Effects of natural micro-fracture morphology, temperature and pressure on fluid flow in coals through fractal theory combined with lattice Boltzmann method

Highlights

• Dominant channels in the natural micro-fractures greatly improve the permeability.

• Flow features in micro-fractures with various morphologies are quite different.

• Pressure and temperature have opposite influence on coal permeability.

Abstract

The fluid flow behaviors during the production of coalbed methane (CBM) are generally restricted by the pre-existing natural fractures in coal seams. To better understand the effect of natural micro-fracture morphology on the flow capability, nine coals collected from Ordos Basin were subjected to optical microscope observations to obtain micro-fractures morphology. And then, the box-counting method (BCM) was used to quantify the complexity of the micro-fracture network planar distribution. Besides, the lattice Boltzmann method (LBM) was adopted to simulate the flow in the complex micro-fracture network under different pressures and temperatures. Finally, factors affecting the flow capability in micro-fracture were elaborated. The results show that the micro-fractures generally present dendritic, reticular, filamentous and orthogonal structures. The natural micro-fracture morphology has a remarkable impact on flow behavior, in which the presence of dominant channels with a length of ~498.26 μm and a width of ~10.96 μm has a significant contribution to permeability, while the orthogonal micro-fracture network normally is not conducive to fluid flow. The fractal dimension extracted from the nine coals varies from 1.321 to 1.584, and the permeability calculated from LBM method varies from 0.147 to 0.345 D; in contrast to other studies, a non-monotonic change, an inverted U-shaped, of permeability on fractal dimension was observed. Moreover, permeability decreases as pressure increases and increases with increasing temperature due to the physical properties of methane and coal matrix. Therefore, this work may contribute to understanding the process of hydrofracturing and hydrothermal methods for improving CBM reservoirs during enhancing CBM recovery.

Introduction

Coalbed methane (CBM) is an essential component of the unconventional energy system due to its huge reserves, the reservoir of which is deemed as a dual-porous medium with pores in matrix and fractures/cleats [1], [2], [3]. Pores are generally associated with the processes of gas storage, desorption and diffusion [4]. For fractures, composed by micro-fractures and macro-fractures, they are the most important physical attribute governing gas flow in a CBM reservoir [5], [6]. Generally speaking, natural fractures primarily contributed to the permeability of coal, while the pores in coal matrix have very limited influence [7]. Extensive works including experiments and numerical simulations have been conducted to understand the performance of micro-fracture with the width at micron scale due to its importance on CBM production [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24]. Multiple experimental methods can be used to characterize micro-fractures properties, including low-field nuclear magnetic resonance (NMR) [8], [9], X-ray computed micro-tomography (X-ray μCT) [10], [11], [12] and the classic optical microscopy [13]. NMR is a non-destructive measurement and has been adopted successfully to detect and quantify the pore-fracture structure of coals [8], where the T₂ spectrum larger than 100 ms represents micro-fracture [9]. However, the detailed morphological features of micro-fracture are not accessible through NMR. X-ray μCT can provide realistic three-dimensional digital images and different components reconstruction [10], [11], [12]. Jenkins et al. [12] utilized X-ray μCT to dynamically measure the deformation behavior of tested rock under various loading conditions. However, X-ray μCT is expensive and time-consuming. Compared with the above techniques, the micro-fracture morphology observation by optical microscopy is not only economically suitable but also easy to obtain clear morphologies [13]. Besides, the fractal dimension can extend the qualitative description of the micro-fracture network to a quantitative description, which quantifies its complexity of distribution [14], [15]. The box-counting method (BCM) is one of the most popular algorithms [16], [17] to acquire the complexity, namely fractal dimension, through the images of pore-fracture structure. Herein, the BCM will be utilized to quantify the complexity of micro-fractures. On the other hand, direct numerical methods including finite difference method (FDM) [18], finite element method (FEM) [19] and finite volume method (FVM) [20] can be effectively adopted to simulate the flow behavior in micro-fracture networks. But these traditional simulation methods on the basis of Navier-Stokes equations require complicated meshing process to define the simulation domain and are challenging to solve complex geometric boundaries and have low parallel efficiency [18], [19], [20]. The lattice Boltzmann method (LBM), as a typical mesoscopic method, has a strong advantage in simulating the flow behavior of porous media with irregular boundaries [21], [22]. For example, Wang et al. [23] decomposed the three-dimensional fracture geometry into primary and secondary roughness through wavelet analysis, and investigated the role of the latter in the flow of rock fractures using LBM. And Zhao et al. [24] adopted LBM to discuss the effect of structure, surface roughness and aperture on flow in constructed fracture networks with rough surfaces.

The previous works on coal fractures/cleats can be classified into two parts: characterization of micro-fracture networks [8], [9], [10], [11], [12], [13] and the exploration of gas flow behavior in the micro-fracture networks [18], [19], [20], [21], [22], [23], [24]. It is significant for understanding the effect of natural fracture network on permeability through investigating the characteristics and distribution of natural fractures in coal. Besides, owing to the complexity of the natural fracture network in coal, much related work has performed flow simulation in the fracture network constructed by algorithms such as Voronoi tessellations method [24], [25] and Fracture Pipe Network Model (FPNM) [26], whereas rare researches have been conducted on the real complex natural fracture networks with specific morphologies. Many studies adopted an idealistic tube model with a circular cross-section to simplify the flow simulation [27], [28]. However, in most cases, the shape of micro-fractures is non-circular and irregular in coal, which is much complicated. Therefore, Yuan et al. [29] compared the realistic shape with the permeability characteristics of circle, square and equilateral triangular cross-sections, which found that the permeability of the network with circle cross-section is the highest, followed by the realistic shape, and the final are square and equilateral triangular. This finding corroborates the importance of accurately acquiring morphological features in micro-fracture networks.

In this study, we aim to investigate the flow behavior in natural micro-fractures with various morphologies under different pressures and temperatures. To detailed address the flow behavior in micro-fractures, the specific morphologies of natural micro-fractures were firstly obtained by optical microscopy. And then, the BCM was used to quantify the complexity of the natural micro-fracture network. After that, the LBM was applied to simulate the flow behavior in the natural micro-fracture network with specific morphologies in coals, and the controlling factors were revealed. This study may provide insights into the flow mechanisms of natural micro-fracture networks with complex morphologies in unconventional reservoirs.