An Integrated Multi-Scale Numerical Simulation of Transient Gas Flow in Shale Matrix

Abstract

The gas flow in shale matrix is of great research interest for optimizing shale gas development. Due to a nano-scale pore radius, the gas flow in the shale matrix may fall in flow regimes which include viscous flow, slip flow and Knudsen diffusion. On top of that, gas adsorption/desorption and stress-sensitivity are some other important phenomena in shale. In this paper, we introduce an integrated multi-scale numerical simulation scheme to depict the above phenomena which is crucial for the shale gas development. Instead of Darcy's equation, we implement the apparent permeability in the reservoir-scale continuity equation to depict the gas flow (viscous flow, slip flow and Knudsen diffusion) in shale matrix. A Langmuir adsorption/desorption term is included in the reservoir-scale continuity equation as a generation term. To ensure the real-time desorption and adsorption equilibrium with gas production, an iterative mass balance check of pore wall surfaces (pore scale) is introduced. At each time step, the pore-scale and reservoir-scale mass balance should be satisfied simultaneously in each grid block. On top of that, the lab data of a Bakken reservoir which provides a relationship between a matrix pore radius reduction and the effective stress is integrated into the two-way coupling geomechanical process to simulate a stresssensitive shale formation. This methodology examines the influence of each mechanism for the shale gas flow in the matrix. Instead of conventional pressure-independent Darcy permeability, the apparent permeability increases with the development of a shale gas reservoir. With the gas adsorption/desorption, the reservoir pressure is maintained via the supply of released gas from nano-scale pore wall surfaces. With the consideration of geomechanics, the apparent permeability is decreased due to the compaction of nano-scale pore radii, which leads to the maintenance of reservoir pressure. Due to the difference of compaction magnitude for each grid block, geomechanics create additional heterogeneity for a nano-pore network in shale matrix, which we should pay more attention to. A novel integrated multi-scale methodology is introduced to examine the crucial phenomena in the shale matrix, which simultaneously takes into account the influence of flow regimes, gas adsorption/desorption and stress-sensitivity. An effective way is provided to quantify the above effects for the transient gas flow in shale matrix.

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