A Study on the Thermal Physical Property Changes in Formation Rocks during Rapid Preheating of SAGD

Abstract

The incorporation and application of SAGD rapid preheating technology effectively solve the problem of the long preheating cycle in the SAGD steam cycle. The thermal properties of reservoir rocks are an important factor affecting the heat transfer law governing their formation during the rapid preheating process of SAGD. During the rapid preheating process of SAGD, the expansion of the reservoir and the steam cycle process will cause changes in the pore permeability, oil-water saturation, and temperature of the reservoir rocks, which will inevitably lead to differences in the changes that occur in the thermal properties of the reservoir rocks, compared to those under the influence of a single factor. In this study, experiments were conducted to determine the thermal properties of reservoir rocks under the combined influence of pore permeability, oil-water saturation, and temperature, quantitatively characterizing the changes in the thermal properties of reservoir rocks. Using the orthogonal method to design and carry out experiments for determining the thermal properties of reservoir rocks, the main factors affecting the thermal properties of reservoir rocks and the significance of each factor’s impact on the thermal properties of reservoir rocks were determined through intuitive analysis and variance analysis of the experimental results. Finally, a regression equation that can characterize changes in the thermal properties of reservoir rocks under the influence of multiple factors was obtained through multiple nonlinear regressions of the experimental results.

1. Introduction

Cyclic steam stimulation and steam circulation are commonly used as SAGD preheating methods. Compared to cyclic steam stimulation preheating, steam circulation preheating heats the formation relatively uniformly and has better connectivity, so steam circulation preheating is the most widely used preheating technology. Although the preheating effect of the steam cycle is better, its long preheating time not only leads to huge steam consumption but also produces a large amount of difficult-to-treat oil residue during the circulation process. These problems increase the development cost of SAGD technology to some extent and have a negative impact on the improvement of economic benefits. In order to solve the problem of the long preheating time, the BitCan Company in Canada proposed the use of SAGD rapid preheating technology in 2015 and it has been adopted rapidly both domestically and internationally. The SAGD rapid preheating technology utilizes the stress dilatation principle in rock mechanics to expand the rock of the reservoir near the wellbore before preheating, causing changes in the rock particle structure of the reservoir, forming a dilatation area with roughly the same increase in permeability and porosity. This allows the steam to develop thermal connectivity between the two wells more quickly, achieving the goal of shortening the preheating time. During the rapid preheating process of SAGD, parameters such as reservoir porosity, oil-water saturation, and temperature will change, all of which will cause changes in the thermal properties of the reservoir, thereby affecting the application of the heat transfer law in the reservoir. The thermal properties of reservoir rocks mainly include thermal conductivity, specific heat capacity, and the thermal diffusion coefficient. There are many factors that can affect the thermal properties of reservoir rocks, including their petrological characteristics, porosity, oil-water saturation, pressure, and temperature. Xu Zhenzhang from China [1] systematically elaborated on the factors affecting the thermal properties of reservoir rocks in 1992 and analyzed the mechanisms of changes in reservoir rock thermal properties under the influence of various factors based on research data at that time. However, due to the limited testing technology and instrument conditions of early rock thermal properties testing, testing could only be conducted at room temperature and pressure, which cannot effectively simulate geological conditions. Therefore, the accuracy of rock thermal property testing results is poor [2]. In recent years, there has been significant development in testing technology and instruments, with significantly improved accuracy of test results and the ability to effectively simulate various temperature and pressure conditions for determining rock thermal properties.

Considering the influence of temperature on the thermal properties of rocks, Sun et al. [3] measured the thermal properties of dry sandstone under different temperature conditions and described the changes in thermal properties of the sandstone under conditions of 25 °C to 900 °C in four stages, based on the measurement results. The thermal conductivity of the rock showed an overall decreasing trend, while the specific heat capacity was proportional to temperature before 200 °C, fluctuating between 200 °C and 400 °C, and was inversely proportional to temperature after 600 °C. Abdulagaov [4] and Emirov [5] also reached similar research conclusions. Geng et al. [6] investigated the effect of temperature on the thermal diffusion coefficient through experimental measurements and found that the thermal diffusion coefficient of sandstone is inversely proportional to temperature and tends to stabilize when the temperature reaches 600 °C or above. As a result of such analysis, it is believed that the decrease in thermal diffusion coefficient from 25 °C to 300 °C is mainly due to the escape of attached water, bound water, and structural water. Between 300 and 600 °C, the thermal response of minerals in sandstone increases the development of microcracks and weakens the thermal diffusion coefficient of sandstone. Unlike in previous research, Liu et al. [7] conducted experimental and modeling studies on heat transfer in sandstone under low-temperature conditions, and conducted thermal property tests on saturated water, saturated oil, and dry sandstone under low-temperature conditions (−196.13–19.85 °C). The test results show that the thermal conductivity of dry sandstone under low-temperature conditions increases with an increase in temperature, which is different from the situation where the thermal conductivity decreases with an increase in temperature under high-temperature conditions. Analysis suggests that this is mainly related to the strong phase transition, which absorbs a large amount of latent heat.

Considering the influence of oil-water saturation on the thermal properties of rocks, Guo Yeping et al. [8] measured the thermal conductivity of sandstone under different temperature and water-content conditions. The analysis showed that the thermal conductivity of sandstone is inversely proportional to temperature, and the thermal conductivity of sandstone in a saturated state will undergo a sudden change near 0 °C due to the influence of the water phase change. However, under a constant temperature, the thermal conductivity of sandstone is directly proportional to the water content, and the growth rate of thermal conductivity is inversely proportional to the ambient temperature. Hu Rong et al. [9] conducted a measurement study on the thermal properties of rocks in the Chunguang Oilfield, analyzing the effects of oil-water saturation and rock density on thermal properties. The study found that the thermal conductivity and specific heat capacity of rocks are directly proportional to their water saturation and density, and are inversely proportional to their oil saturation. In addition, by regressing the results of thermal property testing, a regression relationship equation was obtained for calculating rock thermal properties through the difference in logging acoustic time. Song Xiaoqing et al. [10] conducted a study on the thermal properties of the main rocks in Guizhou, and the results showed that the thermal conductivity of rocks under saturated water conditions increased by 2–17% compared to those under dry conditions, the thermal diffusion coefficient increased by 1–16%, and the specific heat capacity decreased by 3.08–21.79%. Analysis suggests that in addition to the petrological characteristics, the water content of rocks is the main factor affecting their thermal properties. Zhen Zuolin et al. [11] conducted experiments to determine the thermal properties of underground transportation surrounding certain rocks in Lanzhou. The experimental results showed that the thermal conductivity of the surrounding soil samples increased linearly with the increase in water content; the volumetric specific heat capacity decreased first and then increased with the increase in water content, and the thermal diffusion coefficient increased first and then slowly decreased with the increase in water content.

In terms of the impact of changes in pore permeability on the thermal properties of rocks, Scharli et al. [12] and Sayed et al. [13] conducted studies on the influence of rock porosity on rock thermal properties in 1984 and 2011, respectively. The results showed that the porosity of rocks was inversely proportional to their thermal conductivity, but this result was only based on data analysis and did not provide empirical evidence. In 2020, Zhu et al. [14] used scanning electron microscopy to obtain images of rock samples, analyzed the microstructure of different rock types, and studied the relationship between thermal conductivity and porosity using eight different thermal conductivity porosity models. The results indicate that the thermal conductivity decreases with an increase in porosity, confirming the previous research findings.

Given the impact of changes in pore permeability on the thermal properties of rocks, studies by Scharli et al. [12] in 1984 and Sayed et al. [13] in 2011 investigated the relationship between rock porosity and thermal properties. These findings indicated that the porosity of rocks is inversely proportional to their thermal conductivity, though these results were solely based on data analysis and were not empirical. In 2020, Zhu et al. [14] utilized scanning electron microscopy to capture images of rock samples and examined the microstructure of various rock types. They further examined the correlation between thermal conductivity and porosity using eight distinct thermal conductivity-porosity models. Their results suggest that thermal conductivity decreases as porosity increases, corroborating the previous research findings.

In predicting the thermal properties of rocks, various models have been proposed [15,16,17,18,19,20,21], all of which are obtained through regression methods based on a large amount of experimental data, and these models only consider the influence of single factors for thermal property prediction. However, there are many factors that affect the thermal properties of reservoir rocks, and the direction of their influence is also different. Therefore, many prediction models that only consider the influence of single factors have significant limitations.

Overall, there is currently a wealth of research on changes in reservoir thermal properties, and scholars have conducted quantitative or qualitative studies on the various factors that affect reservoir rock thermal properties. They have summarized the mechanisms and predictive models of reservoir thermal property changes under the influence of corresponding factors. However, the shortcomings are that currently, most research conclusions are obtained through experimental analysis under the control of single-factor variables, and there is no research on the changes in reservoir thermal properties under the joint influence of multiple factors. For the rapid preheating process of SAGD in the F reservoir studied in this study, factors affecting the thermal properties of reservoir rocks include increased local reservoir porosity and permeability after expansion, as well as changes in oil-water saturation and temperature that are caused by steam entering the formation. From previous research, it can be seen that the influence of these factors on thermal properties, especially thermal conductivity, is not consistent. Therefore, the changes in rock thermal properties under the combined action of multiple factors is a problem worthy of in-depth research, and it is also the basis for conducting subsequent research on heat transfer laws in reservoirs.

2. Apparatus and Procedures

2.1. Materials

The oil for the experiments (Figure 1) was taken from reservoir F; the viscosity of crude oil was 39,952 mPa·s under reservoir temperature (22 °C) conditions. The rock cores used in the experiment are shown in Figure 2.

2.2. Apparatus and Procedures

2.2.1. Oil-Water Core Saturation

Before conducting thermal property measurements, it is necessary to fully saturate the core sample with oil and water according to the experimental design requirements and slice it into slices. The core saturation device used in the experiment includes a formation fluid saturation system (Figure 3) and an oil-water saturation device (Figure 4).

The formation fluid saturation system is mainly used in experiments to saturate the formation water of artificial rock cores. The specific steps are as follows:

(1)

Prepare a sufficient amount of formation water according to the experimental requirements and fill a water tank with it;

(2)

After placing the rock core into the rock ventricle, close the rock ventricle and turn on the rock ventricle vacuum pump, continuously vacuuming it for 48 h;

(3)

Turn off the vacuum pump and open the valve between the formation water tank and the rock core chamber;

(4)

Slowly apply pressure to the rock ventricle using a hand pump;

(5)

Stop pressurization when the pressure of the rock ventricle remains unchanged for 12 h;

(6)

Reduce the pressure of the rock ventricle to 0 MPa, open the vent valve to drain excess formation water, remove the rock core, inspect and clean the equipment, and prepare for the next experiment.

Due to the strict requirements for core oil-water saturation in thermal property testing experiments, conventional oil-water saturation methods cannot accurately control the oil-water saturation of artificial cores. Therefore, by referring to the steady-state method for measuring the oil-water permeability of rock cores, the oil-water saturation of the saturated water rock cores was controlled. The experimental setup flowchart is shown in Figure 4. Two constant flow pumps are used to pump oil and water into the rock core. During this process, the proportion of the oil and water injection rate remains constant. When the pump pressure is stable and the produced oil-water ratio remains consistent with the injected oil-water ratio for 20 min, it can be considered that the oil-water ratio in the rock core pores is the same as the injected oil-water ratio, which achieves the goal of controlling the oil-water saturation of the core. The specific steps are as follows:

(1)

Connect up the equipment and open the constant temperature box at least 30 min before the experiment, then adjust the temperature of the constant temperature box to 80 °C;

(2)

Place the saturated formation water core into the core gripper, then connect the core gripper to the device according to the flowchart;

(3)

Close the outlet valve of the rock core gripper, open the ISCO pump to inject formation water into the rock core, and check the sealing;

(4)

After confirming the sealing of the device, open the outlet valve of the gripper, and after the water stabilizes, close the ISCO pump and all valves;

(5)

Turn on two ISCO pumps, adjust to the specified flow rate according to experimental requirements, open all valves, and saturate the core with oil and water simultaneously;

(6)

After the oil and water at the outlet end of the core gripper are discharged for 5 min, use a measuring cylinder at the outlet end to collect the produced liquid in time intervals (10–20 min each time) and observe the pressure changes of the ISCO pump. When the pump pressure is basically stable and the oil-water ratio of the produced liquid is the same as the injected oil-water ratio, close the ISCO pump and all valves;

(7)

Close the constant-temperature box, lower the temperature of the gripper to room temperature, then open the gripper and remove the rock core;

(8)

Clean the device and prepare for the next experiment.

2.2.2. Thermophysical Property Determination

The experimental device for measuring thermal properties adopts the LFA467 laser thermal conductivity instrument produced by the NETZSCH company in Selby, Germany, as shown in Figure 5.

The specific testing steps are as follows:

(1)

Turn on the instrument power and wait for about 10 s before the “unlock” light turns on. Simultaneously press the “close + safety” button until the “close” light remains on and the instrument is ready;

(2)

Turn on the computer and water bath, set the water bath temperature to 2 °C above room temperature;

(3)

Add liquid nitrogen to the infrared detector and stabilize it for 30 min before testing begins;

(4)

Use nitrogen as the blowing gas and set the output pressure to 0.05 MPa;

(5)

Cut the saturated oil and water core into rock sample slices according to the experimental requirements (as shown in Figure 6), and spray graphite on the upper and lower sides of the slices;

(6)

Simultaneously press the “close + safety” button to open the injection port, place the sample into the instrument, and prepare for testing (as shown in Figure 7);

(7)

Open the measurement software, set the measurement parameters, and start the test (as shown in Figure 8);

(8)

After the test is completed, open the analysis software to analyze the test results and output the test report;

(9)

When the temperature of the sample tray cools to below 100 °C, open the furnace and take out the sample.

During the experiment, attention should be paid to protecting the eyes and other parts of the human body from ultra-low-temperature burns when adding liquid nitrogen; similarly, be careful of high-temperature components when opening the furnace body to avoid high-temperature burns.

2.2.3. Experimental Plan and Parameter Design

In order to study the changes in reservoir thermal properties under the influence of multiple factors through experiments, based on survey data and laboratory conditions, three influencing factors were selected: pore permeability change amplitude, water saturation, and temperature (

Table 1. Orthogonal experimental factor level table.

Level	Factors
	A	B	C
	Amplitude of Changes in Porosity and Permeability, %	Water Saturation	Temperature, °C
1	5	0.2	60
2	10	0.4	120
3	15	0.6	180
4	20	0.8	240
5	25	1	300

). Five levels were selected for each factor, and a six-factor five-level orthogonal design table (three empty columns) was used to carry out a three-factor five-level orthogonal experimental design (

Table 2. Experimental scheme design table of thermal property measurement.

No.	Amplitude of Changes in Porosity and Permeability, %	Water Saturation	Temperature, °C
1	5	0.2	60
2	5	0.4	120
3	5	0.6	180
4	5	0.8	240
5	5	1	300
6	10	0.2	120
7	10	0.4	180
8	10	0.6	240
9	10	0.8	300
10	10	1	60
11	15	0.2	180
12	15	0.4	240
13	15	0.6	300
14	15	0.8	60
15	15	1	120
16	20	0.2	240
17	20	0.4	300
18	20	0.6	60
19	20	0.8	120
20	20	1	180
21	25	0.2	300
22	25	0.4	60
23	25	0.6	120
24	25	0.8	180
25	25	1	240

).

Due to limitations in the experimental conditions, it is necessary to manufacture artificial rock cores as thermal property measurement samples, based on the pore permeability conditions, when conducting thermal property measurement experiments. The parameters of the core samples are shown in

Table 3. Experimental scheme design table of thermal property measurement.

No.	Permeability, D	Porosity
1	0.885	0.3175
2	0.885	0.3175
3	0.882	0.312
4	0.882	0.312
5	0.899	0.3559
6	0.916	0.3605
7	0.916	0.3605
8	0.924	0.327
9	0.924	0.327
10	0.924	0.312
11	0.965	0.346
12	0.965	0.346
13	0.965	0.331
14	0.965	0.331
15	0.975	0.3632
16	1.008	0.3637
17	1.008	0.3637
18	1.009	0.3650
19	1.009	0.3650
20	1.015	0.378
21	1.050	0.358
22	1.050	0.358
23	1.050	0.364
24	1.050	0.364
25	1.050	0.3507

.

3. Results and Discussion

The experimental results for the samples’ thermal properties obtained from the LFA thermal conductivity tester are shown in

Table 4. Experimental scheme design table of thermal property measurement.

No.	Amplitude of Changes in Porosity and Permeability, %	Water Saturation	Temperature, °C	Thermal Diffusion Coefficient, mm2/s	Thermal Conductivity Coefficient, W/(m·K)	Specific Heat, J/(g·K)
1	5	0.2	60	0.751	1.422	1.790
2	5	0.4	120	0.690	1.360	1.820
3	5	0.6	180	0.622	1.330	1.829
4	5	0.8	240	0.540	1.331	1.811
5	5	1	300	0.469	1.360	1.770
6	10	0.2	120	0.601	1.199	1.800
7	10	0.4	180	0.570	1.180	1.830
8	10	0.6	240	0.544	1.180	1.820
9	10	0.8	300	0.500	1.220	1.801
10	10	1	60	0.711	1.301	1.570
11	15	0.2	180	0.480	0.990	1.833
12	15	0.4	240	0.480	1.000	1.850
13	15	0.6	300	0.492	1.050	1.840
14	15	0.8	60	0.690	1.270	1.590
15	15	1	120	0.620	1.190	1.572
16	20	0.2	240	0.387	0.793	1.880
17	20	0.4	300	0.430	0.840	1.890
18	20	0.6	60	0.630	1.220	1.611
19	20	0.8	120	0.602	1.141	1.610
20	20	1	180	0.560	1.100	1.590
21	25	0.2	300	0.330	0.600	1.910
22	25	0.4	60	0.533	1.120	1.647
23	25	0.6	120	0.530	1.050	1.673
24	25	0.8	180	0.540	1.020	1.660
25	25	1	240	0.540	1.149	1.630

.

3.1. Intuitive Analysis and Analysis of Variance

3.1.1. Intuitive Analysis

Based on the orthogonal experimental factor level table and experimental results, a visual analysis is conducted on the test results for the thermal diffusion coefficient, thermal conductivity coefficient, and specific heat. The vacant columns (D, E, F) are used as error columns and have no practical significance. In the intuitive analysis table (

Table 5. Thermal diffusivity experimental results: intuitive analysis table.

No.	Factor						Thermal Diffusion Coefficient, mm2/s
	A	B	C	D	E	F
1	1	1	1	1	1	1	0.75
2	1	2	2	2	2	2	0.69
3	1	3	3	3	3	3	0.62
4	1	4	4	4	4	4	0.54
5	1	5	5	5	5	5	0.47
6	2	1	2	3	4	5	0.6
7	2	2	3	4	5	1	0.57
8	2	3	4	5	1	2	0.54
9	2	4	5	1	2	3	0.5
10	2	5	1	2	3	4	0.71
11	3	1	3	5	2	4	0.48
12	3	2	4	1	3	5	0.48
13	3	3	5	2	4	1	0.49
14	3	4	1	3	5	2	0.69
15	3	5	2	4	1	3	0.62
16	4	1	4	2	5	3	0.39
17	4	2	5	3	1	4	0.43
18	4	3	1	4	2	5	0.63
19	4	4	2	5	3	1	0.6
20	4	5	3	1	4	2	0.56
21	5	1	5	4	3	2	0.33
22	5	2	1	5	4	3	0.53
23	5	3	2	1	5	4	0.53
24	5	4	3	2	1	5	0.54
25	5	5	4	3	2	1	0.54
K1	3.072	2.549	3.315	2.821	2.885	2.955
K2	2.926	2.703	3.043	2.820	2.840	2.814
K3	2.762	2.818	2.772	2.883	2.745	2.662
K4	2.609	2.872	2.491	2.690	2.726	2.691
K5	2.473	2.900	2.221	2.628	2.646	2.720
k1	0.614	0.510	0.663	0.564	0.577	0.591
k2	0.585	0.541	0.609	0.564	0.568	0.563
k3	0.552	0.564	0.554	0.577	0.549	0.532
k4	0.522	0.574	0.498	0.538	0.545	0.538
k5	0.495	0.580	0.444	0.526	0.529	0.544
R	0.120	0.070	0.219	0.051	0.048	0.059

,

Table 6. Thermal conductivity experimental results: intuitive analysis table.

No.	Factor						Thermal Conductivity Coefficient, W/(m·K)
	A	B	C	D	E	F
1	1	1	1	1	1	1	1.42
2	1	2	2	2	2	2	1.36
3	1	3	3	3	3	3	1.33
4	1	4	4	4	4	4	1.33
5	1	5	5	5	5	5	1.36
6	2	1	2	3	4	5	1.2
7	2	2	3	4	5	1	1.18
8	2	3	4	5	1	2	1.18
9	2	4	5	1	2	3	1.22
10	2	5	1	2	3	4	1.3
11	3	1	3	5	2	4	0.99
12	3	2	4	1	3	5	1
13	3	3	5	2	4	1	1.05
14	3	4	1	3	5	2	1.27
15	3	5	2	4	1	3	1.19
16	4	1	4	2	5	3	0.79
17	4	2	5	3	1	4	0.84
18	4	3	1	4	2	5	1.22
19	4	4	2	5	3	1	1.14
20	4	5	3	1	4	2	1.1
21	5	1	5	4	3	2	0.6
22	5	2	1	5	4	3	1.12
23	5	3	2	1	5	4	1.05
24	5	4	3	2	1	5	1.02
25	5	5	4	3	2	1	1.15
K1	6.803	5.004	6.333	5.792	5.652	5.942
K2	6.080	5.500	5.940	5.524	5.939	5.510
K3	5.500	5.830	5.620	5.788	5.372	5.653
K4	5.094	5.982	5.453	5.521	5.800	5.512
K5	4.939	6.100	5.070	5.791	5.653	5.799
k1	1.361	1.001	1.267	1.158	1.130	1.188
k2	1.216	1.100	1.188	1.105	1.188	1.102
k3	1.100	1.166	1.124	1.158	1.074	1.131
k4	1.019	1.196	1.091	1.104	1.160	1.102
k5	0.988	1.220	1.014	1.158	1.131	1.160
R	0.373	0.219	0.253	0.054	0.113	0.086

and

Table 7. Visual analysis table of specific heat tests: experimental results.

No.	Factor						Specific Heat, J/(g·K)
	A	B	C	D	E	F
1	1	1	1	1	1	1	1.79
2	1	2	2	2	2	2	1.82
3	1	3	3	3	3	3	1.83
4	1	4	4	4	4	4	1.81
5	1	5	5	5	5	5	1.77
6	2	1	2	3	4	5	1.8
7	2	2	3	4	5	1	1.83
8	2	3	4	5	1	2	1.82
9	2	4	5	1	2	3	1.8
10	2	5	1	2	3	4	1.57
11	3	1	3	5	2	4	1.83
12	3	2	4	1	3	5	1.85
13	3	3	5	2	4	1	1.84
14	3	4	1	3	5	2	1.59
15	3	5	2	4	1	3	1.57
16	4	1	4	2	5	3	1.88
17	4	2	5	3	1	4	1.89
18	4	3	1	4	2	5	1.61
19	4	4	2	5	3	1	1.61
20	4	5	3	1	4	2	1.59
21	5	1	5	4	3	2	1.91
22	5	2	1	5	4	3	1.65
23	5	3	2	1	5	4	1.67
24	5	4	3	2	1	5	1.66
25	5	5	4	3	2	1	1.63
K1	9.020	9.213	8.208	8.704	8.732	8.700
K2	8.821	9.037	8.475	8.770	8.695	8.730
K3	8.685	8.773	8.742	8.739	8.769	8.729
K4	8.581	8.472	8.991	8.734	8.688	8.777
K5	8.520	8.132	9.211	8.680	8.743	8.691
k1	1.804	1.6264	1.642	1.741	1.746	1.740
k2	1.764	1.6944	1.694	1.754	1.738	1.746
k3	1.736	1.7546	1.748	1.748	1.754	1.746
k4	1.716	1.8074	1.798	1.746	1.738	1.754
k5	1.704	1.8426	1.842	1.736	1.748	1.738
R	0.100	0.216	0.200	0.018	0.016	0.016

), Ki is the sum of the experimental values of the level i of the corresponding factors in the column; ki is the average experimental value of the level i of the corresponding factors in the column, ki = Ki/number of levels; R is the range of the mean values at each level.

From the data in the table above, it can be seen that the range values R_A, R_B, and R_C, corresponding to the amplitude of pore permeability change (A), water saturation (B), and temperature (C), are arranged in descending order: R_C > R_A > R_B. This indicates that the change in temperature (C) has the greatest impact on the thermal diffusion coefficient of the reservoir among the three factors studied in this article and is the main factor affecting changes in the thermal diffusion coefficient. Therefore, the order of the degree of influence on the thermal diffusion coefficient of the reservoir among the three factors is: temperature (C) > amplitude of pore permeability change (A) > water saturation (B). Similarly, the range of factors that affect the thermal conductivity of reservoirs is ranked as follows: R_A > R_C > R_B, and the amplitude of pore permeability change (A) is the main factor affecting the thermal conductivity of reservoir rocks. The order of magnitude of the impact of the three factors on the thermal conductivity of reservoir rocks is: pore permeability change amplitude (A) > temperature (C) > water saturation (B). The range order of factors affecting the specific heat of reservoir rocks is R_B > R_C > R_A, and the water saturation (B) is the main factor affecting the specific heat of reservoir rocks. The order of the degree of influence of the three factors on the specific heat of reservoir rocks is: water saturation (B) > temperature (C) > pore permeability change amplitude (A).

We can map the effect curves of each indicator based on the data in the table as follows.

According to Figure 8, Figure 9 and Figure 10, it can be seen that within the parameter range studied in this article, the thermal diffusion coefficient is negatively correlated with the amplitude of pore permeability changes, positively correlated with water saturation, and negatively correlated with temperature. The thermal conductivity is negatively correlated with the amplitude of pore permeability changes, positively correlated with water saturation, and negatively correlated with temperature. The specific heat is negatively correlated with the amplitude of pore permeability changes, positively correlated with water saturation, and positively correlated with temperature. The variation trends of the thermal diffusion coefficient, thermal conductivity coefficient, and specific heat obtained from orthogonal experiments with respect to each factor are consistent with the research results for single-factor influences in References [6,7,8], indicating that the results of this study are consistent with those in previous studies.

3.1.2. Variance Analysis

The main influencing factors of each indicator and the changing trends of the three indicators with each factor were determined through intuitive analysis in the previous section. However, intuitive analysis can only determine the magnitude of the impact of different factors on the indicators and cannot quantify the degree of impact. Therefore, an analysis of variance was chosen to determine the significance of the impact of each factor on different indicators. For this, we calculate the sum of squared deviations, degrees of freedom, and mean square of each factor that affects the thermal diffusion coefficient, thermal conductivity coefficient, and specific heat, based on the intuitive analysis table’s F-value. The F-critical value and p-value were used for the analysis of variance, and the calculation results are shown in

Table 8. Thermal diffusion coefficient variance analysis table.

Factor	Sum of Squared Deviations	Degree of Freedom	Mean Square	F-Value	F0.05	p-Value	Significance
A	0.0459	4	0.0115	5.0295	3.260	0.0129	Significant
B	0.0166	4	0.0041	1.8156	3.260	0.1907	Not significant
C	0.1502	4	0.0375	16.4378	3.260	0.0001	Significant
Error	0.0274	12

,

Table 9. Thermal conductivity variance analysis table.

Factor	Sum of Squared Deviations	Degree of Freedom	Mean Square	F-Value	F0.05	p-Value	Significance
A	0.4692	4	0.1173	17.3986	3.260	0.0001	Significant
B	0.1559	4	0.0390	5.7806	3.260	0.0079	Significant
C	0.1842	4	0.0461	6.8319	3.260	0.0042	Significant
Error	0.0809	12

and

Table 10. Specific heat variance analysis table.

Factor	Sum of Squared Deviations	Degree of Freedom	Mean Square	F-Value	F0.05	p-Value	Significance
A	0.0321	4	0.0080	1.1911	3.260	0.3639	Not significant
B	0.1507	4	0.0377	5.5879	3.260	0.0089	Significant
C	0.1274	4	0.0319	4.7245	3.260	0.0160	Significant
Error	0.0028	12	0.0002

below.

In the above analysis of variance table, the significance level is α = 0.05 (confidence level of 95%), and the calculated F-critical value at F_0.05 is 3.260.

According to Table 8, if the F-means of the pore permeability variation amplitude (A) and temperature (C) factors are greater than F_0.05, then the pore permeability variation amplitude (A) and temperature (C) have a significant impact on the thermal diffusion coefficient of reservoir rocks at a confidence level of 95%. According to Table 9, the F-values of the pore permeability variation amplitude (A), water saturation (B), and temperature (C) factors are all greater than F_0.05. Therefore, at a confidence level of 95%, the pore permeability variation amplitude (A), water saturation (B), and temperature (C) have a significant impact on the thermal conductivity of reservoir rocks. According to Table 10, if the F-values of water saturation (B) and temperature (C) factors are greater than F_0.05, this indicates that water saturation (B) and temperature (C) have a significant impact on the specific heat of reservoir rocks at a confidence level of 95%.

Based on the experimental results and literature research results, we analyzed the mechanism of changes in reservoir rock thermal properties under the influence of multiple factors. The amplitude of pore permeability changes has a significant impact on the thermal diffusion coefficient and thermal conductivity of reservoir rocks. This is mainly because when there are more pores in the reservoir rocks, the fluid in the pores will occupy a larger proportion of space and form a continuous phase. At this point, more resistance and dispersion effects need to be overcome when transferring energy inside the medium, thereby slowing down the speed of heat transfer. Therefore, as the porosity and permeability increase, the thermal diffusion coefficient and thermal conductivity of reservoir rocks will decrease. Water saturation has a significant impact on the thermal conductivity and specific heat of reservoir rocks, mainly because water has a higher specific heat and thermal conductivity. As the water saturation of reservoir rocks increases, their average thermal conductivity and specific heat will gradually increase. It should be noted that in practical situations, the influence of water saturation on the thermal conductivity and specific heat of reservoir rocks of different types, pore structures, and permeability may also vary. For example, when the pore connectivity of reservoir rocks is good and the morphology is regular, the fluid flow in them is better, and the thermal conductivity of reservoir rocks is also better. When the pores of reservoir rocks are small, dispersed, or fractured, this will affect the contact area between liquid water and solid rocks, thereby reducing the total specific heat of reservoir rocks. Temperature has a significant impact on the thermal diffusion coefficient, thermal conductivity, and specific heat of reservoir rocks, mainly because as the temperature increases, the internal microstructure and oil-water saturation of the rocks change. Firstly, as the temperature increases, the vibration frequency of molecules and atoms inside the rock increases, which enhances the rate of energy transfer and diffusion. In theory, the thermal conductivity and thermal diffusion coefficient should increase with the increase in temperature. However, in reality, the small pores and cracks inside the rock can form thermal barriers, hindering the transfer and diffusion of heat. Therefore, the thermal conductivity and thermal diffusion coefficient will actually decrease with the increase in temperature. In addition, as the temperature increases, atoms and molecules in the rock begin to vibrate more violently, leading to an increase in the interaction force between atoms and molecules in the reservoir rock. This interaction force creates a tendency in the rock to resist external changes; that is, the specific heat of the reservoir rock increases.

3.2. Regression Analysis

After determining the impact trend and significance of each factor on different indicators through intuitive analysis and an analysis of variance, regression analysis of experimental data is also necessary to establish regression equations to characterize the quantitative relationship between each factor and different indicators. When conducting regression analysis on experimental data, multiple regression is used to characterize the relationship between each variable and the dependent variable, with the dependent variables being Y₁ (thermal diffusion coefficient), Y₂ (thermal conductivity), and Y₃ (specific heat), while the independent variables are X_A (pore permeability change amplitude), X_B (water saturation), and X_C (temperature).

3.2.1. Multiple Linear Regression

A multiple linear regression method was used to perform regression analysis on the data, and the regression results analysis table is as follows.

According to

Table 11. Multivariate linear regression analysis table.

	Regression Equation	R2	F-Value	p-Value
Thermal diffusion coefficient	$\begin{array}{l}{Y}_1=0.7554-0.00604X_{\mathrm{A}}\\ + 0.087X_{\mathrm{B}}-0.00091X_{\mathrm{C}}\end{array}$	4	0.0080	1.1911
Thermal conductivity	$\begin{array}{l}{Y}_2=1.4388-0.01884X_{\mathrm{A}}\\ + 0.268X_{\mathrm{B}}-0.001X_{\mathrm{C}}\end{array}$	4	0.0377	5.5879
Specific heat	$\begin{array}{l}{Y}_3=1.8318-0.00496X_{\mathrm{A}}\\ + 0.273X_{\mathrm{B}}+0.00084X_{\mathrm{C}}\end{array}$	4	0.0319	4.7245

, the fitting degree of the regression equations for the thermal diffusion coefficient and thermal conductivity coefficient obtained by the multiple linear regression method is relatively low (below 0.9). Although their p-values meet the significance test requirements, the fitting degree of the regression equation is poor and cannot meet the accuracy requirements of the prediction results. The regression equation of specific heat obtained from multiple linear regressions has a high degree of fit (greater than 0.95), and the p-value meets the significance test requirements. This indicates that the linear regression equation has a good fit and can meet the accuracy requirements of the prediction results.

The results of multiple linear regressions indicate that there is no non-linear relationship between the three factors involved in this article and the thermal diffusion coefficient and thermal conductivity coefficient, and that linear regression cannot be used for quantitative analysis. The regression equation of specific heat obtained from multiple linear regression meets the requirements of fitting and significance, and a linear relationship can be considered to characterize the quantitative relationship between specific heat and the three factors involved in this article.

3.2.2. Multiple Nonlinear Regression

The multiple nonlinear regression method used in References [22,23] was used to perform multiple nonlinear regression on the experimental results. The Levenberg–Marquardt method was chosen as the estimation method, and the regression results are shown below (

Table 12. Multivariate nonlinear regression equation coefficient table.

Coefficient	Thermal Diffusion Coefficient Equation	Thermal Conductivity Equation	Specific Heat Equation
n	1	2	3
a	0.966	1.776	1.832
b	−10,293.401	10,301.728	−10,271.272
c	10,293.402	−10,301.727	10,271.273
d	4.234 × 10−6	5.533 × 10−6	1.164 × 10−6
e	0.031	0.035	0.011
f	2.762 × 10−5	−8.954 × 10−5	−3.524 × 10−5
g	0.001	1.11 × 10−4	−0.001
h	−0.032	−0.045	−0.022
i	−1.41	−0.344	−0.221
j	−0.001	−0.01	−0.002

).

According to

Table 13. Multivariate nonlinear regression analysis table.

	Regression Equation	R2	F-Value	p-Value
Thermal diffusion coefficient	$\begin{array}{l}{Y}_{\mathrm{n}}=\mathrm{a}+b{X}_{\mathrm{A}}^2+\mathrm{c}{X}_{\mathrm{B}}^2\\ + d{X}_{\mathrm{C}}^2+e{X}_{\mathrm{A}}{X}_{\mathrm{B}}+f{X}_{\mathrm{A}}{X}_{\mathrm{C}}\\ + g{X}_{\mathrm{B}}{X}_{\mathrm{C}}+h{X}_{\mathrm{A}}+i{X}_{\mathrm{B}}+j{X}_{\mathrm{C}}\end{array}$	0.999	7.89 × 104	1.59 × 10−33
Thermal conductivity		0.991	6211.5	3.02 × 10−25
Specific heat		0.998	1.78 × 105	3.6 × 10−13

, the fitting degree of the multiple nonlinear regression equations for the three indicators is relatively high (greater than 0.99), and their p-values are far less than 0.05. This indicates that the results of multiple nonlinear regressions are superior to those of multiple linear regression in terms of fitting degree and significance.

From the analysis results, it can be seen that the influence direction and significance of the three factors of pore permeability change amplitude, water saturation, and temperature on the thermal diffusion coefficient, thermal conductivity coefficient, and specific heat of reservoir rocks are different. Moreover, during the rapid preheating process of SAGD, reservoir expansion and the steam circulation process will cause simultaneous changes in pore permeability, oil-water saturation, and the temperature of reservoir rocks. Therefore, it is only by analyzing the changes in thermal properties of reservoir rocks and establishing corresponding multiple nonlinear regression equations to characterize them before conducting SAGD rapid preheating operations that we can more accurately predict the changes in reservoir rocks during production and construction and can further evaluate the effectiveness of SAGD rapid preheating construction more accurately.

3.3. Prediction Model for the Thermal Properties of Reservoir Rocks

The main controlling factors, significance, and regression equations affecting the thermal diffusion coefficient, thermal conductivity coefficient, and specific heat of reservoir rocks have been determined through intuitive analysis, variance analysis, and regression analysis in the previous section. Taking into account the accuracy and significance of the regression results, a multiple nonlinear regression equation was ultimately chosen to characterize the quantitative relationship between the thermal diffusion coefficient, thermal conductivity coefficient, and specific heat indicators and the changes in porosity and permeability, water saturation, and temperature.

The regression equation for thermal diffusion coefficient is as follows:

$$\begin{array}{l}\alpha =0.966-10,293.401x^2+10,293.402S_{\mathrm{W}}^2+4.234\times {10}^{-6}{T}_{\mathrm{f}}^2+0.031x{S}_{\mathrm{W}}\\ +2.762\times {10}^{-5}x{T}_{\mathrm{f}}+0.001S_{\mathrm{W}}{T}_{\mathrm{f}}-0.032x+-1.41S_{\mathrm{W}}-0.001T_{\mathrm{f}}\end{array}$$

(1)

The regression equation for thermal conductivity is as follows:

$$\begin{array}{l}{\lambda }_{\mathrm{f}}=1.776+10,301.728x^2-10,301.727S_{\mathrm{W}}^2+5.533\times {10}^{-6}{T}_{\mathrm{f}}^2+0.035x{S}_{\mathrm{W}}\\ -8.954\times {10}^{-5}x{T}_{\mathrm{f}}+1.11\times {10}^{-4}{S}_{\mathrm{W}}{T}_{\mathrm{f}}-0.045x+(-0.344S_{\mathrm{W}})-0.01T_{\mathrm{f}}\end{array}$$

(2)

The regression equation for specific heat is as follows:

$$\begin{array}{l}{M}_{\mathrm{R}}=1.832-10,271.272x^2+10,271.273S_{\mathrm{W}}^2+1.164\times {10}^{-6}{T}_{\mathrm{f}}^2+0.011x{S}_{\mathrm{W}}\\ -3.524\times {10}^{-5}x{T}_{\mathrm{f}}-0.001S_{\mathrm{W}}{T}_{\mathrm{f}}-0.022x+-0.221S_{\mathrm{W}}-0.002T_{\mathrm{f}}\end{array}$$

(3)

α—Thermal diffusion coefficient of reservoir rocks, mm²/s

x—Increase in pore permeability, %

S_W—Reservoir rock water saturation, dimensionless

T_f—Reservoir rock temperature, °C

λ_F—Thermal conductivity coefficient of reservoir rock, W/(m·K)

M_R—specific heat of reservoir rocks, J/(g·K)

4. Conclusions

(1) The main factor affecting the thermal diffusion coefficient of reservoir rocks is the amplitude of pore permeability changes. The main factor affecting the thermal conductivity of reservoir rocks is temperature. The main factor affecting the specific heat of reservoir rocks is water saturation.

(2) The thermal properties of reservoir rocks are influenced by the amplitude of pore permeability changes, water saturation, and temperature. An increase in porosity and permeability will cause the fluid to form a continuous phase, resulting in the need to overcome more resistance and dispersion when transferring energy within the medium, thereby slowing down the rate of heat transfer. The specific heat and thermal conductivity of water are relatively high. As the water saturation of reservoir rocks increases, the average thermal conductivity and specific heat of reservoir rocks will gradually increase. An increase in temperature will increase the vibration frequency of molecules and atoms inside the rock, increasing the rate of energy transfer and diffusion. However, the small pores and cracks present in the rock will form thermal barriers, which, in turn, reduce the thermal conductivity and thermal diffusion coefficient. In addition, the specific heat of reservoir rocks increases due to the increased temperature, which enhances the interaction forces between atoms and molecules in the reservoir rocks.

(3) Taking into account the accuracy and significance of the regression results, a multiple nonlinear regression equation was ultimately chosen to characterize the quantitative relationship between reservoir thermal properties and pore permeability changes, water saturation, and temperature.