Liquid mixing on bubble-cap and sieve plates

Experimental frequency-response results and their interpretation by the diffusion equation lead to a correlation of liquid mixing with operating conditions for large-scale bubble-cap and sieve plates, in terms of a modified Péclet number and the liquid hold-up and froth density. Other mixing concepts are critically discussed. A simple method of predicting the effect of liquid mixing on plate efficiency is proposed, assuming complete mixing of the vapour between plates.     

Residence time distribution of a purely viscous non-Newtonian fluid in helically coiled or spatially chaotic flows

This work is dedicated to an experimental study of residence time distributions (RTD) of a pseudoplastic fluid in different configurations of helically coiled or chaotic systems. The experimental system is made up of a succession of bends in which centrifugal force generates a pair of streamwise Dean cells. Fluid particle trajectories become chaotic through a geometrical perturbation obtained by rotating the curvature plane of each bend of ±90° with respect to the neighboring ones (alternated or twisted curved ducts). Different numbers of bends, ranging from 3 to 33, were tested. RTD is experimentally obtained by using a two-measurement-point conductimetric method, the concentration of the injected tracer being determined both at the inlet and at the outlet of the device. The experimental RTD is modeled by a plug flow with axial dispersion volume exchanging mass with a stagnant zone. RTD experiments were conducted for generalized Reynolds numbers varying from 30 to 270. The Péclet number based on the diameter of the pipe is found to increase with the Reynolds number whatever the number of bends in the system. This reduction in axial dispersion is due to both the secondary Dean flow and the chaotic trajectories. Globally, the flowing fraction, which is one of the characteristic parameters of the model, increases with the Reynolds number, whatever the number of bends, to reach a maximum value ranging from 90% to 100%. For Reynolds numbers less than 200, the flowing fraction increases with the number of bends. The stagnant zone models fluid particles located close to the tube wall. The pathlines become progressively chaotic in small zones in the cross section and then spread across the flow as the number of bends is increased, allowing more trapped particles to move towards the tube center. Results have been compared with those previously obtained using Newtonian fluids. The values of the Péclet number are greater for the pseudoplastic fluid, the local change of apparent viscosity affecting the secondary flow. For pseudoplastic fluids, the apparent viscosity is lower near the wall and higher at the center of the cross section. The maximum axial velocity is flattened as the flow behavior index is reduced, inducing a decrease of the secondary flow in the central part of the pipe and an acceleration of it near the wall, which reduces the axial dispersion. These results are encouraging for the use of this system as continuous mixer for complex fluids in laminar regime, particularly for small Reynolds numbers.     

Liquid phase mixing in turbulent bed contactor

Axial mixing of the liquid phase in turbulent bed contactor (TBC) is studied through residence time distribution (RTD) experiments over a large range of variables such as flow rate of gas and liquid phases, static bed heights, diameter and density of particles and number of stages in presence of downcomer using air water system. Since all the liquid exits only through the downcomer, it enables the correct estimation of exit concentration of the tracer. The experimental RTD curves are satisfactorily compared with the axial dispersion model. The Peclet numbers evaluated by axial dispersion model and the Peclet numbers reported in the literature are used to propose a unified correlation in terms of operating and geometric parameters. Correlation is also developed for predicting the axial dispersion coefficient. It was observed in the present study that almost plug flow conditions can be achieved in multistage TBC.     

Hydrodynamic Behavior and Residence Time Distribution of Industrial‐Scale Bale Packings

The hydrodynamic behavior of bale packing was tested in a catalytic distillation column. Models and empirical equations for predicting pressure drop and dynamic liquid holdup were proposed and compared with experimental results. The examination of residence time distribution (RTD) relied on the pulse method and a conductivity meter which deduced the axial Péclet number, axial dispersion coefficient, and dynamic liquid holdup. The relations of dynamic liquid holdup obtained from gravimetric draining experiments and RTD studies were discussed with static and total liquid holdup. Potential impacts of the liquid distributor and conductivity cell were also assessed. The results prove that models and empirical equations fit well and are reliable in design and scale‐up.     

Trickle bed hydrodynamics and flow regime transition at elevated temperature for a Newtonian and a non-Newtonian liquid

Despite the hydrodynamics of trickle beds experiencing high pressures has become largely documented in the recent literature, trickle bed hydrodynamic behavior at elevated temperatures, on the contrary, largely remains terra incognita. This study's aim was to demonstrate experimentally the temperature shift of trickle-to-pulse flow regime transition, pulse velocity, two-phase pressure drop, liquid holdup and liquid axial dispersion coefficient. These parameters were determined for Newtonian (air-water) and non-Newtonian (air-0.25% Carboxymethylcellulose (CMC)) liquids, and the various experimental results were compared to available literature models and correlations for confrontation and recommendations. The trickle-to-pulse flow transition boundary shifted towards higher gas and liquid superficial velocities with increasingly temperatures, aligning with the findings on pressure effects which likewise were confirmed to broaden the trickle flow domain. The Larachi-Charpentier-Favier diagram [Larachi et al., 1993, The Canadian Journal of Chemical Engineering 71, 319-321] provided good predictions of the transition locus at elevated temperature for Newtonian liquids. Conversely, everything else being kept identical, increasingly temperatures occasioned a decrease in both two-phase pressure drop and liquid holdup; whereas pulse velocity was observed to increase with temperature. The Iliuta and Larachi slit model for non-Newtonian fluids [Iliuta and Larachi, 2002, Chemical Engineering Science 46, 1233-1246] predicted with very good accuracy both the pressure drops and the liquid holdups regardless of pressure and temperature without requiring any adjustable parameter. The Burghardt et al. [2004, Industrial and Engineering Chemistry Research 43, 4511-4521] pulse velocity correlation can be recommended for preliminary engineering calculations of pulse velocity at elevated temperature, pressure, Newtonian and non-Newtonian liquids. The liquid axial dispersion coefficient (D_ax) extracted from the axial dispersion RTD model revealed that temperatures did not affect in a substantial manner this parameter. Both Newtonian and power-law non-Newtonian fluids behaved qualitatively similarly regarding the effect of temperature.     

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     

Longitudinal mixing of the liquid phase in packed columns with countercurrent two phase flow

Axial mixing of the liquid phase in trickle flow through two columns packed with Raschig rings was determined by least square fitting of the experimentally obtained F-curve applying the Fibonacci optimal search method. The Péclet number was found to be independent of the gas flow rate and proportional to the liquid Reynolds number. The one parameter axial dispersed plug flow model was shown to be acceptable in describing axial mixing of the liquid phase. A simple correlation of the Péclet number is proposed for application in mass transfer design calculations     

Gas/Flüssig-Reaktoren

Gas-liquid reactors . The gas hold-up in bubble columns increases in proportion to the gas flux density in the homogeneous flow regime and rises less than proportionally in the heterogeneous flow regime. Both the gas and the liquid axial dispersion coefficient increase with gas flow. Gas phase dispersion becomes more intensive with increasing liquid viscosity, while liquid dispersion drops slightly. Experimental results for mass transfer in low viscosity liquids show that the two-range turbulence model best fits experimental data. When aerating highly viscous Newtonian and non-Newtonian liquids, mass transfer in the liquid phase is well described by known relations valid for very low bubble-Reynolds number and very high Schmidt number.     

Dimensional Analysis of Particle and Liquid Dispersion in Draining Foam

A dimensionless correlation for the axial dispersion of particles and liquid tracer in draining foam has been developed that expresses the dimensionless dispersion as a function of Peclet and Stokes numbers. The correlation is fitted to the data of Lee et al., Coll. and Surf. A. 263 , 320‐329 (2005). The value of the axial dispersion coefficient is independent of the self‐dispersivity. It is seen that Saffman, J. Fluid. Mech. 6 , 321‐349 (1959) model for the dispersion coefficient in solid porous media only provides order of magnitude prediction of the axial dispersion coefficient but it can inform about the dominant mechanisms of dispersion.     

Axial dispersion characteristics in three phase fluidized beds

Axial dispersion coefficients in three-phase fluidized beds have been measured in a 0.152 m-ID x 1.8 m high column by the two points measuring technique with the axially dispersed plug flow model. The effects of liquid velocity (0.05–0.13 m/s), gas velocity (0.02–0.16 m/s) and particle size (3-8 mm) on the axial dispersion coefficient at the different axial positions (0.06–0.46 m) in the bed have been determined. The axial dispersion coefficient increases with increasing gas velocity but it decreases with an increase in particle size and exhibits a maximum value with an increase in the axial position from the distributor. The axial dispersion coefficients in terms of the Peclet number have been correlated in terms of the ratio of fluid velocities, the ratio of the panicle size to column diameter, and the dimensionless axial position in the bed based on the isotropic turbulence theory.     

Taylor dispersion in finite-length capillaries

The solute transport in a core-annular geometry is studied. A Newtonian or non-Newtonian (i.e., power-law) liquid flows through the core, while the solute can exchange between the liquid and the surrounding tissue. The permeability of the phase interface depends on the nature of the solute, i.e., relatively low for lipids and macromolecules but high for ions and gases. We analyse the moment’s equations of the residence time distribution (RTD). The solution of the equation for the second moment provides the exact formula for the Taylor dispersion coefficient. Unlike previous studies using a perturbation procedure where coefficient of axial dispersion cannot be defined at low permeability, the current study gives Taylor coefficient of dispersion for any value of the permeability. It is found that the coefficient in shear-thinning fluid is lower than in the Newtonian one, although the relative importance of non-Newtonian effects decreases when other factors, e.g. inter-phase transport and solubility, become dominant. The equations for the higher moments are analysed and the general structure of the solution is obtained in the form of integrals, which can be easily evaluated numerically. When the analysis is applied to solute transport between capillaries and surrounding tissues, it is shown that the classic Taylor expression does not describe dispersion of solute, e.g. glucose and albumin, in the capillary, except in situations where the Péclet number is very low. For the range of parameters typical for microvascular circulation in tissues, the higher moments play an important role and need to be considered.     

充填式浮选柱二维返混特性的实验研究

以二维扩散模型为基础，采用点源脉冲示踪法对开式浮选柱和装有不同类型规整填料的充填式浮选柱内液相的轴向与径向返混进行了实验研究，得到了各种填料内轴向和径向彼克列准数与气相、液相表观雷诺数的关联式。通过比较发现，在所用填料中，装有250Y或350Y型填料的浮选柱不仅轴向返混最小，而且径向返混最大，最有利于提高回收率。另外，对起泡剂的影响进行了实验研究，发现起泡剂可以减小返混，但当起泡剂浓度大于一定值时反而会增大径向返混。     

Residence times in fluidized beds with secondary gas injection

Experiments were carried out to determine the effects of secondary gas injection on the gas residence time and macromixing characteristics in a bubbling fluidized bed. Primary gas is introduced via a bottom distributor plate, while secondary gas is introduced via a fractal injector submerged in the bed. Results indicate that the average residence time decreases only slightly. Calculated overall reactor Péclet numbers indicate that the gas experiences less back-mixing with secondary gas injection. The bubble size was observed to decrease by up to 70%, indicating improved gas–solid contact. Taking this improved contact and plug flow behavior into account, the conversion in a fluidized bed with secondary gas injection is expected to increase significantly, particularly for mass-transfer limited reactions.     

Low Péclet number behavior of the transfer rate in packed beds

The asymptotic behavior of the mass-transfer coefficient in a packed bed reactor at low Péclet numbers is dependent upon how the coefficient is defined. A singular perturbation approach coupled with heuristic arguments is used to demonstrate that the film mass-transfer coefficient in deep beds approaches a constant value as the Péclet number decreases. The film coefficient is utilized in the one-dimensional model of a bed as a sink term in the governing equation. The volumetric, or effective, mass-transfer coefficient which relates the overall reactant conversion to a logarithmic mean concentration driving force, decreases linearly with the Péclet number as the Péclet number approaches zero. The distinction between the two coefficients is important in the low Péclet number region. Analogous results apply to beat transfer. Reported experimental data support these predicted trends.It has been, demonstrated that the low Péclet number behavior of the Sherwood number in a packed bed reactor is dependent upon its defining equation. A rigorous singular perturbation approach coupled with heuristic arguments indicates that for a deep bed the effective mass-transfer coefficient (defined by eqn 1) is directly proportional to the Péclet number. The film coefficient (defined by eqn 3) approaches a constant in the same limit. These conclusions are independent of the detailed geometric void structure in the bed.     

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

Residence time distribution and modeling of the liquid phase in an impinging stream reactor

Based on some experimental investigations of liquid phase residence time distribution (RTD) in an impinging stream reactor, a two-dimensional plug-flow dispersion model for predicting the liquid phase RTD in the reactor was proposed. The calculation results of the model can be in good agreement with the experimental RTD under different operating conditions. The axial liquid dispersion coefficient increases monotonously with the increasing liquid flux, but is almost independent of gas flux. As the liquid flux and the gas flux increase, the liquid dispersion coefficient of center-to-wall decreases. The axial liquid dispersion coefficient is much larger than that of center-to-wall, which indicates that the liquid RTD is dominated mainly by axial liquid dispersion in the impinging stream reactor.     

On axial dispersion in fixed beds

The primary purpose of this paper is to show that the criticisms by Tsotsas and Schlünder (1988) of an earlier paper (Gunn, 1969) are based upon elementary mathematical errors of the part of Tsotsas and Schlünder. A summary of experimental data on axial dispersion in liquids and gases shows that the dependence of the axial dispersion coefficient upon the Schmidt group predicted by Tsotsas and Schlünder is not observed despite the large number of emperical factors in their expressions. In particular, the strong dependence of the axial Peclet group upon the Schmidt group for axial dispersion in liquids predicted for Re> 1 is not observed, since the consensus of expirimental data is that for this range the dependence of Pe upon Re is slight.

The experimental dependence of Pe upon Re for different values of the Schmidt group agrees with the expressions of Gunn (1969)     

Effect of impeller type on the mixing in torus reactors

Torus reactors are characterized by a homogeneous fluid circulation without dead zones. Torus reactors were used for applications in biotechnology, food processing, polymerization and liquid waste treatments. The relatively simple extrapolation of performances, due to the absence of dead volume, is one of the main advantages of this reactor, with low shear stresses and an effective radial mixing allowing efficient heat dissipation. This study is based on the mixing in order to analyse the fluid circulation, mainly in turbulent flow regime, and to characterize the torus reactor with the axial dispersion plug flow model. The objective of this study is to characterize the flow and the mixing in the torus reactors in batch and continuous modes. The mixing analysis was made according to the flow parameters and to the geometrical characteristics of the reactor and impeller. The mixing in the torus reactor can be characterized by the Péclet number, Pe_D, defined with torus diameter. A representative model based on plug flow with axial dispersion and partial recirculation was proposed.     

Correlating parameters for axial dispersion in liquid fluidized systems

The dispersion coefficient, the time delay and the time constant, as parameters associated with models of liquid phase axial dispersion in fluidized systems, have been correlated using available literature data for fluidization involving a wide range of fluid and particle properties. The results permit prediction of these parameters from only a knowledge of the bed voidage. A comparison with Chung and Wen's¹ correlation demonstrates the superiority of the present correlation.     

Unsaturated liquid percolation flow through nonwetted packed beds

The unsaturated flow of liquid through packed beds of large particles was studied using six different liquids, all with contact angles greater than 90° on the bed packing (wax spheres of 9, 15 and 19.4 mm diameter). The liquidflow was discrete in nature, as drops for low flow rates and rivulets for high flow rates. For unsaturated liquid flows, the actual percolation velocity, not superficial velocity, should be used to characterize the flow. The percolation velocity did not vary with packed-bed depth, but was a strong function of liquid flow rate, liquid and particle properties. Effects of liquid and particle properties (but not flow rate) are well captured by a simple correlation between the liquid-particle fiction factor and Reynolds number based on actual percolation velocities. Liquid dispersion, characterized by the maximum dispersion angle, varies significantly with liquid and particle properties. The tentative correlation suggested here needs further validation for a wider range of conditions.