Critical Rate for Water Coning: Correlation and Analytical Solution

Abstract

Summary Two methods are presented for predicting critical oil rate for bottomwater coning in anisotropic, homogeneous formations with the well completed from the top of the formation. The first method is based on an analytical solution where Muskat's assumption of uniform flux at the wellbore has been replaced by that of an infinitely conductive wellbore. The potential distribution in the oil zone, however, is assumed unperturbed by the water cone. The method is derived from a general solution of the time-dependent diffusivity equation for compressible, single-phase flow in the steady-state limit. We show that very little difference exists between our solution and Muskat's. The deviation from simulation results is caused by the cone influence on potential distribution. The second method is based on a large number of simulation runs with a general numerical reservoir model, with more than 50 critical rates determined. The results are combined in an equation for the isotropic case and in a single diagram for the anisotropic case. The correlation is valid for dimensionless radii between 0.5 and 50 and shows a rapid change in critical rate for values below five. Within the accuracy of numerical modeling results, Wheatley's theory is shown to predict the correct critical rates closely for all well penetrations in the dimensionless radius range from 2 to 50.