Modeling Annular Flow Behavior for Gas Wells

Abstract

Summary A mechanistic model is developed for the prediction of annular two-phaseflow behavior in gas wells. The model can predict annular flow characteristics, such as liquid film thickness, gas void fraction, and pressure gradient. It wasevaluated against a data bank of 75 wells for pressure gradient. It wasevaluated against a data bank of 75 wells for which the pressure drop betweenthe bottom of the well and the wellhead was available. The model was alsocompared with data from two wells with measured pressure profiles. Modelpredictions are in agreement with these data and superior to most commonly usedcorrelations. Introduction Gas/liquid two-phase flow occurs in a wide range of engineering applicationsin the petroleum, nuclear, chemical, and geothermal industries. Two-phase flowin the petroleum industry is very common because of the simultaneous productionof gas, oil, and water from hydrocarbon reservoirs. When gas and liquid flow simultaneously in a pipe, various flowconfigurations or patterns may form, each with different spatial dis-tributionsof the gas/liquid interface. The existing flow patterns depend on theoperational variables-namely, the liquid and gas flow rates, the physicalproperties of the two phases, and the geometry of the conduit (diameter andinclination angle). Knowledge of the flow regime that will occur in a pipe isessential to the design engineer because the flow hydrodynamics and thetransfer mechanisms of momentum, mass, and heat differ significantly from onepattern to another. For upward vertical flow, the flow patterns encountered art bubble, dispersed bubble, slug, churn, and annular flow. Flow-pattern prediction hasbeen studied extensively by two-phase-flow prediction has been studiedextensively by two-phase-flow researchers. Recent models enable prediction offlow patterns for all inclination angles. These models, which are givenelsewhere beyond the scope of this paper. Annular flow occurs under conditions of high gas flow raw and low to mediumliquid flow rate. The liquid flows as a film around the pipe wall, surroundinga high-velocity gas core, which may contain entrained liquid droplets. Theinterface between the gas and the liquid film is very wavy. Atomization anddeposition of liquid droplets occur through this interface. Predicting flow behavior under annular conditions is important for properdesign of systems, such as gas wells. Earlier predictive means for two-phaseflow were empirical correlations. These correlations have been usedextensively, but their validity is limited because they depend strongly on theconditions under which the experimental data were taken. An attempt has beenmade recently to develop models to predict flow behavior on the basis ofphysical principles. These models can be applied for different flow principles. These models can be applied for different flow conditions with more confidencebecause they include such important parameters as pipe diameter, inclinationangle, physical properties, parameters as pipe diameter, inclination angle, physical properties, and flow rates. Wallis and Hewitt and Hall-Taylor gave general discussions of annular flow. Dikler presented an early attempt to model annular flow that considered fallingfilm in vertical pipes. Hewitt later extended this work to upward flow. Morerecently, other models have been published for vertical upward annular flow. Hasan and Kabir developed a comprehensive model for predicting two-phase flowin wellbores that includes treatment of annular predicting two-phase flow inwellbores that includes treatment of annular flow with previously publishedmethods. Yao and Sylvester presented a simple model to predict film thicknessand pressure drop presented a simple model to predict film thickness andpressure drop for vertical flow. The Oliemans et al model is based on atwo-fluid model supported by empirical correlations far both entrainment andinterfacial shear stress. Finally, Caetano presented a model for annular flowin an annulus configuration. Physical mechanisms associated with annular flow have also been studiedextensively. Turner et al. and Ilobi and Ikoku studied the minimum gas velocityrequired for liquid removal from verbical pipes. Taitel et. al.. used this sameconcept to predict the tran-sition boundary to annular flow. Wallis, Henstockand Hanratty, Whalley and Hewitt, and Asali et al developed interfacial shearrelationships. Various studies" have focused on the entrainment process. These phenomena are essential to model development. Oliemans et al gave acomprehensive review of both interfacial shear and entrainment. They concludedthat most of the correlations for entrainment do not give satisfactory resultsand apply only in the test range in which they were derived. The objective of this study is to present a general model for the predictionof annular flow behavior in vertical pipes. This includes prediction of annularflow behavior in vertical pipes. This includes the prediction of liquid filmthickness, gas void fraction, and pressure bent. The model is presented in adimensionless form, thus pressure bent. The model is presented in adimensionless form, thus making its application easy and straightforward to anyflow condition. Analysis Fig. 1a is a schematic of annular flow, and Fig. lb shows the generalapproach of separating the flow into two fluids. This includes the liquid filmflowing around the pipe wall and the core, which consists of the gas phase andentrained liquid droplets. The proposed model is for fully developed annular flow in vertical andoff-vertical upward pipes under isothermal conditions. The liquid film isassumed to have a uniform thickness, hF, and to be free of gas. The fluid inthe core is considered homogeneous i.e., no slip occurs between the liquiddroplets and the gas phase. The average-velocity concept is used in both theliquid film and gas core regions. Although the model assumes incompressibleflow, gas compressibility can be taken into account in the numericalintegration to calculate total pressure drop. From the above simplified assumptions, the conversation laws of linearmomentum and mass are used to derive the model The approach taken is similar to Taitel and Dukler's for horizontal and near-horizontal stratified flow and Barnea et al. for downward vertical annular flow. Linear Momentum. Eqs. 1 and 2 represent the conservations of the linearmomentum applied to the liquid film and gas core, respectively (refer to Fig.1b): Assuming equilibrium condition between the liquid phase and the gas core, wecan combine Eqs. 1 and 2 by eliminating the pressure gradient. SPEPE P. 435