Intermittent two phase flow in horizontal pipes: Predictive models

A semi-mechanistic model for two phase gas-liquid slug flow proposed recently by Dukler and Hubbard has been modified and extended to apply to the entire intermittent flow regime. Flow predictions of the model proposed in this paper are compared with detailed experimental data recently obtained for an air-oil system. The model requires the use of empirical correlations for the slug velocity and the in situ liquid volume fraction in the slug. In addition, either the slug frequencies or length corresponding to the given design conditions must be known. However, calculated values of average pressure gradient and in situ liquid volume fraction are relatively insensitive to these latter parameters, and in fact, good results are obtained assuming a constant slug length. The paper includes a discussion of the limitations of the proposed model and the expected direction of further study required to extend its mechanistic aspects.     

Flow pattern in horizontal and vertical two phase flow in small diameter pipes

New data on flow pattern transition for gas liquid flow in small diameter tubes (4 to 12 mm) is presented. The experimental results are compared with previously published models for horizontal and vertical flows considered to be valid for medium and large diameter pipes. The effect of surface tension which might be expected to be important in small diameter pipe flow has been found to affect only the stratified-slug transition in horizontal flow. A modification to the model to include this effect is proposed.     

Identification of stratified liquid-liquid flow through horizontal pipes by a non-intrusive optical probe

The stratification during the simultaneous flow of two immiscible liquids through a horizontal conduit has been investigated. For the identification of different flow patterns, an indigenously developed unique optical probe has been used. The presence of different phase contents and various interfacial features along the optical path gives rise to attenuation and scattering and makes the identification possible. The probability density function (PDF) analysis and the wavelet multiresolution technique have been adopted for development of an objective flow-pattern indicator. The range of existence of the different stratified distributions as predicted by the indicator is in close agreement with the maps reported in literature.     

Numerical modeling of three-phase stratified flow in pipes

The simultaneous flow of water, oil and gas is of practical importance for the oil and gas industry. These three phases are present in varying degrees of concentration in many oil and gas pipelines. In this work, a model has been developed to predict the values of the hold-up and pressure gradient for three-phase stratified flow prevailing in a horizontal pipeline. This information is usually the first step for analyzing the stability of stratified flow and developing transition criteria. The concept of extended velocity has been applied to compute the wall shear stresses in three-phase flow. The effect of process variables such as gas to liquid ratio, pipe diameter, oil viscosity and non-Newtonian character of oil on hold-up and pressure gradient has been studied to simulate the oil well conditions. Structural stability analysis was also carried out to check for the sensitivity of the model.     

Void fraction and pressure drop in two phase stratified flow

A procedure for computing the void-fraction and pressure drop in two-phase stratified flow over the whole range of flows from turbulent-turbulent to laminar-laminar, has been put forth. The results are in excellent agreement with those of previous investigators in flow situations where data are available. Simple curve fits of the theoretical results have been developed to compute the required quantities, as functions of the Lockhart - Martinelli parameters.     

Adiabatic homogeneous bubbly flow in horizontal pipes

The usual one dimensional method of analysis based upon the equations of continuity, energy and momentum is applied to the flow of homogeneous bubbly liquid-gas mixtures in horizontal pipes. The analysis results in a set of equations which are adequate insofar as they are able ro explain known phenomena of the flow. It is shown that the concept of the Mach number, applied to bubbly pipe flow, is physically meaningful in the same way as it is in gas dynamics and that the condition, Mach number equal to one represents a realistic criterion for flow choking. A friction-length formula is derived and verified experimentally.     

Stratified turbulent-turbulent gas-liquid flow in horizontal and inclined pipes

A two-dimensional model for stratified turbulent-turbulent gas-liquid flow in inclined pipes is proposed. The gas phase is treated as bulk flow, but an exact solution is carried out for the liquid phase, applying the eddy viscosity theory to model the turbulent viscosity. The interfacial structure is taken into consideration using appropriate correlations for the interfacial shear stress. The model is capable of predicting the liquid velocity field, holdup and pressure drop given gas and liquid flow rates, physical properties, pipe size, and angle of inclination. The results are substantially better than the prediction of Lockhart and Martinelli (1949) correlation and better than the Taitel and Dukler (1976) model for stratified flow.     

Characterization of foam flow in horizontal pipes by using two-flow-regime concept

Foam has been widely used in numerous scientific and engineering applications. Although foam has relatively low fluid density because of high gas content, it can exhibit a viscosity value enormously higher – often several orders of magnitude higher – than that of bulk gas or liquid phase. Since foam typically exists as a complex fluid system with internal gas bubbles and external liquid phase, understanding and characterizing its flow behavior is very challenging.The objective of this study is to investigate the characteristics of foam rheology in horizontal pipes in a wide range of experimental conditions—two different pipe materials (stainless steel and nylon pipes with about 0.5 in in outer diameter and 12 ft in length), three surfactant formulations (Cedepal FA-406, Stepanform-1050, and Aquet-944), and three surfactant concentrations (0.1, 0.5, and 5 wt%). The experimental data can be collected in terms of (i) pressure measurements at several positions along the pipes and (ii) visual analysis of bubble size and bubble-size distribution during the shear flow. The concept of “two foam-flow regimes” consisting of high-quality regime and low-quality regime is at the heart of interpreting the experimental outcome.The experimental results showed that there were two distinct high-quality and low-quality foam flow regimes which could be identified by both pressure responses and direct visual observations. The results further showed that the high-quality regime was characterized by unstable and oscillating pressure responses represented by the repetition of fine-textured foam and free gas (i.e., slug flow), while the low-quality regime was characterized by stable pressure responses represented by either the flow of fine-textured foams (i.e., plug flow) or the flow of upper-layer foams and lower-layer liquid (i.e., segregated flow). These two regimes, separated by a locus of f_g^? in the contour plot, were shown to have different sensitivities to the change in gas and liquid velocities: (1) foam rheology in the high-quality regime was dependent upon both gas and liquid velocities because the lengths of fine-textured-foam and free-gas sections were altered to adjust to the new flow conditions, and (2) foam rheology in the low-quality regime was primarily dependent upon gas velocity because of the development of fine-textured foams with increase in shear rates, and was relatively independent of liquid velocity because of lubricating effect and drainage effect.The implication of these experimental findings is discussed for applications such as foam-assisted underbalanced drilling processes and foam fracturing treatments in the petroleum industry.     

水平管气液二相分层流移动壁面模型的改进

针对基于Standard k-ε湍流模型的移动壁面模型在预测水平管气液二相分层流气相封闭关系时的不足,利用Launder-Spalding和Launder-Sharma低雷诺数k-ε湍流模型对移动壁面模型进行改进,其中湍流黏度和湍流雷诺数由修正湍流耗散率替代原定义的耗散率。通过数值模拟结果拟合出新的气壁和界面摩擦因子Blasius形式公式,计算结果发现,湍流模型的选择对固定壁面和移动壁面剪切的预测都有明显影响,其中Launder-Spalding低雷诺数k-ε湍流模型得到的气相封闭关系预测精度最高,在气、液相雷诺数9 000≤ReG≤50 000和20 000≤ReL≤30 000,压降预测相对均根误差为10.6%,为理论和实验研究提供了有价值的参考。     

Analysis of stratified laminar flow of immiscible liquids in circular and non-circular pipes

A numerical analysis has been made of laminar stratified flow of two immiscible Newtonian liquids in circular and certain non-circular pipe configurations. Solutions are given far viscosity ratios of 10, 100, and 1000 and for various volumetric flow rate fractions. Five pipe configurations are studied. In each case volumetric flow rate factors and power reduction factors are computed. It is shown that the circular pipe is the best pipe configuration for the two-phase flow having a viscosity ratio of about 10 or less. A flat bottomed pipe configuration is found to give higher volumetric flow rate factors as well as higher power reduction factors than the circular pipe when the viscosity ratio is about 100 or more.     

An improved two layer model for horizontal slurry pipeline flow

A model for predicting head losses for coarse-particle or settling slurries has been obtained. Experimental data for isothermal flows of sand, gravel and coarse coal slurries in pipes of industrial scale have been used to obtain the correlations in the model. The model differs from previous versions in the way it deals with the concentration of the lower layer and in the role ascribed to the finest (–74 μm) particles. The fraction of contact load, which contributes sliding friction at the pipe wall, is found to be primarily a function of the ratio of the mean flow velocity to the settling velocity of the mass median particle size in the (+74 μm) fraction. The correlations are restricted to mixtures containing less than 35% (+ 74 μm) particles by volume.     

Flow pattern transition for downward inclined two phase flow; horizontal to vertical

Data on the flow pattern transition for gas liquid flow in pipes for downward 0–90° inclination was collected. Mathematical models were developed to predict the flow pattern in the whole range of downward inclination.     

Prediction of flow pattern for the co-current flow of gas and non-newtonian liquid in horizontal pipes

Previous work on delineating flow patterns for the horizontal two-phase flow of gas and Newtonian liquid is briefly described. One of the flow pattern maps has been slightly adjusted to take account of the evidence from more recent studies. It is shown that physical properties of the system have relatively little influence on flow regime. It is then established that this map is also applicable when the liquid shows shear-thinning non-Newtonian properties.     

Holdup for two-phase flow of gas-non-newtonian liquid mixtures in horizontal and vertical pipes

The paper deals with the experimental investigations carried out to evaluate holdup for gas-non-Newtonian (pseudoplastic) liquid mixtures in vertical and horizontal flow in pipes. Correlations developed predict holdup in slug flow regime with acceptable statistical accuracy.     

Experimental validation of a simple model for gas-liquid slug flow in horizontal pipes

In this work, the simple submodel of Taitel and Barnea (Chem. Eng. Sci. 45 (1990) 1191) for horizontal gas-liquid slug flow has been reformulated. An additional source of pressure loss suggested by Cook and Behnia (Chem. Eng. Sci. 55 (2000) 4699) was incorporated in the model, thus improving its predictive accuracy. The proposed model was tested extensively against 12 pressure gradient and eight liquid holdup data sources for both air-water and air-oil slug flow in smooth and rough pipes over a wide range of operating conditions. The very good agreement between the predicted and experimental results substantiates the general validity of the model.