Experimental Determination of Gas Relative Permeability Considering Slippage Effect in a Tight Formation

Abstract

In this paper, the gas relative permeability considering slippage effect has been experimentally examined under various experimental conditions (i.e., ambient, high confining pressure, and high temperature). Experimentally, Klinkenberg permeabilities of 12 core samples have been measured by using steady-state flow experiment. It has been found that the Klinkenberg permeability is independent of the experimental temperature and dramatically decreases as confining pressure is increasing. Furthermore, linear correlations have been newly developed between the Klinkenberg permeability and the gas-measured permeability under various conditions. Subsequently, the developed correlations are correspondingly applied to calibrate the gas relative permeability. It has been found that the gas relative permeability can be overestimated without consideration of the slippage effect, i.e., Klinkenberg effect. In addition, the newly developed correlations have been applied to analyze the sensitivity of gas-water relative permeability to gas-measured permeability, confining pressure, and temperature. It is demonstrated that mobile water greatly alleviates the gas relative permeability in comparison to irreducible water. Although an increased confining pressure simultaneously reduces the effective water phase and gas phase permeability, the gas relative permeability increases and the water relative permeability decreases as the confining pressure increases. It is attributed to the fact that the effective water phase permeability is more sensitive to the confining pressure. Given an elevated experimental temperature, the gas relative permeability is reduced while the water relative permeability is enhanced, implying the significance of temperature effect on gas-water relative permeability measurements.

Evolutionary Model and Experimental Validation of Gas-Bearing Coal Permeability under Negative Pressure Conditions

“…According to the principle of energy minimum, coal reduces its surface chemical energy by adsorption of gas, forming a certain attraction potential, and the mutual attraction between molecules (carbon atoms) on the surface of the coal matrix and molecules (carbon atoms) inside the matrix decreases, leading to the expansion of the coal matrix, while the desorption process is the opposite, and the chemical energy of the coal surface increases the contraction of the coal matrix. Many scholars have theoretically derived and verified by laboratory experiments combining thermodynamics and elastic dynamics 35,36 and found that the adsorption of gas leads to two-thirds of the total strain in the coal matrix expansion strain, as shown in formula 8…”

“…According to the principle of energy minimum, coal reduces its surface chemical energy by adsorption of gas, forming a certain attraction potential, and the mutual attraction between molecules (carbon atoms) on the surface of the coal matrix and molecules (carbon atoms) inside the matrix decreases, leading to the expansion of the coal matrix, while the desorption process is the opposite, and the chemical energy of the coal surface increases the contraction of the coal matrix. Many scholars have theoretically derived and verified by laboratory experiments combining thermodynamics and elastic dynamics , and found that the adsorption of gas leads to two-thirds of the total strain in the coal matrix expansion strain, as shown in formula ε normalm = 4 italica ρ R T ln ( 1 + b p ) 9 V normalm E normalm where ε m denotes the expansion strain and is a dimensionless value, a is the Langmuir model gas adsorption volume constant in m 3 /t, b is the gas adsorption constant in the Langmuir model in MPa –1 , ρ is the apparent density of coal in t/m 3 , R is the gas constant, taken as 8.31415 J/(kg K), T is the experimental temperature in K, V m is the molar volume of gas, taking a value of 22.4 L/mol in the standard state, and E m is the modulus of elasticity of the coal matrix in MPa.…”

“…Some scholars calculated the quantitative relationship between strain, specific surface area, and surface free energy of the coal body under the action of gas by the principle of elasticity mechanics, and the principle of energy conservation can be shown in formula . , ε normalc = 2 normalΔ π S ρ 3 E normalm …”

Thermal Expansion and Adsorption Characteristics of Coal Based on Temperature Change and Its Influence on the Slippage Effect

“…In addition to the stress state and seepage gas, the temperature also changes the slippage effect. The temperature is higher, and the slippage effect is more obvious. ,, Gupta et al found that compared to the temperature, the impact of pore pressure on the gas slip is much greater, and the effect of temperature on gas slip becomes more obvious at low pore pressure. As for the influence mechanism of temperature on the slippage effect, Qu et al believed that as the temperature rises, in addition to the change of the mean free path of gas will make the change in the slippage effect, and the thermal expansion deformation will also cause the enhancement of the slippage effect.…”

Applicability Analysis of Klinkenberg Slip Theory in the Measurement of Tight Core Permeability

“…Additionally, Yue et al [50] measured the permeability of tight cores under the average pressure of 0-1 MPa, and they found that the measured apparent permeability was bigger than the value predicted by Klinkenberg slip theory, unlike other scholars. Liu et al [51] carried out gas-water two-phase seepage experiments on compact cores. They believe that the relative permeability of gas phase may be overestimated if slippage effect is not dealt with in the process of determining effective gas permeability.…”