Numerical Modeling of Low Permeability Oil Flow with the Threshold Pressure Gradient

Abstract In this article, the authors present partial differential equation models for linear transient oil flow that include a threshold pressure gradient (TPG) assumption for low permeability flow. Results of numerical simulations developed for the dimensionless PDEs are compared to a conventional model and to each other to determine the effect of including the TPG. A conventional PDE model was non-dimensionalized and coded using finite difference methods and a conjugate gradient algorithm. Then a two-grid approach was developed to solve the same problem with the addition of a threshold boundary condition. This method is described, and the results are compared on two test problems, one a field scale problem and one a lab scale problem. The results of this work can inform more advanced modeling of oil flow by determining when and how a threshold pressure gradient should be applied.