3D Numerical Modeling of Linear Flow of Non-Newtonian Fluid in Porous Media: Application to Non-Newtonian Draw-Down Pressure Transient Analysis

In this study, a 3-Dimensional non-linear partial differential equation (PDE) describing flow of non-Newtonian fluid in porous media was developed for a no-flow boundary reservoir. Non-Newtonian fluid flow in porous media has direct applications in polymer flooding for secondary oil recovery operations and flow of heavy crude in the reservoir. This novel work presents the pressure behavior of horizontal wells with non-Newtonian fluid flow in porous media as well as the methodology for analyzing pressure transient data from non-Newtonian reservoirs. The main assumptions in the mathematical modeling of the differential equation are; permeability anisotropy with directional permeabilities kx, ky and kz horizontal well is in the y-direction perpendicular to direction of maximum permeability kx effects of gravity, skin and wellbore storage were neglected and the reservoir fluid was considered to be a non-Newtonian pseudo plastic fluid that obeys power law model in an isothermal condition. The derived equation was discretized using finite difference approach; A 3D numerical simulator was developed with the aid of MATLAB to solve the system of linear equations obtained from the discretization of a 15 X15 × 15 grid system to obtain pressure transient data. Type curves in terms of PwD and tD were generated for different power law flow index n ranging from 0.1 to 1 for horizontal well length of 600ft, 1000ft and 1200ft. The developed type curves in this study were validated with a Newtonian case using Tiab Direct synthesis (TDS) technique to analyze the radial flow regime for the determination of average permeability as well as the early linear flow for determining kx The results obtained from the Newtonian fluid case were very close to the actual property been determined.