Critical and Subcritical Flow of Multiphase Mixtures Through Chokes

Abstract

Summary Equations that describe isentropic (adiabatic with no friction loss) flow of multiphase mixtures through chokes can be deduced from the general energy equation. These flow equations are valid for both critical and subcritical flow. Equations, physical property correlations for oil/water/natural gas systems, and a property correlations for oil/water/natural gas systems, and a computer method that will handle both flow regimes are described. The procedure will determine whether flow will be in the critical or subcritical regime. The analysis method has been tested by comparing measured and calculated flow rates of 1,432 sets of literature data comprising both critical and subcritical air/water, air[kerosene, natural gas, natural gas/oil, natural gas/water, and water flows. An average discharge coefficient of 0.826 gave a negligible average error with a 15.4% standard deviation. Introduction In oil fields, it is a common practice to flow liquid and gas mixtures through chokes. Both surface and subsurface chokes may be installed to control flow rates and to protect the formation and surface equipment from unusual pressure fluctuations. In addition to installed chokes, irregular choke-like constrictions also may play a dominant role in limiting the flow rate from a blown-out play a dominant role in limiting the flow rate from a blown-out well. System that involve condensation of the gaseous phase, such as steam/water, are not considered in this paper. Also, flow conditions that would lead to choke throat pressures equal to or less than the vapor pressure of the water phase are not considered. Under "subcritical" flow conditions, the mass flow rate of a stream will be a function of the pressure downstream of the choke when the upstream pressure is held constant. If the pressure drop across the choke becomes sufficiently large, the flow regime will become "critical" and the mass flow rate will be independent of the downstream pressure when the upstream pressure is held constant. Several investigators have described studies of critical and subcritical flow. A thermodynamically based theory and empirical correlations have been reported. The empirical correlations generally are valid over the range where experimental data were available but may give poor results when extrapolated to new conditions. The literature shows little success in correlating the conditions that determine the boundary between critical and subcritical flow. The purpose of this paper is to review the thermodynamic basis, develop a theoretical framework, and show that this approach is valid for both subcritical and critical flow. Correlations of oil, gas, and water properties then are combined with the thermodynamic framework to yield a computer program for calculating isentropic flow. Discharge coefficients, which relate actual flow to ideal frictionless flow, were determined by use of experimental data available in the literature. Energy Balance for Multiphase Mixtures The thermodynamic framework for multiphase critical flow is based on the principal of conservation of energy. As a flowing mixture approaches a constriction, its velocity will increase and the pressure will fall. Little time or area is available for heat pressure will fall. Little time or area is available for heat transfer; thus, the expansion of the gaseous fraction is essentially adiabatic. Consequently, the temperature of the flowing mixture also changes. Beginning with the general energy equation, the relationship between variables at any point in the flowing system can be determined based on these assumptions (1) that temperature varies with position, but at any point, all phases are at the same temperature; (2) that velocity varies with position, but at any point, all components are moving with the same velocity; (3) that the gas compressibility factor is constant; (4) that the liquids have a negligible compressibility compared to gas; (5) that elevation changes are negligible; and (6) that the flow process is adiabatic and frictionless. Appendix A shows the derivation of equations that relate the pressure in the throat of the choke to the mass flow when the upstream pressure is known. The necessity to conserve energy leads to the pressure is known. The necessity to conserve energy leads to the interesting phenomenon that a maximum mass flow rate is achieved at a specific throat/upstream pressure ratio; the critical pressure ratio, however, depends on inlet conditions. As Appendix A shows, this critical flow condition can be determined by differentiation of the general energy equation.