Discontinuities in the Orkiszewski Correlation for Predicting Pressure Gradients in Wells

Abstract

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, T, 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 T 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 T 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. IntroductionThe Orkiszewski method [1] for prediction of two-phase pressure gradients in vertical pipe is primarily a modification of the Griffith and Wallis correlation [2] for the slug flow region. The modification was to develop a liquid distribution coefficient, T, to account for the distribution of the liquid in the slugs, in the films around the gas bubbles, and as entrained droplets in the gas bubbles. Orkiszewski applied the liquid distribution coefficient to the equation for mixture density proposed by Griffith and Wallis and also used it in a new equation for friction pressure gradient. This work supposedly extended the Griffith and Wallis correlation into the high velocity range of slug flow and resulted in more accurate predictions of friction loss and mixture density.Using data primarily from Hagedorn and Brown [3], Orkiszewski correlated T with superficial mixture velocity v m , liquid viscosity \i L , and pipe diameter d. For oil as the continuous liquid phase, T is determined from equation (1) if v m < 10 ft/sec and from equation (2) if v m > 10 ft/sec. Similar equations were developed for the case

Pressure Drop Determination for Multiphase Flow in a Vertical Well Tubing

“…[1][2][3] While others dealt with the problem of predicting pressure gradients in an oil wells, where the flowing fluid may be gas, oil or water mixture with interphase mass transfer. The complexity of fluids encountered, the large diameters, long lengths of pipe and often times in hostile environments, make multiphase flow unique in the petroleum industry 4 .…”