Analytical Study of Permeability Properties of Loose Sandstone Based on Thermal-Hydraulic-Mechanical (THM) Coupling

Abstract

The permeability of reservoirs is a key factor affecting the exploitation and utilization of geothermal resources. This test used a core flow meter and other advanced experimental devices to investigate the evolution of the permeability characteristics of loose sandstone samples (with a diameter of 25 mm and a length of 50 mm) in the Zijiao Town area under various temperatures, confining pressures, injection rates, and cyclic loading and unloading conditions. The results show that (1) as the temperature increases, the overall trend of rock permeability decreases, which is mainly related to the thermal expansion of rock particles. In addition, the higher the temperature, the greater the gravel outflow. (2) The critical pressure for pore closure in the unconsolidated sandstone in the region is approximately 15 MPa. (3) The permeability change of loose sandstone under low injection rate conditions is relatively small and can be neglected. However, there is reason to believe that under high-flow injection conditions, the permeability of this type of rock mass will undergo significant changes. (4) Under the condition of loading and unloading, the permeability ratio curve of the unloading stage at three temperatures is almost a straight line. The higher the temperature, the smaller the slope, and the permeability at 20 °C with the highest recovery degree is only about 50% of the initial one.

1. Introduction

One of the most significant challenges that the world faces in the 21st century is mitigating climate change and the greenhouse effect while simultaneously meeting the growing demand for energy [1]. As we all know, the issue of energy scarcity is a crucial factor that constrains the survival and progress of human society [2]. Since the Industrial Revolution, the world’s demand for coal, oil, natural gas, and other fossil fuels has been on an upward trajectory, with projections indicating that global energy demand will increase by more than one-third by 2035 [3]. Huge energy consumption has brought not only convenience to human production and life but also caused rather serious environmental pollution. Simultaneously, fossil energy is a primary energy source, but its excessive development and utilization are not beneficial for the sustainable and healthy development of human society. Therefore, the search for renewable energy that can replace fossil energy has become an important issue in today’s human society.

Because it is green, clean, and pollution-free, with a wide distribution, high efficiency and stability, and renewable and flexible development, geothermal energy has attracted the attention of many scientists and decision makers [4]. Compared with renewable energy sources such as solar energy, hydro energy, wind energy, biomass energy, and ocean energy, geothermal energy is basically unaffected by geographical, climatic, and seasonal factors. It features relatively consistent temperatures, immense reserves, stable output, and long effective working hours. With the introduction and implementation of innovative geothermal utilization technologies such as ground-source heat pumps and dry hot rock systems, geothermal energy has revealed its vast application prospects and development potential [5]. Currently, about 252.6 metric tons (1 metric ton = 1,000,000 tons) of CO₂ emissions are avoided by geothermal energy use worldwide each year [6]. In addition, this figure is expected to reach more than 800 metric tons by 2050 [7].

In the process of geothermal energy extraction, the permeability of reservoirs is of great importance. Good permeability conditions can enhance the efficiency of heat extraction and reduce the cost of extraction. Therefore, it is of great significance to explore the permeability of geothermal reservoirs.

Numerous experts and scholars have conducted extensive research in related areas. Feng Zijun et al. [8] studied the permeability characteristics of nitrogen in anthracite and gas coal within 600 °C. As the temperature increases, the permeability decreases initially and then increases sharply. Under high-temperature conditions, the coal undergoes severe pyrolytic cracking, which significantly increases the pore cracks in the coal body and greatly improves its permeability. Zhao Yangsheng et al. [9] conducted experimental research on the acoustic emission characteristics and permeability evolution of sandstone and granite in the range of room temperature to 600 °C. As the temperature increases, intermittent and multiphase thermal fracturing occurs, leading to synchronous multi-peak segments in the permeability of rocks. Through experimental research, Xi Baoping et al. [10] found that the permeability of granite after applying high temperatures is closely related to the temperature experienced and the stress state in which it is located. S. Chaki et al. [11,12] studied the microscopic characteristics of rock mass after exposure to high temperatures and found that thermal damage leads to changes in the internal microstructure of the rock mass, which further affects its permeability characteristics. Xu Jiang et al. [13,14,15] studied the relationship between coal sample permeability and temperature under different effective stresses and gas pressures. Compared with dense rock mass, loose rock mass has a looser internal particle structure and is more susceptible to the influence of extrusion and shear stress during mining, resulting in compaction deformation and particle migration, thereby altering its seepage resistance [16,17,18,19,20,21,22].

During the process of geothermal exploitation, adhering to the principle of “taking heat instead of water”, filtered geothermal tail water is reinjected into the well for heat exchange, which may cause issues such as reservoir blockage. Through their research, Gao Baozhu and their colleagues [23,24] discovered that suspended matter particles, chemical precipitates, and microorganisms present in the geothermal recharge tailwater were the main causes of blockages. Among these factors, suspended matter particles were found to contribute the largest proportion, accounting for up to 50%. However, loose rock masses are mostly dominated by pores. Although the porosity of pore-type thermal reservoirs is much higher than that of bedrock fractures, their pore diameters are smaller than fractures, making it easier for suspended matter and chemical precipitation to accumulate and block the aquifers.

Currently, the permeability of rock mass is extensively studied in dense rock masses such as granite, while the study of loose rock masses has rarely been introduced. Shandong Province is rich in geothermal resources in China, with four geothermal areas. According to Li’s study, more than 73% of Shandong’s geothermal resource reserves are in the northwestern depression geothermal district [25]. Lying in the Linqing depression, Dezhou is a geothermal exploitation demonstration city in Shandong Province [26,27]. Geothermal exploration in Dezhou began in the 1990s. By 2020, 29% of geothermal wells and 32% of the geothermal heating areas in Shandong were in Dezhou [28]. So in this paper, sandstone samples taken from Zijiao Town, Huimin County, Shandong Province are studied to explore the permeability of loose sandstone changes with time and the influencing factors.

2. Test Introduction

2.1. Test Sample

The samples were taken from Zijiao Town, Huimin County, Shandong Province, and the sampling depth was 1172–1173 m. The prepared sample is shown in Figure 1, and its section diameter and length are 25 mm and 50 mm, respectively.

Due to the fact that the samples drilled in the local thermal reservoir are loose rock samples, they are more friable than rocks that are strictly defined. In order to mitigate the influence of the mud content within the samples and their inherent characteristics on the test, each test group requires individual sampling, followed by weighing after sampling to ensure an error margin of ±0.1 g.

In this test, the fluid used is recharge water sourced from the geothermal project site. The utilization of geothermal recharge tail water to examine the permeability transformation pattern of loose sandstone offers a more accurate representation of actual conditions. This approach aims to provide guidance for the geothermal development of similar reservoir types.

2.2. Test System

The core flow meter (Figure 2a) jointly produced by Jiangsu Kedi Petroleum Instrument Co., Ltd. (Nantong, China) and Jilin University is used in this test device. Its internal principle is shown in Figure 2b. The balance measures the mass of fluid flowing out of the core gripper, and the inlet and outlet pressure detectors measure the pressure difference between the two ends of the gripper. Before the rock sample is placed in the clamp, it is wrapped with a layer of waterproof tape to ensure that the fluid flows only from the inside of the rock mass. The specific stress situation of the porous medium rock mass is shown in Figure 3. The outermost layer is a rubber sleeve, and the inner layer is waterproof tape. The hand pump sends water between the gripper and the gum sleeve to control the confining pressure, with an upper limit of 25 MPa. The heating box is used to heat the ambient temperature, with an upper limit of 180 °C. In addition, after the fluid flows out of the heating box, it passes through the condenser to ensure the collection of high-temperature fluids.

2.3. Computing Formula

The flow of fluid in a pipe can be categorized into laminar flow and turbulent flow. It is widely believed that Darcy’s law is only applicable when the fluid flow remains in the laminar flow state. The Reynolds number (Re) [29] is often used to distinguish between laminar flow (Re < 2300) and turbulent flow (Re > 4000) conditions. It is a dimensionless number group used to determine the flow state of viscous fluid [30]. The specific calculation method is shown in Equation (1).

$$\begin{array}{l}Re=\frac{\rho vL}{\mu }\\ v=\frac{Q}{A}\\ Re=\frac{2\rho Q}{\mu \pi r}\end{array}$$

(1)

where Re is the Reynolds number, dimensionless; ρ is the fluid density, kg/m³; v is the fluid velocity, m/s; L is the characteristic length, where the diameter of the rock sample is taken, m; and μ is the fluid dynamic viscosity coefficient, Pa·s.

Since the fluid flow in this test is very small, on the order of 10⁻⁸ m³/s, the Reynolds number Re is also very small, so it can be determined that the fluid flow is in a laminar flow state. Therefore, the fluid flow in this test follows Darcy’s law. The process of deducing rock mass permeability by Darcy’s law is shown in Equation (2).

$$k=\frac{Q\mu \Delta L}{A\Delta P}$$

(2)

where Q is the fluid flow rate, m³/s; A is the cross-sectional area of the rock sample, m²; μ is the hydrodynamic viscosity coefficient, Pa·s; k is permeability, m²; ΔL is the length of rock mass, m; and ΔP is the pressure difference between the inlet and outlet of the fluid, Pa.

3. Test Results and Analysis

Due to the uniqueness of the selected sandstone samples, the permeability fluctuates over time during the test. It is worth noting that the loose rock mass contains more mobile particles compared to the dense rock mass, and the phenomenon of their movement within the rock mass is known as particle migration at the microscopic level [31]. This migration can cause the blockage or dredging of the seepage channels. At the laboratory scale, the gravel follows the fluid through the pipe until it is finally discharged from the grippers, resulting in an abnormal increase in permeability. In a real reservoir, the gravel only moves from one location to another, so the blockage caused by these mobile particles will be prolonged and extensive in the reservoir.

Compared with tight rock masses, loose sandstone reservoirs possess a looser rock particle structure, rendering them more susceptible to factors such as temperature, pressure, and fluid movement rates during geothermal extraction. This exposure can result in thermal expansion, compaction deformation, and particle migration, ultimately impacting the reservoir’s permeability. This test aims to investigate the effects of temperature, confining pressure, injection rate, and cyclic loading and unloading conditions on the permeability of loose sandstone.

3.1. Effect of Temperature on Permeability of Sandstone Aquifer

To investigate the impact of temperature on the permeability of a sandstone aquifer, five sets of comparative tests are designed, and the experimental setups are presented in

Table 1. The experimental scheme of the influence of temperature on permeability of sandstone aquifer.

Test Number	Temperature (°C)	Confining Pressure (Mpa)	Injection Rate (mL/min)
1	20	10	1.0
2	40	10	1.0
3	60	10	1.0
4	80	10	1.0
5	100	10	1.0

. In this test, all conditions involving temperature are heated to the specified temperature by the heating box and then maintained for 4 h to ensure a constant internal temperature during the test.

Since the thermal reservoir temperature is below 100 °C, the temperature range for this study is selected to be between 20 and 100 °C. The confining pressure is calculated from the depth at which the rock sample is buried.

As can be seen from the analysis of Figure 4, when the temperature is 20 °C and 40 °C, the permeability of the sandstone aquifer follows a similar trend with time. Both cases are relatively stable at the beginning. After approximately one hour of testing, the permeability of both begins to decrease and remains low for about half an hour, before returning to its previous level. The reason for this is that suspended matter in the recharge water accumulates over an hour, resulting in the blockage of some of the rock pores. This is further supported by the observation that the water discharged from the gripper is clearer than the injected fluid (see Figure 5 for a comparison of water samples). In addition, between 1.0 and 1.5 h, the permeability at 40 °C is closer to the mean compared to that at 20 °C. This is because the higher temperature of 40 °C results in a lower hydrodynamic viscosity (as shown in Figure 6), leading to a faster flow rate, which impacts the blocked suspended matter to a certain extent and causes the permeability to be closer to the mean.

The hydrodynamic viscosity coefficient is mainly affected by temperature and has almost nothing to do with a change in pressure [32,33,34]. Therefore, the influence of pressure on it is not considered in this test, and the empirical formula for calculating the coefficient is shown in Equation (3) [35]:

$$\mu =\left\{\begin{array}{l}1.3799-0.0212T+1.3604\times {10}^{-4}{T}^2-4.6454\times {10}^{-7}{T}^3\\ +8.9043\times {10}^{-10}{T}^4-9.0791\times {10}^{-13}{T}^5+3.8457\times {10}^{-16}{T}^6\\ T\in [273,413]\\ 0.0040-2.1075\times {10}^{-5}T+3.8577\times {10}^{-8}{T}^2-2.3973\times {10}^{-11}{T}^3\\ T\in [413,553]\end{array}\right.$$

(3)

$$\begin{array}{l}\rho =838.4661+1.4005T-0.0030T^2+3.7182\times {10}^{-7}{T}^3\\ T\in [273,553]\end{array}$$

(4)

where T is temperature and the unit is K. Figure 6 shows the dynamic viscosity coefficient and density-change curve of water.

When the temperature increases to 60 °C and 80 °C, the permeability remains low during the first half hour of the test, with most values falling below the mean. This is due to the higher test temperature, which causes a thermal expansion effect in the rock particles (as shown in Figure 7), resulting in a lack of good hydraulic connection within the rock sample. Therefore, high pressure is required during fluid injection. According to Equation (2), when ΔP is large, the calculated permeability k value is small, and the relationship between the two is inversely proportional. In the subsequent period, the permeability of sandstone aquifers at both temperatures fluctuates around the mean value. The absence of suspended matter blockage issues compared to 20 °C and 40 °C is attributed to the temperature-induced changes in the dynamic viscosity of the fluid.

When the temperature reaches 100 °C, the permeability changes with time are relatively stable. However, there are several large permeability changes between 0.75 and 1.5 h. This is not limited to the 100 °C condition, and similar occurrences have occurred under all four other temperature conditions. This is caused by part of the gravel draining out of the gripper with the fluid. In addition, the test found that the higher the temperature, the more sand and gravel are discharged from the gripper, which is mainly related to two factors: The first is due to the decrease in the dynamic viscosity coefficient of the fluid, μ, with increasing temperature (as shown in Figure 6). As μ decreases, the internal cohesion force between fluid molecules becomes weaker [36]. With the other conditions being equal, the higher the flow rate, the more sand and gravel will be carried out of the gripper. The second is that with the increase in temperature, the sandstone will undergo thermal expansion, resulting in mutual compression between the sand and gravel. During this process, a small number of sand and gravel will be dislodged and carried out of the gripper by the fluid (Figure 7). During the heating process of the test, it was also observed that as the temperature increased, the monitoring pressure gauge pointer showed a slight increase, which fully indicates that the sandstone undergoes thermal expansion with the increase in temperature.

COMSOL Multiphysics 6.0 numerical simulation software was employed to simulate the volume strain and displacement of the rock mass prior to water injection, in order to reveal the influence of temperature on thermal expansion. The simulation parameters are given in

Table 2. Basic simulation parameters.

Parameters	Numerical Value	Unit
Injection temperature	10	°C
Confining pressure	10	MPa
Thermal expansivity (αT)	1 × 10−5	K−1
Thermal conductivity of rock (λs)	2.1	W m−1 K−1
Thermal conductivity of water (λw)	0.5	W m−1 K−1
Specific heat capacity of rock (cs)	909	J (kg−1 K−1)
Specific heat capacity of water (cw)	4200	J (kg−1 K−1)
Density of rock (ρ)	2000	kg m−3
Young’s modulus (E)	1	GPa
Poisson ratio (v)	0.22	1
Bulk modulus of rock skeleton (Ks)	1.701	GPa
$\mathrm{Initial}\mathrm{porosity}({\phi }_0)$	0.20	1
Initial permeability (k0)	1 × 10−14	m2

; certain parameters have been sourced from Xu [37]. The coordinate system for this simulation is a rectangular coordinate system. The simulation simplifies the rock into a two-dimensional model, and in order to ensure the accuracy of the result, the mesh is divided by a very fine free triangle mesh; the boundary conditions and results are shown in Figure 8.

The changes in permeability are represented by Equation (5), which comprehensively takes into account pore pressure, temperature, and rock mass strain. The specific meanings of each parameter can be found in Table 2.

$$k=k_0\cdot {\{\frac{1}{{\phi }_0}-(\frac{1}{{\phi }_0}-1)\exp [-\frac{1}{K_s}(p-p_0)+{\alpha }_T(T-T_0)-({\epsilon }_v-{\epsilon }_{v0})]\}}^3$$

(5)

Because the conditions of 20 °C are similar to those of room temperature, and due to the presence of external stress (confining pressure), the volumetric strain at this temperature is primarily caused by the mutual compression of rock particles. Therefore, the volumetric strain at this temperature is negative. At 60 °C and 100 °C, the temperature is much higher than room temperature. Under the same external stress conditions, thermal expansion is dominant, resulting in positive volume strain under the two temperature conditions. The higher the temperature, the greater the volume strain, that is, the higher the degree of thermal expansion. Furthermore, as shown in Figure 8, under the same confining pressure condition, the higher the temperature, the smaller the maximum displacement of the model, further indicating the influence of the thermal expansion effect on the movement of rock particles.

The midpoint of the model was selected (25 mm, 12.5 mm) and the ratio of the permeability at this point to the initial permeability was calculated. The calculation equation is referred to in Equation (5).

Permeability variation curves based on THM coupling under different temperature conditions are shown in Figure 9. All three curves show a trend of rising first, then falling, and then stabilizing. The permeability at the initial stage of simulation is lower than the initial permeability, and it can be seen from the local magnification map that the higher the temperature, the lower the initial permeability. In conjunction with Figure 8, thermal expansion has been taken into account in steady-state calculations before transient calculations. Then, the permeability increases, mainly because the cold water injection causes the shrinkage of rock particles [38], thus increasing the porosity, and the larger the difference between injection temperature and simulated temperature, the higher the peak permeability. After the curve has stabilized, again the higher the temperature, the lower the permeability; the main acting factor is still the thermal expansion effect.

By means of numerical simulation, the performance of the thermal expansion effect and its influence on permeability at different temperatures are fully demonstrated.

Figure 10 shows the variation curve of the mean permeability of the test with temperature. Except for 60 °C and 100 °C, the overall trend of the curve decreases with the increase in temperature. There are two main reasons for this result [8]: (1) As the temperature rises, the rock particles and their internal component minerals will undergo thermal expansion, causing a decrease in the pore volume of the sample. The thermal expansion of the rock will develop in all directions within the rock mass. Due to the limiting effect of confining pressure and the two ends of the clamp on the rock mass, the thermal expansion cannot be freely carried out in the outer space and can only squeeze more pores inside the rock mass. The permeability decreases greatly with the continuous increase in thermal expansion, and the two have obvious consistency, so it can be considered that thermal expansion is the main factor affecting the permeability reduction in this temperature range. (2) The pores of natural sandstone samples contain water and adsorbed gas, etc. After the temperature rises, the water and adsorbed gas are continuously discharged, and the seepage channel is opened, but due to the effect of confining pressure and thermal expansion, the seepage channel that is opened is closed again, resulting in lower permeability.

Figure 11 shows the curve of inlet pressure changing with temperature. The overall trend of the curve also decreases with the increase in temperature. This is mainly because the higher the temperature, the smaller the dynamic viscosity of the fluid, resulting in less friction applied to the fluid flow. As can be seen from the figure, the inlet pressure gradually decreases with the increase in temperature, because the thermal expansion of rock particles blocks the flow of fluid when the temperature is higher. The two factors together shape this trend of change. Comprehensive analysis based on Equation (2) and Figure 11: When calculating the permeability of sandstone aquifers, the influence of ΔP on the permeability k at 60 °C is greater than that of the dynamic viscosity coefficient μ of the fluid. At 100 °C, the main factor affecting the calculation of the permeability of sandstone aquifers is fluid flow Q, as a large amount of sand and gravel are discharged at this time.

3.2. Effect of Confining Pressure on Permeability of Sandstone Aquifer

In order to explore the influence of confining pressure on the permeability of sandstone aquifers, four sets of comparative tests are conducted. The temperature and injection rate are set at 60 °C and 1 mL/min, respectively, and the confining pressure is set at 5 MPa, 10 MPa, 15 MPa, and 20 MPa. The temperature is set according to local geological data. The average ground temperature gradient in northwestern Shandong is about 0.034 °C/m, and the annual average temperature is about 20 °C. After comprehensive calculation, the test temperature is set at 60 °C.

When the confining pressure is set at 5 MPa, the sandstone sample is still relatively loose. After 15 min of the test, the permeability increases slightly, considering that a hydraulic connection is established within the rock sample during this period. However, after about an hour of the test, the permeability increases significantly. The reason for this is that after about an hour of fluid flushing, the mud inside the sandstone sample is partially cleared, the pores become larger, forming a dominant channel for fluid flow, and the long-term water injection also expands the original pores [39], all of which lead to an increase in permeability. In comparison, the fluctuation amplitude of permeability in the first hour before the test is significantly smaller than that in the second hour. Considering that water, adsorbed gases, and mud in the pores of the rock samples are discharged during this period, the seepage channels are opened, resulting in a larger fluctuation amplitude of permeability in the second hour.

The permeability curve at 10 MPa is generally more stable than that at 5 MPa, mainly distributed in the range of 8–10 mD. Because the confining pressure is greater than 5 MPa, the adsorbed gas in the pores inside the rock sample is expelled during the loading process. After half an hour of fluid scouring, the percolation channel expands, and the permeability also rises, fluctuating around the average value.

As shown in Figure 12c, when the external confining pressure reaches 15 MPa, the sandstone sample is significantly compressed. Compared with that at 10 MPa, its permeability decreases significantly and is more stable. In the first half hour of the test, the permeability is in a rising state. This is because, at the beginning of the test, a large inlet pressure is needed to pump the recharge water into the rock sample. In the subsequent test process, the permeability changes are relatively stable, mainly ranging from 0.5 to 0.7 mD.

When the confining pressure increases to 20 MPa, the sandstone sample is completely compressed, and the internal pore structure tends to close. From the curve in Figure 12d, the change in permeability was relatively stable throughout the entire test, with no significant increases or decreases. Moreover, the magnitude of the change in permeability was relatively small, ranging from approximately 0.1 mD.

By analyzing the curve shown in Figure 13, the permeability of the sandstone aquifer decreases with increasing confining pressure. The permeability at 10 MPa decreases by 22.89% compared to that at 5 MPa. Although the permeability decreases, the rock sample still maintains a high porosity at this time. The permeability suddenly decreases at 15 MPa, which is 93.65% lower than that at 10 MPa, indicating that the porosity of the sandstone sample at this time is already very small. In contrast, at 20 MPa, the rock samples are completely compacted, and the mean permeability value is only 0.1345 mD; this is consistent with the stable curve of permeability change over time. From Figure 14, the inlet pressure at 15 MPa is 11.79 times that at 10 MPa, while the inlet pressure at 20 MPa is almost the same as that at 15 MPa, only 0.53% higher. Therefore, it can be considered that the sandstone aquifer in this area has been completely compacted and the internal pores are closed when the confining pressure is 15 MPa.

3.3. Effect of Injection Rate on Permeability of Sandstone Aquifer

Due to the influence of the accuracy of the test instrument, large flow injection would lead to unstable data transmission. Therefore, to assess the influence of injection rate on the permeability performance, four schemes are set in the test: 1.0 mL/min, 1.5 mL/min, 2.0 mL/min, and 2.5 mL/min, and the temperature and confining pressure are set at 60 °C and 10 MPa, respectively.

For a consolidated rock sample, the impact of changes in injection rate on its permeability is minimal, as the pressure at the inlet is also changing, resulting in only a slight difference in the final calculation results. However, for unconsolidated sandstone samples, different injection rates have different impact degrees on gravel, so the final calculation results are not the same.

As shown in Figure 15a, when the injection rate is 1 mL/min, the permeability decreases first and then increases in the first half hour, and then fluctuates around the mean value in the subsequent time period. When the injection rate increases to 1.5 mL/min, 2.0 mL/min, and 2.5 mL/min, the curve of permeability versus time tends to be more stable overall. This is mainly because the relatively high injection rate passes through the pores between rocks more quickly, exerting a greater impact force on the adherents within the pores, resulting in a rapid increase in the curve after a short decline. The test also found that different injection rates would lead to different sand production, resulting in an abnormal increase in permeability. Schubert et al. [40,41] also found through tests that excessive moisture content can lead to an increase in sand production, which is consistent with the results of this study.

The variation curves of mean permeability and inlet pressure with injection rate are shown in Figure 16 and Figure 17.

Similar to the fact that the permeability of consolidated rock does not change with injection rate, the change in permeability of loose sandstone at low injection rates is very small and negligible. After increasing the injection rate to 2.5 times the initial value, the permeability increases by only about 0.11 mD (1.26%). The maximum difference in permeability at the selected injection rate for the test is only 0.26 mD, indicating that low injection rates have less impact on the permeability of unconsolidated sandstone than temperature and confining pressure.

Through the above research, and considering the impact of high injection rates on the internal particles of unconsolidated sandstone, when high flow rates are injected, the permeability of this type of rock mass will undergo significant changes [42].

3.4. Effect of Cyclic Loading and Unloading on Permeability of Sandstone Aquifer

As is well known, with the exploitation of geothermal energy, the injection and extraction of fluids are cyclically carried out, which leads to a continuous change in reservoir pressure. In order to understand the impact of pressure cycle increase and decrease on reservoir permeability, we use cyclic loading and unloading to explore its changes. Considering that the test samples are easier to compact than hard rock such as granite, a cycle is used first, and the confining pressure changes follow the loading and unloading path shown in Figure 18. Unlike the previous test where a sample was replaced for each condition, in this test, the sample is only replaced under different temperature conditions, while the confining pressure change is conducted in the same sample.

In this test, fluid flow tests are conducted at 20 °C, 60 °C, and 100 °C, and the ratio of permeability under different confining pressures to that at 5 MPa is calculated. The results are shown in Figure 19. During the unloading stage at the three temperatures, unlike the permeability evolution of fractured granite bodies (Figure 20), the permeability of unconsolidated sandstone only slightly recovers.

It can be clearly concluded from the evolution curve in Figure 19 that during the loading stage, under the same confining pressure, the higher the temperature, the greater the decrease in the permeability of the sandstone aquifer compared to 5 MPa. The permeability of fractured granite rapidly decreases at the beginning of loading, and then the decrease rate slows down. Similarly, the permeability of the sandstone aquifer rapidly decreases at the beginning of loading and then shows a turning point at 15 MPa. However, its decrease rate is much smaller than that of the fractured granite, and can even be neglected. This also indicates that such pore media have a higher permeability compared to fractured media. Even under high confining pressure conditions, the ability of fluids to pass through the unconsolidated sandstone pore media is higher than that of fractured media.

In the unloading process, unconsolidated sandstone and fractured granite also have completely different behaviors: At the beginning of loading, the permeability of fractured granite can recover to the original level. However, as the confining pressure decreases, only part of the deformation can recover, and the unrecovered deformation is plastic deformation. When the confining pressure decreases to 5 MPa, the recovery degree at 25 °C is the highest, reaching about 86%. With the increase in test temperature, the recovery degree decreases, and all are less than 50%. The recovery degree of unconsolidated sandstone is far less than that of fractured granite. As can be seen from the evolution curve, the curves of the permeability ratio in the unloading stage at three temperatures are almost in a straight line. The higher the temperature, the smaller the slope, and the permeability at 20 °C with the highest degree of recovery is only about 50% of the initial one.

For the unconsolidated sandstone, the higher the confining pressure, the higher the degree of squeeze between the rock particles, and the lower the permeability. At the same time, under the same confining pressure, the higher the temperature, the higher the degree of thermal expansion of the rock, and the lower the permeability. After the rock experiences high confining pressure and the pressure decreases, its permeability only shows a slight recovery in a short period of time. With the injection of fluids, the inter-particle pores in the rock gradually expand, leading to a gradual increase in permeability, but this process takes a relatively long time.

4. Conclusions

Unconsolidated sandstone is a type of loose rock mass with low compaction. In this test, we mainly investigated the influence of temperature, confining pressure, injection rate, and cyclic loading and unloading on its permeability. Based on the experimental results, we draw the following conclusions:

• The influence of temperature on the permeability of unconsolidated sandstone is primarily manifested in two aspects. Firstly, as the temperature increases, the overall tendency of permeability decreases. This trend is primarily attributed to the reduction in internal pore volume of the sandstone samples due to the influence of thermal expansion. Secondly, the higher the temperature, the greater the amount of gravel outflow.
• The critical pressure for the internal pore closure of the original unconsolidated sandstone in Zijiao Town is approximately 15 MPa.
• Compared to temperature and confining pressure, the effect of low injection rate on permeability is negligible. However, the higher the injection rate, the greater the amount of gravel carried by the fluid, which requires the selection of an appropriate injection rate during geothermal extraction. The injection rate selected in this test is low, and it is reasonable to believe that this type of sandstone will show different permeability properties when injected with a large flow rate.
• Under the condition of loading and unloading, the permeability ratio curve of the unloading stage at three temperatures is almost a straight line. The higher the temperature, the smaller the slope, and the permeability at 20 °C with the highest recovery degree is only about 50% of the initial one.
• Under laboratory-scale conditions, temperature and injection rate are the most direct factors affecting sand production, while confining pressure has a relatively small impact. Future research should focus on changes in the permeability of unconsolidated sandstone under higher temperature and high injection rate conditions. Moreover, the rock samples used in this experiment had a relatively small size of φ25 mm × 50 mm. Future research should increase the sample size and further investigate the influence of different conditions on the permeability of unconsolidated sandstone, in order to guide the exploitation of geothermal resources in similar types of reservoirs.