Discontinuities in the Orkiszewski Correlation for Predicting Pressure Gradients in Wells

The Orkiszewski correlation is used extensively in the petroleum industry for predicting pressure gradients when gas and liquid flow simultaneously in wells. Unfortunately, the correlation contains a parameter called the liquid distribution coefficient, Γ, that can be discontinuous at a superficial mixture velocity of 10 ft/sec. The liquid distribution coefficient is used to predict both the elevation and friction components of the pressure gradient for slug flow. The accepted trial and error method for integrating the pressure gradient to obtain pressure loss in wells can fail to converge when pressure gradients are discontinuous. Examples of discontinuities in Γ for oil as the continuous phase are presented for several liquid viscosities ranging from 0.3 to 200 cp and for pipe diameters of 1.049, 2.441 and 6.049 in. It was found that a constraint recommended for Γ when mixture velocity <10 ft/sec was essentially useless. It was also found that a constraint for velocities >10 ft/sec could actually increase the magnitude of pressure gradient discontinuity. Convergence of pressure loss calculations when the discontinuity was encountered was possible only if the convergence tolerance was temporarily relaxed.