Predicting Multiphase Flow Behavior in a Deviated Well

Abstract

Summary In deviated wells of an offshore producing environment, flow of two- or three-phase mixtures is invariably encountered. While many investigators have studied vertical multiphase flow behavior, few studies, often entirely empirical, deal with deviated well systems. The main objective of this work is to present a model that predicts both flow regime and pressure gradient in a deviated wellbore. In the modeling of flow-pattern transition and void fraction, an approach similar to that for vertical flow is taken; i.e., four principal flow regimes are recognized: bubbly, slug, churn, and annular. The transition from bubbly to slug flow is found to be at a local void fraction of 0.25. This transition criterion in terms of gas and liquid superficial velocities is found to be significantly affected by the well deviation, particularly in highly deviated wells. The transitions from slug to churn flow and churn to annular flow occur at high fluid velocities and are unaffected by the well deviation. The velocity-profile-distribution parameter for bubbly, slug, and churn flows is found to be unaffected by the well deviation angle. Similarly, the terminal rise velocity for small bubbles also appears to be insignificantly affected by the well deviation. In contrast, the "Taylor" bubble-rise velocity changes dramatically as deviation angle is increased. Thus, the characters of slug and churn flows in a deviated well differ from those in a vertical well. Data on gas void fraction were obtained both from a 5-in. [127-mm] circular pipe and from annular flow channels for deviation angles up to 32° from the vertical. The validity of the proposed model is demonstrated with these data and with laboratory data from other sources. Several field examples are presented to show the application of the model. Introduction The importance of multiphase flow to chemical and petroleum industries needs no elaboration. For a vertical system, the major contributor to the pressure drop is, in most cases, the static head. Prediction of the total pressure drop in a multiphase system therefore requires accurate estimation of the in-situ gas void fraction. The flow of multiphase fluids in vertical pipes is fairly well understood. A number of available models allow determination of the flow pattern at any position in the pipe, which in turn allows estimation of void fraction and pressure drop with models appropriate for the given flow regime. Multiphase flow behavior in an inclined pipe, however, currently is not very well understood. Wellbore deviation adds another dimension to the already complex multiphase flow phenomena generally observed in vertical wells. Correlations available for determining flow-pattern transition and estimating void fraction and pressure gradient in inclined pipes are largely empirical. We discuss some of these correlations here before presenting our model for deviated wells. The classic studies of Beggs and Brill1 and Beggs2 probably give the most comprehensive method currently available for predicting void fraction and pressure drop in deviated wells. That correlation is based on a predictive method for the horizontal system and modifications to account for the system's inclination. For estimating liquid holdup for a horizontal system, fL90 (=in-situ liquid fraction=1- fg90), they propose the following equation in terms of mixture Froude number, NFrm(=nM2/gd), and the input liquid volume fraction, fLi(=nLs/nM): Equation 1 The values of the parameters a, b, and c depend on the flow regime. For inclined systems, Beggs and Brill1 used the holdup calculated by Eq. 1 and multiplied it by the Factor F(q). The value of the multiplier, Fq, depends on the pipe inclination, input liquid fraction, dimensionless liquid velocity number, the Froude number, and the flow pattern that would exist in an equivalent horizontal system. Note that the flow pattern thus calculated does not correspond to the actual pattern observed in the inclined system and is used by Beggs and Brill only as a correlating parameter. The predictions of the Beggs and Brill correlation are usually good, as shown by Payne et al.3 for inclined systems and by Lawson and Brill4 for vertical systems. However, the complications involved in the calculation procedure and the method's exclusive reliance on empiricism make it less than completely satisfactory. One problem with the correlation is that liquid input fraction, fLi, is used to determine the horizontal flow pattern and the correction factor, F(q). For stagnant liquid columns, when FLi=0, the method cannot be used, and for small values of fLi, the predictions of the method are unreliable. A second difficulty arises from the dependence of the deviation correction factor, F(q), on the dimensionless liquid velocity number, NvL. Danesh5 points out that for gas-condensate lines, consideration of the physical system indicates a decrease in F(q) with increasing NvL, while the opposite is predicted by the Beggs and Brill correlation. Perhaps this shortcoming of the Beggs and Brill method may be overcome by use of the density difference between the phases, rL-rg, instead of liquid density, rL, to define NvL. A number of other workers have proposed methods for predicting void fraction and pressure drop in inclined systems. The earliest attempts made by Baker6 and Flanigan7 are rather simplistic; their methods are applicable only for systems slightly inclined from horizontal, and are not expected to be very accurate. The more recent work of Guzhov et al.8 is more sophisticated but is still limited to systems very close to the horizontal and quite inaccurate at low values of liquid holdup.9. Mukherjee10 and Mukherjee and Brill11 present a correlation similar in approach and accuracy to that of Beggs and Brill. Methods based on the flow-pattern approach have also been proposed, but these methods generally are incomplete and address only one flow regime. For example, a number of researchers12–17 have proposed methods for calculating void fraction and pressure drop in inclined slug flow. For predicting void fraction during slug flow in deviated systems, Singh and Griffith12 propose a method similar to that for vertical flow. Using data from a system inclined at 5, 10, and 15° [0.087, 0.17, and 0.26 rad] from the horizontal, they obtained a value of 0.95 for the flow parameter C1, which is slightly lower than that for vertical systems. They also obtained a constant value of 1.15 for the terminal rise velocity, v¥T, for pipe sizes ranging from 0.43 to 0.84 in. [11 to 21.3 mm]. Singh and Griffith, however, did not actually gather bubble-rise velocity data; they used v¥T as a parameter in the void-fraction model.