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.     

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.     

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.     

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.     

Post-combustion CO2 capture process: Equilibrium stage mathematical model of the chemical absorption of CO2 into monoethanolamine (MEA) aqueous solution

This paper deals with the modeling and optimization of the chemical absorption process to CO₂ removal using monoethanolamine (MEA) aqueous solution. Precisely, an optimization mathematical model is proposed to determine the best operating conditions of the CO₂ post-combustion process in order to maximize the CO₂ removal efficiency. Certainly, the following two objective functions are considered for maximization: (a) ratio between the total absorbed CO₂ and the total heating and cooling utilities and (b) ratio between total absorbed CO₂ and the total amine flow-rate.Temperature, composition and flow-rate profiles of the aqueous solution and gas streams along the absorber and regenerator as well as the reboiler and condenser duties are considered as optimization variables. The number of trays or height equivalent to a theoretical plate (HETP) on the absorber and regenerator columns as well as the CO₂ composition in flue gas are treated as model parameters. Correlations used to compute physical-chemical properties of the aqueous amine solution are taken from different specialized literature and are valid for a wide range of operating conditions. For the modeling, both columns (absorber and regenerator) are divided into a number of segments assuming that liquid and gas phases are well mixed.GAMS (General Algebraic Modeling System) and CONOPT are used, respectively, to implement and to solve the resulting mathematical model.The robustness and computational performance of the proposed model and a detailed discussion of the optimization results will be presented through different case studies. Finally, the proposed model cannot only be used as optimizer but also as a simulator by fixing the degree of freedom of the equation system.     

Synthesis of Fe2O3-coated and HCl-treated bauxite ore waste for the adsorption of arsenic (III) from aqueous solution: Isotherm and kinetic models

The present work has focused on the removal of arsenic (III) using two effective adsorbents such as red mud treated with HCl and coated with Fe₂O₃. Adsorption of As (III) was performed by the function of pH, adsorbent dose, contact time, initial ion concentration, and the appropriate conditions for adsorption were determined. The characterization studies of the adsorbent were analyzed using X-ray diffraction, X-ray fluorescence, Brauner–Emmett–Teller, scanning electron microscope, and FTIR spectroscopy. The result of the studies shows that the adsorbent is suitable for the effective removal of As (III) ions. Batch adsorption process showed that the maximum adsorption occurred at Fe₂O₃-coated red mud. The equilibrium data were well fitted to the nonlinear Langmuir isotherm model and the maximum adsorption capacity (q_m) of Fe₂O₃-coated red mud was found to be 21.85?mg?g^?1 which indicates that Fe₂O₃-coated red mud had more adsorption capacity. In the Freundlich isotherm, the experimentally obtained n value of Fe₂O₃-coated red mud was 2.393 which indicates the favorable adsorption of As (III) on the adsorbent. Dubinin–Radushkevich isotherm confirms that the adsorption process is physical in nature. Furthermore, the adsorption kinetic studies followed the pseudo-first-order model. All the results concluded that Fe₂O₃-coated red mud can be considered as a cost-effective and potential adsorbent for As (III) removal.     

Development of a model for the anodic behavior of T60 titanium in chlorinated and oxygenated aqueous media. Application to the specific conditions of hydrothermal oxidation (1 MPa<pressure<30 MPa, 20 °C<temperature<400 °C)

This work evaluates the anodic electrochemical behavior of titanium metal in hydrothermal oxidation conditions (up to 400 °C and 28 MPa) in chlorinated media in order to estimate the supercritical water oxidation reactors reliability for the treatment of less than 10% organic-waste waters. The titanium room temperature dissolution mechanism in chlorinated acidic medium (pH<0) is not fundamentally modified by oxygen. Deduced from the ‘current-potential’ and ‘valence-potential’ curves, it is based on four crucial elementary steps leading to two branches: a so-called active branch corresponding to a trivalent dissolution (its effect is inversely proportional to the pH), and a passive branch (TiO₂ oxide formation with a very limited tetravalent dissolution). In hydrothermal oxidation (pH>1), only the second branch is effective. The titanium protection is directly related to the oxide stability in high pH systems. The mechanism model is expressed in terms of ‘current-potential’ laws, which provide kinetic parameters using optimization calculations. The different elementary steps reaction rates were estimated as well as the evolution of the reaction intermediates coverage ratios with the potential. The quantification of each elementary step was performed to understand and/or orient the materials behavior according to different factors (pH, chloride ions contents, potentials…).     

Optimizing ethanolic hot compressed water (EHCW) cooking as a pretreatment to glucose recovery for the production of fuel ethanol from oil palm frond (OPF)

The objective of this work is to study the effects of reaction temperature, reaction time and ethanol percentage on the pretreatment of oil palm fronds (OPF) using ethanolic hot compressed water (EHCW) to enhance sugar recovery in enzymatic hydrolysis. A central composite rotatable design was used to optimize the pretreatment process conditions. All variables (individual and interactive) were found to affect glucose recovery significantly. A quadratic polynomial equation was modelled for glucose recovery by multiple regression analysis using response surface methodology (RSM). Using a 10 bar pressurized reactor, the optimum conditions for pretreatment of OPF were obtained at 180 °C, 42 min and EtOH wt.% of 26.4%. At the optimum conditions, the predicted glucose recovery was 88.48%. Experimental verification of the optimum conditions gave glucose recovery well within the estimated value of the model.