We implement a novel up-winding scheme for the mobility calculation using the computed velocities in a finite element (FE) unstructured-mesh simulator for fractured reservoirs. In the finite-element finite-volume (FEFV) numerical discretisation 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 (2D-fractures) and four for tetrahedral (3D-matrix). Consequently, the saturations used in calculating the 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 two-dimensional radial 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. We compare the results of this new mobility calculation against other FEFV fractured reservoir simulators. We test the new method on a fracture network outcrop meshed using discrete fractures and matrix elements. This novel approach produces more accurate saturation profiles than previous methods even with higher order methods and better models multi-phase displacements in complex reservoir. It can be easily implemented in current FEFV based simulators.


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