A New Approach for Reducing Numerical Dispersion in Reservoir Simulation

Abstract

Abstract During history matching of observed production data of brown fields, one of the key matching parameters is the water break-through time. Water break-through time is the time at which significant water production begins at a producing well. During the simulation of an immiscible displacement process, numerical dipersion is a well known undesirable simulation artifact which makes water flood-front to move faster when the simulation grid-blocks are coarser. In this paper, we present an approach to reduce numerical dispersion and ensure that the simulated flood-front movement is similar, whether we use coarse grid-blocks or fine grid-blocks in simulation. The approach is based on the correction of laboratory relative permeability data, using the shock front water saturation (Swbt) obtained from fractional flow curve. Swbt is the water saturation at the contact point between a tangent drawn from the connate water saturation (Swi) to the fractional flow curve. Once we obtain Swbt, we then set the critical water saturation of the water relative permeability curve to Swbt. We created different scenarios of grid block sizes and simulated a steady state water injection process using the corrected water relative permeability curve. We based our study conclusions on results from both line drive and 5-spot water injection patterns. The result showed six (6) months difference in predicted water break-through dates when we used the laboratory relative permeability data as is, but with this new approach, the various scenarios of grid block sizes showed similar water break-through dates. This new methodology effectively eliminates the impact of simulation grid size on water break-through prediction results. During geo-model construction, we do not know in advance what impact our chosen grid size would have on flow dynamics, and once the geo-modeling is finalized it could be time consuming to re-do the gridding and layering of the geo-model. We also take note that many times we are constrained to build simulation models with large grid-sizes because of computational limitations, especially in large reservoirs. The new approach presented in this paper would ensure that any size of grid-block used in simulation, would predict similar flood-front movement and hence similar water break-through time as fine grid simulation. Our approach helps to ensure better reliability of simulation results in cases where computational limitations or large size of reservoir makes it necessary to build coarse grid simulation models.