Peaceman's numerical productivity index for non-linear flows in porous media

From Darcy’s law to Darcy-Forchheimer equation, there have being a lot efforts finding solutions for flows in porous media. Peaceman used a system of well blocks to replace the well bore in finding numerical solutions for linear flows. Our work uses a single well block to find the pressure distribution throughout the well for non-linear flows. In the process we found a block invariant which can be used to build the pressure distribution formula. From it, we can find the productivity index, one of the important factors in petroleum engineering.

Theoretical derivation and numerical data are also presented in this report.