We implement a novel up-winding scheme for finite element mobility calculation using the computed velocities in a finite element finite volume (FEFV) unstructured-mesh simulator. In FEFV numerical method, the pressure and transport equations are decoupled. The pressure is calculated using finite elements, and the saturation is calculated using finite volumes. Each element is shared between several control volumes -- three for triangles and four for tetrahedrals. Consequently, the saturations used in calculating element mobilities - hence updating pressure - are unclear. Some researchers use the average value between the elemental control volumes, or the integration points of the finite elements. For three-dimensional spherical flow, this does not produce accurate saturations profiles when compared to the Buckley-Leverett reference solution.

In this paper, we present a new formulation to calculate the FE mobility. We use the velocity vector, which is piece-wise constant in first order elements, to find the upstream saturation–where the tail of velocity vector intersects an element. This novel approach produces more accurate saturation profiles than previous conventional method, and it better models multi-phase displacements in complex reservoirs. It can be easily implemented in current FEFV based simulators.

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