Influences of test method and loading history on permeability of tight reservoir rocks

Highlights

• Characteristics of the downstream pressure build-up curve are analysed.

• Pseudo pressure-based permeability is lower than that for real pressure.

• Ignoring the sample pore volume results in an underestimate of permeability.

• Water permeability is lower than that for gas due to the water-rock interactions.

Abstract

Steady-state and unsteady-state (downstream pressure build-up) gas permeability tests were conducted on low permeability siltstone at a series of upstream pressures during the loading and unloading processes. The characteristics of downstream pressure build-up curves are analysed in detail, and the permeability is calculated based on the data in the stabilization stage. Analysing approaches with and without consideration of the sample pore volume are used to obtain the unsteady-state permeability for both the real pressure and the pseudo pressure. Findings suggest that the permeability based on the pseudo pressure is generally lower than that based on the real pressure, with their ratio ranging from 0.75 to 0.98. The sample pore volume corrected permeability is 1.42–1.51 times of that without the consideration of sample pore volume. The apparent steady-state gas permeability is higher than the sample pore volume corrected permeability due to slip flow, while its intrinsic permeability is lower as the pore pressure is smaller in the steady-state test. The permeabilities decrease with the confining pressure in the loading path especially at lower confinements, while only part of the reductions is recovered during the unloading process. Increase of pore pressure enhances permeability under low confinement conditions. Water permeability is lower than gas permeability in steady-state test due to the water-rock interaction and the residual gas inside the sample.

Introduction

Explorations of unconventional oil and gas reservoirs have attracted more attentions in recent years [1]. Their deep burial depths result in low porosities and permeabilities, therefore artificial fractures are often created by hydraulic fracturing for field exploration [2]. However, majority of the rock mass remains intact and the long-term production depends on the matrix permeability. Compared with conventional reservoir rocks, the accuracy of flow rate measurement suffers and the time duration is prolonged for steady-state permeability test of unconventional reservoir rocks. Therefore, many researchers used unsteady-state permeability tests for tight rocks, which are based on pressure variations instead of the flow rate measurement [3].

The pulse decay method proposed by Brace et al. [4] is a widely used unsteady-state approach to obtaining the permeability of tight rocks. It is more representative of the in situ pressure conditions, and the variation of the sample pore pressure is small resulting in relatively stable fluid properties. Furthermore, only the reservoir pressures need to be recorded which simplifies the testing process. However, Brace et al. [4] ignored the sample storage volume, which results in the underestimation of permeability [5]. Dicker and Smits [6] proposed an analytical approach which takes the sample pore volume into consideration. Researchers found that its discrepancy with Brace’s method increases with the porosity [7]. Metwally and Sondergeld [8] made the experiment and analysis simpler by observing the downstream pressure build-up from the atmosphere condition while maintaining a constant upstream pressure. Both steady-state and unsteady-state permeability test methods can be used to measure the permeability of tight rocks, but the obtained results are usually different. Some researchers found that the permeability measured by the pulse decay method is higher than that measured by the steady-state method [9,10], while others observed the opposite trend [11,12]. Therefore, further investigation is needed to compare the permeability derived by the steady-state and unsteady-state methods.

In addition to permeability test methods [9,11,13,14] and their analysis approaches [5,7], laboratory-measured permeability also depends on the fluid properties [5], [16], [41]. It is found that gas permeability is always higher than liquid permeability for tight rocks, which is attributed to the gas slip flow at the surface of solid wall [17]. The relationship between the gas apparent permeability and intrinsic permeability is expressed by Eq. [1], which shows that gas permeability is linearly related to the reciprocal of the gas pressure. The slippage effect is determined by the gas mean free path and pore radius, while the gas mean free path is a function of gas type, pressure, viscosity and temperature as shown in Eq. [2]. The mean pore radius can be obtained from mercury intrusion porosity test [18], or statistical 2-D or 3-D image analysis [19]. In addition to the first-order Klinkenberg correction, second-order [20] or even higher-order corrections [21] are proposed to account for the relationship between gas permeability and the average pore pressure.

$$k_g=\left(1+\frac{b}{P_a}\right)k_{\infty }=\left(1+\frac{4c\lambda }{r_m}\right)k_{\infty }$$

$$\lambda =\frac{\mu }{P}\sqrt{\frac{\pi R_{g}T}{2M}}$$

where, $k_g$ and $k_{\infty }$ are the gas’s apparent and intrinsic permeabilities respectively, $b$ is the gas slip coefficient, $P_a$ is the average gas pressure, $\lambda$ is the gas mean free path, $r_m$ is the mean pore radius, $c$ is a constant close to unity, $\mu$ is the gas viscosity, $R_g$ is the universal gas constant, $T$ is the absolute temperature, $M$ is the gas molecular mass, and $P$ is the gas pressure.

Gas properties, like viscosity and compressibility factor, change significantly with pressure. Therefore, pseudo pressure was proposed by Al-Hussainy, Rafi et al. [22] to account for the variations of gas property with pressure, especially for tests with high pressure gradients. However, few studies have uncovered the differences between permeabilities based on pseudo pressure and real pressure.

Effective stress is the main influencing factor for variations of intrinsic permeability [23,24], and unconventional oil and gas reservoirs are more sensitive to changes in the effective stress than conventional formations. The laboratory-measured sandstone permeability varies between 10⁻¹⁴ to 10⁻¹³ m², while the silty shale permeability varies from 10⁻²⁰ to 10⁻¹⁵ m² under the same confining pressure range [25]. Changes of matrix porosity and permeability with the effective stress are usually expressed by exponential or power relationships [15,26]. Permeability and porosity are not only functions of the current stress but also depend on the stress history. Researchers found that porosity and permeability are always lower in the unloading path than in the loading path at the same effective stress due to inelastic deformation [25], and their stress sensitivities are also smaller in the unloading path.

Although both steady-state and unsteady-state permeability tests can be used for tight rocks, their comparisons are still not very clear. The analysis of unsteady–state permeability tests needs to be better understood for their appropriate use. The influences of confining pressure and pore pressure on permeability need further investigation in order to better predict the gas and oil production during exploration.