a basic approach to wellbore two-phase flow modeling

Abstract This study presents a simplified two-phase flow model using the drift-flux approach to well orientation, geometry, and fluids. For estimating the static head, the model uses a single expression for liquid holdup, with flow-pattern-dependent values for flow parameter and rise velocity. The gradual change in the parameter values near transition boundaries avoids discontinuity in the estimated gradients, unlike most available methods. Frictional and kinetic heads are estimated using the simple homogeneous modeling approach. We present a comparative study involving the new model as well as those that are based on physical principles, also known as semimechanistic models. These models include those of Ansari et al, Gomez et al., and OLGA. Two other widely used empirical models, Hagedorn and Brown and PE2, are also included. The main ingredient of this study entails the use of a small but reliable dataset, wherein calibrated PVT properties minimizes uncertainty from this important source. Statistical analyses suggest that all the models behave in a similar fashion and that the models based on physical principles appear to offer no advantage over the empirical models. Uncertainty of performance appears to depend upon the quality of data input, rather than the model characteristics. Introduction Modeling two-phase flow in wellbores is routine in every-day applications. The use of two-phase flow modeling throughout the project life cycle with an integrated asset modeling network has rekindled interest in this area. Plethora of models, some based on physical principles and others based on pure empiricism, often beg the question which one to use in a given application. Although a few comparative studies (Ansari et al. 1994; Gomez et al. 2000; Kaya et al. 2001) attempt to answer this question, often reliability of the data base has left this issue unsettled. One of the main objectives of this paper is to present a simplified two-phase flow model, which is rooted in drift-flux
approach. The drift-flux approach (Hasan and Kabir, 2002, pp. 21-62, Shi et al. 2005a, 2005b) has served the industry quite well, as exemplified by its simplicity, transparency, and accuracy in various applications. The second objective is to show a comparative study with a few models using a small but reliable data base to get a perspective on relative performance. Here, data reliability stems from two elements: rate and fluid PVT properties. Pressure data are typically gathered with permanent downhole and wellhead sensors while rate data are measured with surface flow meters or test separators. In each case, the black-oil fluid PVT model was conditioned with laboratory data to ensure reliability and consistency. Proposed Model Total pressure gradient during any type of fluid flow is the sum of the static, friction, and kinetic gradients, the expressions for which are given in Eq. A-1 in the Appendix. For most vertical and inclined wells, the static head component–which directly depends on the volume average-mixture density–dominates. Thus, in simple terms, two-phase flow modeling boils down to estimating density of the fluid mixture or gas-volume fraction. Because gas-volume fraction depends on whether the flow is bubbly, slug, churn, or annular, we individually model each flow regime. However, for all flow regimes the gas (or lighter) phase moves faster than the liquid (or heavier) because of its buoyancy and its tendency to flow close to the channel center. This allows us to express in-situ gas velocity as the sum of bubble rise velocity, v∞, and channel center mixture velocity, Covm. However, in-situ velocity is the ratio of superficial velocity to volume fraction. Therefore, the generalized form of gas-volume fraction relationship with measured variables– superficial velocity of gas and liquid phases–can be written as
Copyright 2007, Society of Petroleum Engineers This paper was prepared for presentation at the 2007 SPE Annual Technical Conference and Exhibition held in Anaheim, California, U.S.A., 11–14 November 20ቤተ መጻሕፍቲ ባይዱ7. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, Texas 75083-3836 U.S.A., fax 01-972-952-9435.