Analytical coupled axial and radial productivity model for steady-state flow in horizontal wells

A new analytical model for coupled radial well inflow and axial flow has been developed and applied to horizontal well productivity calculations. This analytical model results in a linear pressure distribution in the axial direction and a logarithmic pressure distribution in the radial direction. The analytical solution is investigated for two special cases where a one-dimensional analytical solution already exists. It is proven that the model reduces to the classical radial inflow model in the case when the axial pressure gradient is zero and to the linear Darcy equation when there is zero radial inflow. The new equations are also used to evaluate the well flow rates when the skin effect is included. The analytical solution verifies that the axial flow in the reservoir, in general, cannot be ignored, particularly in reservoirs with high permeability and high well productivity. The analytical model is used to quantify the importance of frictional losses in well productivity calculations. An example on how the analytical model can be used in hand calculations to determine well productivity and frictional losses is presented.