Critical Flow of Wet Steam Through Chokes
Authors: Chien Sze-Foo 
Published: December 2007

Summary
Analytical models and experimental results of the critical flow of steam areinvestigated. A new parameter, the dimensionless critical steam flux derivedfrom the perfect-gas model, has proved to be useful and convenient forcorrelating critical-flow data. Based on both analytical and experimental data, empirical correlations of the dimensionless critical steam flux and thecritical-pressure ratio are established as functions of stagnation steamquality.

Introduction
Energy management for large steam stimulation and steamflood oil recoveryprojects requires improved measurement and control techniques for both steamquality and steam flow rate. Such measurements and controls are necessary toensure the efficient and effective use of heat distributed to the injectionwells. Inexpensive and accurate steam-quality measurement devices for fieldwideapplications are still being developed. Most injection wells, however, areequipped with a flow-rate control device at the wellhead, usually an adjustablecontrol valve or a static choke. The adjustable control valve is designed forsteam flow at a relatively low velocity and causes only minor pressure lossacross the valve. It is used when the steam-distribution system can afford onlya slight pressure loss across the flow-rate control device. Of course, suchvalves can also be used for high flow rates or even at critical-flow conditionsif the flow system can afford a substantial pressure loss across the controlvalve. The static choke is a popular steam-flow-rate control device for almostall shallow steam-injection wells. To achieve a constant flow rate, the staticchoke is always used under a critical-flow condition. Because of the choke'sdesign, the downstream pressure at which the critical flow of the static chokeoccurs is fairly low compared with its upstream pressure. Thus, the staticchoke involves a large pressure loss, which limits its applications to shallowwells. Fig. I depicts a typical static choke. The essential part of the chokeis the choke bean, which is a short tube (normally 6 in. [15.2 cm] long). Thechoke-bean diameter may vary from 1/8 to 3/4 in. [0.3 to 1.9 cm], depending onthe flow rate desired. Before steamflooding became an oilfield practice, staticchokes were used extensively and satisfactorily on gas wells to control the gasflow rate. The flow-rate equations and critical-pressure information weredeveloped for gas, a single-phase fluid. Most steam used in steam EOR projectsis a wet steam that is a two-phase liquid. The flow rate and pressure of thecritical flow of wet steam are not fully understood. This paper investigatesthe critical-flow rate and critical-pressure ratio of the wet steam by use ofanalytical models and experimental data and establishes empirical correlationsfor the critical flow rate and critical pressure. Focusing on practicaloilfield applications, this study covers the critical flow of steam with steampressures ranging from 50 to 2,000 psia [0.3 to 13.8 MPa] and steam qualityranging from 10 to 100%.

Analytical Approaches for the Critical Flow of Steam
Critical flow refers to a situation where, for a given stagnation (orupstream) condition and a given flow-rate control device, further reduction inthe downstream pressure of the choke fails to increase the mass flow rate. Thismass flow rate is defined as the critical mass flow rate, and the pressure atthe exit end of the flow-rate control device when the critical flow firstoccurs is defined as the critical pressure. For convergent/divergent-typecontrol devices, however, the throat pressure when critical flow first occursis defined as the critical pressure. The critical mass flow rate per unitcross-sectional area of flow is known as the critical mass flux; the ratiobetween the critical pressure and the stagnation pressure is thecritical-pressure ratio. In practice, the pressure downstream of a flow-ratecontrol device may be less than the critical pressure. Under such a condition, the criteria for the critical-pressure ratio and the critical mass flux stillhold. Two basic analytical approaches are used to study critical steam flow: aperfect-gas model and a homogeneous-equilibrium model. Results serve as basesfor comparison with experimental data and for establishing the empiricalcorrelations of the critical flow.