General Multi-Porosity simulation for fractured reservoir modeling

• New formulation for shape factor to consider matrix subdivision is derived and validated through numerical examples.
• A general Multi-Porosity Model is proposed with two features: conventional Multi-Porosity Model and Multi-Porosity Model with Subdivision.
• In the Multi-Porosity Model, binary connection table to flexibly control arbitrary inter-porosity and intra-porosity connections.
• The application of porosity subdivision in the Multi-Porosity Model significantly improve the solution to capture the transient flow between matrix and fracture.

In the area of fractured reservoir modeling, conventional Dual Porosity Models is challenged to flexibly simulate more than two porosity systems and it is also difficult to capture the transient fluid transfer between matrix and fracture. This work aims to solve those problems in fractured reservoir simulation. The newly introduced Multi-Porosity Model honors any number of porosity types with different properties, such as permeability, porosity and wettability thus achieving significant improvements over conventional Dual-Porosity Models. Arbitrary connections for intra-porosity flow and inter-porosity flow are incorporated into the design to allow for the convenient transformation between Multi-Porosity and Multi-Permeability formulations. The addition of a flexible subdivision in each porosity system has allowed us to characterize the transient flow for inter-porosity flow. Due to the low permeability in the matrix, transient flow between matrix and fracture dominates, and thus matrix spatial subdivision is necessary to accurately capture the dynamics. The formulation is designed to allow the proposed scheme to be generalized. To quantify the improvements available with the new formulation, several typical Multi-Porosity Models are compared with Fine-Grid Single-Porosity Models. Consistent results have been obtained with those similar cases from literature, and the robustness and efficiency of the model is validated. Besides, the extra matrix subdivision is proven to accurately capture the transient fluid transfer between matrix and fracture.