Higher Resolution Unstructured Spectral Finite-Volume Method for Flow in Porous Media
- Yawei Xie (Henan University) | Michael G. Edwards (Swansea University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Simulation Conference, 10-11 April, Galveston, Texas, USA
- Publication Date
- Document Type
- Conference Paper
- 2019. Society of Petroleum Engineers
- 5.6 Formation Evaluation & Management, 5.6.5 Tracers, 5 Reservoir Desciption & Dynamics, 5.3 Reservoir Fluid Dynamics, 5.3.1 Flow in Porous Media, 5.5 Reservoir Simulation
- Spectral, Higher resolution, CVD-MPFA, Finite-volume
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- 76 since 2007
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A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection equation coupled with an elliptic pressure equation resulting from Darcy's law together with mass conservation. The spectral volume (SV) method is a locally conservative, efficient high-order finite volume method for convective flow. In 2D geometry, the triangular cell is subdivided into sub-cells, and the average state variables in the sub-cells are used to reconstruct a high-order polynomial in the triangular cell. The focus here is on an efficient strategy for reconstruction of both a higher resolution approximation of the convective transport flux and Darcy-flux approximation on sub-cell interfaces. The strategy involves coupling of the SV method and reconstructed CVD-MPFA fluxes at the faces of the spectral volume, to obtain an efficient finer scale higher resolution finite-volume method which solves for both the saturation and pressure. A limiting procedure based on the Barth-Jespersen limiter is used to prevent non-physical oscillations on unstructured grids. The fine scale saturation/concentration field is then updated via the reconstructed finite volume approximation over the sub-cell control-volumes. The method is also coupled with a discrete fracture model. Performance comparisons are presented for tracer and two phase flow problems on 2D unstructured meshes including fractures. The results demonstrate that the spectral-volume method achieves further enhanced resolution of flow and fronts in addition to that of achieved by the standard higher resolution method over first order upwind, while improving upon efficiency.
|File Size||2 MB||Number of Pages||18|
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Y. Xie and M. G. Edwards, Higher resolution total velocity Vt and Va finite-volume formulations on cell-centred structured and unstructured grids, Comput Geosci, 921-936 21, 2017, https://doi.org/10.1007/s10596-017-9669-5.