Stress-dependent permeability of organic-rich shale reservoirs: Impacts of stress changes and matrix shrinkage

Effective stress is gradually increased and permeability is gradually reduced during reservoir depletion caused by hydrocarbon production, while the organic-rich matrix might experience a shrinkage process that will boost the permeability. The main objective of this paper was to develop a mathematical simulator coupling gas flow process, geomechanics effects, and matrix shrinkage in order to evaluate their influences on reservoir permeability and production performance of organic-rich shale reservoirs. The mesh was divided into three different continuums: organic matter, non-organic matter, and natural fractures. Matrix shrinkage was only considered for organic matter because of gas desorption process, and the stress-dependent permeability was considered for all three sub-pore media. The flow and stress-equilibrium equations were solved by the fixed-stress sequential method, where the flow equations are solved first, followed by the mechanics equations. The displacements are solved for each grid node by finite element method, and the grid pressure is solved by the integral finite difference method. Different stress-dependent correlations are chosen to separately apply to these three sub-pore media. Based on the correlations, the porosity and permeability are updated at end of each time step. A synthetic reservoir model was built, where the permeability change and the cumulative gas production is calculated at each time step. Besides, the sensitivity analyses were investigated for Total Organic Carbon (TOC), matrix permeability, Young's modulus, Poisson's ratio, and bottom hole pressure. The coupled model was validated by comparing with the analytical solution of Mandel's consolidation problem. Numerical results show that the permeability and cumulative production is significantly reduced when the stress-dependent permeability is considered. The matrix shrinkage on organic matter could provide an obvious rebound on cumulative production at the late producing stage, because the permeability is boosted by the media shrinkage at low pressure. However, the production enhancement is highly related to bottom hole pressure and Total Organic Carbon. Due to large permeability decline, a higher TOC does not necessarily bring a higher cumulative production. When the stress-dependent permeability is considered, a larger matrix permeability encounters a bigger loss of production rate. A higher cumulative production is predicted from a lower either Young's modulus or Poisson's ratio. A large bottom hole pressure could offset certain production loss caused by the permeability decline. Overall, the triple-porosity coupled simulator can quantitatively interpret the impacts of matrix shrinkage and geomechanics on permeability change and gas production performance for organic-rich shale reservoirs. That provides more realistic production performance evaluation and economic assessment when the stress-dependent permeability needs to be considered. Additionally, this coupled flow-geomechanics model is also available to simulate the permeability change when water injection is performed to maintain reservoir pressure and prevent the permeability decline.