Multidomain Two-Phase Flow Model to Study the Impacts of Hydraulic Fracturing on Shale Gas Production

Abstract

Hydraulic fracturing enhances the recovery of gas from ultralow permeability shales, into which water-based fracturing fluids, proppants, and activators are typically injected. However, the impacts of the existing complex multidomain response of a heterogeneous mineral and organic matrix and fractures on the resulting heterogeneity of reservoir transport properties caused by the hydraulic fracturing remain poorly understood. To address this defect, a multidomain multiphysics model is constructed to represent a two-phase flow within a three-component heterogeneous solid system (mineral and organic matrix and fractures) representing the functional complexity of the medium. This model partitions the shale reservoir into a stimulated reservoir volume (SRV) enclosed within an unstimulated reservoir volume (USRV). Different from the previous work, the shape of the SRV is treated as the spheroid instead of the rectangular shape and the size can be determined from the spatial distribution of microseismic events rather than artificially assumed. A two-phase flow model is established for both regions with the impacts of the effective stress variation on the fracture permeability considered and solved with a finite element formalism. The fidelity of the model is first verified using two field data sets from the Barnett and Marcellus shales with good fits achieved against time histories of production. Numerical studies then investigate the impacts of relevant parameters on shale gas production behavior; specially, the impacts of the effective stress and the existence of proppants are first reported. The variations in relative permeability and intrinsic permeability within the SRV are shown to dominate the early-time response of the gas flow rate. The long-term response is mainly dependent on the mass supply from the matrix system and the encapsulating USRV region. The effectiveness of hydraulic fracturing optimized as the SRV region is maximally extended in the horizontal direction and where the increase in permeability is a convex function against a concave function. The distal transport and placement of the proppant remarkably enhance the gas production rate and resist its decline as a result of the evolving high formation stress developed by pressure drawdown. For the selection of proppant type and placement, the resulting permeability and compressibility are of complementary importance as the first controls the initial gas flow rate, whereas the second determines the permeability trend with time. Proppant permeability decreases near-linearly for a constant compressibility but exponentially where compressibility is updated to represent the true response of the proppant pack. The proposed model applies a new approach for optimizing the hydraulic fracturing process and for analyzing the shale gas production behavior.

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“…Based on the Langmuir adsorption theory, the adsorbed gas mass can be defined as where θ is the surface coverage of the adsorption layer, and P L is the Langmuir pressure. Chen and Yang 57 developed a kinetic model based on the random walk theory, which can be expressed as 56 The adsorbed gas content in equilibrium, m e (p wall ), is determined using the Langmuir isotherm:…”

“…The aforementioned relationship can be solved through the iterations of the four subequation. 56 To this end, the General Form PDE Interface in the COMSOL with four variables (velocity vα in the three directions and the liquid pressure) was used. A desktop computer, with an Intel(R) Core (TM) i7-6700 @ 3.40 GHz as the CPU and 24.0 GB of memory, was used for the computation.…”

“…The mass transfer between the matrix and fracture system can be defined in terms of the diffusion time as follows 53,56 :where subscript m refers to the matrix system. The diffusion time for the matrix system can be expressed aswhere D (m 2 /s) and ω denote the diffusion coefficient of the matrix and the shape factor (m −2 ), respectively.…”

“…Based on the Langmuir adsorption theory, the adsorbed gas mass can be defined aswhere θ is the surface coverage of the adsorption layer, and P L is the Langmuir pressure. Chen and Yang 57 developed a kinetic model based on the random walk theory, which can be expressed as 56 …”

“…To address this issue, four subequations must be solved simultaneously: three subequations for the velocity vector in the three directions (Equation 9 and Equation ), in contrast to the one equation to be solved in the case of Darcy flows. The aforementioned relationship can be solved through the iterations of the four subequation 56 . To this end, the General Form PDE Interface in the COMSOL with four variables (velocity vα in the three directions and the liquid pressure) was used.…”