [26] as:

$$\frac{\delta 2T_g}{\delta Z^2}-\frac{1}{{\alpha }_s}\frac{\partial T_g}{\partial t}=0$$

(1)

Prediction of in-ground temperature (T_g) exhibits a sinusoidal pattern due to the cyclic variation of the meteorological parameters above. In Equation (1), Z is the soil depth in meters, (Z = 0 at the ground surface), and the thermal diffusivity (α_s) is expressed either in m² s⁻¹, m² day⁻¹, or m² month⁻¹; this is in accordance with the purpose of predicting the in-ground temperature, T_g (either instantaneous, daily average, or monthly average).

Kusuda et al. [27], Moreland et al. [28] and Labs [29] have reported a mathematical solution for Equation (1) and mathematically modelled the annual in-ground temperature profile based on heat conduction theory applied to a semi-infinite homogenous solid. Herein, their model has been adapted for desert conditions in arid climate areas. For a homogeneous soil with constant thermal diffusivity (α_s), the monthly average of the in-ground temperature (T_g) at any depth (z) and month number (t) can be estimated by using the following formula:

$$T_g\left(z,t\right)=T_m-T_{amp}\times Exp\left[-z\sqrt{\left(\frac{\pi }{12{\alpha }_s}\right)}\right]\times cos\left\{\frac{2\pi }{12}\left[t-t_o-\frac{z}{2}\sqrt{\frac{12}{\pi {\alpha }_s}}\right]\right\}$$

(2)

where T_g (z,t) is the soil temperature at depth z and month number t (t = 1, 2, 3, …12); T_m is the annual mean soil surface temperature (°C); T_amp is the amplitude of soil surface temperature [(max-min)/2] in (°C); z is the depth below the ground surface (m); α_s is the thermal diffusivity of the in-ground soil (m²/month); t is time (the month number that the in-ground temperature is calculated for); and t_o is the time shift (month of the year of the lowest ground surface temperature). For the desert of the KSA, the value of α_s was estimated to be 2.736 (m²/month) and the thermal conductivity of soil as 2.2–2.8 (W m ⁻¹ °C⁻¹) [11,12]. The measured in-ground temperature at 0.1-m depth was considered the ground surface temperature. From 1 November 2020 to 31 October 2021, the values of T_m and T_amp were estimated (from measurements) to be 30 °C and 12 °C, respectively. Moreover, in January, the lowest ground surface temperatures were recorded; thus, t_o in Equation (1), is equal to one. In a similar manner, the daily average of the in-ground temperature (T_g) at any depth (z) and a Julian day number (t) can be expressed as:

$$T_g\left(z,t\right)=T_m-T_{amp}\times Exp\left[-z\sqrt{\left(\frac{\pi }{365{\alpha }_s}\right)}\right]\times cos\left\{\frac{2\pi }{365}\left[t-t_o-\frac{z}{2}\sqrt{\frac{365}{\pi {\alpha }_s}}\right]\right\}$$

(3)

where t is the Julian day number (1, 2, 3, …365); t_o is the time shift (i.e., the Julian day number of the lowest ground surface temperature). In Equation (3), the thermal diffusivity α_s was taken as 0.0912 m²/day. Similarly, the hourly average value of in-ground temperature at a depth z (m) and time t (h), T_g (z, t) is given by:

$$T_g\left(z,t\right)=T_m-T_{amp}\times Exp\left[-z\sqrt{\left(\frac{\pi }{8760{\alpha }_s}\right)}\right]\times cos\left\{\frac{2\pi }{8760}\left[t-t_o-\frac{z}{2}\sqrt{\frac{8760}{\pi {\alpha }_s}}\right]\right\}$$

(4)

In Equation (4), α_s was taken as 0.0038 m²/h, and the time shift t_o is calculated in hours.

3. Results and Discussion

3.1. The Measured In-Ground Temperature Profile

In the surface zone of the ground (0–1-m depth), the in-ground temperature (T_g) is strongly influenced by the short-time cyclic variation of the climatic parameters (i.e., solar radiation, ambient air temperature, wind speed, humidity, local rainfall, and snow, etc., if any). The annual variation of the ground temperature T_g (monthly averaged), measured at different depths, is illustrated in Figure 2. This figure shows that the annual cyclic variation of T_g is maximum at a 0.1-m depth, with an amplitude of about 26 °C. This variation as well as its amplitude decreases as the depth into the ground increases. When the depth increased to 3 m, the maximum annual variation of T_g reduced to 5 °C (from 28 °C in winter to 33 °C in summer). The results shown in Figure 2 proved that at a certain depth (>3 m), T_g would become nearly constant, unaffected by the cyclic variations of the climatic parameters (T_g = GUT). Designers of geothermal systems for domestic indoor space heating and cooling applications are always looking for the GUT value which is the essential parameter in designing earth-to-air heat exchanger systems.

In the desert, it was quite difficult to dig deep enough to reach the GUT because digging in rocky soil is quite hard and expensive. Therefore, instead of measurements, Equations (2)–(4) have been proposed for predicting T_g for depths greater than 3 m. Their parameters were justified according to the climate and soil properties of the desert in arid regions and validated to show the accuracy of the predictions.

3.2. Validation of the Proposed Equations

The numerical Equations (2)–(4) have been used to predict the hourly average, daily average, and monthly average values of the in-ground temperature (T_g) for a depth of up to 15 m. To check the accuracy of the predictions, the maximum and minimum errors can be estimated by accounting for the maximum and minimum differences between the measured and predicted values of T_g. For a practical and more common methodology, Equations (2)–(4) were validated by estimating the mean absolute error (E_MA) and the root mean square error (E_RMS) of the simulated value of T_g (T_g−sim) within a certain time, referring to reference (measured) values of T_g (T_g−meas); these can be expressed as:

$$E_{MA}={\displaystyle \sum }abs\left(T_{g-meas}-T_{g-sim}\right)/N$$

(5)

$$E_{RMS}=\sqrt{{\displaystyle \sum }{\left(T_{g-meas}-T_{g-sim}\right)}^2/N}$$

(6)

where N is the number of data points during the specified time (i.e., day, month, and year).

3.2.1. Daily Average Validation

Figure 3 illustrates the daily average of the measured values of the in-ground temperature (T_g−meas) at different depths compared to the simulated values (T_g−sim). To cover a wide range of T_g and for a large span of comparison, two cold winter days (15 December and 15 January) and two hot summer days (15 July and 15 August) were selected to represent the two extreme weather conditions. In Figure 3, a reasonable agreement is observed between the measured and simulated values of T_g on summer and winter days. In summer, T_g decreases as the in-ground depth (z) increases; however, in winter T_g increases as the in-ground depth (z) increases. According to the results shown in Figure 3, Equation (3) can be used successfully to predict the daily variation of the in-ground temperature (T_g) with a mean absolute error (E_MA) of 0.46–1.1 °C, and a root mean square error (E_RMS) of 0.5–1.2 °C. This is based on the four days tested. Moreover, to show the validity of Equation (3) throughout the year, day 15 in each month was chosen to calculate the daily average values of T_g at 0.1-m and 3-m depths, and they were compared with the corresponding measured values (Figure 4).

In Figure 4, the daily average value of T_g was calculated, using Equation (3), as being at 0.1-m and 3-m depths, for day 15 of each month, and compared with the corresponding measured values at these times. Reasonable agreement between the measured and the predicted value of T_g is observed in Figure 4, throughout the year. The difference between the measured and predicted values of T_g decreases as the depth in the ground increases, due to the increasing stability of T_g and decreasing fluctuation. Based on the presented results in Figure 4, values of E_MA and E_RMS were estimated to be 1.16 and 1.29 °C at a 0.1-m depth. These values decreased to 0.98 and 1.12 °C at a 3-m depth for E_MA and E_RMS, respectively. Therefore, the greater the depth in the ground, the more stable the in-ground temperature, and lower the estimation error.

3.2.2. Monthly-Average Validation

Figure 5 illustrates the monthly average variation for the calculated results, using Equation (2) and the measured values of T_g at different depths, from 0.1 m up to 3 m, in the ground. Two months in hot summer (July and August) and two months in cold winter (December and January) were selected for the comparison. Temperature variation with depth showed similar trends as the daily average trends illustrated in Figure 3 (T_g increases with depth in winter and decreases with depth in summer). Using the presented data in Figure 5, the values of E_MA and E_RMS were estimated to be in the range of 0.44–0.92 °C and 0.46–0.96 °C, respectively. Values of E_MA and E_RMS are relatively lower than those estimated for the daily average results (Figure 3 and Figure 4) because the number of data points for the monthly average calculation is much higher than those of the daily average.

To examine the validity of Equation (2) for predicting the annual variation of T_g at different depths precisely, the monthly average of T_g was calculated at 0.5-m and 3-m depths using Equation (2). Figure 6 presents the comparison with the corresponding measured values of T_g. The annual variation of T_g was presented based on the monthly average values of T_g. In Figure 6, at a depth of 0.5 m, the annual cyclic variation of T_g is relatively high as it is affected by the cyclic variation of the climatic factors. However, at a 3-m depth, the fluctuation attenuated, and the T_g was about 29 °C in cold winter (January) and about 32 °C in hot summer (August). Based on the results in Figure 6, at a depth of 0.5 m and 3 m, the values of E_MA were estimated as 1.1 and 1.0 °C, respectively. In addition, the values of E_RMS were estimated as 1.42 and 1.28 °C at 0.5-m and 3-m depth, respectively.

In general, and based on the previous discussion, Equations (2)–(4) can be used successfully to predict the in-ground temperature (T_g) of gravely sand, rocky soil at any depth under arid climatic conditions. Moreover, under extreme weather conditions, the mean absolute error of prediction (E_MA) will never exceed 1.2 °C, and the root mean square error will never exceed 1.42 °C. This result is in accordance with that reported by Al-Ajmi et al. [4]. They adopted a numerical equation to predict the in-ground temperature in the desert of Kuwait which is similar to the desert in KSA in terms of soil and climate arid conditions.

3.3. Prediction of the In-Ground Temperature for z > 3 m

Equation (2) was used to predict the monthly average values of T_g at different depths. The simulated results obtained for 12 months and depths of ≥3.5 m are presented in Figure 7. In addition, the measured values of T_g for depths of 0.1–3 m are also presented to show the whole temperature profile. An interesting shape for the in-ground temperature profile was obtained. This profile is similar to the profile reported in [30] for the simulated in-ground temperature profile in the Maslak/Istanbul, Turkey region. As illustrated in Figure 7, at a depth (z) greater than 13 m, T_g becomes constant at 30 °C throughout the year. Because the seasonal variation of the arid climatic parameters is almost similar every year in the deserts of KSA, the GUT can be considered constant at 30 °C throughout the year at a depth of 13 m or more. According to Figure 7, and for economic considerations, burying the geothermal heat exchanger pipes at a 10-m depth is acceptable for effective operation of the heat exchanger throughout the year. A medium having a large heat capacity, as the in-ground soil, and its temperature is constant at 30 °C (the GUT) through the year, is very adequate for cooling and heating purposes in a climate the ambient air temperature drops below 10 °C on winter nights and exceeds 47 °C on summer days. These levels of temperature differences would create excellent geothermal energy potential for domestic heating and cooling purposes. Under such conditions, if an earth to air heat exchanger is implemented, the cooling and heating capacity is expected to reach 900 and 1000 MJ per m³ of flowing air per day [18].

4. Conclusions and Recommendation

This study attempts to provide clear and essential information about the in-ground temperature profile in surface and shallow zones (0–8 m). This information is an essential requirement for designing geothermal heat exchangers or heat pumps for domestic heating and cooling for the indoor spaces in the desert of arid regions. The temperature profile was measured up to 3 m in depth. For a depth of >3 m, numerical equations were adopted, validated, and used to simulate the in-ground temperature up to 15 m. The main conclusions can be summarized as follows:

The annual variation of the climatic parameters significantly affects the in-ground temperature (T_g) up at to 3-m depth, after which the cyclic variation of T_g decreases, and the vertical profile of T_g increases with depth in winter and decreases with depth in summer.

For a depth > 3 m, the in-ground temperatures (T_g) were simulated using the numerical Equations (2)–(4). These equations were validated by comparing the measured values of T_g (for depths ≤ 3 m) with the simulated values. The validation yields mean absolute errors (E_MA) of no more than 1.2 °C and root mean square errors (E_RMS) of no more than 1.42 °C under extreme weather conditions.

The daily, monthly, and annual variation of T_g decreased as the depth increased and became constant as 30 °C at 13 m depth; this temperature can be considered the ground undisturbed temperature (GUT). A GUT of 30 °C is adequate for cooling and heating purposes, throughout the year, in a climate where the ambient air temperature drops below 10 °C on cold winter nights and exceeds 47 °C on hot summer days. Under these conditions, if an earth to air heat exchanger were implemented, considerable heating and cooling capacity is expected to be achieved.

The potential of geothermal energy is promising for cooling and heating applications in arid regions such as in the Arabian Peninsula for sustainable development and environmental protection. Therefore, researchers should focus on developing earth-to-air geothermal heat exchangers and heat pumps for heating and cooling residential buildings, greenhouses, and poultry houses in the rural areas of the deserts, where the electrical network is not available.