About one numerical model for reservoir flow near a horizontal well at nonlinear law of fluid motion

The article relates to the problem of a horizontal well productivity estimation under the condition that the near-well flow if effected by nonlinear phenomena. The mathematical model is developed which effectively resolves the problem of fieldscale reservoir simulations taking into account the difference between a wellbore radius and a characteristic collector size. This model incorporates the nonlinear Forscheimer's law of porous flow. For the flow around a single horizontal well the physically reasonable but simplified model of flow structure is proposed which allows to solve analytically the problem of the nonlinear reservoir flow and to construct the analytical expression for the well productivity as the dependence on the reservoir and well properties. We analysed the correctness of this solution and made the comparison between the analytical estimations and well-known numerical results related to flows in homogeneous and stratified reservoirs. By means of such comparative work we defined the admissible as well as optimal macroblock dimensions shapes depending on reservoir shapes and required accuracy of productivity calculations.