Friction factor improved correlations for laminar and turbulent gas–liquid flow in horizontal pipelines

We develop improved correlations for two-phase flow friction factor that consider the effect of the relative velocity of the phases, based on a database that includes 2560 gas–liquid flow experiments in horizontal pipes. The database includes a wide range of operational conditions and fluid properties for two-phase friction factor correlations. We classify the experiments by liquid holdup ranges to obtain composite analytical expressions for two-phase friction factor vs. the Reynolds number by fitting logistic dose curves to the experimental data with. We compute the liquid holdup values used to classify the experimental data using correlations proposed previously. The Reynolds number is based on the mixture velocity and the liquid kinematic viscosity. The Fanning friction factor for gas–liquid is defined in term of the mixture velocity and density. Additionally, we sort the experimental data by flow regime and obtain the two-phase friction factor improved correlations for dispersed bubble, slug, stratified and annular flow for different holdup ranges. We report error estimates for the predicted vs. measured friction factor together with standard deviation for each correlation. The accuracy of the correlations developed in this study is compared with that of other 21 correlations and models widely available in the specialized literature. Since different authors use different definitions for friction factors and Reynolds numbers, we present comparisons of the predicted pressure drop for each and every data point in the database. In most cases our correlations predict the pressure drop with much greater accuracy than those presented by previous authors.     

Heat transfer measurements and correlations for air–water flow of different flow patterns in a horizontal pipe

Heat transfer coefficients were measured and new correlations were developed for two-phase, two-component (air and water) heat transfer in a horizontal pipe for different flow patterns. Flow patterns were observed in a transparent circular pipe using an air–water mixture. Visual identification of the flow patterns was supplemented with photographic data, and the results were plotted on the flow regime map proposed by Taitel and Dukler and agreed quite well with each other. A two-phase heat transfer experimental setup was built for this study and a total of 150 two-phase heat transfer data with different flow patterns were obtained under a uniform wall heat flux boundary condition. For these data, the superficial Reynolds number ranged from 640 to 35,500 for the liquid and from 540 to 21,200 for the gas. Our previously developed robust two-phase heat transfer correlation for a vertical pipe with modified constants predicted the horizontal pipe air–water heat transfer experimental data with very good accuracy. Overall the proposed correlations predicted the data with a mean deviation of 1.0% and an rms deviation of 12%.     

Experimental investigation and theoretical modeling of liquid entrainment in a horizontal tee with a vertical-up branch

This article describes a comprehensive literature review of liquid entrainment in horizontal pipes with vertical-up branches. Deficiencies in the available data and correlations were identified. The Air–water Test Loop for Advanced Thermal–hydraulic Studies (ATLATS) was constructed and entrainment onset and steady-state data were collected for a wide range of flow conditions. Using new insights gained from experimental testing, the authors developed a model for predicting the onset of entrainment and steady-state entrainment rate. Previously published correlations, along with the new model, are compared against all available data. The new model shows very good agreement with the onset data, but is not very good at predicting branch quality at high liquid flow rates.     

The split of vertical annular flow at a large diameter T junction

Measurements and observations have been made of the split of gas—liquid flow at a T junction where the main pipe was vertical and the side arm horizontal. All three pipes connecting to the junction were of 0.125 m dia. The gas and liquid flow rates were chosen to ensure annular flow in the inlet pipe. The resulting data have been compared with existing models.     

An appraisal of liquid–liquid slug flow in different pipe orientations

Gas–liquid slug flow occurs over a wide range of phase flow rates and in a variety of practical applications during gas–liquid two-phase flows. The range of slug flow increases further in narrow pipes (<0.0254 m), undulated pipelines, riser tube, etc. On the other hand, the past literature shows that slug flow is rarely observed for liquid–liquid cases. In the present study, an interest was felt to investigate whether liquid–liquid slug flow occurs in situations known for excessive slugging in gas–liquid cases. For this, experiments have been performed in narrow (0.012 m ID) vertical and horizontal pipes and an undulated pipeline of 0.0254 m internal diameter where the V-shaped undulation comprises of an uphill and a downhill section between two horizontal pipes. The studies have been performed for both peak and valley orientation of the undulation. Kerosene and water have been selected as the test fluids and the optical probe technique has been used to supplement visual observations especially at higher flow rates. The studies have revealed the existence of the slug flow pattern over a wide range of phase flow rates in all the three geometries. Interestingly, it has been noted that the introduction of an undulation induces flow patterns which bear a closer resemblance to gas–liquid flows as compared to liquid–liquid flows through a horizontal pipe of 0.0254 m diameter.     

Development of a new temperature measuring system for gas–liquid flow in spraying field

Based on previous work, a new temperature measuring system for gas–liquid flow, composed of shielded and unshielded thermocouples, on-line laser detection device for liquid droplets, vacuum pump and wavelet analysis data processor, is developed in this work. The necessity of vacuum pump and the criterion of mesh size selection are also described. Through an application of measuring temperature in saturator, it shows that the system can evaluate the separation of gas–liquid two-phase flow and measure the liquid droplet temperature and the gas temperature effectively in counter-current spraying field.     

Prediction of void fraction for gas–liquid flow in horizontal,upward and downward inclined pipes using artificial neural network

In this work, the ability of artificial neural networks (ANNs) to predict void fraction of gas–liquid two–phase flow in horizontal and inclined pipes was investigated. For this purpose, an ANN model was designed and trained using a total of 301 experimental data points reported in the literature for inclination angles between –20° and +20°. Pipe inclination angle as well as superficial Reynolds number of gas (Re_sg) and liquid (Re_sl) were chosen as input parameters of different structures of multilayer perceptron (MLP) neural networks, while the corresponding void fraction was selected as their output parameter. A hyperbolic tangent sigmoid and a linear function were employed as transfer functions of hidden and output layers, respectively, and Levenberg–Marquardt back propagation algorithm was used to train the networks. By trial–and–error method, a three–layer network with 10 neurons in the hidden layer was achieved as optimal structure of the ANN which made it possible to predict the void fraction with a high accuracy. Mean absolute percent error (MAPE) of 1.81% and coefficient of determination (R²) of 0.9976 for training data and MAPE of 1.52% and R² value of 0.9948 for testing data were obtained. Also for all data, MAPE of 1.95% and R² value of 0.9972 were calculated, and 96% data were within ±5% error band. In addition, the accuracy of the proposed ANN model was compared with the predictions from 17 void fraction correlations available in the literature for different flow patterns and horizontal and inclined flows. For all cases, the proposed ANN model gave better performance than all of the studied correlations. The results confirm the very good capability of the ANNs to predict the void fractions of gas–liquid flow in inclined pipes, regardless of flow pattern. Finally, by performing interpolation using the trained network, the void fraction values for some other conditions were predicted.     

Studies on two-phase co-current air/non-Newtonian shear-thinning fluid flows in inclined smooth pipes

In this work, co-current flow characteristics of air/non-Newtonian liquid systems in inclined smooth pipes are studied experimentally and theoretically using transparent tubes of 20, 40 and 60 mm in diameter. Each tube includes two 10 m long pipe branches connected by a U-bend that is capable of being inclined to any angle, from a completely horizontal to a fully vertical position. The flow rate of each phase is varied over a wide range. The studied flow phenomena are bubbly flow, stratified flow, plug flow, slug flow, churn flow and annular flow. These are observed and recorded by a high-speed camera over a wide range of operating conditions. The effects of the liquid phase properties, the inclination angle and the pipe diameter on two-phase flow characteristics are systematically studied. The Heywood–Charles model for horizontal flow was modified to accommodate stratified flow in inclined pipes, taking into account the average void fraction and pressure drop of the mixture flow of a gas/non-Newtonian liquid. The pressure drop gradient model of Taitel and Barnea for a gas/Newtonian liquid slug flow was extended to include liquids possessing shear-thinning flow behaviour in inclined pipes. The comparison of the predicted values with the experimental data shows that the models presented here provide a reasonable estimate of the average void fraction and the corresponding pressure drop for the mixture flow of a gas/non-Newtonian liquid.     

An extension of the Lockhart-Martinelli theory of two phase pressure drop and holdup

The Lockhart-Martinelli model is extended for the case of seperated flow, enabling theoretical relationships to be developed for holdup and pressure loss. For the stratified flow case the analytical solution gives close agreement with pressure loss data and with the results of the analyses of both Johannessen and of Taitel and Dukler. The holdup relation which was derived gave good agreement with data for the situation where interfacial shear is unimportant. For the case of annular separated flow the analytical solution gives close agreement with pressure loss data for large diameter pipes where liquid surface effects are minimal. The holdup relation on the other hand was severely in error but an empirical modification did serve to give good agreement with experimental data.

A further theoretical extension of the Lockhart-Martinelli approach enabled a general pressure loss correlation to be developed for annular type flows. Lack of systematic data for large diameter pipes, particularly for the steam-water case, hampers the application of the derivation, but, despite this draw-back, a general correlation is developed which accounts for the effect of pipe diameter and is useful for prediction of pressure loss in steam-water systems.     

Water-lubricated transport of high-viscosity oil in horizontal pipes: The water holdup and pressure gradient

This paper has investigated the water holdup and the pressure gradient of water-lubricated transport of high-viscosity oil flow in horizontal pipes. Experimental results on the water holdup and the pressure gradient of water-lubricated high-viscosity oil two-phase flow in a horizontal 1 in. pipe were discussed. Models for the prediction of the water holdup and/or the pressure gradient of core flow or water-lubricated flow were reviewed and evaluated. It was found that the water holdup of the water-lubricated flow is not only closely related to the input water volume fraction but also the degree of the oil phase eccentricity which is attributed to the oil phase Froude number. This can explain the inconsistency of the experimental results with regard to the relationship between the water holdup and the input water volume fraction in the literature. The applicability of the existing empirical or mechanistic models of water-lubricated high-viscosity oil flow were discussed and demonstrated. A modified correlation to the water holdup correlation of Arney et al. (1993) which was shown to be exclusively applicable for concentric core flow was introduced for stable water-lubricated flow, including both concentric and eccentric core flows. This correlation was evaluated and a fair applicability was shown. The accuracy of different models for the prediction of the pressure gradient of water-lubricated transport of high-viscosity oil was demonstrated to be not high in general. This is closely associated with the difficulty in accurately accounting for the influence of oil fouling on the pressure gradient.     

Interfacial flows in corrugated microchannels: Flow regimes,transitions and hysteresis

We report simulations of gas–liquid two-phase flows in microchannels periodically patterned with grooves and ridges. A constant effective body force is applied on both fluids to simulate a pressure-driven creeping flow, and a diffuse-interface model is used to compute the interfacial evolution and the contact line motion. Depending on the body force, capillary force and the level of liquid saturation, a number of flow regimes may appear in the corrugated microchannel: gas flow, blockage, liquid flow, bubble–slug flow, droplet flow, annular flow and annular-droplet flow. A map of flow regimes is constructed for a set of geometric and flow parameters starting from a prescribed initial configuration. Some of the regimes are new, while others have been observed before in straight tubes and pipes. The latter are compared with previous experiments in terms of the regime map and the holdup ratio. The transition among flow regimes shows significant hysteresis, largely owing to the pinning of the interface at sharp corners in the flow conduit. Hysteresis is reduced if the sharp corners are rounded. Under the same operating conditions, different flow regimes can be realized from different initial conditions. The roles of geometry and wettability of the channel walls are also elucidated.     

Two-phase discharge from a stratified region through two horizontal branches with centerlines falling on an inclined plane

The main objective of this study was to obtain new experimental data for conditions not previously tested for discharging two-phase flow through two 6.35 mm diameter branches with centerlines falling in an inclined plane. The present results are relevant to many industrial applications including headers and manifolds, multichannel heat exchangers and small breaks in horizontal pipes. In the experimental investigation, the critical heights for the onsets of liquid and gas entrainment (OLE and OGE, respectively) were obtained, analyzed and correlated for two different branch spacings and two different angles between the branches. For each combination of branch spacing and angle between the branches, a wide range of Froude numbers was used. Two-phase mass flow rate and quality results were also obtained and analyzed for a range of interface heights for 16 different combinations of branch spacing, inclination angle, test section pressure and pressure drop across each branch. New empirical correlations were developed to predict the dimensionless mass flow rate and quality. The new correlations show good agreement with the present data and with previous correlations.     

Exact solutions of core-annular laminar inclined flows

An exact solution for laminar two-phase eccentric core-annular flows (CAF) in inclined pipes is derived. This solution complements the exact solutions that were obtained for inclined stratified flows with curved interfaces as to provide a set of solutions for two-phase laminar separated flows. A unified set of three dimensionless parameters for separated flows is defined and used to explore the effects of the system parameters and separated flow configurations on the velocity profiles and the resulting holdup, pressure gradient and pumping power requirement in horizontal and inclined concurrent and countercurrent flows. It is shown that similarly to stratified flows, also in CAF multiple solutions for the holdup and the associated flow characteristics can be obtained in inclined flows. The boundaries of the multiple solution regions are mapped and the effect of the core eccentricity and system parameters boundaries are demonstrated and discussed.The benefits of adding a lubricating phase for transportation of a viscous fluid in inclined CAFs is investigated. An adverse effect of the upward pipe inclination on the power savings in all of the separate flow configurations is demonstrated. Independently of the density of the lubricant, namely, whether it is lighter or heavier than the viscous fluid, the effect of hydrostatic pressure gradient always hinders the possibility of reducing the pumping requirement for transporting the viscous phase. However, surprisingly, a heavier lubricant is preferable form the view point of power saving. The implications of turbulent flow of the lubricating phase and the susceptibility to Ledinegg instability on the potential power savings are also considered and discussed. The application of the model for the analysis of experimental data of the holdup and pressure drop obtained in horizontal and inclined CAF is also demonstrated.     

Slip between the phases in two-phase water–oil flow in a horizontal pipe

This paper is devoted to slip phenomenon between the phases that occurs in unstable two-phase water–oil flow systems in a horizontal pipe. The emphasis is placed on the relation between the slip and the real (in situ) water fraction in a flowing mixture, as well as the substitute physical properties of the whole two-phase system. The experimental data collected throughout research served for the evaluation of the accuracy of the methods of real phase fraction in a water–oil flow system in horizontal pipes as they were referred to in the bibliography. Subsequently we have suggested the author indicate a method of determination of the fraction for two-phase liquid systems like O/W, W/O and W + O. In order to establish the specific equations, the drift-flux model has been used here.     

Effect of pipe diameter on flow patterns for air-water flow in horizontal pipes

New results are presented on interfacial patterns observed for air and water flowing in horizontal 2.54 and 9.53 cm pipelines close to atmospheric conditions. This work differs from previous studies in that measurements of pressure fluctuations at two locations separated in the streamwise direction are used to detect slugs. The liquid flow needed to initiate slugs at low gas velocities is strongly affected by pipe diameter and appears to depend on a linear instability. At high gas velocities the transition is approximately independent of pipe diameter and is explained by a nonlinear mechanism associated with the coalescence of roll waves. The initiation of slugs in the annular flow regime is determined to occur at much lower liquid flows than had been reported by previous investigators. The transition from stratified to annular flow is different in smaller-diameter pipes than in larger pipes because wave wetting plays a more important role.     

Interfacial level gradient effects in horizontal newtonian liquid-gas stratified flow—i

The analysis of reported Newtonian liquid-gas stratified flow data for horizontal circular ducts indicated that an interfacial level gradient (ILG) and therefore non-uniform flow tended to exist over a wide range of test conditions. Significant ILG can be present if high-viscosity liquids and low gas velocities' are used to produce stratified flow. ILG can reduce the liquid holdup and can possibly expand the stratified flow regime by delaying the transition to wavy stratified and/or intermittent flow. Use of the Lockhart-Martinelli parameters Φ²_L and Φ²_G is invalid in stratified flow if ILG is present because of unequal axial pressure gradients in the gas and liquid phases. During uniform stratified flow, especially in the laminar liquid-turbulent gas ftow regime, the combined one-dimensional mechanical energy equations can be used in dimensionless form to accurately predict the liquid holdup and pressure drop. In future stratified flow experiments, the axial pressuregradient in both phases should be measured.     

Experimental investigation on the slip between oil and water in horizontal pipes

This work is devoted to study of the slip phenomenon between phases in water–oil two-phase flow in horizontal pipes. The emphasis is placed on the effects of input fluids flow rates, pipe diameter and viscosities of oil phase on the slip. Experiments were conducted to measure the holdup in two horizontal pipes with 0.05 m diameter and 0.025 m diameter, respectively, using two different viscosities of white oil and tap water as liquid phases. Results showed that the ratios of in situ oil to water velocity at the pipe of small diameter are higher than those at the pipe of big diameter when having same input flow rates. At low input water flow rate, there is a large deviation on the holdup between two flow systems with different oil viscosities and the deviation becomes gradually smaller with further increased input water flow rate.     

The rivulet flow pattern during oil–water horizontal flow through a 12 mm pipe

The present study reports the hydrodynamics of the rivulet pattern during oil–water flow through a 12 mm horizontal acrylic pipe. The interfacial distribution has been observed visually and characterized from signals obtained from an optical probe as well as by isokinetic sampling. The probability density function (PDF) and fast Fourier transform (FFT) of the signals have provided an understanding of the flow configuration. The experiments have revealed that although rivulet flow is a typical separated flow pattern, it has different characteristics as compared to the stratified and annular flow patterns. The holdup and pressure drop under such conditions have been compared with the drift flux model for horizontal flow as well as the two-fluid model as proposed by Brauner and Maron [9] for liquid–liquid flows.     

Planar dynamics of inclined curved flexible riser carrying slug liquid–gas flows

Flexible risers transporting hydrocarbon liquid–gas flows may be subject to internal dynamic fluctuations of multiphase densities, velocities and pressure changes. Previous studies have mostly focused on single-phase flows in oscillating pipes or multiphase flows in static pipes whereas understanding of multiphase flow effects on oscillating pipes with variable curvatures is still lacking. The present study aims to numerically investigate fundamental planar dynamics of a long flexible catenary riser carrying slug liquid–gas flows and to analyse the mechanical effects of slug flow characteristics including the slug unit length, translational velocity and fluctuation frequencies leading to resonances. A two-dimensional continuum model, describing the coupled horizontal and vertical motions of an inclined flexible/extensible curved riser subject to the space–time varying fluid weights, flow centrifugal momenta and Coriolis effects, is presented. Steady slug flows are considered and modelled by accounting for the mass–momentum balances of liquid–gas phases within an idealized slug unit cell comprising the slug liquid (containing small gas bubbles) and elongated gas bubble (interfacing with the liquid film) parts. A nonlinear hydrodynamic film profile is described, depending on the pipe diameter, inclination, liquid–gas phase properties, superficial velocities and empirical correlations. These enable the approximation of phase fractions, local velocities and pressure variations which are employed as the time-varying, distributed parameters leading to the slug flow-induced vibration (SIV) of catenary riser. Several key SIV features are numerically investigated, highlighting the slug flow-induced transient drifts due to the travelling masses, amplified mean displacements due to the combined slug weights and flow momenta, extensibility or tension changes due to a reconfiguration of pipe equilibrium, oscillation amplitudes and resonant frequencies. Single- and multi-modal patterns of riser dynamic profiles are determined, enabling the evaluation of associated bending/axial stresses. Parametric studies reveal the individual effect of the slug unit length and the translational velocity on SIV response regardless of the slug characteristic frequency being a function of these two parameters. This key observation is practically useful for the identification of critical maximum response.     

Correlation of the liquid volume fraction in the slug for horizontal gas-liquid slug flow

Experimental data for gas holdup in liquid slugs are reported for two different pipe sizes (2.58 cm and 5.12 cm I.D.). A simple empirical correlation is developed and is shown to be a significant improvement over the only other published correlation proposed by Hubbard (1965). The results of this investigation are important for the development of a mechanistic model for the prediction of pressure drop and holdup for slug flow in pipes.