Geofluids

Volume 2018, Article ID 7049830, 17 pages

https://doi.org/10.1155/2018/7049830

## A Fluid-Solid Coupling Mathematical Model of Methane Driven by Water in Porous Coal

State Key Laboratory of Coal Resources and Safe Mining, Xuzhou, Jiangsu 221116, China

Correspondence should be addressed to Weiyong Lu; moc.qq@155896984

Received 30 April 2018; Revised 14 July 2018; Accepted 25 July 2018; Published 16 September 2018

Academic Editor: Joaquín Jiménez-Martínez

Copyright © 2018 Bingxiang Huang and Weiyong Lu. 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

The existence of the water-driven-methane effect in gassy coal has been verified by field tests and laboratory experiments. However, a water-driven-methane mathematical model that considers methane adsorption and desorption has not yet been established. Based on the water-driven-methane process, a fluid-solid coupling mathematical model of methane driven by water is established. The model’s reliability is verified by the results of a water-driven-methane physical experiment and by using a solution of the COMSOL Multiphysics software. The space-time distribution regularities of the pore pressure, water-methane two-phase saturation, and pore pressure gradient in the water-driven-methane process are analysed. The results reveal the following. (1) The water-driven-methane fluid-solid coupling mathematical model for porous coal is reliable. (2) In the water-driven-methane process, there is an increasing zone and a decreasing zone of pore pressure in the coal sample. The increasing zone of pore pressure is closest to the side of the water inlet, and its area gradually decreases. The decreasing zone of pore pressure is closest to the side of the methane outlet, and its area gradually increases. Over time, the methane pressure in the increasing zone of pore pressure first increases and then decreases, and the methane pressure in the decreasing zone of pore pressure continuously decreases. The change (increase or decrease) rate of the methane pressure gradually decreases from both ends towards the middle of the coal sample. (3) The curve of the water saturation over time changes from a lower concave curve to a straight line, while the curve of the methane saturation with time changes from an upper convex curve to a straight line. The methane saturation in the decreasing zone of pore pressure is greater than that in the increasing zone of pore pressure. Over time, the water saturation of a specific point in space continuously increases while its methane saturation continuously decreases. Both of the increase rate of the water saturation and the decrease rate of the methane saturation gradually reduce over time. (4) The pore pressure gradient along the driving direction first decreases and then increases. The decreasing zone of the pore pressure gradient is located in the increasing zone of pore pressure, and the increasing zone of the pore pressure gradient is located in the decreasing zone of pore pressure. Over time, the pore pressure gradient at the side of the water inlet increases, and its increase rate decreases. The pore pressure gradient at the side of the methane outlet decreases, and its decrease rate decreases. The rate of increase in the pore pressure gradient at the side of the water inlet is greater than the rate of decrease in the pore pressure gradient at the side of the methane outlet.

#### 1. Introduction

During the process of water injection or hydraulic fracturing in gassy coal, the methane concentration of the airflow in the roadway clearly increases. This phenomenon is known as the water-driven-methane effect [1]. The existence of this phenomenon has been shown in laboratory experiments. The effect has both advantages and disadvantages in production practice. On the one hand, it can provide new ideas and technology for the exploitation of coalbed gas, and the hydraulic measures are used to eliminate methane outbursts. On the other hand, it can increase the methane concentration of the airflow in the roadway in addition to the methane content and methane pressure of the local region in the coal seam, which is detrimental to the prevention of coal and methane outbursts and methane explosions [2–7]. In fact, the negative effect of the water-driven-methane process has always existed, but it has not been an obvious cause of a disaster and has not attracted the attention of fieldworkers and researchers. With an increase in the exploitation depth of coal seam gas and coal resources, the positive and negative impacts of the water-driven-methane effect have become more and more obvious [8, 9]. However, at present, a mathematical model considering the effect of methane adsorption and desorption in coal has not been established to describe the water-driven-methane effect in coal. Therefore, during the water-driven-methane process, the distribution regularities of water and methane saturation in addition to the pore pressure and its gradient are still not clear. Therefore, to describe the water-driven-methane process accurately, a mathematical model should be established. Based on this mathematical model, the distribution regularities of water and methane saturation and of the pore pressure and its gradient can be analysed. A more comprehensive and in-depth understanding of the effect of this process will be useful for making the best use of this phenomenon’s advantages and overcoming its disadvantages.

At present, a mathematical model has been established to describe water-gas or water-oil two-phase driving processes in conventional porous medium reservoirs [10–12]. Of course, coal rock masses are also porous media. The water-driven-methane process in a coal rock mass also belongs to water-gas two-phase flow in porous media. However, the effect of methane adsorption and desorption in coal is significantly different from that of the water-driven-gas process in coal rock masses and conventional porous media. During the processes of water drainage, decreasing pressure, and desorption of coalbed methane, there is a stage of water-gas two-phase flow. A coupled fluid-solid mathematical model that considers the effects of methane adsorption and desorption has already been established to describe this stage, but it still cannot be directly used to describe the water-driven-methane process in coal because of the following reasons. (1) The coupled fluid-solid model of coalbed methane drainage is used to describe the process of water-methane two-phase flow with a decrease in the water pressure and adsorbed coalbed methane becoming free coalbed methane. However, a coupled fluid-solid model of methane driven by water is required to describe the process of driving out methane in coal by the injected water, which is injected into the coal. The boundary conditions of the above two processes are different. In addition, the injected water will also cause an increase in methane pressure, resulting in the transformation of free methane to adsorbed methane. (2) For the coupled fluid-solid mathematical models of coalbed methane drainage, some equations are only listed but not solved, and for the other equations, only the numerical solutions are offered. However, the reliability of these mathematical models has not been verified. Furthermore, these models primarily study the evolution regularities of reservoir permeability and methane production but rarely address the distribution regularities of water-methane two-phase saturation and of the pore pressure and its gradient [13–15].

To clarify the distribution regularities of water-methane two-phase saturation and the pore pressure and the mechanism of the pore pressure gradient in the water-driven-methane process, pure porous coal rock without fractures is selected in this study, thereby excluding the effects of fractured structures. Based on the elastic theory of porous media, the principle of effective stress, the principle of methane adsorption and desorption, and the principle of conservation of mass and Darcy’s law, a coupled fluid-solid mathematical model of methane driven by water is established. This model considers the effect of coalbed methane adsorption and desorption, the deformation field of the coal rock mass, and the seepage field of water and methane. The reliability of the mathematical model is verified by physical experiments of artificially suppressed briquette coal. On the basis of the mathematical model, a further study is developed on the distribution regularities of water-methane two-phase saturation and the pore pressure and the mechanism of the pore pressure gradient. Scientific understanding is provided for the water-driven-methane process in the porous coal.

#### 2. Conceptual Model

Porous coal rock (Figure 1(a)) is characterized by a pore structure of air pores and mold pores and similar structures (Figure 1(b)), which can provide space for free methane and adsorbed methane (Figure 1(c)) [16–18]. In a porous coal rock, there are many interconnected pores, which can be regarded as the migration channels of fluid [19, 20].