A new coupled multiphysics model and partitioned time-stepping method for the triple-porosity-Stokes fluid flow model

This paper proposes a new coupled multiphysics model and decoupled finite element method for the realistic naturally fractured reservoir consisting of the triple-porosity medium combined with a free flow region. More specifically, the triple-porosity medium consists of three transmittable, interacting contiguous porous mediums with more-permeable macrofractures, less-permeable microfractures, and stagnant-matrix region, respectively, which is described by the dual-fracture-matrix equations. Moreover, the free fluid flow region is governed by the evolutionary Stokes equation. To couple the triple-porosity medium with the conduit region, five physically valid coupling conditions, are utilized to capture the interfacial phenomena efficiently. The variational formulation and the well-posedness of the model are reported. To lay a solid ground, a fully-implicit algorithm is proposed in a traditional format. On the other hand, based on the idea of partitioned time-stepping, the five interface conditions, and the mass exchange terms in the triple-porosity model, the second algorithm is decoupled into four levels. The decoupling technique allows a non-iterative splitting of the coupled problem into four parallel subproblems. The unconditional stability and optimal convergence analysis are derived for the partitioned time-stepping scheme. For the petroleum engineering applications, we design two numerical experiments and perform parameter sensitivity analysis, which shows the applicability and complicated flow characteristics of the triple-porosity-Stokes interface system.