Cone Breakthrough Time for Horizontal Wells

Abstract

Summary: Recovery from an oil zone underlying a gas cap, overlying an aquifer, or sandwiched between gas and water can be improved by repressing the coning problem through horizontal-well drainage. Literature methods to predict coning behavior are limited to steady-state flow conditions and determination of the critical rate. The results in this paper are based on new semianalytical solutions for time development of a gas or water cone and of simultaneous gas and water cones in an anisotropic infinite reservoir with a horizontal well placed in the oil column. The solutions are derived by a moving-boundary method with gravity equilibrium assumed in the cones. For the gas-cone case, the semianalytical results are presented as a single dimensionless curve (time to breakthrough vs. rate) and as a simple analytical expression for dimensionless rates > ⅓. For the simultaneous gas- and water-cone case, the results are given in two dimensionless sets of curves: one for the optimum vertical well placement and one for the corresponding time to breakthrough, both as functions of rate with the density contrast as a parameter. The validity of the results has been extensively tested by a general numerical simulation model. Sample calculations with reservoir data from the Troll field and comparison with test data from the Helder field demonstrate how the theory can be used to estimate the time to cone breakthrough and its sensitivity to the uncertainties in reservoir parameters.