An Evaluation of Critical Multiphase Flow Performance Through Wellhead Chokes

Abstract

A multiphase flow equation describing the behavior of orifice flow may be used directly to evaluate well performance as a function of choke size; upstream choke pressure; choke temperature; producing and solution GOR; gas, oil, and water gravities; and a discharge coefficient. The coefficient compensates for nonideal factors excluded in the development of the equation and relates theoretical oil production rates through chokes to field-measured rates. Discussion Various developments have been published that present theory and correlations for describing simultaneous liquid and gas flow though a restrictive orifice. The correlations of Poettmann and Beck were intended to aid in the prediction of gas-liquid flow through chokes. Their development followed the original presentation by Ros and was derived for an average orifice discharge coefficient. Poettmann and Beck considered the polytropic expansion of the gaseous phase of the fluid expanding through the choke. The polytropic expansion theory was used successfully by Ros and is perhaps the most rigorous development in the application of orifice flow theory to oilfield conditions. Basically, the derivation of any orifice relationship is dependent on two main criteria. First, an expression must be written relating the flowing fluid specific volume and velocity to the mass flow rate. Second, an independent equation must be written incorporating the behavior of the gaseous phase of the fluid with pressure. The above stipulations are met by the following relationships. The energy balance around a fluid flowing through an orifice may be written as(1)144 = 0 The polytropic expansion equation relating the specific volume of the gas, (Vf - Vl), to the confining pressure, p, the polytropic expansion constant, b, and the ratio p, the polytropic expansion constant, b, and the ratio of specific heat at constant pressure to specific heat at constant volume, n, is(2)n p(Vf - Vl) = b When an expression for the orifice velocity, v2, is achieved with Eqs. 1 and 2, a relationship for the mass rate of flow through the choke is achieved by using the resulting relationship:(3)v2 qm = CA (3) vf2 where C is the orifice discharge coefficient, and Subscript 2 denotes downstream orifice throat conditions. The solution of Eqs. 1 through 3 is given in Appendix A. The results are summarized below. For critical orifice flow, the critical pressure ratio, Ec, defined as the ratio of the upstream pressure to the downstream choke pressure, occurs when(4)= = 0; = critical pressure ratio. The condition following from the solution of Eqs. 1 and 3 for flow is(5) JPT P. 843