The Development and Application of Novel Apparatus for Relative Permeability Measurement

Abstract

Relative permeability plays a crucial role in understanding the characteristics of gas and water seepage in porous media and in establishing production schedules in practical engineering applications. However, accurately determining water saturation in the relative permeability measurement is challenging due to the minimal detectable amount of movable water in ultra-low-permeability rocks. This chapter introduces a novel method to determine water production during relative permeability measurement. We developed an apparatus that combines a separator with a high-precision differential pressure transducer (DPT) to measure the variation in water production during the experiment. The repeatability of measurements using this apparatus was tested, and the results demonstrated high stability. In addition, we used this apparatus to investigate the gas−water relative permeability in high-rank coal. The results indicate that the effect of displacement pressure on the relative permeability properties depended on the type of gas. The carbon dioxide–water system exhibited a significantly larger two-phase flow span compared to the helium–water or methane–water system at the same displacement pressure. Moreover, the relative permeability of the carbon dioxide–water system showed a higher sensitivity to the displacement pressure compared to the helium–water and methane–water systems.

1. Introduction

To address the global challenge of climate change, many researchers have shifted their focus toward unconventional clean energy extraction [1] and carbon dioxide geological sequestration technologies [2, 3, 4]. These technologies aim to mitigate carbon emissions or enhance clean energy production by injecting carbon dioxide into various subsurface formations such as saline aquifers, coal beds, and shale formations. As these reservoirs typically contain both liquid and gas phases, it is essential to understand the multiphase flow characteristics in reservoirs for effective project assessment. Relative permeability plays a vital role in characterizing the flow potential of each phase within the reservoir. It represents the ratio of the effective permeability of each phase (gas or liquid) to the absolute permeability of the reservoir. This parameter is crucial for reservoir simulation, where accurate modeling of fluid flow behavior is necessary for optimizing carbon dioxide storage or enhanced energy production. By quantifying the relative permeability of different phases, researchers can better understand how fluids move and interact within the reservoir. This knowledge is essential for predicting the performance and efficiency of carbon dioxide sequestration or energy extraction projects.

In the measurement of relative permeability using the unsteady state method [5, 6], accurate determination of water saturation was challenging for reservoirs with low porosity and permeability. This is because rocks with small porosity and high irreducible water saturation tend to displace only a small amount of water during the experiment. Over the past 50 years, researchers have developed various equipment and measurement techniques to address this challenge. One approach is to collect the displaced water in a graduated fluid receiver tube and estimate the volume based on the change in water level. Dabbous et al. [7] designed an apparatus specifically for measuring the relative permeability of coal using this method. Similarly, Durucan et al. [8] developed an apparatus for measuring the relative permeability, and the change in water volume was measured by conventional volumetric method. However, it is important to note that the gas–water interface during the experiment is unstable, which may affect the accuracy of data determination. Another widely used method is the gravimetric method [9, 10, 11, 12], where the weight change of water in the separator is measured using an electronic balance. However, the presence of pipelines between the separator and the core holder can introduce volatility in the electronic balance readings. Nuclear magnetic resonance (NMR) relaxation has been employed by Sun et al. [13] to measure the gas–water relative permeability of coal. In this method, the water content in the pores is estimated using the total amplitude of T₂. Schembre and Kovscek [14] and Zhao et al. [15] have utilized X-ray CT measurement to calculate the relative permeability. Water saturation data is obtained from images of the core slices at a certain time. Both NMR and CT provide direct measurements of water saturation, avoiding potential errors caused by dead volumes in the apparatus. However, the limited resolution of NMR and CT imposes constraints on the sample size used in the experiment, which may affect the representativeness of the results. Additionally, the high cost of NMR and CT poses a significant barrier to their widespread adoption.

In this chapter, a novel apparatus for measuring the gas–liquid relative permeability of ultra-low-permeability rocks was introduced. This apparatus combined a specially engineered separator and a high-precious DPT in the relative permeability measurement system. The separator was designed to withstand high-pressure conditions, ensuring the simulation of a real reservoir environment. The DPT, on the other hand, was capable of monitoring the water content in real time, providing continuous and precise data during the experiment. Importantly, the DPT offered a more cost-effective solution for relative permeability measurement compared to NMR and CT. To validate the performance of the apparatus, thorough verification tests were conducted. These tests aimed to assess the accuracy, reliability, and stability of the measurements obtained using the apparatus. Additionally, the impact of displacement pressure and gas type on the gas–water relative permeability of coal was investigated. The findings from these experiments contribute to a better understanding of fluid flow behavior in ultra-low-permeability rocks.

2. Apparatus

2.1 The design of relative permeability apparatus

We developed a novel apparatus designed to accurately measure the gas–water relative permeability of ultra-low-permeability rocks. The schematic diagram of the apparatus can be seen in Figure 1(a). The apparatus is composed of five main components: a gas injection and control system, a core holder system, a separation system, s back-pressure control system, and a data acquisition system (DAQ). Based on the schematic diagram of the novel apparatus, we constructed the relative permeability device, as shown in Figure 1(b). The gas injection and control system comprises a gas source and a syringe pump. The syringe pump can withstand high pressure, with a maximum capacity of 25.86 MPa. This system allows precise control over the gas injection process, ensuring accurate measurements. Within the core holder system is a core holder itself, along with a confining pump. The core holder guarantees secure placement of the rock sample, and the confining pump applies a maximum confining pressure of 25 MPa. The separation system comprises a gas–water separator and a DPT. The back-pressure control system incorporates a back-pressure valve and a flow meter. The back-pressure valve serves the purpose of maintaining a consistent back-pressure during the experiment, while the flow meter, with a measurement range of 50 ml/min and an accuracy of ±0.5%RD + ±0.1%FS, accurately measures the flow rate. For effective data acquisition, the DAQ system was equipped with various pressure sensors and a data acquisition card. This configuration allows simultaneous data collection from each sensor, thereby enhancing the reliability of the acquired data.

Figure 1.

The diagram of the novel apparatus [16]. (a) the structure diagram of the relative permeability measurement system; and (b) picture of the apparatus for relative permeability measurement.

The characteristic of our device lies in two aspects: the design of the gas–water separation system and the arrangement of the downstream pipeline. The gas–water separation system in our apparatus consists of a cylindrical separator and a high-precision differential pressure transducer (DPT). The separator was specifically designed to efficiently collect the displaced water, while the DPT accurately monitors changes in the water level, enabling precise determination of water production. To prevent water evaporation and minimize system errors, a small amount of oil was added to the separator. This ensures that the collected water remains intact throughout the measurement process. Furthermore, the arrangement of the pipelines connecting the core holder and the separator plays a crucial role in reducing residual water in the pipelines. By arranging these pipelines vertically, we can effectively minimize the amount of residual water, enhancing the accuracy of the measurements.

One key advantage of our device is its adjustability in terms of measurement range and accuracy. The measurement accuracy of the displaced water is influenced by both the inner diameter of the separator and the precision of the DPT. As a result, we have the flexibility to design separators with different diameters to meet specific measurement requirements. This adjustability allows for precise and tailored measurements based on the unique characteristics of different rock samples. The relationship between the differential pressure and the displaced water volume follows the liquid pressure formula:

$$\mathrm{\Delta }p={\rho }_{w}g\mathrm{\Delta }h={\rho }_{w}g\frac{4\mathrm{\Delta }V}{\pi d^2}$$E1

where $\mathrm{\Delta }p$ is the change of differential pressure, Pa; ${\rho }_{\mathrm{w}}$ is the density of water, kg/m³; g is the acceleration of gravity, m/s²; $\mathrm{\Delta }h$ is the change of liquid level in the separator, m; $\mathrm{\Delta }V$ is the change of water volume in the separator, m³; d is the inner diameter of the separator, m.

In theory, it is indeed possible to enhance the measurement accuracy by reducing the inner diameter of the separator indefinitely, as demonstrated by Eq. (1). However, it is important to consider practical limitations and avoid potential capillary effects. We recommend a minimum inner diameter of 5 mm for the separator. In our specific study, we utilized a separator with an inner diameter of 6 mm. To ensure accurate measurements, we employed a high-precision DPT with a measurement range of 1.4 kPa and an accuracy of ±0.25 FS. This DPT provides reliable and precise data that is essential for calculating the relative permeability. For researchers conducting relative permeability measurements using a similar device, we advise designing a specialized separation system to meet their specific requirements. This customization allows researchers to optimize the measurement accuracy and range based on their unique experimental conditions and objectives.

2.2 The performance of the novel apparatus

Measurement repeatability is indeed a crucial requirement for experimental equipment, and we have conducted assessments to evaluate it for gas permeability measurements on different rock types, including sandstone and coal. Additionally, we have performed verification experiments to assess the repeatability of water production during relative permeability measurements.

To measure the gas permeability of sandstone, we employed the steady state method while maintaining a constant gas injection rate throughout the measurement process. The differential pressure between the upper and lower sides of the sample was recorded in Figure 2(a). In Test 1, nitrogen gas was injected at a rate of 20 ml/min, and the differential pressure eventually stabilized at 30.330 kPa. In Tests 2 and 3, nitrogen gas was injected at a rate of 10 ml/min, resulting in coinciding differential pressure curves. The final differential pressure reached 14.548 kPa. Using Darcy’s law, we calculated the gas permeability, as depicted in Figure 2(b). The gas permeabilities were measured to be 11.20, 11.07, and 11.07 mD for Test 1, Test 2, and Test 3, respectively. The average gas permeability across the three tests was found to be 11.11 mD, with a corresponding standard deviation of 0.0613.

Figure 2.

The measurement results of gas permeability of sandstone by the steady-state method. (a) the differential pressure curves; and (b) the measured gas permeability.

In our study, we employed the pulse-decay method to measure the permeability of coal. The decay curves of the differential pressure over time were plotted in Figure 3(a). These curves exhibited an exponential decay pattern. Using the fitted results obtained from the decay curves, we applied the equation proposed by Jones [17] to calculate the gas permeability of the coal sample. The gas permeabilities were determined to be 5.56, 5.49, and 5.45 μD for Test 1, Test 2, and Test 3, respectively. These values are presented in Figure 3(b). The average gas permeability across the three tests was found to be 5.5 μD, with a corresponding standard deviation of 0.0437. This indicates that the measurements are consistent and repeatable, as evidenced by the small standard deviation.

Figure 3.

The measurement results of gas permeability of coal by the pulse-decay method. (a) the differential pressure curves; and (b) the measured gas permeability.

After verifying the repeatability of gas permeability, we conducted nitrogen–water relative permeability experiments on sandstone using the unsteady state method. The sandstone samples were subjected to a confining pressure of 8.5 MPa, with the downstream connected to the atmosphere. To maintain consistency, the displacement pressure was kept at 0.24 MPa throughout the experiments. The relative permeability experiment was repeated three times, and the water and gas production data obtained from each repetition are presented in Figure 4. The data demonstrate good agreement across the three repetitions, indicating repeatability and reliability in the measurements. To quantitatively evaluate the differences between the three measurements, we calculated the global coefficient of variation (GCV) using the following formula:

Figure 4.

The water and gas production during the relative permeability measurement [16]. (a) Water production; and (b) gas production.

$$\mathit{GCV}=\frac{1}{\mathrm{n}}\sum _{i=1}^n\frac{\sqrt{\frac{1}{m}\sum _{j=1}^m{\left(y_i^j-\overline{y_i}\right)}^2}}{\overline{y_i}}$$E2

where n represent the time. j represents the test number. $y_i^j$ represents the j th measurement result at the time i. $\overline{y_i}$ represents the average data at the time i.

The GCV for water production was 0.05, and for gas production was 0.06. The results obtained for both gas permeability and gas–water relative permeability, along with the stability observed in the measurements, further confirm the repeatability of the experimental apparatus used in this study.

3. Application

3.1 Experimental design and process

In this section, we utilized the previously evaluated novel apparatus to investigate the impact of displacement pressure and gas type on gas–water flow characteristics in coal. Coal is known for its unique swelling behavior induced by gas adsorption [18, 19, 20, 21], and the extent of swelling is influenced by gas pressure [22, 23, 24, 25]. Therefore, studying the effect of gas type and gas pressure on gas–water seepage behavior in coal is a logical step. The experiments used helium, methane, and carbon dioxide as the injected gases. The experimental conditions are summarized in Table 1. The injection pressure (P_in) ranged from 1.9 to 3.9 MPa, while the outstream pressure (P_out) remained constant.

Gas type	Pin/MPa	Pout/MPa	Effective stress/MPa
He, CH4, CO2	1.9, 2.9, 3.9	0.1	5.9

Table 1.

The experimental conditions of relative permeability measurement.

The anthracite coal sample used in this investigation was collected from SiHe Coal Mine in the Qinshui Basin. The vitrinite reflectance of the coal sample was measured to be 3.37%. Prior to measuring the relative permeability, the coal sample was dried at 60°C for 24 hours to remove residual water. Subsequently, the gas permeability was measured using the pulse-decay method with helium. The confining pressure and pore pressure were set at 7.9 MPa and 2 MPa, respectively. After the gas permeability measurement, the coal sample was saturated with water for 3 days. Once complete water saturation was achieved, the measurement of relative permeability was conducted. Water production was determined by the DPT, while gas production was recorded by a gas flow meter. The relative permeability of gas and water was calculated based on the recorded data, using the calculation method described in our previous study [26]. By investigating the gas–water flow characteristics in coal under different gas types and pressures, this study aims to provide insights into the behavior of coal reservoirs and enhance our understanding of gas and water migration in such porous media.

3.2 Results of the displacement experiment

The gas permeability of the dried coal, measured with helium, was found to be 18.26 μD. Figure 5 illustrates the recorded gas and water production for different gas–water systems at varying displacement pressures. For the helium–water and methane–water systems, it was observed that the total accumulated water flow remained below 1 ml, and the effect of displacement pressure on this flow was negligible. In the case of the helium–water system, the total accumulated water flow ranged from 0.238 ml to 0.327 ml as the displacement pressures varied. Similarly, for the methane–water system, the total accumulated water flow ranged from 0.179 ml to 0.387 ml with increasing displacement pressures. However, for the carbon dioxide–water system, the total accumulated water flow exceeded 1 ml, and it exhibited a significant increase with increasing displacement pressures. Specifically, as the displacement pressures increased from 1.8 MPa to 3.8 MPa, the total accumulated water flow increased from 1.488 ml to 5.178 ml.

Figure 5.

The accumulated water/gas flow at different displacement pressures for different gas–water systems. (a) Helium–water system; (b) methane–water system; and (c) carbon dioxide–water system. Reprinted (adapted) with permission from reference [26]. Copyright 2023 American Chemical Society.

Based on the analysis of accumulated water/gas flow, we were able to calculate the gas–water relative permeability. The results of the helium–water relative permeability at different displacement pressures are presented in Table 2. It was observed that the irreducible water saturation was extremely high, ranging from 90.2% to 92.1%, indicating a narrow two-phase flow span for the helium–water system. Additionally, the maximum relative permeability of gas was found to be significantly higher than that of water. Specifically, the maximum relative permeability of gas ranged from 13.97% to 15.48%, while the maximum relative permeability of water was much lower, ranging between 1.82% and 2.77%. It should be noted that the influence of displacement pressures on the characteristic parameters of relative permeability was not apparent. Across different displacement pressures, the irreducible water saturation remained relatively consistent, ranging from 90.2% to 92.1%. Similarly, the gas relative permeability at the irreducible water saturation varied only slightly, ranging from 13.97% to 15.48%.

∆p = 1.8 MPa			∆p = 2.8 MPa			∆p = 3.8 MPa
Sw/%	krw/%	krg/%	Sw/%	krw/%	krg/%	Sw/%	krw/%	krg/%
95.2	2.70	7.97	94.6	5.45	2.77	95.4	1.82	3.26
94.3	1.79	8.12	93.8	3.48	3.05	95.0	1.75	3.23
93.9	0.62	8.58	93.0	1.04	3.84	94.6	1.38	3.51
93.5	0.32	9.39	92.6	0.59	4.76	94.2	1.00	4.12
93.1	0.19	10.50	92.2	0.48	5.72	93.8	0.87	4.72
92.7	0.10	11.95	91.8	0.26	7.01	93.4	0.55	5.63
92.3	0.08	13.50	91.4	0.15	8.76	93.0	0.18	7.90
91.9	0.067	14.85	91.0	0.10	10.94	92.5	0.07	11.77
91.5	0.066	15.48	90.6	0.06	13.67	92.1	0.04	13.97
			90.2	0.05	15.21

Table 2.

Relative permeability measurement results for helium–water system.

Reprinted (adapted) with permission from reference [26]. Copyright 2023 American Chemical Society.

The results of methane–water relative permeability under different displacement pressures are presented in Table 3. The irreducible water saturation ranged from 90.7% to 91.8%. This indicates a narrow two-phase flow span, similar to what was observed in the helium–water system. However, it is worth noting that the relative permeability of methane at the irreducible water saturation is significantly lower compared to helium. The methane relative permeability ranged from 4.67% to 5.26%, indicating that methane exhibited lower ability to flow through the coal matrix than helium. Moreover, the impact of displacement pressures on the relative permeability of methane–water showed similar trends to the helium–water system.

∆p = 1.8 MPa			∆p = 2.8 MPa			∆p = 3.8 MPa
Sw/%	krw/%	krg/%	Sw/%	krw/%	krg/%	Sw/%	krw/%	krg/%
97.0	2.40	0.00	93.1	0.46	1.72	96.3	3.14	1.25
96.6	1.93	0.24	92.7	0.39	2.03	95.9	2.12	1.32
96.2	1.34	0.89	92.3	0.26	2.55	95.4	0.84	1.51
95.8	0.91	1.46	91.9	0.15	3.06	95.0	0.60	1.78
95.4	0.58	1.83	91.5	0.08	3.82	94.6	0.63	2.09
95.0	0.50	2.20	91.1	0.05	4.77	94.2	0.55	2.37
94.6	0.46	2.46	90.7	0.04	5.26	93.8	0.42	2.69
94.2	0.38	2.70				93.4	0.27	3.09
93.8	0.28	2.95				93.0	0.15	3.57
93.3	0.22	3.24				92.6	0.07	4.11
92.9	0.19	3.59				92.2	0.05	4.77
92.5	0.16	3.97				91.8	0.03	5.15
92.1	0.10	4.42
91.7	0.09	4.67

Table 3.

Relative permeability measurement results for methane–water system.

Reprinted (adapted) with permission from reference [26]. Copyright 2023 American Chemical Society.

The results of carbon dioxide–water relative permeability under different displacement pressures are listed in Table 4. The irreducible water saturation in the carbon dioxide–water system ranged from 25.7% to 78.7% as the displacement pressure increased from 1.8 MPa to 3.8 MPa. This indicates a wider range of two-phase flow span compared to the helium–water and methane–water systems. Additionally, the carbon dioxide relative permeability at the irreducible water saturation was found to be lower than that of helium and methane. Despite the lower irreducible water saturation in the carbon dioxide–water system, carbon dioxide exhibited lower ability to flow through the coal matrix compared to helium and methane. Unlike the helium–water and methane–water systems, the characteristics of carbon dioxide–water relative permeability were significantly influenced by the displacement pressure. As the displacement pressure increased from 1.8 MPa to 3.8 MPa, the irreducible water saturation decreased from 78.7% to 25.7%. These findings demonstrate that the behavior of carbon dioxide–water relative permeability differs from that of helium–water and methane–water systems. The wider range of irreducible water saturations and the influence of displacement pressure highlight the unique characteristics of carbon dioxide as a displacing fluid in coal.

∆p = 1.8 MPa			∆p = 2.8 MPa			∆p = 3.8 MPa
Sw/%	krw/%	krg/%	Sw/%	krw/%	krg/%	Sw/%	krw/%	krg/%
97.0	0.81	0.00	100.0	0.82	0.00	90.2	1.40	0.00
94.0	0.29	0.02	93.6	0.66	0.00	86.3	1.05	0.00
91.9	0.26	0.10	88.5	0.42	0.01	82.9	1.02	0.02
89.3	0.22	0.26	84.2	0.34	0.04	78.2	0.98	0.07
86.3	0.18	0.45	78.7	0.29	0.09	73.5	0.70	0.11
84.2	0.18	0.61	74.8	0.26	0.15	69.7	0.61	0.17
81.6	0.18	0.66	70.5	0.30	0.22	65.8	0.64	0.26
79.9	0.12	0.69	65.4	0.27	0.33	60.3	0.58	0.43
78.7	0.10	0.71	61.6	0.20	0.45	55.2	0.50	0.65
			57.7	0.22	0.54	50.5	0.46	0.87
			54.3	0.19	0.61	45.3	0.41	1.15
			51.8	0.15	0.65	39.8	0.32	1.45
			50.5	0.18	0.68	34.7	0.25	1.70
						30.4	0.19	1.92
						27.8	0.15	2.13
						25.7	0.12	2.22

Table 4.

Relative permeability measurement results for carbon dioxide–water system.

Reprinted (adapted) with permission from reference [26]. Copyright 2023 American Chemical Society.

3.3 Impact of displacement pressure and gas type on gas–water relative permeability

The relative permeability curves of different gas–water systems at various displacement pressures are illustrated in Figure 6. It was observed that the gas type significantly affected the relative permeability of anthracite coal. For the helium–water and methane–water systems, the shapes of the gas–water relative permeability curves were almost identical, while curves for the carbon dioxide–water system were flatter. Furthermore, the carbon dioxide–water system exhibited a substantial increase in the span of the two-phase flow.

Figure 6.

The effect of displacement pressure on gas–water relative permeability curves. (a) the relative permeability of water; and (b) the relative permeability of gas. Reprinted (adapted) with permission from reference [26]. Copyright 2023 American Chemical Society.

The effect of gas type and displacement pressure on the characteristic parameters of relative permeability is presented in Figure 7. It was observed that the variation of irreducible water saturation with displacement pressure is influenced by the gas type. In the case of the helium–water and methane–water systems, there was little change in irreducible water saturation with the increase in displacement pressure. This finding was consistence with the study conducted by Yang et al. [27], who examined the effect of gas (N₂) displacement pressures on the displaced water content in low-permeability coal. They found that the irreducible water content stabilized when the displacement pressure exceeded 2 MPa. However, for the carbon dioxide–water system, the irreducible water saturation showed a significant and rapid decrease as the displacement pressure increased from 1.8 MPa to 3.8 MPa. This indicates that the impact of displacement pressure on irreducible water saturation is more pronounced in the carbon dioxide–water system compared to the helium–water and methane–water systems. The difference in irreducible water saturation with displacement pressure can be attributed to the variation in the interfacial tension between different gas–water systems. Previous studies [28, 29, 30] have indicated that the interfacial tension between helium and water, as well as methane and water, remains relatively close within the pressure range of 0.1–4 MPa (approximately 66–73 mN/m). However, the interfacial tension between carbon dioxide and water decreased rapidly, from 72 to 46.8 mN/m [31, 32], as the pressure increased to 4 MPa. The decline in interfacial tension promotes water displacement in the experiment. Additionally, the dissolved carbon dioxide alters the contact angles between carbon dioxide, water, and coal [33], resulting in a shift in coal wettability from water-wet to carbon dioxide wet [34]. The change in wettability enhanced water recovery efficiency during the drainage process, leading to a decrease in irreducible water saturation in the carbon dioxide–water system with increasing displacement pressure.

Figure 7.

The characteristic parameters of relative permeability curve at different displacement pressures. (a) Irreducible water saturation; and (b) gas relative permeability at irreducible water saturation.

Furthermore, it was observed that the gas permeability at irreducible water saturation exhibited a more pronounced variation with gas type rather than displacement pressure. The sequence of swelling induced by gas adsorption in coal is widely recognized as CO₂ > CH₄ > He [35]. Consequently, the gas permeability in the helium–water, methane–water, and carbon dioxide–water systems followed the same sequence.

4. Limitations

Precision determining the relation between the accumulated gas/water flow and water saturation is essential in the relative permeability experiment. However, experimental errors were present in this study. The accumulated gas/water curves indicated that the gas preferentially penetrated the sample during the drainage process for measuring helium–water and methane–water relative permeability. It was recognized as an illusion caused by errors in the experimental system. During the drainage process, the displaced water initially accumulates on the sample outlet surface and then fills the dead volume, which is unavoidable in the device design. The accumulated water overcomes the adhesion between the water and the surface of the coal sample and flows into the separator due to gravity and pressure gradient. This leads to the illusion that an early gas breakthrough occurs in relative permeability measurement. Furthermore, it is well-known that the absolute permeability of coal is influenced by gas adsorption [21]. Relative permeability is defined as the ratio of effective permeability to absolute permeability. Therefore, the results of relative permeability are affected by the choice of absolute permeability. In this study, the absolute permeability used for the calculations was based on He permeability. As a result, the calculated relative permeability values obtained in the experiment were extremely small.

5. Conclusion

In this chapter, the development of a novel apparatus for measuring gas–water relative permeability in ultra-low-permeability rocks was presented. The apparatus utilized high-precision DPT to determine the water saturation of the rock samples. This combination of DPT and separator allows the relative permeability measuring device to adjust the water measurement range and measurement accuracy according to specific requirements. To ensure the reliability of the measurement results, gas permeability tests were conducted three times on sandstone and coal samples, and the relative permeability of sandstone was also tested three times. The repeatability of the measurements was confirmed, providing confidence in the accuracy and consistency of the obtained data. The investigation then focused on studying the impact of displacement pressures and gas types on the relative permeability of anthracite coal. The findings and conclusions drawn from this study can be summarized as follows:

1. The combination of DPT and a separator is a feasible method for determining the water saturation of ultra-low-permeability rocks during relative permeability measurements.

2. The gas permeability and relative permeability measurements exhibit good repeatability, with low standard deviations and GCV values, indicating the accuracy and consistency of the obtained data.

3. The impact of displacement pressure on relative permeability properties varies depending on the gas type. Helium–water and methane–water systems show no significant differences in two-phase flow span with increasing in displacement pressure, while the carbon dioxide–water system exhibits an increase in two-phase flow span.

4. Gas type plays a significant role in influencing the relative permeability of coal. Carbon dioxide–water relative permeability demonstrates a substantial two-phase flow span compared to helium–water or methane–water systems under the same displacement pressure.

Acknowledgments

This work was supported by the Central Guidance on Local Science and Technology Development Fund of Inner Mongolia Autonomous Region (No.2022ZY0018), the National Key Research and Development Program of China (No.2018YFB0605601).

Conflict of interest

The authors declare that they have no conflicts of interest.

Notes/thanks

The authors would like to express their sincere gratitude to the American Chemical Society (ACS) and the Institute of Physics (Great Britain) for granting permission to utilize the figures and tables presented in this chapter. Their generosity allows us to enhance the quality and comprehensiveness of our research findings. We are thankful for their support in disseminating scientific knowledge and promoting collaboration in the academic community.