Geofluids

Volume 2019, Article ID 7474587, 15 pages

https://doi.org/10.1155/2019/7474587

## Interaction of Cleat-Matrix on Coal Permeability from Experimental Observations and Numerical Analysis

^{1}State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, China^{2}State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China^{3}School of Mechanical and Mining Engineering, The University of Queensland, St. Lucia, QLD 4074, Australia^{4}Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang 110004, China

Correspondence should be addressed to Zhongwei Chen; ua.ude.qu@nehc.iewgnohz

Received 9 July 2019; Revised 2 October 2019; Accepted 8 October 2019; Published 18 November 2019

Academic Editor: Paolo Madonia

Copyright © 2019 Chunguang Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Gas transport through porous coal contains gas laminar flow in the cleat network and gas adsorption/diffusion in the matrix block. Since permeable capacity of the cleat is greater than that of the matrix, change of the matrix pressure readily lags behind change in the cleat pressure. Such unsynchronized pressure changes can result in a complex compatible deformation of a cleat-matrix system, significantly affecting the coal permeability. In this paper, we investigated the cleat-matrix interaction on coal permeability by using a modified pressure pulse decay method integrated with numerical analysis. The experimental results indicate that the bulk volume of the coal sample rapidly expanded at the beginning of gas injection, and then the volume expansion rate of the coal sample slowed down as the downstream pressure of the coal sample gradually equilibrated with the upstream pressure. During this process, the coal permeability was observed to gradually decrease with time. Numerical analysis results indicate that gas transport from the cleat to the matrix can attenuate the differential pressure between the cleat and the matrix. A smaller ratio of initial matrix permeability to initial cleat permeability can prolong decay duration of the differential pressure inside the cleat-matrix system. Although the coal sample is subjected to a stress-controlled condition, the coal permeability response to gas diffusion is closer to the case using a constant volume boundary. The dynamic change of coal permeability is significantly affected by the cleat-matrix interaction, in cases where the short-term change is mainly attributable to the cleat network and the long-term change is controlled by matrix swelling/shrinkage.

#### 1. Introduction

Coal bed methane is an unconventional gas whose storage/transport in a coal reservoir is different from that in a carbonate reservoir. Given that coal permeability is predominated by cleats, it is commonly assumed that the Darcy flow is a result of flow in the cleat system and that the contribution of flow in the coal matrix to the Darcy flow can be neglected. According to considerable laboratory measurements and field observations, coal permeability is controlled by two factors: the pore pressure change can alter effective stress and consequently increase or decrease the bulk volume of the coal [1–7]; gas adsorption/desorption can swell or shrink the coal matrix, which can compress or close the cleat aperture. Of these two factors, gas adsorption has a greater impact on coal permeability. During coal bed methane extraction, gas in the cleat network first discharges, causing a drop in the reservoir pressure, which in turn leads to gas transfer due to gas gradients between the matrix and the cleat. Current assumptions on the mass transfer between the matrix and the cleat can be categorized into (i) equilibrium state, (ii) nonequilibrium and pseudosteady state, and (iii) nonequilibrium and nonsteady state. (i)The equilibrium state assumption is that gas adsorption/desorption on the matrix occurs instantaneously. Here, the matrix pressure is always equal to the cleat pressure [8–10]. Under this assumption, the effective stress of the bulk coal is usually expressed as , where is the effective stress, is the total stress, is the Biot coefficient, and is the pore pressure. In order to simplify the calculation, is set to unity. This means that interconnected pores of the coal matrix is well developed. The gas-bearing coal matrix provides a mass source term for the gas flow equation [11] via gas adsorption/desorption. This assumption ignores the gas supply hysteresis effect from the matrix blocks and consequently underestimates coal permeability(ii)The nonequilibrium and pseudosteady state assumption is that a time-dependent gas transfer is driven by pore pressure gradient between the coal matrix and the cleat [12]. The cleat pressure shares the same finite mesh element with the matrix pressure, which is relevant to the numerical modeling of coal permeability evolution. This assumption not only can investigate gas mass exchange between the matrix and the cleat but also can simulate the gas diffusion process in the coal matrix [13–15]. The advantage of this assumption is that it is applicable to dual-porosity media. However, the pseudosteady state assumption is unable to interpret inhomogeneous deformation behavior of the matrix block when the size of the coal matrix becomes larger(iii)The nonequilibrium and nonsteady state assumption is that coal matrix pressure changes dynamically and the gas flow rate is proportional to the pressure gradient. Under this assumption, both the matrix pressure and the cleat pressure can be set as an independent variable in their respective computational domain [16–21]. The geomechanic properties of the matrix block such as size and permeability also affect the tempospatial distribution of pore pressure. For instance, the pressure gradient attenuation will become faster when the matrix permeability increases. As a result, the gas transfer between the matrix and the cleat is likely to decay rapidly. In this case, deviation from the equilibrium state model (Assumption I) and the nonequilibrium model (Assumption II) may be negligible. In fact, gas permeability of the coal matrix is extremely low. Moreover, the coal matrix size is not small enough to ignore. If the equilibrium state model is used, then the gas flow in the cleat is possibly overestimated. Therefore, it is necessary to study tempospatial gas transfer and its impact on the evolution of porosity/permeability of coal

Most permeability measurements on porous media are required to be conducted when the pore pressure reaches the equilibrium state [22–30]. This requirement suggests that both the matrix pressure and the cleat pressure are held constant during testing. Micro-CT imaging shows that the pore structure of the coal matrix consists of connected pores and nonconnected pores [31, 32]. The gas pressure of the connected pore system is readily increased up to the cleat network pressure, while the gas pressure in nonconnected pores remains at the initial value. Under such conditions, the pore pressure of coal is characterized by nonlinear distribution. Gas diffusion in the matrix takes a longer time to reach the equilibrium state, which causes the matrix pressure to lag behind the cleat pressure. The unsynchronized changes in effective stress between the matrix and the cleat can alter coal permeability by the matrix deformation narrowing/widening the cleat aperture. To resolve these issues, several researchers introduced a deformation coefficient into the matchstick model to evaluate the impact of adsorption-induced deformation on the cleat aperture [33–36]. Although these models can investigate the cleat-matrix interactions induced by matrix swelling, the effective stress-controlled matrix deformation on coal permeability has received little attention. Therefore, it is challenging to create accurate reservoir simulations of this behavior. This permeability variation is also important for enhanced coal bed methane such as N_{2} and CO_{2} that are injected to improve recovery of reservoir gases.

In our previous studies [37, 38], gas permeability evolution resulting from competition between gas adsorption effect and mechanical compression has been investigated by using numerical modeling. We also observed the deformation evolution of porous structure of coal sample during gas injection process [39]. It is experimentally found that gas convection between the matrix and the cleat can dynamically control bulk deformation of coal. These findings reveal the gas permeability change induced by gas unsteady flow process. Conventional laboratory permeability measurements only provide relation of permeability and gas pressure/effective stress, which can estimate cleat compressibility under steady-state flow condition.

Therefore, in this paper, we modify the pulse decay method [40, 41] by intermittently measuring coal permeability under two geomechanical conditions: constant confining stress and constant differential pressure, respectively. It is aimed at revealing the impact of dual-pore structure deformation on gas permeability change, due to gas transport from unsteady-state to steady-state flow. In order to minimize the sorption-induced swelling effect on solid deformation, this paper uses helium to measure coal permeability. This method can precisely evaluate the interaction of gas seepage/diffusion and porous structure deformation. Combined with the numerical simulation method, cleat-matrix interaction on the dynamic evolution of coal permeability is investigated for gas flowing from an unsteady state to a steady state. The present work also gives insight into how the evolution of coal permeability is associated with the dual-pore pressure system.

#### 2. Experimental

##### 2.1. Coal Sample and Test Equipment

Coal test samples were collected from the Juye coalfield in Shandong Province in eastern China. The microscopic physical parameters are listed in previous work [39]. Permeability measurements are completed on high-volatile bituminous coal (2.5 cm in diameter and 5.0 cm in length) cored from a block collected from the Juye coalfield in eastern China. To obtain distribution characteristics of coal cleat, the full-sized sample was scanned by using Nano-2000 X-ray machine. The X-ray machine has a resolution of 0.05 *μ*m. The CT voxel data were first converted into a series of CT images and then analyzed using Avizo software. A digital coal sample was reconstructed as shown in Figure 1(a). Threshold segmentation was used to define the cleat network of the coal sample from the voxel data (Figure 1(b)). Mean porosity along the axis of the coal sample is plotted in Figure 1(c). The mean porosity of the overall coal sample is 2.6%. It seems to indicate that the coal sample has few visible cleats.