Multiscale model reduction for shale gas transport in fractured media

Abstract

In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our previous work [1], where we derived an upscaled model in the form of generalized nonlinear diffusion model to describe the effects of kerogen. To model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method [13,17]. In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. In [17], we developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations on a Cartesian fine grid. In this paper, we consider arbitrary fracture orientations and use triangular fine grid and developed GMsFEM for nonlinear flows. Moreover, we develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region represents the degrees of freedom needed to achieve a certain error threshold. Our approach is adaptive in a sense that the multiscale basis functions can be added in the regions of interest. Numerical results for two-dimensional problem are presented to demonstrate the efficiency of proposed approach.

Dynamic diffusion-based multifield coupling model for gas drainage

“…In most of the previous studies, the gas diffusion in coal was viewed as a steady-state process, and the timeliness of this process was not considered, that is, the diffusion coefficient was treated as a constant Akkutlu et a., 2016;Yan et al, 2014). However, the aforementioned analysis indicates that the unipore diffusion model is not suitable for coal masses, so a multistage diffusion model should be used to characterize the dynamic diffusion process.…”

“…where C M is molar mass of CH 4 , kg/mol；R is gas constant, J/(mol·K); 0 D is gas diffusion coefficient, m 2 /s, which in previous studies was generally viewed as a constant Akkutlu et al, 2016), but as discussed in section 1, it changes with the diffusion process. Based on related theoretical analyses and experimental investigations, put forward the dynamic diffusion coefficient model, which is given as follows:…”

Generalized Multiscale Finite Element Method for the poroelasticity problem in multicontinuum media

“…Multiscale finite volume method for solution of the poroelasticity problem is presented in [29]. Generalized multiscale finite element (GMsFEM) for solution of the flow problems in fractured porous media is considered in [30,31]. In [32,33], we considered construction of the coarse grid problem for poroelasticity problem in heterogeneous media.…”

A 3D coupled model of organic matter and inorganic matrix for calculating the permeability of shale

“…have noticed the big differences between kerogen and inorganic matrix in shale and treat them separately [10][11][12][13][14][15][16][17].…”

“…In 2015, Akkutlu [12] adopted multiscale asymptotic analysis method to solve a one-dimensional dual-porosity continuum model and concluded that both the gas in-place and gas production rate depend on the content of kerogen in shale. Later, Akkutlu [13] employed the generalized multiscale finite element method (GMsFEM) to add the influence of fractures and extended the model to 2D. Based on Akkutlu's work, in 2016, Alexey [14] divided shale into kerogen and inorganic matrix and solved both the continuum subdomains by nonlinear parabolic equation, then utilized numerical homogenization technique through local problems to calculate macro parameters.…”