Comprehensive, three-dimensional, anisotropic and transient, reservoir/wellbore coupling models are developed for infinite-conductivity and infinite-conductivity wellbores to calculate the productivity of a horizontal well placed in a box-shaped drainage volume. The finite-conductivity well model considers frictional and accelerational pressure drops in the wellbore. It also takes into account the effects of fluid inflow into the well. These models are semianalytical in nature and can be used under transient or pseudosteady state flow conditions. The infinite-conductivity well model is compared with the uniform flux model to show the differences in well productivity calculations. The effects of wellbore pressure drop on well productivity are shown using the finite-conductivity well model. These models can provide reference solutions to calculate well indices or to check the accuracy of a numerical simulator. Because of their analytical nature they are easier and faster to use than numerical simulators. Using superposition in space and time, these models can be run under a variety of constraints. We believe that our finite-conductivity well model is more general than any published previously.

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