Peaceman Well Block Radius For Different Regimes of Production

We consider sewing machinery between finite difference and analytical solutions defined at different scales: far away and near source of the perturbation of the flow. One of the essences of the approach is that coarse problem and boundary value problem in the proxy of the source model two different flows. We are proposing a method to glue solution via total fluxes, which is predefined on a coarse grid. It is important to mention that the coarse solution "does not see" boundary. From an industrial point of view our report provides a mathematical tool for analytical interpretation of simulated data for fluid flow around a well in a porous medium. It can be considered as a mathematical "shirt" on the famous Peaceman well-block radius formula for linear (Darcy) radial flow but can be applied in much more general scenarios. As an important case, we consider nonlinear Forchheimer flow. We will consider all three regimes of the flow based on new MB equation for compressible fluid: (i) Stationary Flow (ii) Pseudo Stationary(PSS) Flow (iii) Boundary Dominated(BD) Flow