Modeling of the kinetic for the acidolysis of different triacylglycerols and caprylic acid catalyzed by Lipozyme IM immobilized in packed bed reactor

This work proposes a lumped kinetic model for the acidolysis of a triacylglycerol (TAG) and an odd free fatty acid (FFA) in a non-aqueous medium, catalyzed by a 1,3 specific lipase immobilized on a solid support. This model is based on the mechanism of the acidolysis reaction by considering the following hypothesis: (1) only the fatty acids in positions 1 and 3 of TAG are exchanged and these two positions in the glycerol backbone are equivalent and (2) the only intermediate of appreciable lifespan in which the enzyme participates is the acyl-enzyme complex. The kinetic equation obtained for the rate of incorporation of an odd fatty acid to TAG has been applied to the results obtained in the acidolysis of three oils (commercial triolein, cod liver oil (CLO) and a commercial oil enriched in eicosapentaenoic acid (EPA), EPAX 4510TG) with caprylic acid (CA), catalyzed by the immobilized lipase Lipozyme IM contained in a packed bed reactor (PBR). The acidolysis has been carried out by recirculating the reaction mixture through the PBR until the reaction equilibrium was reached. In these conditions it has been proved that the PBR behaves as a perfect mixed dispersion reactor and the experimental results obtained at low TAG concentrations have been acceptably fitted to the kinetic expression obtained from the proposed model, with only two fitting parameters.However, for TAG concentrations higher than , an appreciable reduction of the reaction rate was observed. This result was due to the decrease of the effective diffusivity of reactants within the pores of the support where the lipase is immobilized, since the viscosity of the reaction mixture increases appreciably when the reactant concentration also does. When this phenomenon is included in the developed kinetic model, the experimental results obtained at high TAG concentrations could also be explained, even in absence of the organic solvent (n-hexane). It is observed that the influence of diffusion into the pores increases with the degree of CA incorporation to TAG, which was due to the increase of TAG and native fatty acid concentrations in the particle pores, which determines a continuous decrease in the effective diffusivity of CA.     

Study of gas cavity size hysteresis in a packed bed using DEM

When a high velocity gas jet is introduced into a packed bed a cavity is formed. The size of the cavity shows hysteresis on increasing and decreasing gas flow rates. This hysteresis leads to different cavity sizes at same gas flow rate depending on the bed history. The size of cavity affects the gas flow profiles in the packed bed. In this study the cavity size hysteresis phenomenon has been modeled using discrete element method along with turbulent gas flow. A reasonable agreement has been found between computed and experimental results on cavity size hysteresis. The effect of various parameters, such as nozzle height from the bed bottom and packing height, on the cavity size hysteresis has been studied. It is found that inter-particle interaction forces along with gas drag and bed porosity play an important role in describing the cavity size hysteresis. The injection of gas flow allows the particles to go to an unconstrained state than they were previously in, and their ability to remain in that state, even under decreased gas drag force, leads to the phenomenon of cavity size hysteresis.     

Improved one-dimensional model of a tubular packed bed reactor

The major drawback of one-dimensional models of tubular fixed bed reactors, which are often used if the computational effort should be small, is the fact that the reaction rate is calculated using the average temperature over the cross-section of the reactor. The difference between this reaction rate and the average reaction rate over the cross-section becomes increasingly significant with increasing temperature difference over the radius of the reactor and with increasing activation energy of the reaction(s). Improved versions of the one-dimensional model, such as that of Hagan et al. [1988. A simple approach to highly sensitive tubular reactors. SIAM Journal of Applied Mathematics 48, 1083-1091] are available, which use an analytical approximation of the radial temperature profile to improve the prediction of the average reaction rate. However, application of these models involves solving of implicit equations. Here, a new model is proposed as an alternative to the existing one-dimensional models. It has the same form as the conventional one-dimensional model and contains only explicit functions. It is demonstrated that, at conditions not too close to runaway, the new model performs better than the well-known α-model.     

Non-isothermal modeling of the flue gas desulphurization process using a semi-dry spouted bed reactor

A mathematical model is developed for investigation of SO₂ removal in a powder particle spouted bed (PPSB) for non-isothermal operating condition. For this aim, the stream-tube model which was already validated for such systems is applied for hydrodynamics of solid and gas phases, and then by using the conservation laws of mass and energy, the governing equations for gas and solid phases are derived and solved numerically. The published experimental data in the literature are used to validate the accuracy of the proposed model. The results show that the model is capable of predicting the behaviour of this system properly. Also the optimum performance of this system is investigated by studying the effects of different parameters such as bed height, molar ratio of sorbent to acid gas (Ca/S) and inlet concentration of SO₂.     

Modeling a fluidized bed reactor by integrating various scales: Pore,particle, and reactor

This work proposes a novel population-balance based model for a bubbling fluidized bed reactor. This model considers two continuum phases: bubble and emulsion. The evolution of the bubble size distribution was modeled using a population balance, considering both axial and radial motion. This sub-model involves a new mathematical form for the aggregation frequency, which predicts the migration of bubbles from the reactor wall toward the reactor center. Additionally, reacting particles were considered as a Lagrangian phase, which exchanges mass with emulsion phases. For each particle, the variation of the pore size distribution was also considered. The model presented here accurately predicted the experimental data for biochar gasification in a lab-scale bubbling fluidized bed reactor. Finally, the aggregation frequency is shown to serve as a scaling parameter.     

Modeling of a packed-bed electrochemical reactor for producing glyoxylic acid from oxalic acid

A two-dimensional reactor model was established for a packed-bed electrochemical reactor with cooled cathode (PERCC) for producing glyoxylic acid from oxalic acid based on the system's reaction kinetics, mass conservation equation, and the equation of charge conservation in terms of solution-cathode potential to describe the distributions of glyoxylic acid concentration and electrolyte potential in the cathode compartment of the PERCC. The equation for a circulating mixer was also presented to account for the accumulation of glyoxylic acid in the catholyte of a batch electroreduction process. Using the orthogonal collocation approach, the partial differential equations of the model could be converted into sets of algebraic equations and be numerically solved. The effects of operating temperature, conductivity of catholyte, operating cathode potential, and volumetric flow rate of the catholyte on the current efficiency and concentration of glyoxylic acid were simulated and discussed, with emphasis on the current densities generated from main and side reactions. The model was used in a batch operation process and a continuous operation process, with the predicted results being generally in good agreement with the experimental data for both the cases.     

Simulation of activity loss of fixed bed catalytic reactor of MTO conversion using percolation theory

In this investigation, a reactor model for prediction of the deactivation behavior of MTO's porous catalyst in a fixed bed reactor is developed. Effect of coking on molecular transport in the porous structure of SAPO-34 has been simulated using the percolation theory. Thermal effects of the reaction were considered in the model and the temperature profile of the gas stream in the reactor was predicted. The predicted loss in catalyst activity with time-on-stream was in very good agreement with the experimental data. The resulting coke deposition and gas temperature profiles along the length of reactor suggested a reaction front moving toward the outlet of the fixed bed reactor at the operating experimental conditions of 1 h⁻¹ and 723 K for methanol space velocity and inlet temperature, respectively. Effects of space time, coordination of Bethe network, and effective diffusivity of component in reaction mixture on the reactor performance are presented.     

Tracer investigation of a packed column under variable flow

Tracer techniques are well-established methods in investigations of a flow process dynamics. The concept of experimental evaluation of residence time distribution (RTD) is widely utilized. There exist advanced methods of RTD function analysis. The methods generally assume the constant flow rate in the system. In this work, we aim to determine the flow parameters for a process under variable flow rate using ordinary tracer data. The experimental study analyzed as an illustration of the method is the tracer experiment carried out on a pilot scale system—packed bed reactor.     

Modeling and simulation of a small-scale trickle bed reactor for sugar hydrogenation

Laboratory-scale trickle bed reactor was modeled and simulated, taking into account axial dispersion, gas–liquid, liquid–solid and internal mass transfer as well as catalyst deactivation under isothermal conditions. For catalyst particles dynamic and steady state models were developed, including both mass and heat balances. Catalyst deactivation was included in the model by using the final activity concept for the catalyst particles. A well-working numerical algorithm (method of lines) was applied for solving the reactor model with Matlab 7.1 and the results followed experimental trends very well. The steady-state reactor model was based on simultaneous solution of mass balances. The aim was to illustrate how these parabolic partial differential equations could be solved with a step-by-step calculation for a selected geometry. The final model verification was done against experimental data from the hydrogenation of arabinose to arabitol on a ruthenium catalyst.     

Cationic polymerization in rotating packed bed reactor: Experimental and modeling

On the basis of analysis of key engineering factors predominating in cationic polymerization, butyl rubber (IIR) as an example was synthesized by cationic polymerization in the high‐gravity environment generated by a rotating packed bed (RPB) reactor. The influence of the rotating speed, packing thickness, and polymerization temperature on the number average molecular weight (M_n) of IIR was studied. The optimum experimental conditions were determined as rotating speed of 1200 r min^?1, packing thickness of 40 mm and polymerization temperature of 173 K, where IIR with M_n of 289,000 and unimodal molecular weight distribution of 1.99 was obtained. According to the experimental results and elementary reactions, a model for the prediction of M_n was developed, and the validity of the model was confirmed by the fact that most of the predicted M_ns agreed well with the experimental data with a deviation within 10%. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Spontaneous ignition of wood, char and RDF in a lab scale packed bed

Many municipal waste combustors use preheated primary air in the first zone to dry the waste. In most cases the preheat temperature does not exceed 140 °C. In previous experiments it is found that at temperatures around 200 °C, in some circumstances, self- or spontaneous ignition can be achieved. Using preheated air can be a powerful tool to control the ignition and combustion processes in a waste combustion plant. To use this tool effectively, the influence of the preheated air on the fuel bed needs to be well understood. The present work is done to investigate in a systematically way the spontaneous ignition behaviour of a packed bed heated with a preheated air stream. Experiments on a lab scale packed bed reactor are carried out for various fuel types. Because MSW is an highly inhomogeneous fuel, wood and char are used as model fuels. To include the inhomogeneous character of MWS, also experiments are carried out with RDF. Parameters such as primary air flow velocity and temperature, addition of inert material, moisture content of the fuel (wood chips) and particle size (char) have been changed to see their effect on the spontaneous ignition temperature and on the minimum air temperature needed for ignition. The spontaneous ignition temperature is defined as the bed temperature at which a transition takes place from a negligible or slow fuel reaction rate to a rapid oxidation of either the volatiles or the solid fuel without an external source such as a spark or a flame. The minimum or critical air temperature is defined as the lowest air temperature at which ignition can be obtained. It is found that the type of fuel has influence on the ignition temperatures. Besides both the critical air temperature needed for the spontaneous ignition and the spontaneous ignition temperature increase with an increase in the primary air velocity (between 0.1 and 0.5  m/s) and increasing the added inert fraction (between 0 and 40 wt%), irrespective of the fuel type. The effect of air flow velocity and temperature and also the effect of inert on both the critical air temperature and the spontaneous ignition temperature can be explained qualitatively by using Semenov’s analysis of thermal explosions. Semenov’s theory is quantitatively applied to predict the spontaneous ignition and the critical air temperatures for wood.     

Hydrodynamic study of a toroidal fluidized bed reactor

Hydrodynamic behavior of a newly developed toroidal fluidized bed reactor is studied in this work. The reactor has a gas distributor consisting of angled blades in an annular ring at the reactor bottom. The driving force for particles to move over the distributing blades comes from the velocity head of gas jets accelerated upon entering the blade spacing. Relevant hydrodynamic behaviors are measured with various inert materials in a pilot scale 400-mm toroidal fluidized bed reactor. The observed hydrodynamic behavior is found to be essentially predictable at ambient temperature by conventional hydrodynamic models. Fine particle tracking on the reactor wall is clearly observed through oxidation of zinc dross at a bed temperature of around 1120°C, and is simulated on the basis of a simplified mathematical model. Hydrodynamic issues, such as particle flying trajectory and retention time in the reactor, are discussed based on the developed model.     

Modeling solvent extraction of vegetable oil in a packed bed

A one-dimensional model was developed for solvent extraction of oil from a packed bed of oil-bearing vegetable materials. The equilibrium relationship between the residual oil content of marc and oil concentration of stagnant miscella in pores of the bed material was generated through experiments with rice bran and hexane. The nondimensional parameters recognized from the model describing extraction were initial Reynolds number (Re_i), initial Schmidt number (Sc_i), bed void fraction (ε_b), particle porosity (ε_p), ratio of bed diameter to particle diameter (D_t/d_p), ratio of bed depth to bed diameter (L/D_t), ratio of particle surface area to bed cross-section (a_pAL/A=a_pL), and recycle of solvent and equilibrium distribution coefficient (EDC). For reducing the time required to extract to the same residual oil content of marc, higher values of Re_i, ε_b, and a_pL were beneficial, whereas higher values of Sc_i, ε_p, D_t/d_p, L/D_t, and EDC were detrimental.     

Simulations of chemical absorption in pilot-scale and industrial-scale packed columns by computational mass transfer

A complex computational mass transfer model (CMT) is proposed for modeling the chemical absorption process with heat effect in packed columns. The feature of the proposed model is able to predict the concentration and temperature as well as the velocity distributions at once along the column without assuming the turbulent Schmidt number, or using the experimentally measured turbulent mass transfer diffusivity. The present model consists of the differential mass transfer equation with its auxiliary closing equations and the accompanied formulations of computational fluid dynamics (CFD) and computational heat transfer (CHT). In the mathematical expression for the accompanied CFD and CHT, the conventional methods of k-ε and are used for closing the momentum and heat transfer equations. While for the mass transfer equation, the recently developed concentration variance and its dissipation rate ε_c equations (Liu, 2003) are adopted for its closure. To test the validity of the present model, simulations were made for a pilot-scale randomly packed chemical absorption column of 0.1 m ID and 7 m high, packed with 1/2^″ ceramic Berl saddles for CO₂ removal from gas mixture by aqueous monoethanolamine (MEA) solutions (Tontiwachwuthikul et al., 1992 ) and an industrial-scale randomly packed chemical absorption column of 1.9 m ID and 26.6 m high, packed with 2^″ stainless steel Pall rings for CO₂ removal from natural gas by aqueous MEA solutions (Pintola et al., 1993). The simulated results were compared with the published experimental data and satisfactory agreement was found between them in both concentration and temperature distributions. Furthermore, the result of computation also reveals that the turbulent mass transfer diffusivity D_tvaries along axial and radial directions. Thus the common viewpoint of assuming constant D_t throughout the whole column is questionable, even for the small size packed column. Finally, the analogy between mass transfer and heat transfer in chemical absorption is demonstrated by the similarity of their diffusivity profiles.     

The heat transfer coefficient between a particle and a bed (packed or fluidised) of much larger particles

The heat transfer coefficient has been measured for a heated phosphor-bronze sphere (diam. 2.0, 3.0 or 5.56 mm) added to a bed of larger particles, through which air at room temperature was passed. The bronze heat transfer sphere was attached to a very thin, flexible thermocouple and was heated in a flame to before being immersed in the bed. The cooling of the bronze sphere enabled the heat transfer coefficient, h, to be measured for a variety of U/U_mf, as well as diameters of both the particles in the bed and the heat transfer sphere. It was found that before the onset of fluidisation, h rose with U, but h reached a constant value for U?U_mf. These measurements indicate that in this situation (of a relatively small particle in a bed of larger particles) all the heat transfer is between the hot bronze sphere and the gas flowing over it. Consequently, a Nusselt number, based on the thermal conductivity of the gas, is easy to define and for U?U_mf (i.e. a packed bed), Nu is given by

     

Modelling of gas interstitial velocity radial distribution over cross-section of a tube packed with granular catalyst bed; effects of granule shape and of lateral gas mixing

The previously presented [Zió?kowska, I., Zió?kowski, D., 1993. Modelling of gas interstitial velocity radial distribution over a cross-section of a tube packed with granular catalyst bed. Chemical Engineering Science 48, 3283-3292] mathematical model of gas flow field within a tube packed with a bed of spherical elements has been modernised. The modernisation consists in more rigorous treating of the radial gas dispersion within the bed voids in the fluid dynamic equations and in involving the formulae correlating the flow resistance in beds packed with various non-spherical elements (Raschig rings, cylinders) with their characteristics. The model solution relates the gas interstitial and superficial radial distributions with an empirical parameter—the local effective viscosity or corresponding Reynolds number, dependent on the geometric, aerodynamic and physical properties of the system which are usually known. The effective viscosity is associated with the kinetic energy dissipation due to the interface friction, the shear stresses in molecular and turbulent motion and the radial dispersion in the gas stream. Its knowledge makes possible the evaluation of the radial profiles of the gas interstitial velocity, as well as the dispersion coefficient, or corresponding Péclet number and the drag coefficient for individual element within the bed. The effective viscosity has been determined experimentally for beds of Raschig rings and cylinders by the method presented previously [Zió?kowska, I., Zió?kowski, D., 2001. Experimental analysis of isothermal gas flow field in tubes packed with spheres. Chemical Engineering and Processing 40, 221-233] and the results have been correlated with the system characteristics. Then the correlations have been used, according to the model, in evaluation of the radial distributions of the gas interstitial velocity, the radial dispersion coefficient and the drag coefficient for individual element within the bed.     

Modeling and simulation of non-isothermal catalytic packed bed membrane reactor for H2S decomposition

The recovery of H₂ from H₂S is an economical alternative to the Claus process in petroleum and minerals processing industries. Previous studies [React. Kinet. Catal. Lett. 62 (1997) 55; Catal. Lett. 37 (1996) 167] have demonstrated that catalytic decomposition of H₂S over bimetallic sulfide can proceed at relatively higher rates than over mono-metallic systems due to chemical synergism although conversions are still thermodynamically limited. In the present study, the performance of a catalytic membrane reactor containing a packed bed of Ru–Mo sulfide catalyst has been investigated with a view to improving H₂ yield beyond the equilibrium ceiling. A system of differential equations describing the non-isothermal reactor model has been solved to examine the effect of important hydrodynamic and transport properties on conversion. The results were obtained using a Pt-coated Nb membrane tube as the catalytic reactor enclosed in a quartz shell cylinder. Reynolds number for shell and tube side (Re^s and Re^t) as well as the modified wall Peclet number, Pe_m, dramatically affect H₂S conversions. Membrane reactor conversion rose monotonically with axial distance exceeding the equilibrium conversion by as much as eight times under some conditions.     

Tomographic measurement of breakthrough in a packed bed adsorber

The tomographic measurement technique enables the measurement of local water vapour concentrations at the exit of a packed bed adsorber using near infra-red. This is realized by extending the adsorption column with a hollow glass cylinder that serves as the measurement cross-section. The glass is transilluminated from three directions with three light-sheets. The light absorption by water vapour is measured with three InGaAs photodiode arrays and these projections are used for the tomographic reconstruction of the concentration fields. For low water vapour concentrations () an error below 8% is reported. Concentration field measurements during adsorption show the early breakthrough near the column wall due to channeling effects at a low ratio between tube and particle diameter.