Sedimentation-dispersion Model Research Articles

Liquid and solids phase backmixing in a bubble and slurry bubble column using a virtual tracer response methodology based on the trajectory data of the radioactive particle tracking (RPT) technique

AbstractVirtual tracer response methodology developed based on the trajectory data of the computer aided radioactive particle tracking (CARPT) technique was demonstrated. The demonstrated virtual tracer technique has advantages of non‐invasiveness, near perfect injection/sampling, and flexibility in choosing the sampling/injection boundaries in a specific spatial pattern. With the developed virtual tracer technique, liquid and solids backmixing were investigated at the conditions mimicking Fischer‐Tropsch synthesis. Experiments were conducted at different pressure, solids loading, and superficial gas velocity. The axial dispersion model (ADM) and recirculation and cross flow dispersion (RCFD) models were used to model the liquid mixing. Transient sedimentation dispersion model (SDM) was used to model the solids mixing. It was found that the measured axial dispersion coefficient (Dl) in the ADM model increases with increase in the pressure. The increase of dispersion coefficient was explained with the experimental values of mean axial diffusivity and mean recirculation velocity. Axial dispersion coefficients (Dz,uDz,d) in the RCFD model (compartment model) were apparently lower than the Dl, due to the decoupling of global recirculation from the dispersion coefficients in the RCFD. Further, it was found that the dispersion coefficients in the RCFD model follow the trend of the axial eddy diffusivity with change in the operating conditions revealing the dominance of the turbulence in the upflow and downflow compartments. From the solids backmixing study, axial dispersion coefficient (Ds) of solids was found to increase with increase in the solids loading, pressure, and superficial gas velocity at the studied conditions.

Phase distribution in Fischer-Tropsch mimicked slurry bubble column via computed tomography

This study aims to investigate the phases distribution and hydrodynamics in an air-Therminol LT-glass beads slurry bubble column reactor in bubbly and churn-turbulent flow regimes by implementing a gamma-ray computed tomography. It is found that gas holdup increases with increasing superficial gas velocity and operating pressure while increasing solids loading has an opposite effect on gas holdup measurements. It is noticed that the pressure effect is more significant at high solids loading and the solids loading is relatively more substantial at lower pressure. Solids loading has the most significant a stronger effect on the solids holdup profile than on the gas holdup profile. Current results were compared with the Sedimentation-Dispersion Model (SDM) predictions. The findings of this study advance the knowledge of the true behavior of phases distribution in FT mimicked slurry bubble columns which are pertinent in designing such reactors.

Modeling of a slurry bubble column reactor for Fischer-Tropsch synthesis

On the basis of the global CO consumption rate model, the lumped product distribution model and the sedimentation-dispersion model of a catalyst, a steady-state, one-dimensional mathematical model of the slurry bubble column reactor for Fischer-Tropsch synthesis were established. The mathematical simulation of the slurry bubble column reactor for Fischer-Tropsch synthesis was carried out under the following typical industrial operating conditions: temperature 230 °C, pressure 3.0 MPa, gas flow 5×105 m3/h, catalyst content in slurry phase 30%, reactor diameter 5.0 m and the composition of feed gas: y(H2)=0.60, y(CO)=0.30, y(N2)=0.10. The influences of operating pressure, temperature and m(H2)/m(CO) in feed gas on the reactor’s reaction performance were simulated.

Experimental investigation on solid dispersion, power consumption and scale-up in moderate to dense solid–liquid suspensions

Detailed particle concentration distribution in dense solid–liquid suspension was measured by means of fiber optic probes. The effect of solid loading, impeller speed, and impeller type and clearance was investigated. Results were compared with modeling approaches to show the accuracy of sedimentation–dispersion model and its capability to describe complex phenomena taking place in dense liquid–solid mixing systems. Variation of power numbers by changing impeller clearance and solid loading were also investigated. It was shown that the impeller power number for a slurry system exhibited different trends in a moderate or dense liquid–solid system. In addition, scale-up rules to achieve the same level of homogeneity on a large scale as the laboratory scale were evaluated.

Ultrasonic technique to determine particle size and concentration in slurry systems

Acoustic velocity measurements have been used to estimate particle size and concentration in liquid–solid (LS) and gas–liquid–solid (GLS) systems. The slurries of 34 and 110 μ m particles and their binary mixtures in distilled water are tested in concentration range 2–10 vol% in batch operations. In GLS systems, the superficial gas velocity is varied from 0.03 to 0.10 m/s. The presence of gas bubbles affected the acoustic velocity measurements significantly. A data filtration procedure is developed to minimize the effect of gas phase and estimate variations in gas-free liquid–solid region. The filtered data are used to predict concentration using calibration equations and theoretical velocity prediction models of LS systems. The estimated concentrations are comparable with sedimentation–dispersion model predictions in GLS system. This technique is also used to predict average particle size and composition in binary mixtures of particles.

Dispersion coefficients and settling velocities of solids in slurry vessels stirred with different types of multiple impellers

Equipment dealing with stirred suspensions are broadly used in the process industry. Out of the various aspects affecting their performance, solids distribution is addressed in this paper. The behaviour of a tank of high aspect ratio stirred with multiple impellers of three types is analysed. The purpose is to acquire fundamental information on parameters useful for their description, namely the axial dispersion coefficient of the solids phase and the particle settling velocity. Both transient and steady-state experiments were performed with a variety of dilute suspensions. The data were analysed with the axial sedimentation–dispersion model. The axial dispersion coefficient of the solid phase was found to differ from that of the liquid by less than 15% for all the impellers and conditions tested. The effective particle settling velocity in the stirred medium was then determined. As happens in equipment stirred with multiple radial turbines, the value of this parameter was found to be different, in general, from the terminal settling velocity. It is shown that a correlation among these parameters and Kolmogoroff length microscale and particle size obtained previously for a specific geometric configuration is actually independent of the impeller type.

Diagnosis of Solid Distribution in Vessels Stirred with Multiple PBTs and Comparison of Two Modelling Approaches

AbstractThe features of solids concentration distribution were investigated in two baffled vessels of different scale. The vessels were of high aspect ratio and were stirred with multiple PBTs. Both steady‐ and unsteady‐state experiments were performed. The experimental data were compared with the previsions of the one‐dimensional sedimentation‐dispersion model and of CFD tools. The former approach provides good estimates only of the average, steady‐state vertical profiles, while the latter describes the local variations much more accurately. Both approaches give fairly good estimates of the transient solids concentration distribution. The dynamic CFD simulations allowed us also to tune the value of the turbulent Schmidt number as a relevant parameter. Finally, both simulation approaches have confirmed that the particle settling velocity in a stirred liquid is a correct parameter to be used instead of the terminal settling velocity.

Dispersion coefficient and settling velocity of the solids in agitated slurry reactors stirred with multiple rushton turbines

The feature of solids distribution in tanks stirred with multiple Rushton turbines was investigated. Both transient and steady-state experiments were performed in tanks of two scales with a variety of suspensions. The data were analysed with the axial sedimentation–dispersion model. The axial dispersion coefficient of the solid phase was found not to differ from that of the liquid by more than 20%. The effective particle settling velocity in the stirred medium was then determined. It is confirmed that this parameter is different from the terminal settling velocity. Their ratio exhibits the same dependence on Kolmogoroff microscale and particle size as obtained previously with an indirect, approximate approach.

Axial solid concentration distribution in tapered and cylindrical bubble columns

The distribution of axial solid concentration was investigated experimentally and theoretically in tapered and cylindrical slurry bubble columns using air as the gas phase, tap water as the liquid phase and quartz sands as the solid phase. Based on the sedimentation–dispersion model commonly used in cylindrical columns, a mathematical model was presented to predict the solid concentration distribution in the tapered column. Superficial gas velocities up to 0.28 m/s, slurry concentrations up to 159 kg(solid)/m 3(slurry), and static slurry height from 1.6 to 2.7 m were measured. The axial solid concentration distribution becomes uniform with an increase in superficial gas velocity or average solid concentration and with a decrease in particle diameter or static slurry height. The experiments were carried out in the cylindrical column under similar operating conditions to compare differences in the axial solid distribution measured in cylindrical and tapered columns. The results showed that the tapered column provides a more uniform profile of axial solid concentration than the cylindrical column. An empirical correlation for Peclet number was developed using dimensional analysis, which can predict the axial solid concentration distribution in tapered columns.

SOLIDS DISTRIBUTION IN STIRRED SLURRY REACTORS: INFLUENCE OF SOME MIXER CONFIGURATIONS AND LIMITS TO THE APPLICABILITY OF A SIMPLE MODEL FOR PREDICTIONS

The features of solids concentration distribution were investigated in baffled and unbaffled tanks of high aspect ratio, stirred with multiple radial, mixed-flow or axial impellers. In the baffled tanks the average profiles can be predicted with the sedimentation-dispersion model regardless of impeller type - in spite of slight systematic departures from the average trend at the impeller plane and/or midway between the impellers. This is hardly possible for the unbaffled tanks due to lack of physical foundation of this simple model. When the unbaffled tank is stirred with hydrofoil impellers, an inverted profile is even obtained. The mentioned departures and this last anomalous behaviour are qualitatively discussed with reference to particle-turbulence interaction.

Solid Particles Concentration Profiles in an Agitated Vessel

Local solid concentration profiles were investigated in a contoured bottom cylindrical reactor, mechanically stirred by a 45° pitched blade turbine and equipped with four baffles. The solid-liquid system consisted of a suspension of spherical glass beads or alumina grains in water. The effects of the stirring rate and of the size and density of the solid particles were examined. To interpret the solid distribution profiles in the vessel, a one-dimensional sedimentation dispersion model was employed. The description was based on the continuity equation and made use of the experimental knowledge of the flow velocity distribution of the liquid phase and of the calculated terminal velocity in a still medium of the solid particles.

Hydrodynamic behavior of slurry bubble column at high solids concentrations

Hydrodynamics of a slurry bubble column have been investigated up to slurry concentrations of 40 vol.% and gas velocities of 0.26 m/s. High slurry concentrations represent high catalyst loading to increase reactor productivity, while high gas velocities would be required to increase reactor throughputs. The solid particles used are 35 μm glass beads representing typical particle size for catalytic slurry reactors. The two important hydrodynamic parameters investigated are gas holdup and solids concentration profiles. The average gas holdups decreased with increasing slurry concentration but the rate of decrease slowed down for higher slurry concentrations. The analysis of axial gas holdup profiles indicated that decrease in gas holdup due to solids addition could be attributed to a decrease in bubble breakup rates. The experimental gas holdups are compared with literature correlations and models. The axial distribution of slurry concentration followed the classical sedimentation–dispersion model. Effects of gas velocity on axial solids distribution are found to be minimal over the range of gas velocities investigated.

Flow Behavior of a Gas−Liquid−Solid Fluidized Bed in a Self-Circulating Operation through an External Conduit

Flow behavior of liquid and multicomponent mixtures of solid particles in fluidizing columns with an external conduit was investigated for a self-circulating operation by an airlift effect. Experimental and analytical results are presented for circulating rates of liquid and particles and for axial changes in holdups of gas and solid in the column. From good agreement between both results, it was found that a one-dimensional sedimentation-dispersion model and mechanical energy balance equation were successfully applied to predict the axial change in gas and solid holdups as well as the circulating rates of liquid and solid particles in the columns.

Axial mixing and segregation in a gas-liquid-solid three-phase fluidized bed of solid particles of different sizes and densities

Sieved silica-alumina particles (diameter = 481 μm; density = 1990 kg/m3), glass beads (diameter = 516 μm; density = 2500 kg/m3) or mixtures thereof were fluidized in a vertical bubble column of 7 cm in diameter and 4.50 m in height. The bed was operated batchwise or continuously with respect to the feed of solid particles. Axial changes in gas and solid holdups in the bed were measured by simultaneously sectioning the column with 20 horizontal plates. The measured solid holdup of each component in the column was compared with the analytical results calculated by a one-dimensional sedimentation-dispersion model. Both experimental and calculated results were in satisfactory agreement over the entire column, which consisted of dense and dilute regions, as well as circulating quantities of liquid and solid particles.

Hydrodynamics of semibatch slurry bubble columns with polymer solutions

In this work we perform an experimental study of the hydrodynamics of semibatch slurry bubble columns in which the liquid phase is a solution of a high molecular weight hydrolyzed polyacrylamide. Experiments were conducted in bubble columns with two different diameters (10 and 29 cm.) In gas-liquid operation, the gas holdup decreases as the polymer concentration increases due to the formation of large stable bubbles. In the presence of high solids concentration, this trend is reversed in the larger column due to an increase in the number of small bubbles and an appreciable increase in the residence times of the large bubbles brought about by an increase in slurry circulation. The distribution of solid phase becomes more uniform as the polymer concentration increases. This trend is quantified by means of the application of a modified form of the sedimentation-dispersion model. The macromolecular conformation of the polymer in solution is altered by adding NaCl, whose positive ions screen negative charges in the polymer molecule producing a contraction of the coil. At the concentration levels used in this work, the addition of salt decreases the ability of the polymer to produce a more uniform solids distribution.

Inverted segregation of binary particles in gas-liquid-solid fluidized bed

Two-component mixtures of sieved glass beads (2.2, 3.1 and 4.65 mm) were fluidized by upward concurrent flows of air and water in two vertical columns, one of 7 cm diameter and 4.85 m height, and the other of 15 cm diameter and 2.7 m height. After steady-state operation, axial distributions of gas and solid holdups were measured by sectioning the whole column simultaneously with horizontal plates. When solid particles were fluidized at low liquid velocity and high gas velocity, an inverted segregation whereby small particles became concentrated below large particles was observed at a region where the total solid holdup was larger than 0.4. The axial holdup profile of each component of solid particles was described with a one-dimensional sedimentation-dispersion model. Inverted and normal segregation patterns calculated from the model were in agreement with experimental ones over an entire column consisting of dense and dilute regions.

THE SEDIMENTATION-DISPERSION MODEL FOR SLURRY BUBBLE COLUMNS WITH A CONICAL DISTRIBUTOR

In this work we present a mathematical model to simulate the distribution of solid phase in slurry bubble columns with a conical entrance section. The model is based on the sedimentation-dispersion model that is commonly used to simulate solids distribution in cylindrical columns. The model equations are obtained from a mass balance of solids expressed in terms of a cross-sectional average of the solids concentration. The resultingdifferentialequationsare integrated numerically. We have used the model to analyze the effect of the taper angle of a conical distributor on the suspension of solids in a cylindrical spouted bed with pilot scale dimensions. The effects of gas and slurry flow rates, and average and feed solids concentration are also studied. The results show that there is a range of operating conditions for which the solids concentration profile exhibits a maximum within the conical region. For sufficiently high solids concentration, the vicinity of this maximum would be the place where sedimenta...

Transient behavior of the vertical distribution of solid holdup with a step change in liquid velocity in a long bubble column

Sieved glass beads 480 μm in diameter are suspended by upward concurrent gas and liquid flow in a vertical bubble column of 7-cm diameter and 4.85-m height. Transient changes in the holdups of gas and solid particles are caused by a step change in the liquid velocity, and the time-dependent behavior of the axial distributions of the phase holdups is measured by sectioning the column simultaneously with 20 horizontal plates. A one-dimensional sedimentation-dispersion model is applied to describe the transient response of the solid holdup. The model developed is in good agreement with the data over an entire column consisting of dense and dilute regions

Prediction of minimum gas velocity in suspended bubble columns and airlift reactors

For design and operation of bubble columns and airlift reactors with suspended solid particles it is necessary to know the minimum gas velocity for maintaining the state of complete solid suspension. To predict this critical gas velocity information on flow behaviour of solid particles in gas-liquid dispersions is required. For this purpose a simplified model is proposed which is based on an energy balance containing mean values of liquid velocity in the upstream region. Whereas within the riser region of airlift reactors the solid content was found to be constant, it shows a gradient as a function of height in the upstream region of bubble columns, which is described by the Sedimentation-Dispersion Model. In the this way for each of the two reactor types a relation is obtained in which the minimum gas velocity is given as a function of sedimentation velocity of solid particles and liquid velocity. These functions are confirmed by results from measurements in both a bubble column and an airlift reactor with dispersions of glass particles of different grain size in the system air/water.

Axial mixing and segregation of multicomponent coarse particles fluidized by concurrent gas-liquid flow

Multicomponent solid particles were fluidized by upward concurrent flows of air and water in vertical columns of 7 cm diameter and 4.85 m height, and of 15 cm diameter and 2.7 m height. Solid particles used were sieved glass beads (2.2, 3.1 and 4.65 mm) and mixtures thereof. Axial changes in holdups of gas and solids were determined by sectioning the whole column simultaneously with horizontal plates. The solid holdup of coarse particles was more strongly affected by the liquid velocity than was that of fine particles. A one-dimensional sedimentation-dispersion model was applied to describe the axial holdup profile of each solids component. Calculated results were in agreement with experimental ones over an entire column consisting of dense and dilute regions. Parameters used in the calculation were correlated as experimental equations.