Solid Mass Transfer Research Articles

Effect of foam stirrer design on the catalytic performance of rotating foam stirrer reactors

The liquid–solid mass transfer rate in a rotating foam stirrer reactor and in a slurry reactor is studied using the hydrogenation of styrene as a model reaction. The rotating foam stirrer reactor is a novel type of multi-phase reactor where highly open-celled materials, solid foams, are used as a catalyst support and as a stirrer. The design of the foam stirrer has a strong influence on the liquid–solid mass transfer rate. Using a donut-shaped foam block configuration, the liquid solid mass transfer coefficient, kLS, is five times lower than in a blade configuration. The reduced liquid circulation through the foam block structure is explained by a higher frictional pressure drop. The pore Reynolds number indicates that the flow is in the laminar regime for the foam block stirrer while it is turbulent for the blade stirrer. Local measurements of kLS indicate a mass transfer profile along the height of the foam block structure, allowing a pertinent choice of the catalyst location within the foam block and/or suggesting changes of the foam block design to avoid the bottom effects, for instance, using a conical foam block shape. However, the foam block stirrer offers higher liquid–solid interfacial area than a blade stirrer, resulting in higher kLSaLS. At a power input above 1000W/mL3 and using a 20ppi foam block with the top part catalytically active, the reaction rate is not liquid–solid mass transfer limited. Compared to a Rushton stirrer, the liquid–solid mass transfer rate is enhanced because of a high liquid–solid interfacial area and a fast refreshment of the catalyst surface. kLSaLS values of 0.5s−1 are obtained compared to 0.04s−1 for the slurry system. The same production rate as in the slurry reactor is achieved using 62% less catalyst. As the catalyst is immobilized on the stirrer, an additional advantage of the rotating foam stirrer reactor is the absence of a catalyst separation step. Attrition and agglomeration of the catalyst do not occur and the foam catalyst can be reused.

Numerical and experimental investigation of the effects of impinging streams to enhance Ca-based sorbent capture of SO2

A reactor design combining impinging streams and a circulating fluidized bed reactor (IS-CFB) was developed to improve the gas–solid mixing in fluidized beds. The Eulerian two-fluid model and a sulfation model for a CaO/fly ash sorbent were used for numerical simulations of a pilot-scale IS-CFB reactor, and the simulation results indicate that the introduction of impinging streams to a CFB reactor significantly improves the desulfurization efficiency from 89.5% to 95.1%, due to the more homogeneous radial particle volume fraction distributions and the much larger effective SO2 capture zone. The lateral gas flow in the impingement zone intensifies the gas–solid mass transfer. Effects of the bed bulk density and the impinging particle material on the desulfurization efficiency were also investigated. Experiments were conducted using two Ca-based sorbents in a small-scale IS reactor at 750°C. The experimental results show that the Ca/bio-based sorbent gives higher desulfurization efficiencies than the CaO/fly ash sorbent, for the latter which is large and dense cannot be effectively entrained by the impinging streams. A method for combining experiments and calculations is developed to estimate the gas–solid residence time in the impingement zone. It is found that the residence time is significantly influenced not only by the gas velocity but also by the solid to gas mass ratio.

Mathematical Modeling of a Single-Stage, Downward-Firing, Entrained-Flow Gasifier

Gasifiers are the centerpieces of coal-fired integrated gasification combined cycle (IGCC) plants. Mathematical models of gasifiers have been developed in recent literature to describe the physical and chemical processes taking place inside the reactor vessels. These models range from simple one-dimensional (1D) steady-state equilibrium models to higher-order, sophisticated, dynamic 2D and 3D computational fluid dynamics (CFD) models that describe coupled gas–solid hydrodynamics, heat and mass transfer, and reaction kinetics over the complex gasifier geometry. In the current work, a 1D steady-state model of a single-stage, downward-firing, oxygen-blown, slurry-fed, entrained-flow gasifier has been developed for use in the context of IGCC process simulation. In this mathematical model, mass, momentum, and energy balance equations for solid and gas phases are considered. The model includes a number of heterogeneous and homogeneous chemical reactions along with devolatilization and drying of the slurry feed....

Gas holdup of rotating foam reactors measured by γ‐tomography—effect of solid foam pore size and liquid viscosity

Rotating foam reactors have already shown to give high mass transfer rates compared to stirred tank reactors. For a deeper insight into the hydrodynamics of these reactors, the hydrodynamics of rotating foam reactors were studied using γ‐ray tomography. The two‐phase flow through the foam block stirrer is mainly influenced by the solid foam pore size and the liquid viscosity. For low viscosity, the optimal foam block pore size was identified in the range between 10 and 20 pores per inch (ppi). With smaller pore size, the gas holdup inside the foam block strongly increases due to bubble entrapment. For higher viscosity, pore sizes larger than 10 ppi have to be used to achieve a sufficient liquid flow rate through the foam block to avoid a strong gradient over the reactor height. The effect of the hydrodynamics on the gas–liquid and liquid–solid mass transfer and the reactor performance are discussed. © 2012 American Institute of Chemical Engineers AIChE J, 59: 146–154, 2013

Trickle flow liquid–solid mass transfer and wetting efficiency in small diameter columns

AbstractA novel method to simultaneously measure liquid solid mass transfer and external wetting efficiency was employed at column to particle ratios of 10, 6 and 3. Two prewetting procedures representing the upper (Kan) and lower (Levec) hysteresis branches were used. For a multipoint distributor on a Kan prewetted bed wetting efficiency and the specific mass transfer coefficient were almost unaffected by column diameter. The multipoint distributor on a Levec prewetted bed exhibited a decrease in specific mass transfer with decreasing column diameter. Point source experiments resulted in significantly lower wetting and mass transfer measurements with an increasing trend with respect to decreasing column diameter. The results indicate that with proper distribution and prewetting, the effect of column diameter on averaged wetting and liquid–solid mass transfer is almost negligible, a powerful result considering the importance of these parameters on reaction experiments. © 2012 Canadian Society for Chemical Engineering

Mass transfer modeling of a consecutive reaction in rotating foam stirrer reactors: Selective hydrogenation of a functionalized alkyne

The external and internal mass transfer for a rotating foam stirrer reactor has been studied using the hydrogenation of 3-methyl-1-pentyn-3-ol as a model reaction. Catalytic foam stirrers with different number of pores per linear inch (ppi) and washcoating thicknesses are used and their performance are described in terms of activity and selectivity. The liquid–solid mass transfer does not limit the overall reaction rate when a 20ppi foam is used. For this catalytic foam stirrer, a kLSaLS value of 0.2s−1 is estimated at 300rpm. The use of finer pore foam structures is not convenient due to a drastic decrease of catalyst surface refreshment. As a result, the lower kLS value negates the benefit of a larger area (aLS) resulting in a lower liquid–solid mass transfer. The catalyst accessibility is a controlling factor in this fast reaction. The optimal washcoat thickness to avoid diffusion limitations is 5μm. Gas–liquid mass transfer rate is not a limiting factor. A kGLaGL of 0.6s−1 is measured at 300rpm by the physical absorption method. When compared to the conventional slurry reactor, the liquid–solid and the gas–liquid mass transfer rates are 17 and 6 times higher, respectively. However, the intrinsic activity of the foam catalyst is 4.6 times less than the slurry catalyst prepared with the same palladium loading. This is explained by a difference in palladium dispersion caused by a non-homogenous concentration of active sites along the washcoat layer. On the other hand, the less active foam catalyst leads to higher selectivity. The production rate is then increased by mounting more active blades on the stirrer shaft, thus creating more surface area for catalyst deposition while still keeping the high accessibility of a 4μm washcoat layer. Hence, rotating foam reactors have promising applications for multiphase processes. High mass transfer rates can be easily achieved, catalyst filtering is not longer needed and reusability of the foam catalyst is possible.

Assessment and Modeling of a Sequential Process for Water Treatment—Adsorption and Batch CWAO Regeneration of Activated Carbon

A new sequential process, AD–OX, for (post)treatment of water polluted by poorly biodegradable organic compounds has been investigated. It is based on hybridizing classical adsorption on a fixed bed of activated carbon (AC) followed by batch wet catalytic oxidation at higher temperature and pressure on the same bed of AC, which is then regenerated in situ. The basic idea is to take advantage of both operations: 1-efficient water purification at room temperature by adsorption, 2-effective concentrated pollutant degradation by batch air oxidation achieving simultaneously AC regeneration. A small fixed bed reactor, 10 mm diameter, 0.18 m long, filled with granular activated carbon and equipped with convenient 3-way valves, may achieve successively the two main steps. Several AD–OX cycles have been performed with a phenol solution to quantify the regeneration of the activated carbon adsorption capacity. Results show that activated carbon is quickly damaged during the first cycles, due to oxidative coupling, but then a quasi-steady state is obtained proving that significant oxidative regeneration has been achieved. A dynamic model of the adsorption step has been first developed, including intraparticle diffusion, liquid–solid external mass transfer, and axial dispersion of the liquid phase. It has been applied to simulate the performance of the regenerated activated carbon. Using oxidation kinetics over this aged carbon and its adsorption isotherm, separately determined in an autoclave at reaction temperature, the oxidation step after several cycles has been simulated including the heating period, where desorption and oxidation simultaneously occur. The proposed model conveniently predicts the complex phenol concentration–time profile and gives insight to the hydrodynamic behavior of the recycle reactor and the role of mass transfer resistances.

Estimation of sodium bicarbonate crystal size distributions in a steady-state bubble column reactor

Sodium bicarbonate is a substance which is produced in the middle stages of the soda ash production process. In this precipitation process, carbon dioxide gas is continuously injected into the bubble column reactor, which contains carbonate and bicarbonate solutions. This work deals with the study of the gas–liquid mass transfer, coupled with chemical reactions, and the liquid–solid mass transfer, coupled with crystallization. In this mathematical model, a mole balance has been instituted on flows and components through the bubble column, which also utilized a nucleation and growth formula for the solid phase and the Danckwerts’ theory for mass transfer between the gas and liquid phases. The mathematical model can predict the effects of several parameters on the sodium bicarbonate crystal size distributions. We computed the mathematical simulation model results with the experimental results of the bubble column reactor of the Shiraz Petrochemical Complex for validating the model and investigated the effects of different parameters on the sodium bicarbonate crystal size distributions.

Mass transfer intensification in an annular electrochemical reactor by an inert fixed bed under various hydrodynamic conditions

Rates of liquid–solid mass transfer were measured at the inner surface of an annulus by an electrochemical technique which involves measuring the limiting current of the cathodic reduction of K 3Fe(CN) 6 in aqueous solution with a large excess of NaOH under single and two phase flow using an annulus packed with inert spheres. Variables studied are gas and solution superficial velocities, sphere diameter and physical properties of the solution. For unpacked annulus the two phase mass transfer data are correlated for the conditions: 1253 < Sc < 2778, 28 < Re L < 917 and 285 < Re g < 4187 by the equation: Sh = 0.58 Sc 0.33 Re L 0.62 Re g 0.4 For packed annulus, the two phase mass transfer data are correlated for the conditions: 1253 < Sc < 2778, 7 < Re L < 8, 4 < Re g < 380, 0.8 cm < d p < 1.2 cm and annulus diameter of 17 cm by the equation: Sh = 12.69 Sc 0.33 Re L 0.1 Re g 0.14 The mass transfer enhancement ratio due to the presence of packing spheres ranges from 2.08 to 6.1 depending on Re L, Re g and sphere diameter. Implications of the present work for the design and operation of annular electrochemical reactors suitable for electrochemical synthesis involving gaseous reactants and air pollution control are noted.

Gas-Limited Hydrogenation of 1-Octene in a Fixed Bed: Upflow Versus Downflow

Two downflow operational modes with different hydrodynamic states were compared to upflow operation. Various gas-limited conditions (γ = 15–60) were employed. The downflow mode with the higher wetting efficiency consistently outperformed the downflow mode with the lower wetting efficiency. Both downflow modes outperformed the upflow mode at high gas mass fluxes and underachieved against upflow at lower gas mass fluxes. The results stand in contradiction to the theory on direct gas–solid mass transfer under trickle-flow conditions. The switching behavior of the upflow mode performance was attributed to hydrodynamic regime shifts, hinting that the perceived “poor” performance of upflow reactors under gas limited conditions might be linked to slugging in laboratory-scale reactors.

A Theory of Heat and Mass Transfer in Viscoelastic Solids with Microstructures

In the present work, the linear theory of micropolar thermo-viscoelasticity with mass diffusion is established. The constitutive relations are obtained for a mixture of diffusive masses in the bulk medium, and then the uniqueness theorem is proved using the Laplace transform and the positive definiteness assumptions on the initial case of the thermoelastic modulus. The reciprocity relation is established avoiding Laplace transform. Some consequences on the reciprocity relation are discussed. The variational theorem is proved. The integral representation is obtained for the model equations; hence, the Maysel's, Somigliana's and Green's formulae are derived. Finally, the mixed boundary value problem is considered and reduced to a system of four Fredholm-Volterra integral equations.

Glucose Oxidation in Slurry Reactors and Rotating Foam Reactors

Glucose oxidation using platinum promoted by bismuth was studied as a three-phase model reaction. Using catalyst nanoparticles and measuring the oxygen concentration in the bulk liquid, the kinetic parameters and mass transfer characteristics were determined at a temperature of 333 K. The overall reaction rate was studied experimentally using three different support types: slurry catalysts, pellets, and a solid foam stirrer. The glucose conversion rate and the deactivation rate of the catalyst depend strongly on the ratio between mass transfer and reaction rate. At low catalyst concentrations, the glucose oxidation process is liquid–solid mass-transfer-limited. The block stirrer shows a superior performance over the slurry catalysts due to the high liquid–solid volumetric mass transfer coefficient. The bimodal pore size distribution of the catalyst layer further increases the conversion rate. Using slurry catalysts, a loading of 1 wt % in combination with pure oxygen feed is required to achieve acceptable conversion rates. Under these conditions, the gas–liquid mass transfer and partially the liquid–solid mass transfer are the rate-limiting steps. The foam block stirrer shows good gas–liquid mass transfer rates and high liquid–solid mass transfer rates, which still increase at high power input. Working under external mass transfer control and using this stirrer type, the catalyst loading can be strongly reduced to loadings less than 0.4 wt %, while the conversion rate remains comparable to slurry particles with loadings of 1 wt %. As the catalyst is fixed, attrition and agglomeration in high viscosity liquids are circumvented. There is further no need for filtration, and the catalyst can simply be reused.

Hydrodynamics of gas–liquid Taylor flow and liquid–solid mass transfer in mini channels: Theory and experiment

Hydrodynamics of Taylor (slug) flow in horizontal capillary with an inner diameter of 0.92 mm in water–air and glycerol solution–air systems was studied. Experimental data of bubble velocity, dynamic gas hold-up and void fraction were compared with values that were calculated by proposed earlier mathematical model of slug flow in capillary. This model is in a good agreement with experimental data in the range of capillary numbers between 0.05 and 0.12. Also liquid–solid mass transfer coefficient for slug flow and homogeneous flow was experimentally obtained in horizontal capillary with an inner diameter of 2.26 mm and 2.76 mm in a caustic soda solution–air system.

Supercritical carbon dioxide extraction of Baizhu: Experiments and modeling

In this work, supercritical CO 2 extraction has been carried out on a traditional Chinese herb of Baizhu under pressure of 15–45 MPa, temperature of 40–60 °C, mean powder size of 0.167–0.675 mm, and extraction time of up to 180 min. The maximum extraction yield obtained in 5 h is about 6.76 × 10 −2 g per gram raw materials at 60 °C and 45 MPa. The extraction process is correlated by means of five different mathematical models. The evaluation of these models against experimental data shows that among these models the Sovová model performs the best with an overall average absolute relative deviation of 1.62%, followed by Crank and Naik models, finally the Barton and Martínez models. From the Sovová model, the mass transfer coefficient in solid or fluid are obtained and they are varying in the ranges of 4.02–6.14 × 10 −8 m/s and 0.88–2.87 × 10 −9 m/s, respectively. These results suggest that solute diffusion in solid matrices and solute mass transfer in fluid are both important in affecting the supercritical CO 2 extraction process of Baizhu.

Characteristics of Liquid–Solid Mass Transfer in a Bubble Column Equipped with a Vertical Tube of Circular Fins

The solid-liquid mass transfer rate at a stack of circular fin surfaces in a bubble column was investigated. A diffusion-controlled dissolution technique of copper in an acidified chromate solution was employed. Variables studied included the number of actively exposed fins ranging from 5 to 20, pertinent physical properties of the solution, and air superficial velocity. Experimental data showed that the rate of the diffusion-controlled mass transfer increases with increasing superficial air velocity and decreases with increasing chromate solution acid concentration. Moreover, at relatively low superficial air velocity, increasing the number of actively exposed fins results into a continuous increase in the mass transfer coefficient. At relatively higher superficial air velocity, however, the mass transfer coefficient decreases in the 5 to 10 range of actively exposed fins and then reverts to increase in the 15 to 20 range.

Parallel hydrogenation for the quantification of wetting efficiency and liquid–solid mass transfer in a trickle‐bed reactor

AbstractA novel method for the measurement of wetting efficiency in a trickle‐bed reactor under reaction conditions is introduced. The method exploits reaction rate differences of two first‐order liquid‐limited reactions occurring in parallel, to infer wetting efficiencies without any other knowledge of the reaction kinetics or external mass transfer characteristics. Using the hydrogenation of linear‐ and isooctenes, wetting efficiency is measured in a 50‐mm internal diameter, high‐pressure trickle‐bed reactor. Liquid–solid mass transfer coefficients are also estimated from the experimental conversion data. Measurements were performed for upflow operation and two literature‐defined boundaries of hydrodynamic multiplicity in trickle flow. Hydrodynamic multiplicity in trickle flow gave rise to as much as 10% variation in wetting efficiency, and 10–20% variation in the specific liquid–solid mass transfer coefficient. Conversions for upflow operation were significantly higher in trickle‐flow operation, because of complete wetting and better liquid–solid mass transfer characteristics. © 2010 American Institute of Chemical Engineers AIChE J, 2011.

Osmotic dehydration assisted impregnation of curcuminoids in coconut slices

Osmotic treatment was explored as a method to infuse curcuminoids in coconut slices. The rate of mass transfer of moisture, solid and curcuminoids with or without application of ultrasound were studied over a range of concentration of osmotic solutions (0–50%). The diffusion coefficient of curcuminoids was 1.64 × 10 −10 m 2/s, when water was used in place of osmotic solute which was further enhanced by the application of ultrasound to 1.87 × 10 −10 m 2/s. Increase in the concentration of osmotic solution beyond 25% resulted in reversal in the direction of moisture and solid mass transfer. Ultrasound treatment resulted in higher moisture and solid mass transfer due to the breaking of cell structure as revealed by microstructure examination. HPLC analysis revealed that all the curcuminoids (curcumin, demethoxycurcumin and bisdemethoxycurcumin) were infused into the coconut matrix. The present study concluded that osmotic dehydration is a feasible technology for impregnation of functional ingredients into foods without altering its matrix.

Comparison of structured trickle-bed and monolithic reactors in Pd-catalyzed hydrogenation of alpha-methylstyrene

The so-called structured trickle-bed reactors (STBRs) represented by the combination of a tubular reactor and a structure with straight flow channels packed with catalyst particles have been tested for carrying out multiphase reactions. The highly efficient reactor performance of these reactors is observed in hydrogenation of alpha-methylstyrene by virtue of intensive gas–liquid–solid mass transfer even at moderate gas and liquid velocities. Different variants of STBR have been proven and compared with each other as well as with the conventional reactors. The comparison shows that STBR, especially monoliths packed with particles, demonstrate the highest space-time yield, but at the expense of an elevated pressure drop.

Mass transfer behavior at horizontal cylinder in cross flow under different flow conditions

The rate of liquid–solid mass transfer at a horizontal cylinder placed in a cylindrical vertical column under different hydronamic conditions including gas sparging, single phase liquid flow, and two phase (gas–liquid) flow was studied experimentally by using the electrochemical technique which involves measuring the limiting current of the cathodic reduction of K 3Fe(CN) 6 using a solution containing 0.01 M K 3Fe(CN) 6 and 0.1 M K 4Fe(CN) 6 and a large excess of NaOH as supporting electrolyte. Variables studied were: liquid and gas superficial velocities, cylinder diameter, and solution physical properties. For gas sparging: the data were correlated for the conditions 0.2 < (Re.Fr) < 8.7, and 1253 < Sc < 2778 by the equation: j = 0.11 Re . F r − 0.247 . For single phase liquid flow: the data were correlated for the conditions 1253 < Sc < 2778, and 14 < Re < 516 by the equation: S h = 19 S c 0.33 Re 0.47 d t d c 0.9 . For two phase flow: the data were correlated for the conditions 1253 < Sc < 2778, 21 < Re L < 181, and 139 < Re g < 781 by the equation: S h = 6.34 S c 0.33 Re L 0.1 Re g 0.26 . The possibility of using the present data in the area of heat transfer was noted.

Enhanced liquid–solid mass transfer in microchannels by a layer of carbon nanofibers

AbstractThis paper demonstrates that the observed rate of reaction of the liquid-phase selective hydrogenation of an alkyne is higher for an open and rough carbon nanofiber (CNF) layer positioned on a microchannel wall than for an unsupported flat plate catalyst or dense and smooth CNF layers. This enhancement can be contributed to two phenomena: (1) the kinetic reaction rate increases with a factor of 1.4, due to an increase of the open and freely accessible surface area of the CNF layer available for catalyst deposition; (2) the liquid–solid mass transfer increases with a factor of 2.8, due to an increase in the surface roughness of the CNF layer and the formation of large spherical islands of clustered CNFs. A thin layer of CNFs on a microchannel wall can therefore successfully be used to increase the overall rate of reaction per reactor volume compared to an unsupported flat plate catalyst.