MATLAB programming for Numerical differenciation in Petroleum Engineering

I am trying to simulate an oil production from an inhomogeneous reservoir consisting of three layers with different permeabilities. The middle layer is assumed to be not as permeable as the top and bottom layer leading to a condition called crossflow. A well is drilled through the layers and perforated in the top and lower layers. Mathematically, the the perforated intervals are represented by the Dirichlet boundary conditions on pressure while the no flow layers are represented by Newmann boundary conditions on pressure. I have real life data for two separate cases having this scenerio. The tasks to be accomplished includes Deriving and implementing a 2D finite difference solver for the problem and others on request.