New Correlations For Critical And Subcritical Two-phase Flow Through Wellhead Chokes
Authors: Elgibaly A.A.M. , Nashawi I.S. 
Published: March 2010

Abstract
Several correlations of critical and subcritical two-phase flow through wellhead chokes were evaluated to test their application to Middle East oil fields. Two groups of correlations describing two-phase flow through wellhead chokes were examined. The first group involved simple empirical equations similar to those of Gilbert(1). Two new correlations were proposed: one for critical and the other for subcritical flow regimes. The second group comprised derived equations of two-phase flow incorporating PVT properties. PVT correlations developed for the Middle East crudes were employed. These correlations were tested for a wide range of field data obtained from several Middle East countries.
Selection of the best correlation was justified by statistical error analysis, range of validity, and number of involved variables to be measured in the field. Our simple version of correlations provided more accurate results than any other correlation involving the same variables. Incorporation of the PVT correlations for produced fluid properties of the Middle East oil fields improved the accuracy of the derived models.
The developed correlations were useful for accurate prediction of choke performance of the Middle East oil wells. The proposed empirical correlations are applicable for various types of reservoir fluids, including black oil, volatile oil, and gas condensate fluids. These correlations do not require knowledge of PVT properties of the produced fluids.

Introduction
Chokes are commonly used in oil and gas production systems. A choke is a restriction basically designed to control flow rates of oil and gas wells, to impose a back pressure on the formation protecting it from damage, to prevent the downstream disturbances from propagating upstream (critical flow), and to protect the surface equipment facilities against slugging at high flowing pressures.
Several approaches have been suggested for the prediction of multiphase flow through chokes. These approaches can be classified into four groups. The first group consists of correlations similar to the one originally proposed by Gilbert(1). This equation has been further modified by Ros(2), Secen(3), Baxendell(4), Achong(5), Pilehvari(6), and Osman and Dokla(7). These correlations were developed for the critical flow regime. In such correlations, the PVT properties of the produced fluids were neglected. Some of these correlations are claimed to be valid for downstream to upstream pressure ratios up to 0.7(1).
The second group combines the empirical correlations for critical flow through chokes with fluid properties. The correlations belonging to this group include Poettmann and Beck(8), Al-Attar and Abdul-Majeed(9), and Al-Towailib and Al-Marhoun(10). Poettmann and Beck(8) converted Ros's correlation to graphical forms for 20, 30, and 40 ° API crudes. These correlations are restricted to critical two-phase flow of wells producing clean oil. Al-Attar and Abdul-Majeed(9) modified Gilbert's(1) equation by including the API gravity of the crude oil. However, they recommended the use of more field data to test their correlation. Al- Towailib and Al-Marhoun(10) introduced the effect of gas-oil mixture density into an empirical correlation that describes fluid flow in chokes. This correlation is limited for critical flow, neglects solution GOR, and requires knowledge of the specific gravity of the produced gas and oil.