Streamline Tracing on Curvilinear Structured and Unstructured Grids

Summary The streamline method has proven to be extremely successful for reservoir simulation.1 For a Cartesian grid, the standard five-point (seven-point in 3D) discrete pressure equation is employed within the IMPES streamline method. The accuracy of the velocity field plays a critical role in the success of the technique, which relies on precise determination of streamline paths. Modeling complex geology and geometry requires the use of sophisticated grids, and thus the ultimate power of the streamline method will only be realized when the method is extended to general curvilinear grids. In this paper, a generalization of the Cartesian tracing algorithm is developed for general tensor fields on structured (corner-point) grids and unstructured grids. The extension of the method requires the identification of appropriate volumes and fluxes over which tracing equivalent to the Pollock Cartesian method2 can be performed. Essential components of the method include the use of flux-continuous finite-volume schemes for the different grid types coupled with a novel flux recovery technique and a generalization of streamline tracing to polygons.