Axial mixing and mass transfer investigation in a pulsed packed liquid–liquid extraction column using plug flow and axial dispersion models

In this research work, the volumetric overall mass transfer coefficient based on continuous-phase (K_oca) and axial dispersion coefficients of phases (E_c, E_d) in a pilot Pulsed Packed Liquid Extraction Column (PPLEC) have been studied using plug flow model (PFM) and axial dispersion model (ADM). Experiments have been carried out using standard systems of water/acetone/toluene and water/acetone/n-butyl–acetate. Values of K_oca evaluated by ADM are greater than those of PFM by about 20% indicating that the axial mixing lowers the performance of PPLEC. It was found that the drop-size distribution is the main cause of the axial mixing in PPLEC. Increase in dispersed phase flow rate (Q_d), increases all K_oca, E_d and E_c and the minimum values of both E_d and E_c and the maximum values of K_oca are in pulse intensity ranges of 0.8–1 cm/s. Finally, three empirical correlations are proposed for the prediction of these parameters which are in good agreement with the experimental data.     

Use of axial dispersion and plug flow models for determination of axial mixing and mass transfer coefficient in an l‐shaped pulsed packed extraction column

In this study, the volumetric overall mass transfer and phases axial mixing coefficients have been investigated in a pilot plant of an L‐shaped pulsed packed extraction column by using two liquid systems of toluene/acetone/water and n‐butyl/acetone/water. The mass transfer performance has been evaluated using two methods of axial dispersion and a plug flow model. The effect of the operational variables and physical properties, including the dispersed and continuous phases flow rates, pulsation intensity, and interfacial tension, on mass transfer and phases axial mixing coefficients have been considered. It has been found that the pulsation intensity and the continuous phase flow rate seriously affect the mass transfer coefficient, however, the dispersed phase flow rate has a weaker effect. Also, the axial mixing of a phase is strongly affected by the pulsation intensity and the flow rate of the phase itself and it is not affected by the second phase flow rate. Finally, new correlations are proposed to accurately predict the mass transfer and axial mixing coefficients.     

Design and characterization of a multistage,mechanically stirred column absorber

A multistage, mechanically stirred column absorber has been designed and built with a modular construction, based on preliminary experiments with a test column. The column has been characterized as a gas-liquid contactor by its gas holdup, gas and liquid axial dispersion, mixing times, oxygen transfer coefficients and power consumptions, determined as a function of gas velocity, liquid velocity and impeller speed for one and two impellers per stage.Gassed power was correlated with ungassed power, gas rate and impeller speed. The gas phase axial mixing was essentially plug flow and the liquid phase axial mixing varied between 5 and 12 equivalent stages.Oxygen transfer coefficients were correlated with power consumptions and aeration rates by the equation K_La γ (P/V)^a(υ_sg)^b. The oxygen transfer coefficients with single stiffer stages were 25% above those for the double stirrer stages for equal power consumption and gas rates. Except for the low aeration and high power consumption extremes, the column showed superior oxygen transfer performance. in comparison to tubular loop and tank fermenters.     

Axial Dispersion and Phase Holdup Characteristics in Reciprocating Plate Extraction Columns

Abstract

Axial dispersion and phase holdup characteristics have been determined in a 0.102-m i.d. × 3.5 m high QVF glass column. The axial dispersion coefficient decreases with increasing reciprocating frequency (f) and amplitude (A) in the inhomogeneous dispersed phase flow regime, whereas it increases in the emulsion flow regime. The axial dispersion coefficient with a perforated plate increases with continuous and dispersed phase velocities. However, the effect of phase velocities on axial dispersion is less pronounced with the fan plate. The axial dispersion coefficient can be correlated with A ² f, fluid velocities, and the free fractional opening area of the plates. The dispersed phase holdup increases with an increase in agitation intensity. Af, and decreases with the free opening area of the plate.     

Modelling the liquid-phase adsorption in packed beds at low Reynolds numbers: An improved hydrodynamic model

A hydrodynamic model including only one parameter (λ_O) for the prediction of both axial dispersion and external mass transfer in fixed-bed adsorbers at low Reynolds numbers (creeping flow regime) has been developed. The theoretical analysis is based on the application of the (two-dimensional) uniform dispersion model originally proposed by Bischoff and Levenspiel [1962a. Fluid dispersion—generalization and comparison of mathematical models—I. Generalization of models. Chemical Engineering Science 17, 245-255] to the representative capillary of a tube bundle model for describing the flow and mixing behaviour in packed beds. The combination of this model with the relationship between longitudinal and radial dispersion leads to the definition of the sole hydrodynamic parameter λ_O (one-parameter hydrodynamic model). Furthermore, the detailed investigation reveals that the one-parameter concept may be utilized for the application of the (one-dimensional) axial dispersed plug flow model as well. The functional dependence of the parameter λ_O on the flow conditions is elaborated from axial dispersion measurements. Both the new (one-parameter) hydrodynamic model and the classical model including axial dispersion and external mass transfer coefficients (two-parameter model) are utilized to simulate the breakthrough curves for the adsorption of naphthalene onto silica gel. This simulation study reveals that only the one-parameter hydrodynamic model is able to predict the adsorber dynamics over a large range of flow rates.     

Axial dispersion in a pulsed plate column

A technique involving the indicator colour change in an acidbase reaction has been used to measure axial dispersion coefficients in a 15 cm diameter pulsed column. Data have been obtained mainly for single phase (aqueous) flow with two different types of plate at two different spacings. With coarsely perforated plates, the dispersion coefficient is proportional to (amplitude)² times frequency, but semicircular unperforated baffle plates show a dependence on amplitude times frequency. These results are critically compared with published data, and two types of flow regime for axial dispersion are indicated.     

Numerical determination of fluid-to-particle mass and heat transfer coefficients in packed bed reactors

A method based on particle-resolved CFD is built and validated, to calculate the fluid-to-particle mass and heat transfer coefficients in packed beds of spheres with different tube-to-particle diameter ratios (N) and of various particle shapes with N = 5.23. This method is characterized by considering axial dispersion. The mass and heat transfer coefficients increase by 5%–57% and 9%–63% after considering axial dispersion, indicating axial dispersion should be included in the method. The mass and heat transfer coefficients are reduced as N decreases. The catalyst particles without inner holes show higher mass and heat transfer coefficients than the ones with inner holes, because of unfavorable fluid flow in inner holes. The bed of trilobes has the highest mass and heat transfer coefficients, being 85% and 95% higher than the one of spheres. This work provides a versatile method and some useful guidance for the design of packed bed reactors.     

Laminar heat transfer of non-Newtonian nanofluids in a circular tube

Forced convection heat transfer behavior of three different types of nanofluids flowing through a uniformly heated horizontal tube under laminar regime has been investigated experimentally. Nanofluids were made by dispersion of γ-Al₂O₃, CuO, and TiO₂ nanoparticles in an aqueous solution of carboxymethyl cellulose (CMC). All nanofluids as well as the base fluid exhibit shear-thinning behavior. Results of heat transfer experiments indicate that both average and the local heat transfer coefficients of nanofluids are larger than that of the base fluid. The enhancement of heat transfer coefficient increases by increasing nanoparticle loading. At a given Peclet number and nanoparticle concentration the local heat transfer coefficient decreases by axial distance from the test section inlet. It seems that the thermal entry length of nanofluids is greater than the base fluid and becomes longer as nanoparticle concentration increases.     

RTD studies in trickle bed reactors packed with porous particles

The residence time distribution (RTD) for liquid phase in a trickle bed reactor (TBR) has been experimentally studied for air-water system. Experiments were performed in a 15.2 cm diameter column using commerical alumina extrudates with D/d_p ratio equal to 75 to eliminate the radial flow differences. The range of liquid and gas flow rates covered was 3.76 < Re_L < 9.3 and 0 < Re_G < 2.92. The axial dispersion model was used to compute axial dispersion coefficient. The effect of liquid and gas flow rates on total liquid holdup and axial dispersion was investigated. The total liquid holdup has been correlated to liquid and gas flow rates.     

Determination of K ow of Substituted Polycyclic Aromatic Compounds

Octanol-water partition coefficients (K _ow s) of substituted polycyclic aromatic compounds (PACs), anthracene-, pyrene- and quinoline-derivatives, have been determined using HPLC. The determined K _ow s have been compared with results from theoretical fragment methods, developed by Rekker and Mannhold [1] and by Hansch and Leo [2]. The results showed that if these theoretical methods are to be useful with simple substituted PAHs they must be applied differently than normally supposed, due to intramolecular steric conditions. Comparison of the determined K _ow s with measured K _oc values showed that the relationship between K _oc and K _ow is not straightforward, and that prediction of K _oc from K _ow alone will not give results applicable for substituted polycyclic aromatic compounds.     

Comparison of hydrodynamic and mass transfer performances of an emulsion loop-venturi reactor in cocurrent downflow and upflow configurations

Hydrodynamic parameters (gas-induced flow rate and gas hold-up) and mass transfer characteristics (k_La, k_L and a) have been investigated in a gas–liquid reactor denoted “Emulsair” in which the distributor is an emulsion-venturi and the gas phase is self-aspired by action of the kinetic energy of the liquid phase at the venturi throat. Two configurations, respectively cocurrent downflow and cocurrent upflow were compared. A chemical method involving the dispersion of a CO₂–air mixture in a monoethanolamine (MEA) aqueous solution was used to measure mass transfer parameters. Experimental results showed that only the homogeneous bubbling regime prevailed in the upward configuration, while an annular regime could also be observed for cocurrent downflow at low liquid flow rate. Gas-induced flow rate and gas hold-up were usually smaller for cocurrent upflow, both at constant liquid flow rate and specific power input. The same stood for mass transfer properties. Conversely, specific power requirements were lower at constant liquid flow rate and mass transfer characteristics were enhanced at constant gas-induced flow rate for cocurrent upflow. A comparison with other gas–liquid contacting devices showed that the Emulsair reactor is a versatile tool avoiding the presence of mechanically moving parts when high and quickly adaptable dissolved gas supply is required. The cocurrent upflow configuration can be preferred when high gas flow rates are desired because the evolutions of gas-induced flow rate and mass transfer characteristics exhibit a stronger dependence on specific power input in the homogeneous bubbling regime for this configuration.     

Liquid phase axial mixing in a bubble column with viscous non-newtonian liquids

This paper presents some new data for the liquid phase axial dispersion coefficient in a bubble column with highly viscous non-Newtonian liquids (μ_L > 0.03 Pa · s). The data were obtained in a 0.15 m diameter column operating in the slug flow regime, and the dispersion measurements were conducted using heat aas a tracer. The experimental results show that the dispersion coefficients increase with both gas and liquid velocities and quantitatively they are about three times higher than those obtained for the air-water system. The results are explained based on a known hydrodynamic model of vertical gas-liquid slug flow.     

CFD and experimental studies of single phase axial dispersion coefficient in pulsed sieve plate column

This paper intends to study the single phase axial dispersion in pulsed sieve plate column using a combination of computational fluid dynamics (CFD) simulations and experimental measurements. Experiments and CFD simulations were conducted on 0.076 m diameter pilot scale column having standard geometry of 0.05 m plate spacing, 0.003 m hole diameter and 0.21 fractional free area. The effect of density of tracer solution and radial probe position on axial dispersion coefficient has been studied to ensure precision of the experimental measurement method. The effect of pulse velocity from 0.01 to 0.025 m/s and superficial velocity of water from 0.01 to 0.03 m/s has been studied. Simulations were carried out using commercial CFD software, FLUENT 6.2.16, with standard k–? model for turbulence. An unsteady state tracer injection technique was used for axial dispersion measurement. The range of velocity ratio (ψ = Re_o/Re_n) employed in this work was 1–4 which is very low. Therefore the effect of superficial velocity, V_c was found to be greater than pulse velocity. These results were critically compared with published data and it has been found that single phase axial dispersion coefficient is directly proportional to effective velocity (Af + 0.5 V_c). The presented CFD predictions and validation with experimental data will provide useful basis for further work on single phase axial dispersion with various geometrical parameters and understanding the two phase flow patterns in pulsed sieve plate column.     

Axial dispersion in packed beds: The effect of particle size non-uniformities

The effect of particle size non-uniformities on axial dispersion coefficients during laminar liquid flow through packed beds has been studied. The investigations were carried out for binary mixtures of particles with diameters d₁ = 0.169 mm and d₁ = 0.360 mm.A generalized function to determine the increase of the axial dispersion coefficients in non-uniform beds relative to those obtained in uniform beds has been proposed.     

Mass transfer in trickle-bed reactors at low reynolds number

Mass transfer rates were determined in a 3.4 cm i.d. trickle-bed reactor in the absence of reaction by absorption measurements and in presence of reaction. Gas flow rates were varied from 0-100 l/h and liquid flow rates from 0-1.5 l/h. The catalyst particles were crushed to an average diameter of 0.054 and 0.09 cm. Mass transfer coefficients remained unaffected by change in gas flow rate but increased with liquid rate. The data from absorption measurements were evaluated with predictions based upon plug-flow and axial dispersion model. Mass transfer coefficients were found greater in case of axial dispersion model than that of plug-flow model specially at low Reynolds number (Re₁ < 1).Hydrogenation of α-methylstyrene to cumene using a Pd/Al₂O₃ catalyst was taken as a model reaction. Intrinsic kinetic studies were made in a laboratory-stirred-autoclave. Mass transfer coefficients were determined using these intrinsic kinetic data from the process kinetic measurements in trickle-bed reactor. Mass transfer coefficients under reaction conditions were found to be considerably higher than those obtained by absorption measurements.Correlations were suggested for predicting mass transfer coefficients at low Reynolds number.The gas to liquid mass transfer coefficients for lower gas and liquid flow rates were determined in a laboratory trickle-bed reactor. The effect of axial dispersion on mass transfer was considered in order to evaluate the experimental data. Three correlations were formulated to calculate the mass transfer coefficients, which included the effect of liquid loading, particle size and the properties of the reacting substances. The gas flow rate influences the gas to liquid mass transfer only in the region of low gas velocities. In the additional investigations of gas to liquid mass transfer without reaction in trickle-bed reactor, the mass transfer coefficients were determined under reaction conditions and the intrinsic kinetics was studied in a laboratory scale stirred autoclave with suspended catalyst. A few correlations are formulated for the mass transfer coefficients. A comparison with the gas-liquid mass transfer coefficient obtained by absorption measurements showed considerable deviations, which were illustrated phenomenologically.     

Mixing Time Studies in Multiple Impeller Agitated Reactors

Mixing time studies have been carried in a 0.3m diameter and 0.9m tall vessel equipped with three impellers. Conductivity measurement technique has been used for the measurements of mixing time. Effect of the various parameters i.e. tracer density, tracer volume, speed of rotation and impeller combination on mixing time has been studied for two impeller combinations used viz. PTD‐PTD‐PTD and PTD‐PTD‐DT. A compartment model (with one fitted parameter, the exchange flow rate Q_E) with single compartment per agitation stage has been used to predict the conductivity response and the exchange coefficients are calculated from the model parameter. An attempt has been made to explain the experimental results on the basis of the liquid phase axial dispersion coefficient and cell residence time, calculated from the model parameter Q_E     

Study of Hydrodynamics,Mixing and Gas‐Liquid Mass Transfer in a Split‐Rectangular Airlift Reactor

Global hydrodynamic characteristics, liquid mixing and gas‐liquid mass transfer for a 63 L split‐rectangular airlift reactor were studied. Correlations for gas holdup and overall liquid circulation velocity were derived for the air‐water system as a function of the specific power input; these were compared to data and correlations for reactor volumes between 4.7 L and 4600 L. A partial recirculation of small bubbles in the riser was observed when U_gr > 0.03 m/s, which was attributed to the use of a single‐orifice nozzle as the gas phase distributor. The dimensionless mixing time and the overall axial dispersion coefficient were nearly constant for the range of gas flow rates studied. However, values of K_L/d_B were greater than those reported in previous studies and this is caused by the partial recirculation of the gas phase in the riser. While scale effects remain slight, the use of a gas distributor favouring this partial recirculation seems adequate for mass transfer in split‐rectangular airlift reactors.     

A model for liquid-liquid extraction column performance — The influence of drop size distribution on extraction efficiency

A precise model for predicting liquid-liquid extraction column efficiency based upon assumed hydrodynamic, axial mixing and mass transfer behaviour has been formulated and solved numerically. The complex nature of the dispersed phase can be better described by drop-size-dependent residence time distribution (RTD). Both the variation of axial velocities due to drops of different sizes, i.e. forward mixing, and the axial dispersion for the drops of the same size have been considered in this model. The computed results reveal that the effects of both varying velocities and dispersion of drops on extraction efficiency are appreciable and cannot be neglected, and the efficiency may be overestimated if only a forward mixing model is adopted. The comparison of the experimental values of N_ODP with those predicted shows that the mass transfer data obtained in RDC agree well with the values predicted by the present model for the case of solute transfer in c→d direction, and are slightly higher than the predicted ones for the transfer in d→c direction.     

Liquid‐phase axial dispersion of turbulent gas–liquid co‐current flow through screen‐type static mixers

This article discusses the characteristics of turbulent gas–liquid flow through tubular reactors/contactors equipped with screen‐type static mixers from a macromixing perspective. The effect of changing the reactor configuration, and the operating conditions, were investigated by using four different screen geometries of varying mesh numbers. Residence time distribution experiments were conducted in the turbulent regime (4500 < Re < 29,000). Using a deconvolution technique, the RTD function was extracted to quantify the axial/longitudinal liquid‐phase dispersion coefficient. The findings highlight that axial dispersion increases with an increasing flow rate and/or gas‐phase volume fraction. However, regardless of the number and geometry of the mixing elements, reactor configuration, and/or operating conditions, the recorded liquid‐phase axial dispersion coefficients in the presence of screens was lower than that for an empty pipe. Furthermore, the geometry of the screen was found to directly affect the axial dispersion coefficient in the reactor. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1390–1403, 2017     

Calculation of flow fields in two and three-phase bubble columns considering mass transfer

The dimension of bubble column reactors is often based on empirical correlations. Very popular is the axial dispersion model. However, the applicability of these models is limited to the experimental conditions for which the dispersion coefficients are measured, because backmixing depends strongly on the columns dimension and the flow regime. This paper presents a numerical method for the calculation of the three-dimensional flow fields in bubble columns based on a multi-fluid model. Therefore, the local bubble size distribution is considered by a transport equation for the mean bubble volume, which is obtained from the population balance equation. For comparison with experimental results, the axial dispersion coefficients in the liquid and gas phase are calculated from the instationary, three-dimensional concentration fields of a tracer. The model is then extended to include mass transfer between the gas and liquid phase. Increasing mass transfer rates significantly influence the flow pattern. For several applications, a dispersed solid phase is added. For the calculation of three-phase gas-liquid-solid flow, the solid phase is considered numerically by an additional Eulerian phase.