Partitioned time stepping schemes for the non-stationary dual-fracture-matrix fluid flow model

This paper presents the coupled, and decoupled schemes for the naturally fractured reservoir consists of the triple-porosity medium. More specifically, the triple-porosity medium contains three contagious porous medium with more permeable macrofractures, less permeable microfractures, and matrix region which is often known as dual-fracture-matrix fluid flow model. Since the matrix has fluid communication with less permeable microfractures, and macrofratures are fed by the microfractures only, the global domain is divided into two subdomains by considering the traditional dual-porosity region and more permeable macrofractures region respectively. The flow and mass exchange between less permeable microfractures and more permeable macrofractures are modeled by two-fluid communication interface conditions while no-communication interface condition is imposed on between matrix and macrofractures region. The weak formulation and the well-posedness of the dual-fracture-matrix model are derived. Furthermore, coupled, implicit-explicit and data-passing partitioned schemes are proposed. The stability and the optimal convergence analysis are derived for both decoupled schemes. Five numerical examples are presented to illustrate the accuracy of the numerical methods and the applicability of the dual-fracture-matrix fluid flow model. Moreover, the parameter sensitivity analysis is performed in the fourth numerical example.