Recycle Effect on Double‐Pass Concentric Circular Mass Exchangers under Uniform Wall Fluxes

A study on improvement in device performance of a double‐pass concentric circular mass exchanger with uniform wall fluxes and external refluxes was conducted under counterflow operations. The linear superposition of an asymptotic solution and a homogeneous solution with the use of an orthogonal expansion technique for solving such a conjugated Graetz problem is formulated theoretically and the analytical predictions are applied to investigate a substantial masstransfer improvement. A mathematical expression for the average Sherwood numbers and the outlet dimensionless concentration is given. Comparisons of analytical results are made with the single‐pass operations of the same working dimensions (without permeable barriers inserted and without recycle). Considerable device improvement in mass transfer rate is obtained by introducing the recycle‐effect concept in designing such double‐pass devices. The effect of permeable barriers on the mass‐transfer efficiency improvement as well as on the power consumption increment has also been delineated.     

Device Performance Improvement of Double‐Pass Concentric Circular Mass Exchangers under Uniform Wall Fluxes

A double‐pass concentric circular mass exchanger under uniform wall fluxes is produced by inserting a permeable barrier into a circular tube to improve the device performance. The mathematical formulation was developed theoretically for such double‐pass, forced‐convection, mass‐transfer problems which are referred to as conjugated Graetz problems. The analytical solutions are obtained by the linear superposition of an asymptotic solution and a homogeneous solution which are linear in the axial direction and solved with the use of an eigenfunction expansion in a power series. The analytical results show that the mass‐transfer rate of a double‐pass mass exchanger can be improved compared to that of a single‐pass mass exchanger by suitably adjusting the permeable barrier position. Moreover, the ratio of mass‐transfer efficiency improvement and power consumption increment is also shown to make good economic sense.     

Heat Transfer Phenomena of Power Law Fluids in Double‐Pass Heat Exchangers with Isoflux Conditions

A new design of conjugated heat transfer in double‐pass parallel‐plate laminar countercurrent operations of power law fluids under wall isoflux was investigated experimentally and theoretically. The analytical solutions were obtained with a superposition model by introducing an eigenfunction expansion in terms of a power series for the homogeneous part and an asymptotic solution for the inhomogeneous part. The influence of the power law index on the average Nusselt numbers with the various design and operating parameters is also delineated. The theoretical predictions of the experimental results are represented graphically. The heat transfer performance was considerably improved when compared with a single‐pass parallel‐plate heat exchanger (without inserting a solid separator sheet). Suitable adjustments of the solid separator sheet position can effectively enhance the heat transfer efficiencies for such a recycling double‐pass device, as compared with the efficiencies of single‐ and double‐pass devices.     

A Theoretical Study of the Recycle Effect on Multi‐Pass Mass Exchangers with Three Idealized Membranes Inserted

A new device of multi‐pass mass exchanger was developed by inserting three idealized membranes to divide an open conduit into four subchannels. The mathematical formulations of the device with external recycle, as referred to a well‐known conjugated Graetz problem, were conducted to improve the mass transfer efficiency. The eigenfunction expansion technique with the eigenfunction expanding in terms of an extended power series was used to solve such a conjugated Graetz problem analytically. The theoretical predictions were presented graphically and compared with those in the single‐pass operations (without any idealized membrane inserted and external recycle) of the same working dimensions.     

Liquid‐Solid Mass Transfer Behavior of a New Stirred‐Tank Reactor with a Packed Bed Fixed to its Wall

Rates of liquid‐solid mass transfer at a packed bed of Raschig rings fixed to the wall of a stirred tank were measured by a technique which involves the diffusion‐controlled dissolution of copper in acidified dichromate. Variables studied were impeller rotation speed, impeller geometry, Raschig ring diameter, bed thickness, presence of baffles, physical properties of the solution, and effect of superimposed flow. Mass transfer data for the batch reactor were correlated by a dimensionless equation. For a given set of conditions, the radial‐flow impeller was found to produce higher rates of mass transfer than the axial‐flow impeller. The presence of baffles increased the rate of mass transfer inside the bed. Applications of the suggested reactor in conducting different diffusion‐controlled liquid‐solid reactions were evaluated.     

Hydrodynamics and Mass Transfer in Gas‐Liquid‐Solid Circulating Fluidized Beds

Although extensive work has been performed on the hydrodynamics and gas‐liquid mass transfer in conventional three‐phase fluidized beds, relevant documented reports on gas‐liquid‐solid circulating fluidized beds (GLSCFBs) are scarce. In this work, the radial distribution of gas and solid holdups were investigated at two axial positions in a GLSCFB. The results show that gas bubbles and solid particles distribute uniformly in the axial direction but non‐uniformly in the radial direction. The radial non‐uniformity demonstrates a strong factor on the gas‐liquid mass transfer coefficients. A local mass transfer model is proposed to describe the gas‐liquid mass transfer at various radial positions. The local mass transfer coefficients appear to be symmetric about the central line of the riser with a lower value in the wall region. The effects of gas flow rates, particle circulating rates and liquid velocities on gas‐liquid mass transfer have also been investigated.     

Mass Transfer Coefficients in Mechanically Agitated Gas‐Liquid Contactors

There are a large number of correlations given in literature for the prediction of volume‐related liquid‐side mass transfer coefficients in mechanically agitated gas‐liquid contactors. Significant disagreement can be observed concerning the proposed correlations, so that no single correlation exists representing all of the mass transfer data given in the literature. The observed differences can mainly be ascribed to the differences in the geometry of the system, the range of operational conditions and the measurement method used. On the basis of a comparative study of mass transfer phenomena in agitated Newtonian and non‐Newtonian aerated liquids, a critical discussion of the literature results is presented in this review article, so that final conclusions can be drawn for the k_Lα values in the different single‐ and multiple‐impeller agitated systems studied in the literature.     

Two‐Phase Flow with Mass Transfer in Bubble Columns

Bubble columns are widely used in the chemical and biochemical industries. In these reactors a gaseous phase is dispersed into a continuous liquid phase thus the rising bubble swarm induces a circulating flow field. For the dimension of these reactors the local interfacial area and the residence time of the liquid and the gaseous phase are key parameters. In this paper an Euler‐Euler approach is used to calculate the flow field in bubble columns numerically. Therefore a transport equation for the mean bubble volume based on a population balance equation approach is coupled with the balance equations for mass and momentum. The calculations are performed for three‐dimensional, instationary flow fields in cylindrical bubble columns considering the homogeneous and the heterogeneous flow regime. For the interphase mass transfer the physical absorption of the gaseous phase into the liquid is assumed. The back mixing in the gaseous and liquid phase is calculated from the local and time dependent concentration of a tracer.     

Mass Transfer Characteristics in a Rotor‐Stator Reactor

Mass transfer characteristics in a rotor‐stator reactor in terms of the overall volumetric mass‐transfer coefficient (K_xa) using the N₂‐H₂O‐O₂ system were investigated. The effects of various operating parameters including rotation speed, liquid volumetric flow rate, and gas volumetric flow rate on K_xa were systematically examined, and a gas‐liquid mass transfer model was established to predict K_xa. Results reveal that K_xa increased with higher rotation speed, liquid volumetric flow rate, and gas volumetric flow rate. The results also confirm that the predicted values of K_xa were in agreement with the experimental values with deviation within 15 %. The results contribute to a better understanding of mass transfer characteristics in rotor‐stator reactors.     

Improving Gas‐Liquid Mass Transfer in Bubble Columns by Applying Low‐Frequency Vibrations

We show that application of low‐frequency vibrations, in the 50–200 Hz range, to the liquid phase of an air‐water bubble column causes significantly smaller bubbles to be generated at the distributor plate. For bubble column operation in the homogeneous flow regime, measurements of the volumetric mass transfer coefficient using the oxygen absorption technique show that the increase in the k_La values ranges from 50–100 % depending on the flow rate. It is concluded that application of low‐frequency vibration has the potential of improving the performance of bubble columns.     

Volumetric Mass Transfer Coefficient in non‐Newtonian Fluids in Spout Fluid Beds

The volumetric liquid‐phase mass transfer coefficient, k_La, was determined by absorption of oxygen in air using six different carboxy‐methyl cellulose (CMC) solutions with different rheological values in three phase spout‐fluid beds operated continuously with respect to both gas and liquid. Three cylindrical columns of 7.4 cm, 11.4 cm, and 14.4 cm diameters were used. Gas velocity was varied between 0.00154–0.00563 m/s, liquid velocity between 0.0116–0.0387 m/s, surface tension between 0.00416–0.0189 N/m, static bed height between 6.0–10.8 cm, and spherical glass particles of 1.75 mm diameter were used as packing material. A single nozzle sparger of 1.0 cm diameter was used in the spouting line. The volumetric mass transfer coefficient was found to increase with gas velocity, liquid velocity, and static bed height and to decrease with the increase of the effective liquid viscosity of the CMC solution. A dimensionless correlation was developed and compared with those listed in the literature.     

Hydrodynamics,Mass Transfer and Gas Scrubbing in a Co‐current Droplet Column Operating at High Gas Velocities

The main objective of this work was to propose a new process for household fume incineration treatment: the droplet column. A feature of this upward gas‐liquid reactor which makes it original, is to use high superficial gas velocities (13 m s^–1) which allow acid gas scrubbing at low energy costs. Tests were conducted to characterize the hydrodynamics, mass transfer performances, and acid gas scrubbing under various conditions of superficial gas velocity (from 10.0 to 12.0 m s^–1) and superficial liquid velocity (from 9.4·10^–3 to 18.9·10^–3 m s^–1). The following parameters characterized the hydrodynamics: pressure drops, liquid hold‐ups, and liquid residence time distribution were identified and investigated with respect to flow conditions. To characterize mass transfer in the droplet column, three parameters were determined: the gas‐liquid interfacial area (a), the liquid‐phase volumetric mass transfer coefficient (k_La) and the gas‐phase volumetric mass transfer coefficient (k_Ga). Gas absorption with chemical reaction methods were applied to evaluate a and k_Ga, while a physical absorption method was used to estimate k_La. The influence of the gas and liquid velocities on a, k_La, and k_Ga were investigated. Furthermore, tests were conducted to examine the utility of the droplet column for the acid gas scrubbing, of gases like hydrogen chloride (HCl) and sulfur dioxide (SO₂). This is a process of high efficiency and the amount of pollutants in the cleaned air is always much lower than the regulatory European standards imposed on household waste incinerators.     

CO2 Absorption Using Nanofluids in a Wetted‐Wall Column with External Magnetic Field

A new method for enhancing the mass transfer coefficient in the gas absorption process is reported. CO₂ absorption experiments were carried out in a wetted‐wall column using different aqueous nanofluids as the solvent. The mass transfer characteristics were found to increase by applying Al₂O₃/water nanofluid. The mass transfer coefficient decreased with TiO₂/water nanofluid. In the case of Fe₃O₄/water nanofluid, the mass transfer rate was enhanced by increasing the nanoparticle volume fraction, but the mass transfer coefficient was lower than that obtained with water for all experimental conditions studied. Finally, applying a downward magnetic field resulted in higher mass flux and mass transfer coefficient in comparison with experiments without a magnetic field.     

Modeling of Gas‐Solid Reactions: Kinetics,Mass and Heat Transfer,and Evolution of the Pore Structure

Mathematical models for simulating heterogeneous gas‐solid reactions must describe a complex set of physicochemical and thermal phenomena. These include the chemical reaction itself, at an interface whose area varies during the conversion, the transport of gaseous species by diffusion in the pores of the solid, whose size and number generally change in the course of reaction, diffusional transport in the layer of solid product, the evolution or consumption of heat by the reaction and its transport in the porous solid, etc. The present paper gives details of the equations employed to model each of these processes. Some computed results illustrate how increasingly sophisticated recent models describe the gradual obstruction of pores during reactions, such as the sulfation of lime, or the thermal effects related to the exothermic nature of the oxidation of zinc sulfide.     

Gas Holdup and Solid‐Liquid Mass Transfer in Newtonian and non‐Newtonian Fluids in Bubble Columns

Gas holdup and surface‐liquid mass transfer rate in a bubble column have been experimentally investigated. De‐mineralized water, 0.5 and 1.0% aqueous solutions of carboxy methyl cellulose (CMC), and 60% aqueous propylene glycol have been used as the test liquids. Effects of column diameter, liquid height to column diameter ratio, superficial gas velocity and liquid phase viscosity on gas holdup and mass transfer rate are studied. Generalized correlations for the average gas holdup and wall to liquid heat and mass transfer coefficients are proposed. These are valid for both Newtonian and pseudoplastic non‐Newtonian fluids.     

Mass Transfer in a Flat Gas/Liquid Interface using non‐Newtonian Media

Gas/liquid mass transfer has been investigated using a stirred vessel gas/liquid contactor using non‐Newtonian media and carbon dioxide as absorbent and gas phase, respectively. The volumetric mass transfer coefficients at different operational variables have been determined. Non‐Newtonian media (liquid phase) were prepared as aqueous solutions of sodium carboxymethyl cellulose salt. The influence of the rheological properties, polymer concentration, stirring rate, and gas flow rate on mass transfer was studied for these liquid phases. Kinematic viscosity and density experimental data were used to calculate the average molecular weight corresponding to the polymer employed. The Ostwald model has been used to fit the rheological behavior of aqueous solutions of the polymer employed as absorbent phase. Reasonably good agreement was found between the predictions of the proposed models and the experimental data of mass transfer coefficients.     

Comparison of Overall Gas‐Phase Mass Transfer Coefficient for CO2 Absorption between Tertiary Amines in a Randomly Packed Column

The mass transfer performance of CO₂ absorption into an innovative tertiary amine solvent, 1‐dimethylamino‐2‐propanol (1DMA2P), was investigated and compared with that of methyldiethanolamine (MDEA) in a packed column with random Dixon‐ring packing. All experiments were conducted under atmospheric pressure. The effects of inert gas flow rate, amine concentration, liquid flow rate, CO₂ loading, and liquid temperature on mass transfer performance were analyzed and the results presented in terms of the volumetric overall mass transfer coefficient (K_Ga_v). The experimental findings clearly indicate that 1DMA2P provided better mass transfer performance than MDEA. For both 1DMA2P and MDEA solutions, the K_Ga_v increased with rising amine concentration and liquid flow rate, but decreased with higher CO₂ loading. The inert gas flow rate only slightly affected the K_Ga_v. A satisfactory correlation of K_Ga_v was developed for the 1DMA2P‐CO₂ system.     

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.