Fracture Reservoir Simulation Using Finite Element Method with Logarithmic Shape Functions

This research presents a new numerical method for solving single phase flow in oil reservoirs which is able to forcaste the reservoir behavior. The method uses Galerkin finite element formulation in a logarithmic space for calculation of pressure distribution, which yields a logarithmic approximation of pressure around the wellbore. Due to the consistency of this approximation with the actual behavior of pressure in reservoirs, this method leads to a great enhancement in accuracy of simulation results. The method has been deploved in an object oriented programming environment for solving dual porosity model equations and tested on on some case sample models. Comparison of simulation results with analytical solution and the finite difference method shows the superiority of logarithmic finite element method over conventional methods in reservoir simulation. Combination of this method with other numerical methods (control volume) can be used to simulate multi phase flow.