A Novel Integrated Numerical Simulation Scheme for Transient Gas Flow in Shale Matrix

摘要

The gas flow in shale matrix is of great research interest for optimizing shale gas reservoir 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, the adsorbed and free gas is stored in nano-scale organic pores. The gas molecules are attached as a monolayer to pore walls to form a film of gas which is the thickness of the adsorbed layer. When a reservoir is depleted, the attached gas molecules will be released so that the radius of organic pores in which the free gas flows is changeable. Thus a sorption-dependent radius will be introduced to the apparent permeability which represents the flow regimes. Stress sensitivity will also be investigated via a two-way coupling geomechanics process. In this paper, we introduce a novel integrated numerical simulation scheme to quantify the above phenomena which is crucial for the shale gas reservoir development. Instead of Darcy's equation, we implement the sorption-dependent apparent permeability in the continuity equation to depict the gas flow (viscous flow, slip flow and Knudsen diffusion) in shale matrix. The methodology which was developed by Vasina et al. and validated through comparing with molecular simulation will be implemented to determine the thickness of an adsorbed layer at each time step. The Langmuir adsorption/desorption term is included in the continuity equation as an accumulation term. In addition, lab data for 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 stress-sensitive shale formation. This methodology examines the influence of each mechanism for the shale gas flow in the matrix. Overall, the sorption-dependent apparent permeability is smaller than the sorption-independent apparent permeability, which leads to the pressure maintenance for the sorption-dependent apparent permeability case. The sorption-dependent apparent permeability will lead to additional heterogeneity. The apparent permeability near a wellbore is bigger than the one far away from the wellbore, which causes the pressure transmit more easily around the production side. With the consideration of geomechanics, the apparent permeability is decreased due to the compaction of a nano-scale pore radius, which leads to the maintenance of reservoir pressure. Due to the difference of compaction magnitude for each grid block, geomechanics also creates additional heterogeneity for a nano-pore network in shale matrix, which we should pay more attention to. The sorption-dependent radius is incorporated into the apparent permeability model to depict the sorption- dependent apparent permeability of shale matrix. We provide a novel integrated methodology to quantify the crucial transient phenomena in the shale matrix, which includes flow regimes, gas adsorption/desorption and stress sensitivity.