Comparison of Solutions of the Nonlinear and Linearized Diffusion Equations

Abstract

Summary Analytical solutions to the nonlinear partial-differential equation (PDE) that describes pressure behavior during the flow of slightly compressible fluid through porous media are presented. The solutions are compared with the generally accepted solutions of the linearized version of the original nonlinear PDE. It is shown that for routine engineering applications, the solutions to the linearized equation are satisfactory. However, the nonlinear solutions show that some accepted concepts based on the linear solutions are not valid. Moreover, if one is looking for small differences between the field-measured pressure values and the theoretically calculated ones, the solutions to the nonlinear equation should be used in place of the linear solutions.