# Experimental Study on Gas–Water Relative Permeability Characteristics of Tight Sandstone Reservoir in Ordos Basin

Authors: Xiaoxia Ren; Aifen Li; Asadullah Memon
Journal: Geofluids
 (2022)

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## Abstract

Accurate measurement of relative permeability curve is the basis for evaluating gas reservoir performance. The unsteady-state method could bring significant measurement error for low-permeability cores. However, it is difficult to control the constant gas flow rate in the traditional steady-state method, which obstacles the experimental operation. In this study, an improved steady-state method was proposed. First, the pressure value obtained from the experiment, when the gas permeability no longer changed with the average pressure on the rock core, was set as the testing pressure. Then, the gas was injected under constant pressure, and the water was injected with a constant flow rate. Finally, the relative permeability values of gas and water phases were calculated based on Darcy’s law. Comparative analysis of the results of the relative permeability curves under formation pressure and pressure with negligible slip effect indicates that the relative permeability curves are the same in gas and water phases, proving the feasibility of the new method. Further, the results were compared with those of the test method at normal pressure, the water-phase relative permeability showed no significant change, the relative permeability of gas phase was larger, the two-phase flow area became wider, and the irreducible water saturation was lower than that at the normal pressure. This result reflects that pressure does not significantly affect the flow of wetting phase but tremendously influences the nonwetted phase under low pressure. The relationship between relative permeability and water saturation is linear in the semilogarithmic coordinate diagram and can be described by using the following relationship:lnkrg/krw=aSw+lnb. With the decrease in the core permeability, relative permeability curve, and isotonic point moved to the right, irreducible water saturation gradually increased, and residual gas saturation decreased, indicating that the smaller permeability induced a lower gas-phase flow capacity.


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## Body

## 1. Introduction

Gas–water relative permeability is of great significance in the industrial research on natural gas. Relative permeability can be obtained by direct measurement, capillary pressure curve, production data analysis, and indirect calculation methods by using the empirical formulas [1, 2]. Over the past decades, various experiments have been developed and conducted to systematically explore the gas–water relative permeability curves [3–6]. Currently, steady-state and unsteady-state methods are commonly used to obtain relative permeability at the laboratory scale [2]. In the steady-state method, two fluids are simultaneously injected into the core, and their permeability is calculated separately, according to Darcy’s law [7, 8]. Abaci et al. [9] injected a mixture of gas and liquid into a vertical artificial sandstone column at room temperature and pressure to measure relative permeability of gas and liquid. The results showed that when water saturation decreased slightly, the relative permeability of water decreased sharply, and the relative permeability of the gas phase at irreducible water saturation was higher than that of the water phase at residual gas saturation. Donald et al. [10] improved the fluid saturation test by X-ray computed tomography (CT) scanning technology under indoor conditions. The calculation formula for the steady-state method was simple, and the saturation could be measured directly based on Darcy’s law. However, it was challenging to maintain the constant gas flow rate by conventional methods, which brought errors into the measurement results.In contrast, in the unsteady-state method, the displacing phase is injected into the saturated core along with the wetting phase [11–13]. Berry et al. [14] conducted a series of constant-velocity unsteady-state gas–liquid displacement tests on four reservoir sandstone cores with similar porosity, permeability, and lithological characteristics under reservoir conditions. For short-core experiments, if the unsteady-state method is used, the dead volume generally accounts for about 33% of the pore volume of the core [15]. Thus, this effect cannot be ignored, significantly impacting data processing.Furthermore, the effect of pressure was also studied. However, scholars have different opinions on the effects of overlying strata pressure on relative permeability [16, 17]. Some of the early studies in this area was done by Fatt and Mo et al. [18, 19] and Thomas and Ward [20]. They supposed that the overlying strata pressure would not affect the relative permeability of gas and water phases. However, some literature studies indicated that overlying strata pressure significantly affected the gas–water permeability curves for both gas and water phases [19, 21–25]. Some literature studies also reported that pressure significantly affected the nonwetted phase under the overlying pressure; however, it did not significantly affect the wetting phase [26, 27]. This could be attributed to the increase in the overlying strata that binds sand grains tightly together, resulting in a decrease in the pore throat diameter. For a defined water saturation, this results in redistribution of the wetting phase to occupy more pore throats, which indicates that this cannot cause any significant changes in the water-phase relative permeability (e.g., in water-wet sandstone); however, results in more oil flow blockages thus reduce the relative permeability of nonwet phase [28, 29].The unsteady-state method often provides errors in measuring gas–water relative permeability curve due to volume measurement, and the influence of pressure on gas–water relative permeability is seldom considered in the currently used test methods. Therefore, based on the traditional steady-state method to measure relative permeability, in this study, the steady-state method is improved and modified. Considering the influence of the formation pressure, the relative permeability curve can be measured by the improved steady-state method, during which water is injected at constant flow as gas is injected at constant pressure. The test results at normal pressure were compared with those at formation pressure to verify the feasibility of this method.


## 2. Materials and Methods

### 2.1. Experimental Specimens and Conditions

The specimens used in the experiment were obtained from Sulige gas field, Ordos, Inner Mongolia, with a core diameter of 2.5 cm and length of no more than 5.0 cm. The dimensions, porosities, and permeabilities of the core samples are presented in Table1. The porosity and permeability were tested under N2 at 25°C. The experimental temperature was set to the formation temperature of 95°C. Water used was prepared according to the components of output crude oil at the mouth of a well after electric dehydration, and it showed the density of 1.025 g·cm-3 and the viscosity of 0.334 mPa·s, at 95°C. The components and viscosity of water for experimental use were found to be almost the same as those under the formation conditions, which could avoid plugging damage caused by incompatibility of injected water.Table 1
Basic data of core used in gas–water permeability experiment.
Core numberLength/cmDiameter/cmPorosity/%Perm-plug method/(10-3μm2)Dry weight/gWet weight/gSaturated water/mLContact angle/°14.2402.54017.7101.89647.92051.5043.49745.0524.0582.54013.6291.02452.14054.6642.46249.3834.3242.5309.4730.70352.71754.4631.89937.6544.5492.53315.9700.51653.61456.7843.09350.3653.3802.5408.1400.36042.91144.1161.17632.1563.6582.5365.1320.19447.30048.1120.79240.5673.6812.5403.0300.13048.26248.7580.48438.2184.4242.5406.2400.09057.50358.5571.02836.77The wettability of all cores was tested by contact angle measurements with the Kruss DSA-100 drop shape analyzer. A photograph was taken using a camera when a drop of water attached to the surface of a solid. The contact angle between the water and the solid was then calculated.The confining pressure was set as formation, atmospheric, and pressure with negligible slip effect, respectively.


### 2.2. Experimental Equipment and Process

#### 2.2.1. Experimental Setup

Figure1 shows the simulated displacement equipment used for providing high temperature and high reservoir pressure in the test. The system mainly includes displacement pump, humidifier, core holder, gas–water separator, and gas–water metering device.Figure 1
Flow chart of gas–water phase permeability test by the improved steady-state method.


#### 2.2.2. Experimental Process

(a)
By testing gas permeability of rock specimens under different backpressures, the pressure valuePN (under which gas permeability does not change with pressure) was obtained(b)
A core saturated with formation water was placed in a core holder at 95°C and the backpressure ofPN. Formation water was passed through the rock specimen at the constant flow rate (qw). When the system reached stability, the upstream pressure (P1) was recorded, and water permeability was calculated(c)
Water driven by gas: gas was injected into the core to gradually increase upstream pressure toP1. Displacement was continued at constant pressure P1 until no water was produced, and the gas-phase permeability with irreducible water (Swc) was calculated. The core was sealed, with the conditions reduced to laboratory conditions, and then the core was taken out and weighed to calculate the irreducible water saturation of the core(d)
Simultaneous injection of gas and water: the gas pressure was constantP1, and water was simultaneously injected at a constant flow rate of qw/20. When the system reached pressure equilibrium, the gas flow rate was recorded, and the effective permeability of the water and gas phases was calculated. Then, the core was weighed following the method mentioned in the previous step, and the water saturation was calculated(e)
The water flow rate was adjusted toqw/10, and the gas pressure was kept constant P1. Then, the abovementioned step d was repeated(f)
The gas source was closed, water was injected with a flow rate ofqw, and then the water-phase relative permeability under residual gas saturation (Sgr) was calculated


### 2.3. Experimental Data Processing Methods

Considering the variation of water and gas volume with temperature and pressure, it is necessary to adjust water and gas production at room temperature and normal pressure to that at high temperature and high pressure. Therefore, the formula for calculating the gas–water-phase permeability curve by a steady-state method was improved as follows:The volume of liquid under formation conditions is represented as follows:(1)Qw=QL0⋅Bw,where Qw denotes the flow rate of water under experimental conditions, cm3·s-1, QL0 is the flow rate of water under room temperature and normal pressure, cm3·s-1, and Bw is water volume coefficient under experimental conditions.Therefore, after reaching stability, according to Darcy’s law, liquid-phase permeability is represented as follows:(2)kw=QL0BwμwLAp1−p2,where kw is the liquid-phase permeability, cm2, μw denotes water-phase viscosity under experimental conditions, mPa·s, L and A are the core length and cross-section, with the units of cm and cm2, respectively, and P1 and P2 denote upstream and downstream pressure of core holder at steady gas and water discharge, respectively, 10-1 MPa.Figure2 shows schematic illustration for gas permeability, and Darcy’s formula is expressed as follows:
(3)Qg=−kgAμgdpdL,where Qg is the flow rate of gas under experimental conditions, cm3·s-1, kg is the gas permeability, cm2, μg denotes gas viscosity under experimental conditions, mPa·s, A represents core cross-section, cm2, and dp/dL is the pressure gradient, 10-1 MPa·cm-1.Figure 2
Schematic representation of flow process.From the gas state formula, on the ground,(4)p0Qg0=nRT0,where p0 is the atmospheric pressure, 10-1 MPa, Qg0 is the flow rate of gas under room temperature and normal pressure, cm3·s-1, n is the amount of substance, mol, R denotes proportionality coefficient, J·(mol·K)-1, and T0 is the room temperature, K.Under the ground,(5)pQg=nzRT,where p is the experimental mean pressure, 10-1 MPa, Qg is the flow rate of gas under experimental condition, cm3·s-1, z is the compression factor of gas at experimental temperature and pressure, and T is the experimental temperature, K.Then,(6)Qg=p0Q0zTpT0=−kgAμgdpdL.Gas permeability could be obtained by separating the calculus of variations as follows:(7)kg=2μgp0Qg0zTLAT0p12−p22.In this study, the gas-phase permeability under irreducible water is considered as absolute permeability:(8)krg=kgk,(9)krw=kwk,where krg and krw denote relative permeability of gas and water, respectively, and k is the absolute permeability, cm2. Average water saturation is as follows:
(10)Sw=mi−moVpρwBw,where Sw indicates mean water saturation, mi and m0 denote core mass before and after experiment, respectively, g, ρw represents density of water at room temperature, g·cm-3, and Vp is the pore volume of sample, cm3.


## 2.1. Experimental Specimens and Conditions

The specimens used in the experiment were obtained from Sulige gas field, Ordos, Inner Mongolia, with a core diameter of 2.5 cm and length of no more than 5.0 cm. The dimensions, porosities, and permeabilities of the core samples are presented in Table1. The porosity and permeability were tested under N2 at 25°C. The experimental temperature was set to the formation temperature of 95°C. Water used was prepared according to the components of output crude oil at the mouth of a well after electric dehydration, and it showed the density of 1.025 g·cm-3 and the viscosity of 0.334 mPa·s, at 95°C. The components and viscosity of water for experimental use were found to be almost the same as those under the formation conditions, which could avoid plugging damage caused by incompatibility of injected water.Table 1
Basic data of core used in gas–water permeability experiment.
Core numberLength/cmDiameter/cmPorosity/%Perm-plug method/(10-3μm2)Dry weight/gWet weight/gSaturated water/mLContact angle/°14.2402.54017.7101.89647.92051.5043.49745.0524.0582.54013.6291.02452.14054.6642.46249.3834.3242.5309.4730.70352.71754.4631.89937.6544.5492.53315.9700.51653.61456.7843.09350.3653.3802.5408.1400.36042.91144.1161.17632.1563.6582.5365.1320.19447.30048.1120.79240.5673.6812.5403.0300.13048.26248.7580.48438.2184.4242.5406.2400.09057.50358.5571.02836.77The wettability of all cores was tested by contact angle measurements with the Kruss DSA-100 drop shape analyzer. A photograph was taken using a camera when a drop of water attached to the surface of a solid. The contact angle between the water and the solid was then calculated.The confining pressure was set as formation, atmospheric, and pressure with negligible slip effect, respectively.


## 2.2. Experimental Equipment and Process

### 2.2.1. Experimental Setup

Figure1 shows the simulated displacement equipment used for providing high temperature and high reservoir pressure in the test. The system mainly includes displacement pump, humidifier, core holder, gas–water separator, and gas–water metering device.Figure 1
Flow chart of gas–water phase permeability test by the improved steady-state method.


### 2.2.2. Experimental Process

(a)
By testing gas permeability of rock specimens under different backpressures, the pressure valuePN (under which gas permeability does not change with pressure) was obtained(b)
A core saturated with formation water was placed in a core holder at 95°C and the backpressure ofPN. Formation water was passed through the rock specimen at the constant flow rate (qw). When the system reached stability, the upstream pressure (P1) was recorded, and water permeability was calculated(c)
Water driven by gas: gas was injected into the core to gradually increase upstream pressure toP1. Displacement was continued at constant pressure P1 until no water was produced, and the gas-phase permeability with irreducible water (Swc) was calculated. The core was sealed, with the conditions reduced to laboratory conditions, and then the core was taken out and weighed to calculate the irreducible water saturation of the core(d)
Simultaneous injection of gas and water: the gas pressure was constantP1, and water was simultaneously injected at a constant flow rate of qw/20. When the system reached pressure equilibrium, the gas flow rate was recorded, and the effective permeability of the water and gas phases was calculated. Then, the core was weighed following the method mentioned in the previous step, and the water saturation was calculated(e)
The water flow rate was adjusted toqw/10, and the gas pressure was kept constant P1. Then, the abovementioned step d was repeated(f)
The gas source was closed, water was injected with a flow rate ofqw, and then the water-phase relative permeability under residual gas saturation (Sgr) was calculated


## 2.2.1. Experimental Setup

Figure1 shows the simulated displacement equipment used for providing high temperature and high reservoir pressure in the test. The system mainly includes displacement pump, humidifier, core holder, gas–water separator, and gas–water metering device.Figure 1
Flow chart of gas–water phase permeability test by the improved steady-state method.


## 2.2.2. Experimental Process

(a)
By testing gas permeability of rock specimens under different backpressures, the pressure valuePN (under which gas permeability does not change with pressure) was obtained(b)
A core saturated with formation water was placed in a core holder at 95°C and the backpressure ofPN. Formation water was passed through the rock specimen at the constant flow rate (qw). When the system reached stability, the upstream pressure (P1) was recorded, and water permeability was calculated(c)
Water driven by gas: gas was injected into the core to gradually increase upstream pressure toP1. Displacement was continued at constant pressure P1 until no water was produced, and the gas-phase permeability with irreducible water (Swc) was calculated. The core was sealed, with the conditions reduced to laboratory conditions, and then the core was taken out and weighed to calculate the irreducible water saturation of the core(d)
Simultaneous injection of gas and water: the gas pressure was constantP1, and water was simultaneously injected at a constant flow rate of qw/20. When the system reached pressure equilibrium, the gas flow rate was recorded, and the effective permeability of the water and gas phases was calculated. Then, the core was weighed following the method mentioned in the previous step, and the water saturation was calculated(e)
The water flow rate was adjusted toqw/10, and the gas pressure was kept constant P1. Then, the abovementioned step d was repeated(f)
The gas source was closed, water was injected with a flow rate ofqw, and then the water-phase relative permeability under residual gas saturation (Sgr) was calculated


## 2.3. Experimental Data Processing Methods

Considering the variation of water and gas volume with temperature and pressure, it is necessary to adjust water and gas production at room temperature and normal pressure to that at high temperature and high pressure. Therefore, the formula for calculating the gas–water-phase permeability curve by a steady-state method was improved as follows:The volume of liquid under formation conditions is represented as follows:(1)Qw=QL0⋅Bw,where Qw denotes the flow rate of water under experimental conditions, cm3·s-1, QL0 is the flow rate of water under room temperature and normal pressure, cm3·s-1, and Bw is water volume coefficient under experimental conditions.Therefore, after reaching stability, according to Darcy’s law, liquid-phase permeability is represented as follows:(2)kw=QL0BwμwLAp1−p2,where kw is the liquid-phase permeability, cm2, μw denotes water-phase viscosity under experimental conditions, mPa·s, L and A are the core length and cross-section, with the units of cm and cm2, respectively, and P1 and P2 denote upstream and downstream pressure of core holder at steady gas and water discharge, respectively, 10-1 MPa.Figure2 shows schematic illustration for gas permeability, and Darcy’s formula is expressed as follows:
(3)Qg=−kgAμgdpdL,where Qg is the flow rate of gas under experimental conditions, cm3·s-1, kg is the gas permeability, cm2, μg denotes gas viscosity under experimental conditions, mPa·s, A represents core cross-section, cm2, and dp/dL is the pressure gradient, 10-1 MPa·cm-1.Figure 2
Schematic representation of flow process.From the gas state formula, on the ground,(4)p0Qg0=nRT0,where p0 is the atmospheric pressure, 10-1 MPa, Qg0 is the flow rate of gas under room temperature and normal pressure, cm3·s-1, n is the amount of substance, mol, R denotes proportionality coefficient, J·(mol·K)-1, and T0 is the room temperature, K.Under the ground,(5)pQg=nzRT,where p is the experimental mean pressure, 10-1 MPa, Qg is the flow rate of gas under experimental condition, cm3·s-1, z is the compression factor of gas at experimental temperature and pressure, and T is the experimental temperature, K.Then,(6)Qg=p0Q0zTpT0=−kgAμgdpdL.Gas permeability could be obtained by separating the calculus of variations as follows:(7)kg=2μgp0Qg0zTLAT0p12−p22.In this study, the gas-phase permeability under irreducible water is considered as absolute permeability:(8)krg=kgk,(9)krw=kwk,where krg and krw denote relative permeability of gas and water, respectively, and k is the absolute permeability, cm2. Average water saturation is as follows:
(10)Sw=mi−moVpρwBw,where Sw indicates mean water saturation, mi and m0 denote core mass before and after experiment, respectively, g, ρw represents density of water at room temperature, g·cm-3, and Vp is the pore volume of sample, cm3.


## 3. Results and Discussion

### 3.1. Relation between Gas Permeability and Average Core Pressure

Average pore pressure could affect core permeability due to the Klinkenberg effect [2, 30]. Therefore, in this study, the influence of pressure on gas permeability was tested before conducting experiments on relative permeability.The experimental results show that gas permeability first decreased rapidly with the increase of average pore pressure and then decreased slowly with the further increase of the pressure. When a specific pressure was reached, there was no significant change in permeability, even with the continuous increase in the pressure. Figure3 shows that when the average pressure reached 4.25 MPa, the change in permeability became negligible. Therefore, it is reasonable to set backpressure of 5.0 MPa to eliminate slippage effect for gas–water relative permeability test, which is closer to formation conditions.Figure 3
Change of gas permeability with test pressure.


### 3.2. Comparison of Gas–Water Phase Permeability Curves under Different Backpressures

In order to verify the effectiveness of this method, experiments were conducted on the relative permeability of core 7 under different backpressure conditions, as shown in Figure4. The results reveal that there is no significant difference among the three curves for the water phase, which indicates that pressure has no apparent influence on water-phase relative permeability. Noteworthy, relative permeability curves at the backpressure of 5 and 28 MPa are the same in gas and water phases, thus proving the feasibility of the new method. Compared with the gas-phase relative permeability curve under normal pressure, the two-phase penetration area increased, the gas-phase relative permeability became slightly larger, and the irreducible water saturation was lower than that at the normal pressure, which shows that pressure significantly influences gas-phase relative permeability at low pressure.Figure 4
Influence of pressure on gas–water relative permeability curves.The improved method can provide the accurate gas–water permeability under the condition of lower pressure than the actual reservoir pressure, which is of great significance to design development scheme for tight gas reservoir, and for the prediction of production performance and reservoir simulation.


#### 3.2.1. Effects of Different Permeabilities on Gas–Water Permeability Curve

Figure5 shows the test results of the gas–water permeability curve of core No. 4. With the increase of water saturation, the gas-phase relative permeability shows the variation trend of first decreasing rapidly and then decreasing slowly, while the water-phase relative permeability first increases slowly and then rapidly. The gas–water two-phase penetration area of the low-permeability core was relatively narrow, with irreducible water saturation of 63.69% and residual gas saturation of 14.95%. The water saturation corresponding to the isotonic point was higher (about 78%), while the gas–water-phase relative permeability at the isotonic point was lower, about 0.12.Figure 5
Results of the gas–water permeability curve of core No. 4.Figure6 shows gas–water permeability curves of three cores with different permeabilities. The changing trend of the gas–water permeability curve was the same for conditions with different core permeabilities, and the characteristic parameters of the gas–water permeability curve changed significantly. The gas-phase permeability curve moved to the right in the same coordinate system with the decrease in permeability. The irreducible water saturation increased, the residual gas saturation decreased, the isotonic point moved to the right, and the two-phase region narrowed. At low permeability, the water-phase relative permeability at residual gas saturation increased compared to gas-phase relative permeability at irreducible water saturation [30, 31].Figure 6
Gas–water permeability curves of cores with different permeabilities.X-ray analysis results show that the average clay content of cores with a permeability greater than 0.13 mD was 14%, and that of cores with permeability less than 0.13 mD was 8%. Clay minerals are susceptible to speed sensitivity. The gas flow rate was higher than that of water; thus, gas was more susceptible to speed sensitivity when passed through the pores. Moreover, clay content in low permeability core was high; thus, it was easy for the clay minerals to plug the pores, which led to the decrease of gas permeability.The characteristic parameters for gas–water relative permeability of cores with different permeabilities are listed in Table2, and the results are presented in Figure 7.Table 2
Experiments results of the core samples.
Core No.kg/10-3μm2SwcSgrAbsolute permeabilitykgSwc/10-3μm2krwSgrTwo-phase flow range11.8960.5100.1390.4800.2750.35121.0240.5310.1590.9770.5250.31030.7030.6250.1350.8130.7830.24040.5160.6370.1500.6290.3100.21450.3600.6560.0820.9210.9660.26160.1940.7060.0310.9240.5730.26470.1300.7200.0810.3071.6290.20080.0900.7530.0480.5080.6250.198Figure 7
Relationship between characteristic value and permeability of gas–water relative permeability curves: (a) relationship betweenSwc/Sgr and kg and (b) relationship between krwSgr/two-phase flow area and kg.
(a)(b)Figure7(a) exhibits that the irreducible water saturation increases, and residual gas saturation decreases with the decrease in permeability. Notably, all rocks are hydrophilic; therefore, water is the wetting phase, and gas is the nonwetting phase. Before the test, rock was saturated with water, and thus water occupied all pores and throats. When the gas entered the pores under external pressure, the gas could only overcome the capillary force and enter the main pore throat because of the preoccupation of all the percolating channels with water. The smaller the rock permeability, the fewer the larger pore throats. When water reentered the core and displaced the gas, the gas in the mainstream channel could be easily carried away with only a small amount left. Therefore, the smaller permeability induces minor residual gas saturation.The two-phase flow area narrowed with the decrease in the core permeability (Figure7(b)). The two-phase flow area reflects the flowability of two-phase fluid in the pore. The decrease of the two-phase flow area indicated a decrease in pore size and poor pore connectivity. Figure 7(b) demonstrates that the water-phase relative permeability under residual gas saturation tends to increase gradually with the decrease of rock permeability. When core permeability was below 0.13×10−3μm2, the water-phase relative permeability at residual gas saturation was higher than gas-phase relative permeability at irreducible water saturation. This indicates that the lower permeability induces an increased influence of irreducible water saturation on gas permeability.The relationship between relative permeability and water saturation is shown in Figure8. Clearly, the curve is linear in the semilogarithmic coordinate diagram and can be described by the relation lnkrg/krw=aSw+lnb, where a and b are constants [32–34]. With the increase of water saturation, the relative permeability ratio of the gas–water phase decreases exponentially. When the ratio is 1, the corresponding saturation is the water saturation at the isotonic point. Moreover, the core permeability decreases, and the isotonic point moves to the right. Further, the slope of the eight curves is higher, which indicates that the relative permeability ratio of gas to water decreases rapidly, and the gas-phase permeability is poor. The slope increases gradually with the decrease of permeability, indicating that the smaller permeability induces a lower gas-phase flow capacity.Figure 8
Relationship betweenkrg/krw and Sw of cores with different permeabilities.


## 3.1. Relation between Gas Permeability and Average Core Pressure

Average pore pressure could affect core permeability due to the Klinkenberg effect [2, 30]. Therefore, in this study, the influence of pressure on gas permeability was tested before conducting experiments on relative permeability.The experimental results show that gas permeability first decreased rapidly with the increase of average pore pressure and then decreased slowly with the further increase of the pressure. When a specific pressure was reached, there was no significant change in permeability, even with the continuous increase in the pressure. Figure3 shows that when the average pressure reached 4.25 MPa, the change in permeability became negligible. Therefore, it is reasonable to set backpressure of 5.0 MPa to eliminate slippage effect for gas–water relative permeability test, which is closer to formation conditions.Figure 3
Change of gas permeability with test pressure.


## 3.2. Comparison of Gas–Water Phase Permeability Curves under Different Backpressures

In order to verify the effectiveness of this method, experiments were conducted on the relative permeability of core 7 under different backpressure conditions, as shown in Figure4. The results reveal that there is no significant difference among the three curves for the water phase, which indicates that pressure has no apparent influence on water-phase relative permeability. Noteworthy, relative permeability curves at the backpressure of 5 and 28 MPa are the same in gas and water phases, thus proving the feasibility of the new method. Compared with the gas-phase relative permeability curve under normal pressure, the two-phase penetration area increased, the gas-phase relative permeability became slightly larger, and the irreducible water saturation was lower than that at the normal pressure, which shows that pressure significantly influences gas-phase relative permeability at low pressure.Figure 4
Influence of pressure on gas–water relative permeability curves.The improved method can provide the accurate gas–water permeability under the condition of lower pressure than the actual reservoir pressure, which is of great significance to design development scheme for tight gas reservoir, and for the prediction of production performance and reservoir simulation.


### 3.2.1. Effects of Different Permeabilities on Gas–Water Permeability Curve

Figure5 shows the test results of the gas–water permeability curve of core No. 4. With the increase of water saturation, the gas-phase relative permeability shows the variation trend of first decreasing rapidly and then decreasing slowly, while the water-phase relative permeability first increases slowly and then rapidly. The gas–water two-phase penetration area of the low-permeability core was relatively narrow, with irreducible water saturation of 63.69% and residual gas saturation of 14.95%. The water saturation corresponding to the isotonic point was higher (about 78%), while the gas–water-phase relative permeability at the isotonic point was lower, about 0.12.Figure 5
Results of the gas–water permeability curve of core No. 4.Figure6 shows gas–water permeability curves of three cores with different permeabilities. The changing trend of the gas–water permeability curve was the same for conditions with different core permeabilities, and the characteristic parameters of the gas–water permeability curve changed significantly. The gas-phase permeability curve moved to the right in the same coordinate system with the decrease in permeability. The irreducible water saturation increased, the residual gas saturation decreased, the isotonic point moved to the right, and the two-phase region narrowed. At low permeability, the water-phase relative permeability at residual gas saturation increased compared to gas-phase relative permeability at irreducible water saturation [30, 31].Figure 6
Gas–water permeability curves of cores with different permeabilities.X-ray analysis results show that the average clay content of cores with a permeability greater than 0.13 mD was 14%, and that of cores with permeability less than 0.13 mD was 8%. Clay minerals are susceptible to speed sensitivity. The gas flow rate was higher than that of water; thus, gas was more susceptible to speed sensitivity when passed through the pores. Moreover, clay content in low permeability core was high; thus, it was easy for the clay minerals to plug the pores, which led to the decrease of gas permeability.The characteristic parameters for gas–water relative permeability of cores with different permeabilities are listed in Table2, and the results are presented in Figure 7.Table 2
Experiments results of the core samples.
Core No.kg/10-3μm2SwcSgrAbsolute permeabilitykgSwc/10-3μm2krwSgrTwo-phase flow range11.8960.5100.1390.4800.2750.35121.0240.5310.1590.9770.5250.31030.7030.6250.1350.8130.7830.24040.5160.6370.1500.6290.3100.21450.3600.6560.0820.9210.9660.26160.1940.7060.0310.9240.5730.26470.1300.7200.0810.3071.6290.20080.0900.7530.0480.5080.6250.198Figure 7
Relationship between characteristic value and permeability of gas–water relative permeability curves: (a) relationship betweenSwc/Sgr and kg and (b) relationship between krwSgr/two-phase flow area and kg.
(a)(b)Figure7(a) exhibits that the irreducible water saturation increases, and residual gas saturation decreases with the decrease in permeability. Notably, all rocks are hydrophilic; therefore, water is the wetting phase, and gas is the nonwetting phase. Before the test, rock was saturated with water, and thus water occupied all pores and throats. When the gas entered the pores under external pressure, the gas could only overcome the capillary force and enter the main pore throat because of the preoccupation of all the percolating channels with water. The smaller the rock permeability, the fewer the larger pore throats. When water reentered the core and displaced the gas, the gas in the mainstream channel could be easily carried away with only a small amount left. Therefore, the smaller permeability induces minor residual gas saturation.The two-phase flow area narrowed with the decrease in the core permeability (Figure7(b)). The two-phase flow area reflects the flowability of two-phase fluid in the pore. The decrease of the two-phase flow area indicated a decrease in pore size and poor pore connectivity. Figure 7(b) demonstrates that the water-phase relative permeability under residual gas saturation tends to increase gradually with the decrease of rock permeability. When core permeability was below 0.13×10−3μm2, the water-phase relative permeability at residual gas saturation was higher than gas-phase relative permeability at irreducible water saturation. This indicates that the lower permeability induces an increased influence of irreducible water saturation on gas permeability.The relationship between relative permeability and water saturation is shown in Figure8. Clearly, the curve is linear in the semilogarithmic coordinate diagram and can be described by the relation lnkrg/krw=aSw+lnb, where a and b are constants [32–34]. With the increase of water saturation, the relative permeability ratio of the gas–water phase decreases exponentially. When the ratio is 1, the corresponding saturation is the water saturation at the isotonic point. Moreover, the core permeability decreases, and the isotonic point moves to the right. Further, the slope of the eight curves is higher, which indicates that the relative permeability ratio of gas to water decreases rapidly, and the gas-phase permeability is poor. The slope increases gradually with the decrease of permeability, indicating that the smaller permeability induces a lower gas-phase flow capacity.Figure 8
Relationship betweenkrg/krw and Sw of cores with different permeabilities.


## 3.2.1. Effects of Different Permeabilities on Gas–Water Permeability Curve

Figure5 shows the test results of the gas–water permeability curve of core No. 4. With the increase of water saturation, the gas-phase relative permeability shows the variation trend of first decreasing rapidly and then decreasing slowly, while the water-phase relative permeability first increases slowly and then rapidly. The gas–water two-phase penetration area of the low-permeability core was relatively narrow, with irreducible water saturation of 63.69% and residual gas saturation of 14.95%. The water saturation corresponding to the isotonic point was higher (about 78%), while the gas–water-phase relative permeability at the isotonic point was lower, about 0.12.Figure 5
Results of the gas–water permeability curve of core No. 4.Figure6 shows gas–water permeability curves of three cores with different permeabilities. The changing trend of the gas–water permeability curve was the same for conditions with different core permeabilities, and the characteristic parameters of the gas–water permeability curve changed significantly. The gas-phase permeability curve moved to the right in the same coordinate system with the decrease in permeability. The irreducible water saturation increased, the residual gas saturation decreased, the isotonic point moved to the right, and the two-phase region narrowed. At low permeability, the water-phase relative permeability at residual gas saturation increased compared to gas-phase relative permeability at irreducible water saturation [30, 31].Figure 6
Gas–water permeability curves of cores with different permeabilities.X-ray analysis results show that the average clay content of cores with a permeability greater than 0.13 mD was 14%, and that of cores with permeability less than 0.13 mD was 8%. Clay minerals are susceptible to speed sensitivity. The gas flow rate was higher than that of water; thus, gas was more susceptible to speed sensitivity when passed through the pores. Moreover, clay content in low permeability core was high; thus, it was easy for the clay minerals to plug the pores, which led to the decrease of gas permeability.The characteristic parameters for gas–water relative permeability of cores with different permeabilities are listed in Table2, and the results are presented in Figure 7.Table 2
Experiments results of the core samples.
Core No.kg/10-3μm2SwcSgrAbsolute permeabilitykgSwc/10-3μm2krwSgrTwo-phase flow range11.8960.5100.1390.4800.2750.35121.0240.5310.1590.9770.5250.31030.7030.6250.1350.8130.7830.24040.5160.6370.1500.6290.3100.21450.3600.6560.0820.9210.9660.26160.1940.7060.0310.9240.5730.26470.1300.7200.0810.3071.6290.20080.0900.7530.0480.5080.6250.198Figure 7
Relationship between characteristic value and permeability of gas–water relative permeability curves: (a) relationship betweenSwc/Sgr and kg and (b) relationship between krwSgr/two-phase flow area and kg.
(a)(b)Figure7(a) exhibits that the irreducible water saturation increases, and residual gas saturation decreases with the decrease in permeability. Notably, all rocks are hydrophilic; therefore, water is the wetting phase, and gas is the nonwetting phase. Before the test, rock was saturated with water, and thus water occupied all pores and throats. When the gas entered the pores under external pressure, the gas could only overcome the capillary force and enter the main pore throat because of the preoccupation of all the percolating channels with water. The smaller the rock permeability, the fewer the larger pore throats. When water reentered the core and displaced the gas, the gas in the mainstream channel could be easily carried away with only a small amount left. Therefore, the smaller permeability induces minor residual gas saturation.The two-phase flow area narrowed with the decrease in the core permeability (Figure7(b)). The two-phase flow area reflects the flowability of two-phase fluid in the pore. The decrease of the two-phase flow area indicated a decrease in pore size and poor pore connectivity. Figure 7(b) demonstrates that the water-phase relative permeability under residual gas saturation tends to increase gradually with the decrease of rock permeability. When core permeability was below 0.13×10−3μm2, the water-phase relative permeability at residual gas saturation was higher than gas-phase relative permeability at irreducible water saturation. This indicates that the lower permeability induces an increased influence of irreducible water saturation on gas permeability.The relationship between relative permeability and water saturation is shown in Figure8. Clearly, the curve is linear in the semilogarithmic coordinate diagram and can be described by the relation lnkrg/krw=aSw+lnb, where a and b are constants [32–34]. With the increase of water saturation, the relative permeability ratio of the gas–water phase decreases exponentially. When the ratio is 1, the corresponding saturation is the water saturation at the isotonic point. Moreover, the core permeability decreases, and the isotonic point moves to the right. Further, the slope of the eight curves is higher, which indicates that the relative permeability ratio of gas to water decreases rapidly, and the gas-phase permeability is poor. The slope increases gradually with the decrease of permeability, indicating that the smaller permeability induces a lower gas-phase flow capacity.Figure 8
Relationship betweenkrg/krw and Sw of cores with different permeabilities.


## 4. Conclusions

(1)
By changing the simultaneous gas–water constant velocity injection mode to gas constant pressure injection and liquid constant flow injection, respectively, an improved steady-state method for determining the gas–water relative permeability of low-permeability sandstones was proposed in this study. This method simulates the formation temperature and determines the backpressure value when the gas permeability no longer changes with the average pore pressure. With this pressure value considered as backpressure, gas was injected at constant pressure, water was injected at constant flow, and relative permeability was calculated by using Darcy’s formula. Notably, this method could avoid the errors caused by volume measurement in the unsteady-state method and the errors caused by inaccurate control of gas flow rate in the traditional steady-state method(2)
There was no obvious difference between the gas water relative permeability curve measured by this method and that under formation conditions. Compared with the test method at normal pressure, the relative permeability of the water phase did not exhibit any significant change, the gas-phase relative permeability was larger, and the two-phase flow area was wider, which indicates that pressure significantly influences gas-phase relative permeability at low pressure(3)
With the decrease in the core permeability, relative permeability curve, and isotonic point moved to the right, irreducible water saturation gradually increased, and residual gas saturation decreased. When core permeability was below 0.13 mD, the water-phase relative permeability under residual gas saturation was higher than the gas-phase relative permeability at irreducible water saturation



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*Source: 1521837-2022-06-08.xml*