Mathematical Model for Three-Phase Compressible Dual Porosity Streamline Simulation

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.<br><br>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.<br><br>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.<br>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.<br><br>