Abstract
We present a novel velocity based up-winding scheme for the node control volume finite element (NCVFE) method. The NCVFE method solves for the pressure at the vertices of elements and a control volume mesh is constructed around them; where the advection of fluids is modelled. Therefore, each element shares several control volumes, and traditionally the fluid saturations used in calculating the mobilities over each element − hence updating pressure − are arithmetically weighted. In this paper, we use the velocity vector to allocate the upstream direction of the fluid flow in each element and use the upstream fluid saturation in calculating the mobility needed for the pressure equation. We test his novel approach using triangle and tetrahedron elements, and we show that it produces more accurate fluid saturation profiles than the traditional approach. The method can easily be implemented in current NCVFE simulators.
Highlights
Up-scaling is an essential approach when the aim is to reduce simulation time and cost, and UMC allows for better prediction of the movement of the water front in such scenarios
This novel approach can be implemented in current reservoirs simulators and has a wide range of applicability to various fields of hydrocarbon recovery, ground water movement and contaminant transport
The interpolation function N and their derivatives are defined for a triangle and tetrahedron as follows
Summary
Up-scaling is an essential approach when the aim is to reduce simulation time and cost, and UMC allows for better prediction of the movement of the water front in such scenarios. This novel approach can be implemented in current reservoirs simulators and has a wide range of applicability to various fields of hydrocarbon recovery, ground water movement and contaminant transport.
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