A new analytical expression has been developed for the equivalent well block radius for three dimensional (3D) flow. The new equation has the same structure as Peaceman's equation with two new parameters added. Therefore, implementation in a reservoir simulator is straight forward. Numerical experiments have shown that Peaceman's equation for two dimensional (2D) flow can cause high rate errors for the partially penetrating wells. The new formula reduces these errors to a few percent.

In this paper, derivation was presented for a vertical well, steady-state single phase flow with uniform and nonuniform grids. Multiphase, transient flow, horizontal wells and partial completion within a grid block is under development and will be presented in a new paper.

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