A New Coupled Axial-Radial Productivity Model for Horizontal Wells with Application to High Order Numerical Modeling

Abstract

Abstract For long, highly productive wells, frictional pressure loss cannot be ignored. The axial flow along the well trajectory in the near-well region must therefore also be considered. A new, fully analytical model for coupled radial well inflow and axial reservoir flow has been developed. The new model will be briefly reviewed and solutions to steady state flow summarized. A discussion on the usage of the new model in simulation of horizontal wells together with its numerical performance compared to standard finite difference methods will be presented. The new analytical model has been used in the formulation of a numerical scheme for simulation of coupled well inflow and near-well reservoir flow. The analytical model results in a linear pressure distribution in the axial direction and a logarithmic pressure distribution in the radial direction in each near-well reservoir segment. Therefore, the pressure distribution is piecewise linear/logarithmic, contrary to existing piecewise constant distribution resulting from a standard finite difference method. Calculation examples are presented applying both the new method and the standard finite difference method to determine the pressure profiles and flow rates in both the wellbore and the near-well reservoir. Numerical results show that the new method represents a substantial improvement compared to a standard finite difference method, requiring fewer segments to achieve the same accuracy. The new method is more accurate especially near the heel, where accuracy is most important. This numerical scheme has also been proved to be higher order accurate in space discretization than a standard finite difference scheme. Since the axial flow rate is built into the new model analytically, the need for local grid refinements around the well is reduced.