Modeling fluid flow in a porous medium is a challenging computational problem. It involves closely coupled systems of flow transport process consisted of highly heterogeneous distributions of porous medium property, various fluid flow characteristics including injection or production well assemblies, and surface separation and storage facilities. For the design of better flow management scheme, high performance computing tools have been applied as a useful and essential technique in a cost-effective manner. In recent years, grid computing architectures have been emerging as a new computing environment. It allows a powerful computing capability for accurate simulation of complex fluid flow phenomena that occur in porous media. In this paper, grid-enabled simulation approach is presented for modeling a three dimensional, multiphase fluid flow in the grid computing environment. A semi-implicit formulation is used to solve the systems of governing partial differential flow equations, which are discretized in a Cartesian coordinate system. Extensive test results of the code are presented in this paper. The preliminary result shows a significant parallel performance. Based on this preliminary study, we further discuss a future plan for the design of multi-purpose porous media flow simulator, which allows multi-physical simulation capability in grid computing environment..