Mathematical Model for Three-Phase Compressible Dual Porosity Streamline Simulation

Abstract

Flow simulation of fractured reservoirs usually is performed using a dual porosity model. The dual porosity system is modeled by using two coupled grids: one for matrix and one for fracture. These two continua communicate by transfer functions. Until now, there were no mathematical models of dual porosity, three-phase, compressible flow for streamline simulators. To realize this model, it was necessary to reformulate the matrix and fracture pressure equations The conventional transfer function has been incorporated as a source/sink term, not only in the streamline saturation equations (as it was in incompressible case), but also in the pressure equation. The dual porosity model has been implemented into a streamline simulator. This tool has its main application in the geological modeling domain for analyzing uncertainty, model ranking and screening of geologically detailed models, including fractures. This paper describes the mathematical model for a three-phase compressible dual porosity streamline simulator and compares the results and run times of the streamline-based approach with a conventional dual porosity grid-based commercial simulator. The results from the streamline simulator for dual porosity show good agreement with those produced by a commercial finite difference simulator with order of magnitude improvement in simulation time. Streamline methods as a reservoir simulation tool have generated much interest in petroleum engineering because of the capability to calculate fluid flow in multi-million cell geological models with reasonable CPU times. However, important physical properties of geo-scale fluid flow models are still not properly modeled by streamline methods. Enhancing the range of physical properties that can be simulated accurately in a timely manner will enable improved workflows in the geological modeling domain.