Correlations For Holdup Research Articles

Liquid hold-up correlations for trickle beds without gas flow

Dynamic and total liquid hold-up data required for trickle bed reactors without gas flow were gathered from the literature to generate an exhaustive database including over 1100 measurements. The slit model was satisfactorily representational of the evolution of the total liquid hold-up and yielded an average absolute relative error (AARE) of 21.3% for the gravity-driven liquid flow depicted in the database. Similarly, an alternate approach that combined artificial neural networks with dimensional analysis enabled derivation of an empirical dynamic liquid hold-up correlation h D= f( Fr L, We L, Re L, Eo L) yielding an AARE=14%.

Mass transfer and hydrodynamic characteristics in a co-current downflow contacting column

Hydrodynamic and mass transfer characteristics of water–air system in a co-current downflow contacting column (CDCC) were studied for various nozzle diameters at different superficial gas velocities and liquid re-circulation rates. Gas hold-up and liquid-side mass transfer coefficient increased with increasing superficial gas velocity and liquid flow rate but decreased with increasing nozzle diameter. It is shown that correlations developed, which are based on liquid kinetic power per liquid volume present in the column, and superficial gas velocity explains gas hold-up and the mass transfer coefficient within an error 20% for all gas and liquid flow rates and nozzle diameters used. The constants of correlations for gas hold-up and mass transfer coefficient were found to be considerably different from other gas–liquid contacting systems. © 2003 Society of Chemical Industry

Influence of Hydrodynamic Flow Regimes on the Prediction of Gas Hold-up and Liquid Circulation in Airlift Reactors

The influence of the recently identified hydrodynamic flow regimes on the prediction of gas hold-up and liquid circulation velocity in airlift reactors has been investigated. Some hydrodynamic models based on momentum balance are considered. Experiments were conducted on a pilot plant, external loop airlift reactor using air-water system. The generalised equation of Joshi and Lali for the homogeneous regime predicts the overall gas hold-up in this region with satisfactory accuracy and the difference between the experimental and predicted values is lower than ± 8%. Hsu and Dudukovic model predicts the liquid circulation velocity based on the gas hold-up correlations proposed for the homogenous, transition and heterogeneous flow regimes and two-phase friction factor with satisfactory accuracy (within 4.9 %). The results also show that the friction factor has pronounced effect on the model predictions. It would appear, also that the characterisation of various flow regimes has profound effect on the predictions of these important design parameters. Superposition approach is implemented to develop a correlation for the prediction of the axial gas hold-up in the riser as a function of the height and superficial gas velocity. The proposed correlation gives an average error of 4.7%.

Numerical study of stratified oil–water two-phase turbulent flow in a horizontal tube

Stratified oil–water two-phase turbulent flow in a horizontal tube is numerically simulated using a volume of fluid model. A single momentum equation is solved throughout the domain. The RNG k– ε model combined with a near-wall low- Re turbulence model is applied to each phase, and a continuum surface force approximation is adopted for the calculation of surface tension. The simulation is performed in a time-dependent way and the final solution which corresponds to steady-state flow is analyzed. Results of pressure loss, slip ratio, local phase fraction profile and the axial velocity profile are verified by experimental data in literature. Based on the numerical results of extensive calculations, the flow field characteristics are explored and correlations for pressure loss and hold-up are presented.

Hydrodynamic studies in both bi-dimensional and three-dimensional bubble columns with a single sparger

Gas holdup in highly viscous fluid in two-phase bubble column with a single sparger operated continuously with respect to the gas flow and batch wise with respect to the liquid was investigated using bed expansion technique. Two- and three-dimensional columns of the same effective cross-sectional area were investigated. Liquid viscosity varied between 0.063 and 0.320 Pa s, static bed heights between 0.12 and 0.60 m, surface tension between 0.0248 and 0.035 N m −1 and density between 906 and 928 kg m −3. Columns were injected with air at superficial gas velocities between 0.0018 and 0.290 m s −1. A single nozzle sparger of 0.01 m diameter was used. The behavior of bubbles in two-dimensional bubble column was found to fall into the bubble flow regime, whereas the behavior in three-dimensional column was found to fall into the churn turbulent regime. Two correlations for gas holdup in the two- and three-dimensional bubble columns were proposed and compared with correlations listed in the literature.

Integrated Genetic Algorithm−Artificial Neural Network Strategy for Modeling Important Multiphase-Flow Characteristics

Numerous investigations have shown that artificial neural networks (ANNs) can be successful for correlating experimental data sets of macroscopic multiphase-flow characteristics, e.g., holdup, pressure drop, and interfacial mass transfer. The approach proved its worth especially when rigorous fluid mechanics treatment based on the solution of first-principle equations is not tractable. One perennial obstacle facing correlations is the choice of a low-dimensionality input vector containing the most expressive dimensionless independent variables allowing the best correlation of the dependent output variable. Because no clue is known in advance, one has recourse to a laborious, often inefficient, and nonsystematic trial-and-error procedure to identify from a broad reservoir of possible candidates, the most relevant combination of ANN input dimensionless variables. The combinatorial nature of the problem renders the determination of the best combination, especially for multiphase flows, computationally difficult because of the large scale of the search space of combinations. A methodology is devised in this work to cope with this computational complexity by illustrating the potential of genetic algorithms (GAs) to efficiently identify the elite ANN input combination required for the prediction of desired characteristics. The multiobjective function to be minimized is a composite criterion that includes ANN prediction errors on both learning and generalization data sets, as well as a penalty function that embeds phenomenological rules accounting for ANN model likelihood and adherence to behavior dictated by the process physics. The proof of concept of the integrated GA−ANN methodology was illustrated using a comprehensive database of experimental total liquid holdup for countercurrent gas−liquid flows in randomly packed towers for extracting the best liquid hold-up correlation.

Prediction of gas hold‐up in a bubble column filled with pure and binary liquids

AbstractA dimensionless correlation for gas hold‐up in a bubble column filled with pure liquids and binary mixtures has been developed. The criteria of bubble coalescence in pure liquids and foamability of binary mixtures have been included successfully in the proposed correlation. For the first time, comprehensive data of gas hold‐up with respect to concentration in four binary systems are presented. The often‐reported enhancement of gas hold‐up in aqueous alcohol mixtures has been observed experimentally. The proposed correlation is able to predict successfully the trend of gas hold‐up enhancement with respect to concentration. The estimated values are found to be within 7% of the measured values.

A Mechanistic Model for Gas-liquid Two-phase Flow in Slightly Inclined Pipes: To Improve Predictions of Flow Patterns and Pressure Drops.

This paper describes experimental and modeling studies to investigate the behavior of gas-liquid two-phase flow in horizontal and slightly inclined pipelines. The studies were performed with experimental data newly obtained at over 1000 flow conditions that were designed to cover all the flow patterns. The experiments were conducted at a test loop of a 54.9 mm diameter, 105.0 m long pipeline, with 0, 5, and 10 degree inclination of the test section. A new mechanistic model for horizontal and slightly inclined flow was developed implementing transition criteria between the flow patterns, correlation for liquid holdup, and flow models for pressure drop computation. The criteria for the transition boundaries between flow regions were determined for eight flow patterns matching the predicted flow patterns with the experimental observations. For stable dispersed bubble flow, constraints on the bubble size were additionally applied. At the transition between stratified and non-stratified flow, we added such a criterion that slug flow can remain stable at much lower flow rates of liquid. The froth flow region was newly modeled to reproduce the experimental observations between annular and slug flow. The pressure drops were computed for individual conditions of the experimental measurements. Excellent performance of the model was demonstrated by good agreements between the computed results and the experimental data. Correct identification of the flow pattern is crucial for accurate estimation of pressure drops, particularly for those near the transition boundaries. Use of appropriate friction factors is of primary importance for pressure drop calculations in any of the flow patterns.

Scale Effects on the Hydrodynamics of Bubble Columns Operating in the Homogeneous Flow Regime

Measurements of gas holdup were made with the air-water system in bubble columns of 0.1, 0.15 and 0.38 m diameter, equipped with identical distribution devices. For operation with superficial gas velocity in the range 0-0.04 m/s, the total gas holdup was found to decrease with increasing column diameter. Of all the literature correlations for the gas holdup, only the Zehner correlation anticipates this decrease in the gas holdup with increasing column diameter. The reason for this scale dependence is because the strength of the liquid circulations increases with increasing scale. Such circulations accelerate the bubbles travelling upwards in the central core. Computational fluid dynamics (CFD) simulations were carried out using the Eulerian description for both the gas and the liquid phases in order to verify the scale dependence of the hydrodynamics. Interactions between the bubbles and the liquid are taken into account in terms of a momentum exchange, or drag, coefficient. The drag coefficient is determined from the Mendelson correlation for bubble rise velocity. The turbulence in the liquid phase is described using the k-e model. The simulation results verify the trends predicted by the Zehner (1989) correlation. It is concluded that Eulerian simulations are useful tools for scaling up bubble columns.

Predictions of radial gas holdup profiles in bubble column reactors

Gas holdup and its profile are important parameters to be characterized in bubble column reactors. Proper prediction of the radial gas holdup profiles is necessary for determining liquid mixing, flow regime transition, heat and mass transfer. In this study, the following gas holdup profile form, which can be fitted to the observed holdup profiles, is proposed: ε G= ε ̄ G n+2 n+2−2c [1−c(r/R) n]. The parameters n and c needed to describe the gas holdup profile are correlated with appropriate dimensionless groups. n=2.188×10 3 Re G −0.598 Fr g 0.146 Mo L −0.004, c=4.32×10 −2 Re G 0.2492. However, the cross-sectional average gas holdup, ε ̄ G , can be estimated using the available correlations for overall gas holdup. The agreement between the correlation predictions and experimental data is reasonable over wide range of operating conditions.

Improved Liquid Hold-up Correlation for Randomly Packed Towers

The state-of-the-art tools for the evaluation of the total liquid holdup in gas-liquid counter-current randomly dumped packed beds are critically evaluated by thoroughly interrogating a wide hydrodynamic database. This database, consisting of ca. 1,500 experiments on liquid hold-up below the flooding point, represents an important portion of the non-proprietary information released in the literature since the 1930s. Providing access to diversified information, it is dedicated to embracing wide-ranging temperature and gas density levels, and packing shapes extending from classical ones to modern third generation packings. Furthermore, a total of eleven correlations on the total liquid hold-up extracted from the literature are cross-examined using the database. Many limitations regarding the level of accuracy and generalization come to light with this investigation. Artificial neural network modelling and dimensional analysis are then proposed to improve the accuracy in predicting the total liquid hold-up in the pre-loading and the loading regions of packed beds. A combination of five dimensionless groups, comprising the liquid Reynolds (ReL), Froude (FrL), and Ohnesorge (OhL) numbers as well as the gas Froude (FrG) and Stokes (StG) numbers are used as the basis of the correlation. The correlation yields an absolute average relative error of ca. 14% for the whole database and remains in accordance with trends reported in the literature.

Studies of Gas Holdup in Bubble Column Reactors

Gas holdup in bubble columns has been investigated over a wide range of operational and geometrical parameters. A criterion has been developed for the prediction of the transitional velocity from the homogeneous to heterogencous flow regime. Correlations for gas holdup in both regimes are developed and verified against experimental data.

Overall pressure balance and system stability in a liquid–solid circulating fluidized bed

A pressure balance analysis has been carried out, along with a dimensionless empirical correlation for the solids holdup in the riser and a semi-empirical equation for the pressure drop across the non-mechanical control valve derived in this work, to successfully predict the stable operating conditions and explain the origin of the unstable operation phenomena of the liquid–solid circulating fluidized bed. The effects of the total and auxiliary liquid velocity, the solids inventory and the unit geometry on the stable operation range are discussed. Furthermore, this work also reveals the importance of unit structure in improving the performance of the liquid–solid circulating fluidized bed systems.

Correlations for dynamic liquid holdup under pulsing flow in a trickle-bed reactor

Based on theoretical analysis and experimental results, a new attempt has been made to characterize the dynamics of the fluid flowing under conditions of pulsing flow in a trickle-bed reactor (TBR). Two kinds of correlation are proposed for the dynamic liquid holdup under pulsing flow, which can predict the dynamic liquid holdup for a given packing type and given operating conditions.

Heat and mass transfer modeling during the formation and ascension of superheated bubbles

A previously developed model for the heat and mass transfer of a single superheated bubble during the ascension stage was extended to include the formation stage. It allows variable properties and bubble radius changes, solving the gas conservation equations coupled to a bubble dynamics model. Its results were used to predict the existing experimental data in a direct contact evaporator with good agreement. A correction factor for isothermal gas hold-up correlations can be fully calculated by the model enabling good prediction of gas hold-up. The constant property assumption overestimates the gas hold-up and should not be used. Experimental data for steam bubbling process could be reasonably simulated using the superheated bubble model with some additional assumptions.

Prediction of Liquid Holdup in Countercurrent-Flow Rotating Packed Bed

A theoretical analysis of the liquid holdup in the countercurrent-flow rotating packed bed has been developed. It is based on liquid film on a rotating disk in the presence of the gas, with the assumption that the rotating packed bed may be modelled as n layers of hypothetical rotating disks stacked together. Agreement between the predicted values of the liquid holdup and the experimental values was quite good. With this model, the liquid holdup can be estimated in the countercurrent-flow rotating packed bed with data of pressure drop. Furthermore, a correlation for the liquid holdup in the conventional packed bed was extended and modified to estimate that in the countercurrent-flow rotating packed bed.

Simultaneous heat and mass transfer during the ascension of superheated bubbles

A model has been developed for the simultaneous heat and mass transfer during the ascension of superheated bubbles in a liquid column, allowing variable gas physical properties and bubble radius. A correction factor for isothermal gas hold-up correlations, based on bubble model results, has been derived in order to apply them to nonisothermal systems. Results for the bubble volume and the evaporated mass per bubble are used in the prediction of experimental data on gas hold-up and vaporization rate obtained in a direct contact evaporator with fairly good agreement. It has been shown that the constant property and constant bubble radius assumptions lead to overestimation of the vaporization rate and gas hold-up.

Hydrodynamics and computer simulation of an ozone oxidation reactor for treating drinking water

Numerical calculations were conducted to analyze the ozone absorption behavior and removal of odorous materials in the U-Tube ® reactor, which is a bubble column fitted with a concentric down-flow diffuser. A novel calculation model was developed to simulate the reactor by assuming that it is composed of a plug flow section (inner tube) followed by a tanks-in-series section (outer bubble column). The bubble size distribution and gas holdup were measured in the downflow diffuser to obtain correlations for the gas holdup and the Sauter mean bubble diameter. It is found that the ozone absorption efficiency increases with decreasing gas/liquid ratio but is almost independent of the gas-phase ozone concentration. It is also found that the removal efficiency of odorous compounds (2-MIB) significantly increases with both increasing gas-phase ozone concentration and gas/liquid ratio. In order to achieve a high 2-MIB removal efficiency a ozone loading value (=gas-phase ozone conc.×gas/liquid ratio) greater than 0.003 kg/m −3 is required. The numerical calculation well explains the experimental data on the ozone absorption efficiency and the 2-MIB removal efficiency of a pilot plant, showing usefulness of the simulation model proposed.

Some hydrodynamic characteristics of inverse three phase fluidized-bed reactors

Some hydrodynamic characteristics of inverse three-phase fluidized beds were investigated. Using two types of particles having different characteristics ( d s =4 mm, ρ s =920 kg m -3, and d s =0.175 mm and ρ s =690 kg m -3, respectively) allowed us to observe two different expansion mechanisms: a pseudo-fluidized state promoted by the density difference between the solid and the surrounding gas–liquid mixture, and a fluidized state due to the liquid circulation induced by the rise of the bubbles. Both contributed to the solid mixing and axial solid distribution in the system. Systematic holdup measurements were done on two reactor diameter and two types of gas sparger. A correlation for the liquid holdup and bed porosity could be proposed by means of a modified gas drift flux definition. The latest was a function of gas velocity only and gave a good accuracy among the range of solid amount, gas and liquid velocity used.

Gas holdup in homogeneous and heterogeneous gas—liquid bubble column reactors

AbstractThe velocity‐holdup relationship is the most important design parameter for gas—liquid bubble column reactors, providing the basis for the prediction of heat and mass transfer coefficients and information on hydrodynamic conditions. A summary of the literature on gas holdup in bubble columns is supplemented by new experimental results which extend the data range. A criterion for the gas velocity leading to the transition between homogeneous and heterogeneous regimes for perforated plate gas distributors has been developed. Correlations for gas holdup in both regimes are developed and verified against both new and existing data.