Correlation For Liquid Holdup Research Articles

RETRACTED: Modeling a unified slug liquid holdup correlation based on a comprehensive analysis of entering bubble sharpness

Liquid-gas two-phase slug flow is the most complex flow pattern encountered in pipelines, wellbores, and cooling systems in various energy systems. Accurately predicting the slug liquid holdup (HLLS) is vital for the system design and operation because it is a crucial characteristic of slug flow that is closely related to the average liquid holdup and pressure drop. Most existing HLLS models have limited applicability due to a lack of a physical basis for slug aeration mechanisms. This study proposes a new dimensionless number SP to estimate the sharpness of entering bubbles at the liquid slug front and semi-empirically correlates SP to HLLS data, leading to the development of a unified HLLS correlation. We formulate this dimensionless number and its relations using 880 experimental HLLS data points, and the validity of the unified HLLS correlation is tested using 1050 independent data points. The developed semi-empirical model closely agrees with experimental data obtained by varying the fluid properties (0.03 mPa·s ≤ µL ≤ 966 mPa·s, 0.027 N/m ≤ σ ≤ 0.07 N/m) and operating conditions, such as the pipe geometry (1 in. ≤ pipe internal diameter ≤ 3 in., –10° ≤ θ ≤ +90°).

A Modified Model to Predict Liquid Loading in Horizontal Gas Wells

Abstract Liquid loading is inevitable during mature gas-well production, leading the liquids to accumulate at the bottomhole and additional pressure loss. Accurately predicting the liquid-loading initiation is crucial to gas-well production optimization. Significant efforts have been made to model liquid-loading behavior. However, few mechanistic models are capable of easily and accurately tackling the complicated non-uniform liquid-film distribution in the slanted section of horizontal wells. Based on liquid-film inversion, this study developed a simple and comprehensive model to calculate liquid-loading initiation for horizontal gas wells. First, the models for film thickness and critical velocity in the vertical pipe are developed. Then, considering the effect of inclination and velocity difference in liquid-film thickness and liquid-holdup distribution between vertical and inclined pipes, the relationship in vertical and inclined pipes between liquid holdup, liquid-film thickness, and angle correction term is established based on the liquid-holdup correlation for horizontal and inclined pipes described in the empirical model developed by Beggs and Brill, so that the thickness of the film and the corresponding critical velocity at any inclination can be calculated. Finally, the new modified model has been evaluated against both experimental and field-measured data set. In comparison to the Luo et al.’s model, the proposed model has been proven to be simple, accurate, and well-performed in predicting the liquid-accumulation initiation in horizontal wells.

Experimental and Modeling Investigation on Gas-Liquid Two-Phase Flow in Horizontal Gas Wells

Abstract Wellbore pressure gradient in gas wells is significant in designing deliquification technologies and optimizing production. At present, no model has yet to be established specifically for gas wells at a wide gas flowrate range. When calculating pressure gradient in a specific gas field, engineers must evaluate these widely used models and get the best performance model at a certain range. To establish a more comprehensive model in horizontal gas wells, an experimental study was conducted to investigate the flow behavior of liquid-gas two-phase flow at different gas and liquid velocities and inclined angles in a 50 mm visual pipe. The evaluation of these widely used models against the experimental data shows that no model can predict liquid holdup at different gas velocity ranges, and huge deviations due to several reasons can be observed. After conducting a comprehensive analysis, a new liquid holdup correlation was proposed based on the Mukherjee–Brill model by correlating from the experimental results, which have parametric ranges closer to the production of gas wells. This new model adopts a new dimensionless gas velocity number to characterize flow similarities and better scale up pressure from the experiment to the gas wells. By validating against experimental data and field data, the results indicate that the new two-phase flow model has stable performance and can accurately predict pressure gradients at different ranges of pressure and gas/liquid velocities.

The influence of random packed column parameters on the liquid holdup and interfacial area

AbstractCarbon dioxide capture via solvent absorption in packed columns has emerged as a potential technology to mitigate coal‐fired power plant CO2 emissions. Parameters, including packing types, solvent properties, and operating conditions, could potentially affect the packed column CO2 capture efficiency. To understand the importance of those parameters and help packed column optimization, a design of experiments (DoEs) method was proposed to generate input parameter matrix. Combined with multiphase computational fluid dynamics (CFD), the random packed column parameter influence on the liquid holdup and interfacial area can be efficiently investigated. Surrogate‐based sensitivity analysis shows that the solvent flow rate and contact angle are key factors dictating liquid holdup and interfacial area. On the other hand, solvent viscosity has a marginal impact on the interfacial area. The sensitivity scores were calculated for each input parameter to guide the selection of dimensionless numbers for the liquid holdup and interfacial area correlation development.

Modeling of Unified Slug Liquid Holdup Correlation Based on Comprehensive Analysis of Entering Bubble Sharpness

Modeling of Unified Slug Liquid Holdup Correlation Based on Comprehensive Analysis of Entering Bubble Sharpness

Empirical Correlations for Prediction Slug Liquid Holdup on Slug-Pseudo-Slug and Slug-Churn Transitions in Vertical and Inclined Two-Phase Flow

SummaryMost of the existing slug (SL) to churn (CH) or SL to pseudo-slug (PS) transition models (empirical and mechanistic) account for the effect of the SL liquid holdup (HLS). For simplicity, some of these models assume a constant value of HLS in SL/CH and SL/PS flow transitions, leading to a straightforward solution. Other models correlate HLS with different flow variables, resulting in an iterative solution for predicting these transitions. Using an experimental database collected from the open literature, two empirical correlations for prediction HLS at the SL/PS and SL/CH transitions (HLST) are proposed in this study. This database is composed of 1,029 data points collected in vertical, inclined, and horizontal configurations. The first correlation is developed for medium to high liquid viscosity two-phase flow (μL > 0.01 Pa·s), whereas the second one is developed for low liquid viscosity flow (μL ≤ 0.01 Pa·s). Both correlations are shown to be a function of superficial liquid velocity (VSL), liquid viscosity (μL), and pipe inclination angle (θ). The proposed correlations in a combination with the HLS model of Abdul-Majeed and Al-Mashat (2019) have been used to predict SL/PS and SL/CH transitions, and very satisfactory results were obtained. Furthermore, the SL/CH model of Brauner and Barnea (1986) is modified by using the proposed HLST correlations, instead of using a constant value. The modification results in a significant improvement in the prediction of SL/CH and SL/PS transitions and fixes the incorrect decrease of superficial gas velocity (VSG) with increasing VSL. The modified model follows the expected increase of VSG for high VSL, shown by the published observations. The proposed combinations are compared with the existing transition models and show superior performance among all models when tested against 357 measured data from independent studies.

Modeling pseudo-slugs liquid holdup in slightly upward inclined pipes

Pseudo-slug flow is a sub-regime of intermittent flow that is characterized by short, undeveloped, frothy chaotic slugs, with a translational velocity less than the mixture velocity of the fluids. The liquid in the pseudo-slug body is insufficient to reach the upper pipe wall, resulting in large waves with entrained gas bubbles at the bottom part of the pseudo-slug body. This flow phenomenon in the pseudo-slug body is different from the well-known physical model of the conventional unit-cell slug flow. Although pseudo-slug flow occupies a significant area under the intermittent flow region of flow pattern map, theoretical modeling of its characteristics is still limited and scarce in the literature. The objective of this study is to develop a plausible physical model of liquid holdup in pseudo-slugs based on the observed physical and hydrodynamic behavior, based on which a dimensional predictive regression model is developed.This paper discusses liquid and gas entrainment mechanisms within the pseudo-slug body based on experimental observation. It shows that the pseudo-slug body can be divided into two regions, liquid film (wave) with entrained gas bubbles at the bottom, and gas core with entrained liquid droplets at the top. Experimental results show that the proposed dimensionless groups, namely, Stokes, Slippage, and Poiseuille numbers, are strongly correlated to pseudo-slug body liquid holdup experimental data and are capable of describing the experimentally observed physical behavior. A linearized regression model is developed to combine the liquid holdup proportionally in both regions of the pseudo-slug body and correlate them to the experimentally measured total pseudo-slug liquid holdup using a wire-mesh sensor. A validation study of the proposed model with experimental data shows good agreement, outperforming all other existing slug liquid holdup correlations.

Investigation of countercurrent flow profile and liquid holdup in random packed column with local CFD data

Liquid holdup and mass transfer area are critical parameters for packed column design and CO2 capture efficiency prediction. In this paper, a framework was established for modeling the liquid–gas countercurrent flow hydrodynamics in a random packed column with pall rings. Besides the column-averaged information, the radial pall ring distribution, velocity, and liquid holdup profiles are obtained to study the entrance effect and the wall influence in the packed column. With local CFD data, the validated packing specific area ap and liquid velocity uL range for liquid holdup correlation is significantly expanded with respect to existing experimental or column-averaged CFD data. The proposed liquid holdup correlation hL~uL0.44 indicates the random packed column falls in a viscous to turbulent transition regime and it covers a Reynolds Number range of [6.7–40.2]. The derived liquid holdup correlation is in good agreement with existing correlations developed using the column-averaged experimental data.

Shape and maximum volume of static holdup in between two vertical spheres: A modeling study

Static liquid holdup is one of the important parameters in packed bed operations. Packed bed can be fundamentally imagined as an aggregate of two-sphere contacts and liquid is potentially held at the contact points. Between two vertical spheres, existing literature report maximum volume of films either as the geometric limit while solving Young-Laplace equation or the stability limit of static liquid holdup in the presence of asymmetric perturbation. However, it is of fundamental interest to find out the maximum limit of stability of the liquid without any asymmetric perturbation. This work shows a limit, below the geometrical limit of the system, beyond which liquid cannot be stable due to the gravitational force. Axisymmetric film shapes of a given volume, derived using Young- Laplace equation with different boundary conditions, are tested with total energy minimization principle to define the stability limit. Further, a correlation for maximum static liquid holdup is reported with respect to a modified Bond number.

An improved model to predict liquid holdup in vertical gas wells

Accurate prediction of the pressure gradient is crucial for gas-production design and gas well optimization. The most important role in modeling the pressure gradient is generally to calculate the liquid holdup accurately. Currently, numerous mechanistic and empirical models have been developed and modified to deal with all kinds of flow conditions. Due to the chaotic feature in the churn flow, it is difficult for mechanistic models to model this flow pattern accurately. Simplified assumptions for this pattern may lead to large deviations. For empirical models, the range of experimental parameters limits their application. In this study, a variation of liquid holdup with superficial gas velocity is analyzed in order to simplify the liquid-holdup correlation and improve its accuracy. Based on the annular/churn-flow and bubble/slug-flow transition points, a new empirical model is established using a power-law curve. Since the superficial gas velocity and liquid holdup corresponding to the two transition points are obtained from analytical or semi-analytical models, the proposed model is not subject to the experimental ranges, unlike other empirical models. In addition, it avoids dealing with modeling churn flow. The new model has been validated against the laboratory and field data from published studies. For comparison, some widely used models are also evaluated. The result shows that the proposed model, which is capable of predicting the pressure gradient at different pipe sizes, liquid velocities, and gas velocities, has better performance compared with other models.

Validation of mass transfer and liquid holdup correlations for CO2 absorption process with methyldiethanolamine Solvent and piperazine as an activator

In the present study, 24 data sets regarding CO2 absorption by the piperazine (PZ) activated aqueous methyldiethanolamine (MDEA) solution (30% wt) have been obtained from Khan et al.’s work and have been investigated using rate base model. Hence, mass transfer correlations such as Onda’s, Bravo-Fair’s, Billet-Schultes’ correlations and liquid hold-up correlations of Billet-Schultes and Stichlmair have been studies in the current paper. In addition, important parameters like CO2 absorption (%), liquid temperature and rich solvent’s loading have been compared in different mass transfer and liquid hold-up correlations. The results of using the rate-base model in the mass transfer and liquid hold-up correlations in 24 different experimental conditions indicate that the Bravo-Fair mass transfer correlations have higher accuracy compared to other mass transfer correlations. This comparison has been carried out based on CO2 absorption (%) and the rich solvent’s loading. Moreover, studying mass transfer correlations give the following amounts for the average error of Onda’s, Bravo-Fair’s and Billet-Schultes’ mass transfer correlations respectively for CO2 absorption (%) calculation in 16 different experimental conditions: 23.45, 14.63 and 38.59 (%). In the last part of the paper, rich solvent’s loading is compared with real amounts in 12 different experimental conditions. The comparison shows that the average errors of Onda’s, Bravo-Fair’s and Billet-Schultes’ mass transfer correlations are 14.80, 9.70 and 21.75 (%) respectively. Investigating liquid hold-up correlations indicates that Billet-Schultes’ and Stichlmair’s correlations give the same results regarding rich solvent’s temperature, solvent’s temperature profile along the absorption column, CO2 absorption (%) and rich solvent’s loading.

A comparative study of different mass transfer and liquid hold-up correlations in modeling CO2 absorption with MEA

Although CO2 absorption processes have been widely studied in both laboratory and industrial scales, the viability of different relations for the estimation of mass transfer coefficients has not been studied for industrial units. In this paper, the accuracy of different various equations for the estimation of mass transfer coefficients were are evaluated and compared, on the basis of according to the results of an industrial CO2 absorption unit. Therefore, the relations proposed by Onda, Bravo and Billet-Schules were are selected. Also, in some parts of the column pall ring packing was is used. in these parts the Hanley mass transfer coefficients were also used. In addition, Hanley mass transfer coefficients are used for those parts of the column in which pall ring packing is used. Based on the results of rate-based modeling of the column, obtained results show that the Onda equations show have higher accuracy compared to the other mass transfer equations. The comparison was is carried out based on CO2 absorption capacity, temperature profile and rich solvent concentration. The average errors of Onda's mass transfer correlations and Billet & Schultes's liquid holdup correlations in estimating CO2 absorption (%), temperature of rich solvent's temperature, temperature of outlet water's temperature and loading of rich solvent's loading were are 1.153, 2.923, 6.99 and 1.163% respectively. Onda and Billet & Schultes correlations exhibited the most accurate results. Also additionally, liquid film discretization shows indicates that the reaction occurs almost rather instantaneously at liquid-vapor interface and diffusion is the controlling step in the absorption process.

A unified correlation for predicting slug liquid holdup in viscous two-phase flow for pipe inclination from horizontal to vertical

This study presents new measured slug liquid holdup data for liquid viscosity ranging from 200 to 800 mPa s. The experiments were conducted using two different large pipe diameters (0.08 and 0.1 m) and pipe inclination angles of 0°, 30°, 60° and 90° from horizontal. To our best knowledge, most of the existing experimental data were limited to either vertical or horizontal flow and mostly performed using small pipe diameters. Based on the measured data, a new unified empirical correlation is developed to predict slug liquid holdup for viscous two-phase flow in horizontal, vertical and inclined pipes. The proposed correlation is simple and fully consistent with the trends of published experimental data. This study also investigates in details the performance of the existing liquid holdup correlations using different flow conditions. The investigation reveals several discrepancies associated with these correlations. Based on statistical analysis, the proposed correlation performs best as compared to the existing correlations using both the present measured data and data from three independent sources.

Numerical simulation of two-phase flow regime in horizontal pipeline and its validation

PurposeThe purpose of this paper is to investigate oil-gas slug formation in horizontal straight pipe and its associated pressure gradient, slug liquid holdup and slug frequency.Design/methodology/approachThe abrupt change in gas/liquid velocities, which causes transition of flow patterns, was analyzed using incompressible volume of fluid method to capture the dynamic gas-liquid interface. The validity of present model and its methodology was validated using Baker’s flow regime chart for 3.15 inches diameter horizontal pipe and with existing experimental data to ensure its correctness.FindingsThe present paper proposes simplified correlations for liquid holdup and slug frequency by comparison with numerous existing models. The paper also identified correlations that can be used in operational oil and gas industry and several outlier models that may not be applicable.Research limitations/implicationsThe correlation may be limited to the range of material properties used in this paper.Practical implicationsNumerically derived liquid holdup and holdup frequency agreed reasonably with the experimentally derived correlations.Social implicationsThe models could be used to design pipeline and piping systems for oil and gas production.Originality/valueThe paper simulated all the seven flow regimes with superior results compared to existing methodology. New correlations derived numerically are compared to published experimental correlations to understand the difference between models.

Hydrodynamics in a pilot‐scale cocurrent trickle‐bed reactor at low gas velocities

Hydrodynamic data obtained from laboratory‐scale trickle‐beds often fail to accurately represent industrial‐scale systems with high packing aspect ratios and column‐to‐particle diameter ratios. In this study, pressure drop, liquid holdup, and flow regime transition were investigated in a pilot‐scale trickle‐bed column of 33 cm ID and 2.45 m bed height packed with 1.6 mm × 8.4 ± 1.4 mm cylindrical extrudates for air‐water mass superficial velocities of 0.0023 – 0.094 kg/m2s and 4.5 – 45 kg/m2s, respectively, at atmospheric pressure. Significant deviation was observed from pressure drop and liquid holdup correlations at low liquid flows rates, corresponding to gravity‐driven flow limit. Likewise, liquid saturation is overestimated by correlations at high liquid flow rates, owing to significantly reduced wall effects. Lastly, trickle‐to‐dispersed bubble flow and trickle‐to‐pulsing flow regime transitions are reported using a combination of visual observations and analysis of the magnitude of local pressure fluctuations within the column. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2560–2569, 2018

CFD simulation and experimental validation of bubble cap tray hydrodynamics

Abstract In this study, numerical simulations of gas-liquid flow behavior of bubble cap tray have been done. The aim of this work is to develop a Computational Fluid Dynamic (CFD) model enable of predicting the hydrodynamic parameters of any desired system. A transient three-dimensional model in Eulerian framework with standard k-e turbulence model has been developed, ignoring mass and energy transfer equations. For this purpose a new correlation of liquid hold-up with 7.89% average error has been developed using Genetic Algorithm based on the experimental clear liquid height data. By substitution of this correlation in drag force relation, the source term has been added to the momentum equations. Simulations have been carried out over a wide range of liquid and vapor flow rates and the predicted results have been found to be in reasonable agreement with the experimental data. Velocity and pressure distributions, clear liquid height, froth height, and liquid holdup fraction in the froth region have been predicted, which are beneficial in analysis and design of the column trays.

Numerical Validation of Two-Phase Slug Flow and its Liquid Holdup Correlation in Horizontal Pipeline

The transition of one flow regime into another is a very common phenomena in pipeline networks, which can be potentially hazardous for the structural integrity of the pipeline. Literature review showed that there is almost no reported detail investigation of transitional flow whereby the fluid constituents change from one regime to another especially slug transition. Most of the open research papers focused on slug flow regime and its liquid holdup in horizontal pipelines and channels have been carried out on experimental test rigs. The objective of this study is to explore oil-gasoil vapor slug transition and its liquid holdup in a 3.15 inch diameter horizontal straight pipe. The abrupt change in gas/liquid velocities, which causes transition of flow patterns is analyzed using incompressible Volume of Fluid (VOF) method, along with Piecewise Linear Interface Construction (PLIC) technique to capture the sharp front of segregated gas-liquid interface. Slug liquid holdup derived from the present numerical model is compared to existing experimental correlations in the literature.

Investigation of holdup and axial dispersion of liquid phase in a catalytic exchange column using radiotracer technique

Holdup and axial dispersion of liquid phase in a catalytic exchange column were investigated by measuring residence time distributions (RTD) using a radiotracer technique. RTD experiments were independently carried out with two different types of packings i.e. hydrophobic water-repellent supported platinum catalyst and a mixture (50% (v/v)) of hydrophobic catalyst and a hydrophillic wettable packing were used in the column. Mean residence times and hold-ups of the liquid phase were estimated at different operating conditions. Axial dispersion model (ADM) and axial dispersion with exchange model (ADEM) were used to simulate the measured RTD data. Both the models were found equally suitable to describe the measured data. The degree of axial mixing was estimated in terms of Peclet number (Pe) and Bodenstein number (Bo). Based on the obtained parameters of the ADM, correlations for total liquid hold-up (HT) and axial mixing in terms of Bo were proposed for design and scale up of the full-scale catalytic exchange column.

Analysis of the Pressure Drop Through the Bed and Across the Supporting Grid in Type II-TBC: Experimentation and Modelling

Experimental data on pressure drop and bed expansion were collected over a wide range of operating conditions (\({{U}_{{\mathrm{g}}} = 0{-}8\,{m\,s}^{-1}}\), \({{L} = 0{-}27.90\,{kg\,m}^{-2}\,{s}^{-1}}\), \({{H}_{{\mathrm{st}}} /{d}_{{\mathrm{C}}} = 0.5{-}1,\varphi = 0.32{-}0.82, \rho_{{\mathrm{p}}} = 736}\) and \({868\,{kg\,m}^{-3}}\), and \({{d}_{{\mathrm{p}}} = 10}\) and 15 mm) in a type II-TBC. The variations in the pressure drop through the fluidized bed and through the supporting grid were analysed, and the effect of the gas velocity, the liquid spray, the height of the static bed and the free area of the support grid was studied. A model based on an approach including all components of the pressure drop through the fluidized bed and through the support grid has been proposed for the prediction of the pressure drop through the entire column. The predictions for all experimental data were in very good agreement with the experimental data (\({{AARD}_{(-{\Delta}{\mathrm{PC}})} = 10.70}\) %). The choice of the appropriate correlation to estimate the liquid holdup was conducted on the basis of a systematic study for a large number of correlations among the most usual. This study was also aimed to determine the deviations induced by the use of different liquid holdup correlations, when calculating the pressure drops. An interpretation was proposed to explain the disparity in results in the calculation of pressure drop using different correlations to estimate the rate of the liquid holdup.

Effects of Liquid Viscosity on the Wave Velocity and Wave Frequency in Horizontal Annular Flow

An investigation on the liquid holdup, wave velocity, and wave frequency in horizontal annular flow has been experimentally conducted through the measurement of liquid holdup using constant electric current method (CECM) sensors. To investigate the effect of viscosity, water and glycerin were used as working liquid, using superficial liquid velocity and superficial gas velocity of 0.05 to 0.2 m/s and 12 to 40 m/s, respectively. Liquids with higher viscosity give the higher liquid holdup, lower wave velocity, and lower wave frequency. Correlations for liquid holdup and mean film thickness, wave velocity, and wave frequency have been developed with mean average errors (MAE) of 13.5%, 9.2%, and 8.6%, respectively.