Effect of external mass transfer in a packed bed reactor system for a reversible enzyme reaction

A mathematical model was developed to describe the effect of external mass transfer for a packed-bed enzyme reactor in which a reversible, one-substrate, two-intermediate enzyme reaction took place. The model equation was applied to the analysis of an immobilized glucose isomerase reactor system. A Colburn-type mass transfer correlation was obtained from the Colburn j-factor versus Reynolds number plot: i.e., j_D = 0.045N_Re^−0.48. The values of mass transfer coefficient for the system under study ranged from 0.01 to 0.1 cm h⁻¹ depending on the substrate flow rate. Very good agreements were observed between the computer simulation using a plug flow reactor model with the derived mass transfer correlation and the experimental results obtained from the packed-bed reactor operation.     

Co-immobilization of Candida rugosa and Rhyzopus oryzae lipases and biodiesel production

Candida rugosa lipase and Ryzopus oryzae lipase were simultaneously immobilized on silica gel following enzyme pretreatment. The factors affecting the co-immobilization process, such as reaction time and enzyme ratio, were investigated. Biodiesel was then produced by using the co-immobilized enzyme matrix. A batch system was employed with stepwise methanol feeding, and the continuous process involved a packed-bed reactor. Under optimal immobilization conditions, the activity was approximately 16,000 U/g·matrix. When co-immobilized enzyme was used with optimized stepwise methanol feeding, conversion of biodiesel reached about 99% at 3 h and was maintained at a level of over 90% for about 30 reuses.     

Model-based Analysis of Fixed-bed and Membrane Reactors of Various Scale

A packed-bed membrane reactor in a distributor configuration is studied theoretically for the oxidative propane dehydrogenation and compared with a fixed-bed reactor. Based on detailed 2D models considering two different heat and mass transport models the reactor scale-up including various reactor-to-particle diameter ratios (D/d_P) is analyzed with respect to reactor performance, heat transfer and hot spot formation. Higher selectivities at lower hot spot temperatures occur in the packed-bed membrane reactor for the same reaction conditions.     

PERFORMANCE OF A PACKED-BED REACTOR

We examined the conversion rates in a packed bed catalytic reactor with a two phase upward flow in a wide range of operating conditions. The oxidation of ethanol to acetic acid in the liquid phase on a Pd-Alumina catalyst was chosen as the test reaction.

Global reaction rates were measured by changing gas velocities, temperature, and feed concentrations of ethanol in the liquid phase. The observed rates were compared with those calculated using two models, assuming a total external wetting of the catalyst. In the first model, a “kinetic” conversion rate was calculated by neglecting any interphase mass transfer resistance. In the second model the interphase mass transfer resistance was considered and expressed by an overall coefficient evaluated from published correlations. The results show that there is an hydrodynamic influence, probably due to the mass transfer and/or to the partial effective wetting of the catalyst. Mass transfer, on the other hand, is better than that observed in other cases. A comparison with the performances of a downflow trickle-bed reactor operating at the same tested conditions showed a much smaller influence of mass transfer and hydrodynamics on the overall conversion rate for the upflow reactor.     

Performance analysis of an immobilized yeast packed-bed reactor for ethanol fermentation

The performance of an immobilized packed-bed bioreactor for continuous ethanol fermentation was evaluated. Immobilized yeasts were prepared by entrapment in calcium alginate gel. An axial dispersed plug flow model incorporating the effects of substrate and product inhibition on fermentation kinetics was developed. The model equations were solved by the method of orthogonal collocation and the suitability of the reactor model to predict the conversions obtained in this biocatalytic reaction system was assessed.     

A UNIFIED COLLOCATION ALGORITHM FOR PACKED-BED CHEMICAL REACTOR SIMULATION

Mathematical models of packed-bed catalytic reactors are aimed to predict the conversions and temperature profiles in both fluid and solid phases within the reactor. Although very general models can be mathematically formulated, usually several simplifying hypothesis are introduced for the fluid phase and/or the solid phase, in order to overcome computational difficulties

We describe in this paper a computational algorithm based on Orthogonal Collocation Method on finite elements, with elimination of the knot unknown functions, coupled with an integration method for stiff ordinary differential equations. This has been used in the development of a computer code, which allows us to find the transient behavior of the reactor by solving the equation relative to the external field, coupled with those describing the transient behavior in the catalyst particles, for a wide class of reactor models. The most general examined model includes axial dispersion in the external fluid phase, interphase mass and heat transfer resistances, intraphase mass resistance and any given kinetic scheme with complex reaction rate expressions.     

Phenylacetylene hydrogenation in a three-phase catalytic packed-bed reactor: experiments and model

A mathematical model was developed for the cocurrent operation of a three-phase catalytic packed-bed reactor under both trickling- and pulsing-flow regimes. The local fluctuations of liquid-solid mass transfer, liquid flow rate, and liquid holdup in unsteady pulsing-flow were simulated as periodic square-wave functions. The transport properties employed in the model were obtained using published correlations, while expressions for the intrinsic reaction kinetics were taken from our previous work. The model results were found to be in good agreement with experimental data obtained from a laboratory-scale reactor, and verified the advantage of pulsing-flow operation over trickling-flow.     

Facilitated mass transfer in a packed-bed immobilized-cell reactor by using an organic solvent as substrate reservoir

The production of propene oxide from propene and oxygen by non-growing cells entrapped in calcium alginate was used to study the behaviour of a packed-bed immobilized-cell reactor operated with an organic solvent as the substrate reservoir. As a result of the high solubility of propene in the solvent used, n-hexadecane, oxygen was considered to be the limiting substrate. Dilution of the biocatalyst bed with small glass particles appeared necessary to attain a high liquid/solid contacting efficiency between the hydrophilic gel particles and the hydrophobic solvent. The bed dilution had the advantage of avoiding bed compaction and reducing pressure drops. The use of an organic solvent as the transport medium prevented oxygen depletion along the length of the packed-bed reactor. This eliminated the need for a separate gas phase in the bioreactor. A mathematical reactor model was developed to describe the combined effects of contacting pattern and external and internal diffusion limitations on the instrinsic kinetics of the immobilized cells. Experiments with the packed-bed immobilized-cell reactor were performed using an aqueous solution or n-hexadecane as the reaction medium. Predicted oxygen conversions compared favourably to the observed values without the need for fitting factors.     

Intensification principle of a new three-phase catalytic slurry reactor. Part I: Performance characterisation

This paper presents the concept and the performances of a mini horizontal stirred tank reactor, used for hydrogenation reaction. A simple analytical model based on characteristic times of heat and mass transfer illustrates the intensification principle and shows that the relevant intensification parameter is the mass to heat transfer characteristics times ratio. The proof of concept is made through a small scale reactor named RAPTOR^® (French acronym for Reactor with Polyvalent Rectilinear Stirred Reactor with Optimised Transfer). The mass transfer performances are measured and compared to conventional stirred tank reactor and other multiple impeller continuous reactors. In a following second paper, a comparative study is proposed to evaluate the eco-efficiency and the techno-economic advantages of a continuous process involving a RAPTOR^® versus a classical batch process based on a stirred reactor.     

Kinetic studies in a batch reactor using ion exchange resin catalysts for oxygenates production: Role of mass transfer mechanisms

Oxygenated compounds are usually produced by a reversible liquid phase reaction using ion exchange resins with a bidisperse pore structure as catalyst. Mass transport is mainly controlled by diffusion through the macropores and the mass transfer resistance in the gel microspheres is negligible. Therefore, in this paper a mathematical model of the batch reactor considering diffusion of the species in the external film and then macropore diffusion inside the particle and reaction in the gel microspheres was developed. The numerical solution is implemented through the numerical package PDECOL and detailed explanations of the procedure used are presented. The model was applied to the diethylacetal synthesis using ethanol and acetaldehyde as reactants and Amberlyst 18 as catalyst. The experimental data are fitted with a two-parameter model based on a Langmuir-Hinshelwood rate expression in order to get the true reaction kinetics. The influence of the mass transfer mechanisms is evaluated in terms of the effectiveness factor history during the transient state of the batch reactor. The values of the effectiveness factor calculated at equilibrium with the batch reactor model are compared with those calculated from a steady state infinite bath model.     

A study of interfacial polycondensation in a continuous reaction system

A study was made of the interfacial polycondensation of nylon 6–10 in a continuous reaction system since no previous detailed work of this type was reported in the literature. An experimental stirred-flow reactor was used to determine both yield and intrinsic viscosity (molecular weight) as functions of reactant ratio (sebacoyl chloride/hexamethylenediamine) and Reynolds number. It was found that mass transfer was the controlling factor in the reaction system. The yield as a function of Reynolds number correlated directly with the behavior of mass transfer coefficient. In addition, reactant ratio effects on yield were shown to relate to change in organic phase volume. Intrinsic viscosity was a maximum in the same reactant ratio range as for batch and continuous cascade systems studied earlier. Intrinsic viscosity behavior was also shown to relate to mass transfer. The j_D data for the reactor systems were also determined. These values were shown to correlate if normalized for reactant ratio.     

Performance characteristics of a cstr containing immobilised enzyme particles

The effects of internal and external substrate diffusion resistances on the performance of a continuous stirred tank reactor are analysed in this work. Both immobilised enzymatic reactions with and without substrate inhibitions are considered. The substrate conversion for the reaction without substrate inhibition is dependent on four dimensionless parameters: the Thiele modulus, the dimensionless Michaelis constant, the mass transfer Nusselt number and β, which represents a combination of particle hold-up, maximum reaction rate, input substrate concentration and substrate residence time in the continuous stirred tank reactor. For the corresponding reaction with substrate inhibition, the effect of the additional dimensionless inhibition constant on the substrate conversion is also very significant. The substrate conversion generally decreases with decrease in dimensionless parameter β, increase in Thiele modulus and decrease in mass transfer Nusselt number. For the reaction with small Thiele modulus, β and strong substrate diffusion resistances, a multireactor system may be needed if a certain desired substrate conversion is required. The single CSTR model can be extended to describe the multireactor system and the effect of the number of reactors on the substrate conversion for a two- or more reactor system is also examined.     

Investigation of CO2 Reaction with CaO and an Acid Washed Lime in a Packed-Bed Reactor

In this work, a mathematical model was developed for the prediction of packed-bed reactor behavior for CaO+CO₂ reaction based on the random pore model. A natural limestone and a modified sorbent using acetic acid washing were used for the experiments. The performances of these sorbents were initially determined using a thermogravimeter analyzer. Then, the reaction was accomplished in a packed-bed reactor for obtaining CO₂ breakthrough curves and investigation of model predictions. This model was able to successfully predict the effect of process conditions and solid texture on the breakthrough curves of the packed-bed reactor.     

Melt polycondensation of poly(ethylene terephthalate) in a rotating disk reactor

A multicompartment model is proposed for a semibatch melt polycondensation of poly(ethylene terephthalate) in a rotating disk polymerization reactor and compared with laboratory experimental data. The reactor is a horizontal cylindrical vessel with a horizontal shaft on which multiple disks are mounted. The reactor is assumed to comprise N equal sized compartments and each compartment consists of a film phase on the rotating disk and a bulk phase in which disks are partially immersed. The effects of disk rotating speed, number of disks, reaction temperature, and pressure were investigated. It was observed that ethylene glycol is predominantly removed from thin polymer layers on the rotating disks and the enhanced interfacial area exerted by ethylene glycol bubbles accounts for about 30–50% of the total available interfacial mass transfer area. Although the rate of polymerization increases as more disks are used, the maximum number of disks in a reactor must be determined properly in order to prevent the formation of thick polymer films that result in a reduced specific interfacial area and reduced polymerization efficiency. At a fixed reaction pressure, the equilibrium conversion is reached but the rate of reaction can be further increased by increasing the reaction temperature. The results of the proposed multicompartment model are also compared with those predicted by a simple one-parameter model. © 1995 John Wiley & Sons, Inc.     

A study on the ethanol production by immobilized cells ofZymomonas mobilis

Cells ofZymomonas mobilis immobilized in Ca-alginate matrix were used for ethanol production under various conditions. Immobilized cells showed broad optimum pH profile and their operational optimum temperature shifted from 30‡C to 40‡C upon immobilization. As reportedlyZ. mobilis did get the substrate inhibition by glucose, but at high concentration level of glucose the reduction of activity for ethanol production was less severe than that for yeast. The used beads of the immobilizedZ. mobilis were reactivated by incubating them in the activation medium. The increase in cell number and the enhancement of the specific activity per each cell are considered the two major factors responsible for the overall activation. A packed-bed reactor with the feed glucose concentration of 20% (W/V) gave an ethanol productivity as high as 33.0 g/l.hr at the flow rate of 58.5 ml/hr. A comparison between the experimental results from the real packed-bed reactor and the simulation results of an ideal case showed a two-fold inferior performance by the real reactor and this is at least partly attributed to the CO₂ gas effect.     

Mathematical modelling of slow pyrolysis of segregated solid wastes in a packed-bed pyrolyser

Waste segregation is being explored as one of the potential effective ways for waste management, where wastes are separated for either recycling or energy recovery. In this paper, three segregated wastes, contaminated waste wood, cardboard and waste textile are pyrolysed in a slow-heating packed-bed reactor for the purpose of solid, liquid and gas recovery. The effect of final temperature was investigated and product yields and compositions were measured. Mathematical modelling was employed to simulate the heat, mass transfer and kinetic processes inside the reactor. Both a parallel reaction model and a function group model were used to predict the product yields as well as their compositions. Char yield of 21–34%, tar 34–46% and gas 23–43% were obtained. It is found that packed-bed pyrolysis produces 30–100% more char compared to standard TGA tests and the local heating rate across the packed-bed reactor differs remarkably from the programmed wall-heating rate and varies greatly in both time and space. Mathematical modelling suggests that wood has higher tar cracking ability than cardboard and textile wastes during pyrolysis, and the effects of mineral contents in the fuel need to be explored. CO₂, CO, tar and water are the main released species during the major stage of the pyrolysis processes which occurs between 250 and 450 °C, whereas noticeable quantity of hydrogen and light hydrocarbons is observed only at higher temperature levels and at the final stage.     

Determination of process parameters and modelling of lipase-catalyzed transesterification in a fixed bed reactor

Chemical transesterification is of major importance to the edible oil industry. While alkali catalysts randomize all the fatty acids in a triglyceride mixture, the use of a 1,3 specific lipase causes a more selective exchange of fatty acid residues. Basic process parameters for the development of a continuous solvent-free process in a fixed bed reactor have been determined. The kinetics of the transesterfication reaction and the influence of particle diameter, substrate and water concentration on the effective reaction rate were examined in batchwise experiments. Residence time distribution and parameters of inter- and intraparticle mass transfer were determined by modelling of experiments carried out in a fixed bed reactor under transient conditions. Fixed bed reactors with side stream analysis were used for continuous transesterification. A kinetic model was developed for the enzyme catalyzed reaction, thereby showing the analogy between heterogeneous catalytic and enzyme catalyzed reactions. A one-dimensional heterogeneous reactor model was formulated on the basis of the kinetic equation and different process parameters. For numerical calculations, an exponential enzyme distribution inside the carrier was assumed. The simulation of experimental results indicates that they are well described by the developed model. Water concentration and presence of other substances strongly influence the stability of the immobilized enzyme.     

Catalytic hydrogenation of o-nitroanisole in a microreactor: Reactor performance and kinetic studies

Hydrogenation of o-nitroanisole to o-anisidine was conducted in a packed-bed microreactor as a model hydrogenation reaction of importance to the pharmaceutical and fine chemicals industries with the aim of investigating the reactor performance and kinetics of the reaction. The effects of different processing conditions viz. hydrogen pressure, o-nitroanisole concentration, temperature, and residence time on the conversion of o-nitroanisole, space-time yield (STY), and selectivity of o-anisidine were studied using 2% Pd/zeolite catalyst. The kinetic study was undertaken in a differential reactor mode keeping the conversion of o-nitroanisole at less than 10%. During the kinetic study, it was observed that the intermediate 2-methoxynitrosobenzene was present in the reactor at low catalyst loading and low conversions because of short residence time in the reactor. Therefore, for the kinetics study, the overall reaction was treated as comprising two separate reactions: first the reduction of o-nitroanisole to 2-methoxynitrosobenzene and then, the reduction of 2-methoxynitrosobenzene to o-anisidine. Internal and external mass and heat transfer limitations in the microreactor were examined. Different rate laws using different mechanisms from the literature were considered to fit the experimental data. Two rate equations for the two consecutive reactions assuming Langmuir-Hinshelwood mechanism provided the best fit to the experimental data. These two rate equations predicted the experimental rates within 10% error. Experiments were also carried out in an integral reactor, and the reactor performance data were found to be in agreement with the predictions of the theoretical models.     

The unsteady-state solution for a finite dispersion-type catalytic packed-bed tubular reactor

The unsteady-state solution is obtained by an operator theory in functional analysis setting for a general finite catalytic packed-bed tubular reactor model with axial dispersion in the bed, mass transfer between the catalyst particles and the flowing phase, and intraparticle diffusion and surface reaction in the catalyst particles.     

A mass transfer study of a new electrochemical reactor stirred by gases evolved at the counter electrode

Mass transfer coefficients were measured for the deposition of copper from acidified copper sulphate solution at a horizontal cylinder cathode stirred by oxygen evolved at a horizontal lead anode placed below the cylinder. Variables studied were: oxygen discharge rate, electrolyte concentration and cylinder diameter. Oxygen discharge was found to increase the rate of mass transfer by a factor ranging from 1.5 to 5 over the natural convection value depending on the rate of oxygen discharge at the lead anode. The data were correlated by the equation: J = 25.0 Re^?0.53 Mass transfer coefficients measured at an array of horizontal cylinders agreed with the results for single cylinders. A new electrochemical reactor built of a set of parallel arrays of horizontal cylinders and stirred by the counter electrode gases is proposed as offering an efficient way of stirring with no external stirring power requirement.