Abstract
Summary Constant-rate analytical solutions of the one-phase radial-flow equation in two dimensions, including effects of the quadratic gradient term, are derived for an oil reservoir with constant diffusivity and compressibility. The combinations of compressibility contributions to the various terms are analyzed. It is shown that the standard condition allowing the quadratic gradient term to be neglected (cp≪1) is incorrect; pressure, p, should be replaced by a function of the production rate and other reservoir parameters except absolute pressure. The effect of the quadratic gradient term, for which quantitative expressions are given for steady-state and semisteady-state flow, may amount to several percent of the pressure drawdown at the wellbore.
Published Version
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