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Collaborating Authors
Oil & Gas
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 32ยฐ 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 researchers12โ17 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 15ยฐ [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, vยฅT, 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 vยฅT as a parameter in the void-fraction model.
- Europe > United Kingdom > North Sea > Central North Sea > Central Graben > Block 21/10 > Forties Field > Forties Formation (0.94)
- Europe > Norway > North Sea > Central North Sea > Central Graben > PL 018 > Block 2/4 > Greater Ekofisk Field > Ekofisk Field > Tor Formation (0.94)
- Europe > Norway > North Sea > Central North Sea > Central Graben > PL 018 > Block 2/4 > Greater Ekofisk Field > Ekofisk Field > Ekofisk Formation (0.94)
Summary This paper presents a physical model for predicting flow pattern, void fraction, and pressure drop during multiphase flow in vertical wells. The hydrodynamic conditions giving rise to various flow patterns are first analyzed. The method for predicting void fraction and pressure drop is then developed. In the development of the equations for pressure gradient, the contribution of the static head, frictional loss, and kinetic energy loss are examined. Laboratory data from various sources show excellent agreement with the model. Introduction A number of correlations are available for predicting pressure drop during multiphase flow. Because most of these correlations are entirely empirical, they are of doubtful reliability. The calculation procedures involved are also rather complicated. Therefore, a better approach is to attempt to model the flow system and then to test the model against actual data. Proper modeling of multiphase flow requires an understanding of the physical system. When cocurrent flows of multiple phases occur, the phases take up a variety of configurations, known as flow patterns. The particular flow pattern depends on the conditions of pressure, flow, and channel geometry. In the design of oil wells and pipelines, knowledge of the flow pattern or successive flow patterns that would exist in the equipment is essential for choosing a hydrodynamic theory appropriate for that pattern. The name given to a flow pattern is somewhat subjective. Hence, a multitude of terms have been used to describe the various possible phase distributions. In this paper, we will be concerned only with those patterns that are clearly distinguishable and generally recognized. The major flow patterns encountered in vertical cocurrent flow of gas and liquid are listed in standard textbooks and in the classic works of Orkiszewski, Aziz et al., and Chierici et al. The four flow patterns---bubbly, slug, churn, and annular---are shown schematically in Fig. 1. At low gas flow rates, the gas phase tends to rise through the continuous liquid medium as small, discrete bubbles, giving rise to the name bubbly flow. As the gas flow rate increases, the smaller bubbles begin to coalesce and form larger bubbles. At sufficiently high gas flow rates, the agglomerated bubbles become large enough to occupy almost the entire pipe cross section. These large bubbles, known as "Taylor bubbles," separate the liquid slugs between them. The liquid slugs, which usually contain smaller entrained gas bubbles, provide the name of the flow regime. At still higher flow rates, the shear stress between the Taylor bubble and the liquid film increases, finally causing a breakdown of the liquid film and the bubbles. The resultant churning motion of the fluids gives rise to the name of this flow pattern. The final flow pattern, annular flow, occurs at extremely high gas flow rates, which cause the entire gas phase to flow through the central portion of the tube. Some liquid is entrained in the gas core as droplets, while the rest of the liquid flows up the wall through the annulus formed by the tube wall and the gas core. In an oil well, different flow patterns usually exist at different depths. For example, near bottom hole we may have only one phase. As the fluid moves upward, its pressure gradually decreases. At the point where the pressure becomes less than the bubblepoint pressure, gas will start coming out of solution and the flow pattern will be bubbly. As pressure decreases further, more gas may come out of solution and we may see the whole range of flow patterns shown in Fig. 2. Here we discuss the hydrodynamic conditions that give rise to the various flow-pattern transitions. The method for estimating pressure drop in each flow regime is then developed. In developing the equations for pressure gradient, we note that for vertical flow of gas/liquid mixtures, 90 to 99% of the total pressure drop is usually caused by the static head. Accurate estimation of the in-situ gas void fraction is therefore of great importance. Flow Pattern Transition The often chaotic nature of multiphase flow makes it difficult to describe and to classify flow patterns and hence to ascribe criteria for flow-pattern transitions correctly. In addition, although flow patterns are strongly influenced by such parameters as phase velocities and densities, other less important variables---such as the method of forming the two-phase flow, the extent of departure from local hydrodynamic equilibrium, the presence of trace contaminants, and various fluid properties---can influence a particular flow pattern. Despite these deficiencies, a number of methods have been proposed to predict flow pattern during gas/liquid two-phase flow. Some of these methods could be extended to liquid/liquid systems with less accuracy. One method of representing various flow-regime transitions is in the form of flow-pattern maps. Superficial phase velocities or generalized parameters containing these velocities are usually plotted to delineate the boundaries of different flow regimes. Obviously, the effect of secondary variables cannot be represented in a two-dimensional map. Any attempt to generalize the map requires the choice of parameters that would adequately represent various flow-pattern transitions. Because differing hydrodynamic conditions and balance of forces govern different transitions, a truly generalized map is almost impossible. Still, some maps are reasonably accurate. Among these, the map proposed by Govier et al. has found wide use in the petroleum industry. The flow-pattern map of Hewitt and Roberts has also been widely accepted in academia and the power-generating industry. An alternative, more flexible approach is to examine each transition individually and to develop criteria valid for that specific transition. Because this approach allows physical modeling of individual flow patterns, it is more reliable than the use of a map.
- North America > United States > Texas > Permian Basin > Midland Basin > Steen Field (0.89)
- North America > Canada > Northwest Territories > Wallis Field (0.89)
SUMMARY. This work proposes a hydrodynamic model for estimating gas void fraction, fg, in the bubbly and slug flow regimes. The model is developed from experimental work, involving an air/water system, and from theoretical arguments. The proposed model suggests that prediction of fg, and hence the bottomhole pressure (BHP), is dependent on such variables as tubing-to-casing-diameter ratio, densities of gas and liquid, and surface tension. Available correlations do not include these variables as flexible inputs for a given system. Computation on a field example indicates that slug flow is the most dominant flow mechanism near the top of liquid column at the earliest times of a buildup test. As buildup progresses, transition from slug to bubbly flow occurs in the entire liquid column. Beyond the after flow-dominated period, the effect of bubbly flow diminishes as gas flow becomes negligibly period, the effect of bubbly flow diminishes as gas flow becomes negligibly small. Comparisons of BHP's are made with the proposed and available correlations. Because the proposed model predicts fg between those of the Godbey-Dimon and Podio et al. correlations, BHP is predicted accordingly. Introduction Acoustic well sounding has become a well-established method for estimating BHP in a pumping oil well. The method involves determining the gas/liquid interface in the tubing/casing annulus. From the knowledge of the lengths of gas and liquid columns, BHP can be estimated by adding the pressures exerted by these columns to the casinghead pressure. Although simple in concept, this indirect BHP calculation presents potential problems in two areas: resolution of the acoustic device measuring the gas/liquid interface and estimation of the gas-entrained-liquid-column density. Significant progress has been made in the acoustic device's ability to monitor the movement of the liquid column as a function of time during a buildup test. Estimation of the changing liquid-column density, however, is still fraught with uncertainties. The dead-liquid gradient needs to be adjusted by the so-called gradient correction factor, Fg, (= 1 -fg) to reflect the true column density. Three Fgc correlations proposed by Gilbert, Godbey and Dimon, and Podio et al. have found wide use in the petroleum industry. Relative merits of these correlations were addressed recently. Research in two areas-mass transfer in gas/liquid systems and two-phase flow-has produced a wealth of information for predicting gas void fractions in stagnant liquid columns. None of predicting gas void fractions in stagnant liquid columns. None of these correlations, however, account for the effect of casing and tubing diameters on Fgc. Reliable Fgc prediction is critically important because afterflow, during which the gas continues to bubble through the liquid column, dominates a buildup test in a typical pumping well. In most cases, semilog period beyond afterflow is pumping well. In most cases, semilog period beyond afterflow is seldom reached to allow conventional analysis for estimating permeability-thickness product, skin, and static pressure. Thus, permeability-thickness product, skin, and static pressure. Thus, analysis of after flow-dominated transients provides a viable alternative to the conventional semilog analysis. The purpose of this paper is to explore the relevant literature and to develop a hydrodynamic model for a practical range of flow conditions encountered in a pumping-well annulus through theoretical considerations and experimental work. Theoretical and Experimental Models Concerning Bubbly Flow. Researchers of multiphase flow have usually correlated the void fraction with drift flux, u. Drift flux is a way of expressing the difference between the in-situ velocities of the two phases, vg and vt - i.e., "slip" - and is defined by the following expression:Eq. 1 may be written in terms of the measurable superficial velocities of the phases, vgs and vls, by noting that vgs = fgvg and vls = (1 - fg)vl: For ideal bubbly flow, Wallis suggests the following semitheoretical relationship between drift flux, gas void fraction, and terminal rise velocity of a gas bubble, v : For a stagnant liquid column when vls = 0, substituting u from Eq. 2 into Eq. 3 gives There are a number of correlations available for the terminal rise velocity, v, in an infinite medium. The equation proposed by Harmathy, which has been supported by data from independent sources, gives Wallis suggested that the value of n = 2 be used along with Eq. 5 for v; therefore, Eq. 4 becomes There are disagreements over the exact value of n to be used in Eq. 4. The value of n is affected by impurities in the liquid, the way bubbles are introduced into the column, and the distance these bubbles travel from the point of injections Many workers have used a negative value for the exponent n and expressed fg/(1 -fg)m as a function of superficial gas velocity. For example, Mersmann proposes the following relationship: proposes the following relationship: Akita and Yoshida propose a similar equation with slightly different groupings of properties and values of constants. SPEPE P. 113
- North America > United States > Louisiana (0.28)
- North America > United States > California (0.28)