Sammendrag
Numerical smearing is oftentimes a challenge in reservoir simulation, particularly for complex tertiary recovery strategies. We present a new high-resolution method that uses dynamic coarsening of a fine underlying grid in combination with local timestepping to provide resolution in time and space. The method can be applied to stratigraphic and general unstructured grids, is efficient, introduces minimal computational overhead, and is applicable to flow models seen in practical reservoir engineering. Technically, the method is based on three concepts:
Sequential splitting of the flow equations into a pressure equation and a system of transport equations
Dynamic coarsening in which we temporarily coarsen the grid locally by aggregating cells into coarse blocks according to cell-wise indicators on the basis of residuals (gradients and other measures of spatial and temporal changes can also be used)
Asynchronous local timestepping that traverses cells/coarse blocks in the direction of flow
We assess the applicability of the method through a set of representative cases, ranging from conceptual to realistic, with complex fluid physics and reservoir geology, and demonstrate that the method can be used to reduce computational time and still retain high resolution in spatial/temporal zones and quantities of interest.
Sequential splitting of the flow equations into a pressure equation and a system of transport equations
Dynamic coarsening in which we temporarily coarsen the grid locally by aggregating cells into coarse blocks according to cell-wise indicators on the basis of residuals (gradients and other measures of spatial and temporal changes can also be used)
Asynchronous local timestepping that traverses cells/coarse blocks in the direction of flow
We assess the applicability of the method through a set of representative cases, ranging from conceptual to realistic, with complex fluid physics and reservoir geology, and demonstrate that the method can be used to reduce computational time and still retain high resolution in spatial/temporal zones and quantities of interest.