A Study of Multiphase Flow Behavior in Vertical Wells

Abstract

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,1 Aziz et al.,2 and Chierici et al.3 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.4 has found wide use in the petroleum industry. The flow-pattern map of Hewitt and Roberts5 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.