A combination of mass-transfer flow regime methods is presented for predicting two-phase pressure gradients in oil wells with low to medium predicting two-phase pressure gradients in oil wells with low to medium GOR'S. New relationships are proposed for the slug-froth flow regime to improve the accuracy of the calculated local thermodynamic parameters.

Introduction

The polyphasic flow of Newtonian fluids in vertical pipes has been investigated both theoretically and pipes has been investigated both theoretically and experimentally by several authors. Poettmann and Carpenter, Ros, Duns and Ros, and Hagedorn and Brown dealt with the problem of predicting pressure gradients in oil wells, where the flowing fluid pressure gradients in oil wells, where the flowing fluid may be a gas-oil-water mixture with interphase mass transfer Several applications and improvements of the equations proposed by the above authors have been published; empirical relationships have also been published; empirical relationships have also been presented. presented. A method for predicting two-phase pressure drop in vertical pipes was proposed by Orkiszewski. This method, which has been widely accepted in the oil industry, is basically a combination of methods previously proposed by other authors, with some previously proposed by other authors, with some modifications as far as slug flow is concerned. The same basic approach as Orkiszewski's has been adopted in the present work. Theoretical studies as well as experimental results presented in the technical literature have been examined and a set of equations has been selected that has proved to be particularly efficient in predicting pressure gradients in two-phase vertical flow. A new relationship has been developed to deal with the slug-froth flow regime.

Pressure Gradient and Flow Regimes Pressure Gradient and Flow Regimes Starting from the macroscopic mechanical energy balance equation, the elementary pressure drop, dp, in a vertical pipe can be expressed as follows.

(1)
By making some approximations in evaluating the acceleration gradient, p v dv, which is almost always negligible, we have

(2)

Before integrating Eq. 2 numerically, the locally prevailing flow regime must be determined because prevailing flow regime must be determined because the way both p and Tf are to be evaluated depends on the flow regime. The various ways a gas-liquid mixture can flow in a vertical pipe are usually grouped into three main flow regimes; that is, bubble-plug flow, slug-froth flow, and mist flow. A transition zone exists between the last two regimes. By combining the experimental results by Griffith and Wallis with those by Duns and Ros, the following criteria have been proposed by Orkiszewski for determining the flow regime.

Bubble-Plug Flow
$(qg/qt) less than Nv$
(3)
Slug-Froth Flow
$(qg/qt) greater than Nv,$
(4a)

JPT

P. 927

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