Finite Difference Method for two phase fluid flow

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I have the below set of equations and boundary conditions governing two phase fluid flow in an oil well and am struggling to start with a code to solve these with the finite difference method.

I know that I will have to manipulate the equations in order to create arrays in Matlab based on increments of r and t.

I am looking to solve for Sw as function of radial distance r.

The variables are Po, Pw, So, Sw, r & t. The rest are constants which I have expertimetnal values for.

Any help would be highly appreciated as to how to start solving. Thanks

Equations and boundary conditions