The potential distribution around a partially penetrating source is a solution of the diffusivity equation. Presenting a new method "Discrete Flux Element" (DFE) this paper provides the solution to the diffusivity equation with uniform potential as well as uniform flux inner boundary conditions (IBC). This solution provides the ability for modeling any sources with arbitrary geometry. The pressure derivative equations have been derived for uniform potential as well as uniform flux inner boundary conditions. The pressure derivative reflects the wellbore length and the distance of a horizontal well to the no-flow boundary.

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