Effect of catalyst dispersion on performance of slurry bubble column reactors

Using the sedimentation-diffusion model for catalyst dispersion the steady-state performance of semi-batch bubble column reactors has been studied over a wide range of mass transfer and reaction groups for reactions that are described by power law and Langmuir-Hinshelwood (L-H) type of kinetics. The effect of catalyst dispersion on conversion is found to be a complex function of mass-transfer and reaction parameters. Nonuniform catalyst distribution has a detrimental effect on the values of conversion for systems following nth-order kinetics. However, the use of a L-H rate form predicts improved conversions for some values of model parameters in the presence of solid dispersion.Also the reactor model accounts exactly for volume change effects during reaction. It is found that volume contraction enhances conversion for reactions following the nth-order kinetics, but that the opposite is possible with the L-H kinetics.     

Glycerol ethers synthesis from glycerol etherification with tert-butyl alcohol in reactive distillation

This paper presents a study of glycerol etherification with tert-butyl alcohol catalyzed by Amberlyst 15 in reactive distillation (RD). A thermodynamic analysis is firstly investigated by applying three group contribution methods, to determine the equilibrium composition by minimization of the Gibbs free energy and to compare the predicted values against measured data. Next, the kinetic model parameters are regressed by matching measured data from an autoclave reactor. The activity based Langmuir-Hinshelwood model is found to give the best representation of the reaction rate data. The regressed kinetic rate expressions are also compared against independently measured data in fixed bed reactors reported in the literature and found to give a good match. Finally, using the developed models, it is shown by simulation as well as verification by experiments, that the suitable RD configuration for the production of glycerol ethers in RD is the one consisting of 6 rectifying stages and 6 reaction stages without stripping stage.     

Sensitivity analysis applied to independent parallel reaction model for pyrolysis of bagasse

The independent parallel reaction model (IPR model) is applied in this work to study the slow dynamic pyrolysis of sugarcane bagasse, based on a thermogravimetric analysis of three ranges of particle diameters. The kinetic parameters and mass fraction of each principal pseudo-component of biomass (hemicellulose, cellulose and lignin) are estimated using the Differential Evolution Algorithm. A comparison of the estimated mass fractions and Arrhenius parameters against experimental values reported in the literature shows good agreement. The influence of various kinetic parameters of the model is also analyzed by means of sensitivity studies using derivative methods based on the DASPK 3.0 code. The results of the relative parametric sensitivity indicate that activation energies affect bagasse conversion more strongly than other parameters, followed by the pre-exponential factors of Arrhenius equation and mass fractions. The sensitivity of the IPR kinetic model to the orders of reaction is very slight.     

A general integral method for the determination of empirical reaction rates and parameters

A general procedure for the determination of empirical rates and kinetic parameters of irreversible, constant volume reactions is presented which is clearly superior to the conventional methods of kinetic analysis. By nonlinear regression of the integrated potential rate equation for stoichiometrically independent reactions of n the order, the empirical pre-exponential factor, activation energy, and reaction order are obtained. The regression equation relates explicitly the final concentration of the reference component not only to the time parameter of the reaction but also to the initial concentration. This includes an integral method for the determination of reaction orders in concentration. Two limiting cases are treated - the stoichiometric mixture of reactants and a mixture with one reactant in large excess. By analysis of standard Hougen-Watson rate models the dependence of empirical reaction orders on experimental conditions and simulated rate parameters is evaluated. By grouping the data into ranges of monotonous concentration change, conversion rates and rate parameters of reactions with changing volumes are calculated in a less rigorous deduction. The simplified interpretation of published experimental data is demonstated for the total oxidation of methane on Pd-catalysts and the dehydrogenation of cyclohexanol on ZnO.     

锰改性活性焦烟气脱硫本征动力学

利用浸渍法制备了锰改性的活性焦,在消除内外扩散的前提下,用等温积分管式反应器测试了其催化氧化脱硫性能。通过对动力学实验数据分析,运用Langmuir-Hinshelwood和Eley-Rideal模型,推导出了其本征动力学方程,并对模型参数进行了估值。结果表明,活性焦经锰改性后,比表面和孔容均有不同程度的增加,脱硫效率较改性前得到提高。经统计检验,Eley-Rideal模型为较优模型,模型计算值能与实验数据吻合,平均偏差4.3%,反应活化能为40.859 kJ/mol。     

A Film Diffusional Effect on the Apparent Kinetic Parameters in Packed-Bed Immobilized Enzyme Reactors

A film diffusional effect on the apparent kinetic parameters in packed-bed reactors containing the enzyme immobilized on the surface of a nonporous support was investigated. A comparison of the plug-flow reactor model equation, expressed analytically in terms of the apparent kinetic parameters, with experimental data showed that the conventional linearized plot based on the reactor model equation was essentially nonlinear. Simulations for the apparent kinetic parameters were made using the intrinsic kinetic parameters and volumetric mass-transfer coefficient previously determined from experimental data. Consequently, the apparent kinetic parameters were found to decrease monotonically with the increase of liquid flow rate. On the other hand, with the increase of reactor-inlet substrate concentration, these constants first increased, passed through a maximum, and finally decreased toward their respective intrinsic values. © 1997 SCI.     

Kinetics and slurry-type reactor modelling during catalytic hydrogenation of o-cresol on Ni/SiO2

The effect of kinetic parameters (reactant concentrations, temperature) was investigated on the initial reaction rate for the catalytic hydrogenation of o-cresol on Ni/SiO₂, carried out in a batch or semi-batch agitated slurry-type reactor.

The data were interpreted by a kinetic model based on the Langmuir-Hinshelwood mechanism with non-dissociative and non-competitive adsorption of o-cresol and hydrogen on different sites, where the limiting step is due to the reaction of adsorbed reactants. The activation energy (E_a = 82 kJ/mol) is in good agreement with previous literature values reported for the catalytic hydrogenation of phenol.

Taking into account thermodynamic (solubilities) and mass transfer kinetics (k_La) data measured in situ, the integral reactor conversion rate of this three-phase catalytic reaction was simulated accurately in the physical regime by taking into account external and internal mass transfer resistances.     

多孔催化剂有效因子的近似分析解(Ⅱ)近似分析解与数值解的比较

根据本文第Ⅰ部分所提出的多孔催化剂有效因子近似计算式,针对不同形式的幂函数型动力学方程和双曲型动力学方程,计算了等温下Thiele模数不同时非一级反应的有效因子,并且用数值方法求出相应条件下的有效因子以作比较.大量的计算结果证明所提出的近似计算式较之文献上已有的近似式,不但精度高,而且适用范围广.同时近似式中参数估值简便,克服了以往研究者所提出的式子中这方面所存在的困难.     

Estimation of kinetic parameters during pyrolysis from linearized DTA traces

A method which empolys the linearization of DTA traces is presented for the estimation of kinetic parameters during polymer pyrolysis. By this method, two DTA traces are used, changes in mechanism with conversion may be detected, and it is not necessary to measure areas prior to evaluating activation energy and reaction order. The method is applied to polyethylene, polypropylene, and polystyrene. The agreement between observed and reported values of kinetic parameters is good. Advantages and disadvantages of the method are discussed.     

Reaction-induced crystallization kinetics during the anionic polymerization of ϵ-caprolactam

The kinetics of crystallization during anioiiic polymerization of ?-caprolactam was studied by the adiabatic temperature rise method, A new kinetic model for the non-isothermal crystallization was derived and the possibility of its application was Investigated. By evaluating the parameters in the model for the given adiabatic system, the crystallization behavior during the; polymerization process was analyzed. The experimental and calculated temperature rise showed a very good agreement, which indicated that the model equation was appropriate to describe the non-isothermal reaction-induced crystallization kinetics in this study. The melting temperature of the reaction mixture increased steadily due to the change of the crystal structure with conversion. The equilibrium crystallinity was higher when the crystallization started in the presence of unreacted monomer than when the crystallization occurred after polymerization was completed. At lower conversion, the reaction mixture was less viscous, a condition that made transport to the liquid-crystal interlace easier, and thus the activation energy for transport decreased. On the other hand, the increasing mobility resulted in difficulty in forming stable nuclei arid the free energy of nucleation increased.     

Reactor sizing for butane steam reforming over Ni and Ru catalysts

We obtained kinetics data on steam reforming of butane and calculated the appropriate reactor size based on the kinetics data. Using commercial Ni and Ru catalysts, steam reforming reactions of butane were performed while changing the reaction temperature and partial pressure of reactants. After comparing the power law model and the Langmuir-Hinshelwood model by using the kinetics data obtained from the experiment, it is revealed that the reaction rate could be determined by both models in the reforming reaction of butane over commercial Ni and Ru catalysts. Also, calculation of the steam reforming reactor size using a PRO/II simulation with a kinetic model equation showed that the reactor size using the Ni catalyst is smaller than that with the Ru catalyst to obtain the same conversion.     

Numerical Determination of the Thermal Diffusivity and Kinetic Parameters of Solid Explosives

The thermal diffusivity and the kinetic parameters (activation energy and pre-exponential factor) of explosive substances are determined numerically using an iterative method. A numerical modelling based on a finite difference approximation of the equation of unsteady heat allows simulations of the thermal behaviour of the product in the absence of any reaction and phase change. The comparison of simulation and measured results allows the convergence towards the thermal diffusivity of the substance under test. The principle is the same for kinetic parameters. In this latter case, the modelling involves the equation of unsteady heat flow with an internal energy source. The governing partial differential equation is processed using Zinn and Mader's method.     

A LINEAR APPROXIMATION METHOD TO EVALUATE ISOTHERMAL EFFECTIVENESS FACTORS

A linear approximation method to estimate effectiveness factors for isothermal catalytic pellets has been developed. The method is based on the Taylor series expansion of the reaction rate expression above the surface particle concentration for the key component. The application of the method to reaction systems with nonlinear kinetics yields simple analytic expressions for the effectiveness factor equivalent to that found for first order irreversible reaction. The effectiveness factor expressions obtained depend of one parameter analogous to the Thiele modulus. In this work we report the results obtained for a Monod type kinetic equation. The effectiveness factors predicted are compared with those obtained from the numerical solution of the exact boundary value problem. The error is negligible at low Thiele moduli and as this parameter is increased the error grows, reaching an asymptotic value at high Thiele moduli. For the example presented, the error is below 10%. The available results indicate that nonlinear cases such as Langmuir-Hinshelwood type of equations can be treated successfully using the method developed.     

Rubber modified epoxy resin. I: Cure kinetics and chemorheology

The curing and vitrification effect during the reaction of ATBN modified epoxy resin was studied through the dynamic differential scanning calorimetry method and a new reaction kinetic equation containing generalized WLF equation was developed to describe the reaction rate at both glassy and rubbery state. An autocatalytic mechanism was found to describe adequately the cure kinetics of the rubber modified epoxy resin and the overall order of reaction was assumed to be 2. The kinetic parameters were determined from the DSC data through the Marquardt's multivariable nonlinear regression method and Runge–Kutta integration technique. The presence of rubber indicated minor effect on the cure kinetics of epoxy resin. The Arrhenius type viscosity function was employed to establish a relationship between viscosity data measured by RMS and chemical conversion calculated from the reaction kinetic equation.     

Mechanism and Kinetics of the Decomposition of Solids by a Thermogravimetric Method

According to Doyle, the thermogravimetric curve of a decomposition reaction can be expressed by the equation log g(α)–log p(x) = B. The variable x depends on the temperature Tα, at which the fraction of the initial compound decomposed is α. Both g(α) and p(x) depend on temperature; however, B is independent of temperature. The trial-and-error method allows, for a given thermogravimetric curve, the determination of the g(α) and p(x) functions fitting the equation and thus an estimation of the probable mechanism of the reaction and of other kinetic parameters (activation energy and frequency factor). To facilitate the analysis of experimental data, a table of log g(α) values for various decomposition mechanisms and a plot of-log p(x) vs T for various activation energies are presented. The use of the table and the diagram is described.     

Synthesis of esters: Development of the rate expression for the Dowex 50 Wx8-400 catalyzed esterification of propionic acid with 1-propanol

The kinetics of the esterification reaction of propionic acid with 1-propanol over the ion-exchange resin Dowex 50Wx8-400 has been studied in this investigation. Kinetic experiments were conducted using a 1 L Lab-Max system at a stirrer speed of 900 rpm over a temperature range of 303.15 -333.15 K. The catalyst loading was varied from 10 to 60 g dry cat/L and acid to alcohol molar ratios of 1:1, 1:2, 1:4, 2:1 and 4:1 were employed. The equilibrium constants for this reaction were determined in separate experiments at 303.15, 313.15 and 323.15 K. The values were equal to 33.18, 30.62 and 28.37, respectively, with a standard enthalpy change of reaction of 6.4 kJ/mol. These values show the reaction to be mildly exothermic. It was found that both external and internal diffusion limitations did not affect the overall reaction rate. The conversion of propionic acid increased with increasing temperature and catalyst loading and decreased with increasing initial mole fraction of acid. The increase in chain length of acid or alcohol or branching had a retarding effect on the conversion. Several kinetic models were tested to correlate the kinetic data, the pseudo-homogeneous (P-H) model, the Eley-Rideal (E-R) model, the Langmuir-Hinshelwood (L-H) model, the modified Eley-Rideal (M-E-R) model and the modified Langmuir-Hinshelwood (M-L-H) model. In all models, the activity coefficients were estimated using UNIFAC to account for the non-ideal thermodynamic behavior of reactants and products. A correction factor for the resin affinity for water (α) was used in both M-E-R and M-L-H models. The above models predicted the kinetic behavior of the studied system with an overall error ranging from 1.65% to 13.32%. Water was found to be more strongly adsorbed than other species present in the system. The M-E-R model between adsorbed 1-propanol and non-adsorbed propionic acid which assumes surface reaction as the rate controlling step, with α equal to 2, was found to be the best model with the least overall error (1.65%). The activation energy for the esterification was estimated to be 67.3 kJ/mol by this model.     

Kinetics and mechanism of deactivation by fouling of a silica-alumina catalyst in the gaseous phase dehydration of isoamyl alcohol

The kinetics and mechanism of the deactivation by fouling of a silica-alumina catalyst in the dehydration of isoamyl alcohol in gas phase have been investigated. It has been found that deactivation takes place in series with the main reaction by coverage of active sites. The kinetic equation of deactivation is of the Langmuir-Hinshelwood type, and the parameters have been determined from the data obtained in an isothermal reactor.     

A numerical analysis of rate data for packed bed reactors in gas-solid reaction systems

A numerical solution of the pseudo-steady state governing equations on the basis of the Langmuir-Hinshelwood type rate equation was obtained by the approximate finite difference method in packed bed reactors for gas-solid reaction system. It was proved that the numerical method has good accuracy compared with the strict solution in the special case that the reaction rate can be represented by the first-order kinetics in terms of gaseous reactant and the effectiveness factor is unity druing the reaction. The numerical method is proposed to predict the transient of exit-gas compositions of a packed bed reactor used for gas-solid reaction systems. The exit-gas composition can be predicted from the conversion data of a single particle with varying reaction time. The present method can be easily applied to the systems involving adsorptive gaseous reactants and complex reaction behavior with structural changes of particles.     

Comparative study of the cure kinetics of an unsaturated polyester resin using different procedures

The cure kinetics of an unsaturated polyester resin were studied by differential scanning calorimetry (DSC), and different dynamic and isothermal procedures were compared. It was established that the isothermal kinetic analysis through the isoconversional adjustment lnt = A + E/RT is the method that offers the most accurate results for unsaturated polyester resin cure kinetics. From this comparative study it was noted that the activation energy not only varies according to the degree of conversion but also according to the method used to evaluate the kinetic parameters. Furthermore, it was shown that the activation energy cannot be separated from the other adjustment parameters, so the different kinetic procedures used are not generally comparable. Different methods of evaluating the degrees of conversion α and the reaction rates dα/dt according to the experimental reaction heat were also studied. It was found that the method used has a strong influence on the values of α and dα/dt, but only a slight one on the kinetic parameters.     

Cure kinetics of methacrylate-type resin that include cyclohexane moiety

Two methacrylate-type resin including cyclohexane moiety were synthesized and characterized. The curing characteristics of these resins were investigated according to the change of thermal initiator. An autocatalytic kinetic reaction occurs in these systems, and the kinetic parameters of all systems were reported in terms of generalized kinetic equation that considered the diffusion term. It can be shown that the reaction conversion rate of one methacrylate-type resin (NC-9110-MA) is faster than another resin (EHPE-3150-MA), regardless of the kinds of thermal initiator, which is attributed to the reaction rate constant increases of NC-9110-MA with lower activation energy compared with EHPE-3150-MA. It can be seen that the conversion reaction rate of these resin systems with BPO as thermal initiator at low temperature is higher than those with AIBN. A main factor of reaction conversion rate increase for the NC-9110-MA resin system is a reaction rate constant; however, that for the EHPE-3150-MA resin system is a total reaction order. These resin with BPO as thermal initiator represent a lower cure reaction activation energy and collision frequency factor than those with AIBN.