Pseudo Relative Permeability Compensation for Numerical Dispersion

Abstract

Reservoir simulation is an approach of recreating the occurring phenomena of the reservoir by solving the general governing equations that describe the reservoir processes. Finite difference technique is an effective method to get the solution out of the reservoir models for different scenarios. In light of many benefits of using course grid models rather than fine grid and simplification, using the same relative permeability curves from laboratory cannot be applied in the fields having large grid dimensions because of numerical dispersion (smearing) of finite difference modeling. Thus, the relative permeability curves must be modified based on the grid size and then applied into the simulator. The authors introduce a methodology to demonstrate how the lab relative permeability curves can be modified based on coarse grid sizes to honor the same anticipated rock behavior. Thus, an objective function is developed to minimize the numerical dispersion in a synthetic tilted reservoir by automatically changing the relative permeability and comparing the results with the equivalent fine model. By this method, modified relative permeability curves can be obtained and introduced to the coarse model. This modification workflow is almost inevitable for reservoir simulation models with very coarse grids and it eases the history-matching process by approaching more realistic solution.