A mathematical model of a fluidized bed reactor for the continuous production of solvents by immobilized Clostridium acetobutylicum

A fluidized bed reactor has been employed for the continuous production of solvents from whey permeate using cells of Clostridium acetobutylicum immobilized by adsorption onto bonechar. Substrate diffusion equations have been developed for the bioparticles, and a mathematical model has been advanced to describe the operation of the reactor. The model was fitted to the experimental data using the concept that not all of the biomass within the reactor was active in solvent production. On this basis, less than 5% was ‘active’ biomass.     

Optimal design and operation of an industrial three phase reactor for the oxidation of phenol

Among several treatment methods catalytic wet air oxidation (CWAO) treatment is considered as a useful and powerful method for removing phenol from waste waters. In this work, mathematical model of a trickle bed reactor (TBR) undergoing CWAO of phenol is developed and the best kinetic parameters of the relevant reaction are estimated based on experimental data (from the literature) using parameter estimation technique. The validated model is then utilized for further simulation and optimization of the process. Finally, the TBR is scaled up to predict the behavior of CWAO of phenol in industrial reactors. The optimal operating conditions based on maximum conversion and minimum cost in addition to the optimal distribution of the catalyst bed is considered in scaling up and the optimal ratio of the reactor length to reactor diameter is calculated with taking into account the hydrodynamic factors (radial and axial concentration and temperature distribution).     

Development of a mathematical model for Bacillus circulans growth and alkaline protease production kinetics

BACKGROUND: An unstructured mathematical model was developed to understand information on the relationship between Bacillus circulans growth and metabolism‐related protease production (using logistic and Luedeking–Piret equations respectively) in a batch reactor with respect to glucose consumption and fermentation time. The objective was to develop an indispensable tool for the optimisation, control, design and analysis of alkaline protease production. RESULTS: Biomass growth and enzyme production titres changed with a change in substrate concentration. Modelling analysis of biomass and enzyme production titres at different substrate concentrations revealed significant accuracy in terms of statistical consistency and robustness with respect to fermentation kinetic profiles. CONCLUSION: With the B. circulans strain used, an economic protease yield (2837 × 10³ U g^?1) with respect to biomass and glucose ratio was achieved at low substrate concentration (10 g L^?1). The developed model could be effectively utilised for designing, controlling and up‐scaling the protease production process in high‐density fermentation in selected bioreactors with statistical consistency. Copyright © 2008 Society of Chemical Industry     

Thermodynamic analysis of a cyclic water gas-shift reactor (CWGSR) for hydrogen production

The cyclic water gas-shift reactor (CWGSR) is a cyclically operated fixed bed reactor for the removal of carbon monoxide from reformate gases. It is based on the repeated reduction of iron oxide by reformate gases and its subsequent oxidation by steam. To evaluate the thermodynamic limits of this reactor, we develop a model under the assumption of chemical equilibrium. For this purpose, we conduct a wave analysis which shows that the reactor behaviour is dominated by the movement of sharp reaction fronts. Depending on the positions of these fronts at cyclic steady state, five different operating regimes of the CWGSR can be identified. Besides the qualitative analysis of the regimes, the equilibrium model also offers a first quantitative analysis regarding the two performance parameters, i.e. fuel utilisation and product concentration. At 750 °C, a fuel utilisation of 55% can be achieved, and the molar hydrogen fraction in the product stream is up to 70%. The equilibrium model can be used for a first estimate of favourable design and operating parameters of the CWGSR.     

Evaluation of hydrodynamic behavior of the perforated gas distributor of industrial gas phase polymerization reactor using CFD-PBM coupled model

A 2D computational fluid dynamics (Eulerian–Eulerian) multiphase flow model coupled with a population balance model (CFD-PBM) was implemented to investigate the fluidization structure in terms of entrance region in an industrial-scale gas phase fluidized bed reactor. The simulation results were compared with the industrial data, and good agreement was observed. Two cases including perforated distributor and complete sparger were applied to examine the flow structure through the bed. The parametric sensitivity analysis of time step, number of node, drag coefficient, and specularity coefficient was carried out. It was found that the results were more sensitive to the drag model. The results showed that the entrance configuration has significant effect on the flow structure. While the dead zones are created in both corners of the distributors, the perforated distributor generates more startup bubbles, heterogeneous flow field, and better gas–solid interaction above the entrance region due to jet formation.     

Biomass pyrolysis in a circulating fluid bed reactor for the production of fuels and chemicals

An approach for biomass flash pyrolysis in a circulating fluid bed (CFB) reactor with continuous solids regeneration is described in this study. The unit is capable of performing conventional and catalytic biomass pyrolysis with the proper solid selection. The production of improved quality liquid products in a direct step through catalytic pyrolysis is investigated in this work. Both conventional and catalytic biomass pyrolysis can be effectively performed in this CFB unit. Flash pyrolysis conditions were achieved and liquid product yields of ∼70 wt% (on biomass feed) were obtained. The effect of specific operating variables including the type of inorganic solid material and the solid/biomass ratio was established on the final liquid product quality and yield. Solid materials considered included silica sand, a commercial fluid catalytic cracking catalyst and a ZSM-5 additive. Catalytic biomass pyrolysis generally leads to the production of additional water, coke and gases compared to conventional pyrolysis. However, the obtained liquid product quality and composition is improved.     

Kinetic model for the esterification of free fatty acids from palm oil with methanol using sulfuric acid as catalyst and sensitivity analysis in tubular reactors

Industrial biodiesel production from crude palm oil (CPO) by homogeneous transesterification requires some conditioning stages. One is deodorization, where free fatty acids (FFA) are stripped out from the CPO. The FFA from the deodorizer is esterified using a homogeneous acid catalyst to produce more biodiesel and improve process profitability. This work studied the sulfuric acid-catalyzed esterification of FFA with methanol. The factors evaluated were temperature (between 40 and 60°C) and catalyst concentration (between 0.15 and 1.5 wt% based on the mixture). The parameters of a reversible second-order kinetic model were adjusted from experimental data using a genetic algorithm. The kinetic model, which adequately represents the esterification reaction, according to the Fisher–Snedecor test, was used to perform a sensitivity analysis in isothermal, adiabatic, and non-isolated continuous tubular esterification reactors using ASPEN HYSYS V10. The results showed that the highest conversion (~96%) was predicted using an isothermal reactor. However, its installation and operational costs could also be the highest. An adiabatic reactor was preferred, which optimal conversion of 94.5% was predicted at temperature, catalyst concentration, residence time, and methanol-to-FFA molar ratio of 140°C, 0.3 wt%, 47 min, and 6.7, respectively, its predicted operational cost was 0.63 dollars per biodiesel kilogram. Therefore, the adjusted and validated model has a relevant importance in the biofuel sector, not only in Colombia, but also worldwide.     

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.     

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.     

Optimal design of a thermally coupled fluidised bed heat exchanger reactor for hydrogen production and octane improvement in the catalytic naphtha reformers

The present study combines simultaneously the definition of fluidisation and process intensification (thermally coupled heat exchanger reactor) concept and determines the optimum operational conditions in both sides of the reactor, using Differential Evolution (DE) optimisation approach. The exothermic hydrogenation of nitrobenzene to aniline takes place in a set of tubular reactors which is placed inside the naphtha reactors and thermally handle the endothermic reaction of reforming. A single objective function consists of four terms including aromatic mole fraction of the reformate and hydrogen production from each reactor in the endothermic side as well as the total molar flow rate of aniline and nitrobenzene conversion in the exothermic side is defined. Seven decision variables such as inlet temperature of exothermic and endothermic sides, exothermic molar flow rates for the first and the second reactors and the number of tubes are considered during the optimisation procedure. Temperature constraints have been considered in both sides during the optimisation in order to reduce the possibility of rapid catalyst deactivation by sintering. Results show approximately 464.4 and 598.9 kg/h increase in aromatic and aniline production rates in optimised thermally coupled fluidised bed naphtha reactor (OTCFBNR) compared with non‐optimised case (TCFBNR), respectively. Such a theoretical study is necessary prior to designing new pilot plants and revamping industrial units. © 2011 Canadian Society for Chemical Engineering     

Mathematical modeling,steady state simulation,parametric analysis and optimization of SO2 capture in a countercurrent moving bed (CaO and C) reactor

The use of absorbents based on calcium for the reduction of SO₂ emissions from power plants has been studied for the last 30 years. The present work is part of a research project aimed at the development of a moving bed limestone filter. It is placed after burning in order to capture the SO₂ from the flue gases of pulverized lignite combustors. A heterogeneous mathematical model was developed for the steady‐state simulation of a gas–solid countercurrent moving bed reactor. The mathematical model was solved using the method of finite elements and gave results for the temperature and conversion profile along the reactor. Also, parametric analysis (for T_g,in, T_s,in, u_s, q_o, , , d_o, z_o) was performed and useful conclusions concerning the behavior of a moving bed reactor in different conditions were drawn. Finally, optimization of conditions was performed to give an SO₂ conversion higher than 0.95. The results are of important technological interest as a dry process in applications of SO₂ capture. © 2018 Society of Chemical Industry     

A novel process for the ethyl lactate synthesis in a simulated moving bed reactor (SMBR)

A novel approach for the synthesis of ethyl lactate using a simulated moving bed reactor was evaluated by experiments as well as by simulations. A mathematical model considering external and internal mass-transfer resistances and variable velocity due to change of liquid composition was developed to describe the dynamic behaviour of the SMBR and it was validated by the experiments performed; it was observed that the experimental results were well predicted by the model. The effect of operating parameters, as the feed composition, SMBR configuration and switching time on the SMBR performance parameters at the optimal operating points and/or reactive/separation regions was studied. It was shown that the SMBR is a very attractive technology for the production of ethyl lactate, since under appropriate conditions the lactic acid conversion can be driven to completion and productivity as high as and purity of 95% can be obtained.     

Mathematical model for the pultrusion of blocked PU–UP matrix composites

The thermokinetic behavior of blocked polyurethane (PU)–unsaturated polyester (UP)–based composites during the pultrusion of glass‐fiber‐reinforced composites was investigated utilizing a mathematical model that accounted for the heat transfer and heat generation during curing. The equations of continuity and energy balance, coupled with a kinetic expression for the curing system, were solved using a finite difference method to calculate the temperature profiles and conversion profiles in the thickness direction in a rectangular pultrusion die. A kinetic model, dP/dt = A exp(?E/RT)P^m(1 ? P)ⁿ, was proposed to describe the curing behavior of a blocked PU–UP resin. Kinetic parameters for the model were obtained from dynamic differential scanning calorimetry scans using a multiple regression technique, which was able to predict the effects of processing parameters on the pultrusion. The effects of processing parameters including pulling speed, die wall temperature, and die thickness on the performance of the pultrusion also were evaluated. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 1996–2002, 2003     

Experimental, kinetic and 2-D reactor modeling for simulation of the production of hydrogen by the catalytic reforming of concentrated crude ethanol (CRCCE) over a Ni-based commercial catalyst in a packed-bed tubular reactor

Mechanistic kinetic models were formulated based on Langmuir-Hinshelwood-Hougen-Watson and Eley-Rideal approaches to describe the kinetics of hydrogen production by the catalytic reforming of concentrated crude ethanol over a Ni-based commercial catalyst at atmospheric pressure, temperature range of 673-863 K, ratio of weight of catalyst to the molar rate of crude ethanol 3472-34722 kg cat s/kmol crude in a stainless steel packed bed tubular microreactor. One of the models yielded an excellent degree of correlation, and was selected for the simulation of the reforming process which used a pseudo-homogeneous numerical model consisting of coupled material and energy balance equations with reaction. The model was solved using finite elements method without neglecting the axial dispersion term. The crude ethanol conversion predicted by the model was in good agreement with the experimental data (AAD%=4.28). Also, the predicted concentration and temperature profiles for the process in the radial direction indicate that the assumption of plug flow isothermal behavior is justified within certain reactor configurations. However, the axial dispersion term still contributed to the results, and thus, cannot be neglected.     

Performance evaluation of batch and unsteady state fed‐batch reactor operations for the production of a marine microbial surfactant

BACKGROUND: Biosurfactants are microbially derived surface‐active and amphipathic molecules produced by various microorganisms. These versatile biomolecules can find potential applications in food, cosmetics, petroleum recovery and biopharmaceutical industries. However, their commercial use is impeded by low yields and productivities in fermentation processes. Thus, an attempt was made to enhance product yield and process productivity by designing a fed‐batch mode reactor strategy. RESULTS: Biosurfactant (BS) production by a marine bacterium was performed in batch and fed‐batch modes of reactor operation in a 3.7 L fermenter. BS concentration of 4.61 ± 0.07 g L^?1 was achieved in batch mode after 22 h with minimum power input of 33.87 × 10³ W, resulting in maximum mixing efficiency. The volumetric oxygen flow rate (K_La) of the marine culture was about 0.08 s^?1. BS production was growth‐associated, as evident from fitting growth kinetics data into the Luedeking‐Piret model. An unsteady state fed batch (USFB) strategy was employed to enhance BS production. Glucose feeding was done at different flow rates ranging from 3.7 mL min^?1 (USFB‐I) to 10 mL min^?1 (USFB‐II). USFB‐I strategy resulted in a maximum biosurfactant yield of 6.2 g l^?1 with an increment of 35% of batch data. The kinetic parameters of USFB‐I were better than those from batch and USFB‐II. CONCLUSION: Comparative performance evaluation of batch and semi‐continuous reactor operations was accomplished. USFB‐I operation improved biosurfactant production by about 35% over batch mode. USFB‐I strategy was more kinetically favorable than batch and USFB‐II. © 2012 Society of Chemical Industry