General rate equations and their applications for cyclic reaction networks: pyramidal systems

The King-Altman-Hill graphic method has been widely used to derive the rate laws of enzymatic reactions, but the compilation of all the possible pathways is very time-consuming and the reaction rates are not given explicitly. In this study, the network reduction and Y-to-delta transformation techniques were systematically used to derive the general rate equations for pyramidal reaction networks in homogeneous catalysis. The enzymatic reaction of 7,8-dihydrofolate and NADPH to form 5,6,6,8-tetrahydrofolate and NADP, catalyzed by dihydrofolate reductase was taken as an example to illustrate the application of the general reaction rate equations. The calculated overall reaction rate was compared with that obtained from the exact solution by matrix algebra and those obtained from the King-Altman-Hill graphic method.     

General rate equations and their applications for cyclic reaction networks: multi-pathway systems

Many chemical reactions of industrial importance involve complex reaction pathways and networks; and the determinations of the reaction rate laws are very difficult. The accurate or proper rate expression is the most desired information in design phase however. In this study, the network reduction technique and the Bodenstein approximation of quasi-stationary behavior of reaction intermediates were systematically applied to derive general rate and instantaneous rate ratio equations for multi-pathway reaction networks in homogeneous catalysis or enzyme system. Multiple small reaction cycles in a main cycle, and multiple-pathways stemming from an intermediate and ending at different nodes in a cycle were considered. The general rate and rate ratio equations derived in this study are applicable for most homogeneous catalytic reactions and enzymatic reactions. Two examples of multi-pathway cyclic enzyme reaction were used to illustrate the applications of the general rate and rate ratio equations for network elucidation.     

Nanotechnology: applications and potentials for heterogeneous catalysis

Nanotechnology offers the potential to design, synthesize, and control at nanometer length scale. While the catalysis community has many techniques at their disposal to synthesize catalytic materials at such a scale, the ability to fully design and control is still lacking. Examples are presented to illustrate what can nanotechnology do for heterogeneous catalysis to help achieve the goal of designing catalysts for perfect selectivity in a chemical reaction. Some current state-of-the-art approaches and potential limitations are discussed. Some examples of what can catalysis do for nanotechnology are also presented. However, this aspect is much less studied, although it offers rich opportunities for the catalysis community.     

Interaction of kinetics and internal diffusion in complex catalytic three-phase reactions: Activity and selectivity in citral hydrogenation

Kinetics and mass transfer effects were studied for the complex catalytic liquid-phase hydrogenation in a semi-batch reactor, where finely dispersed and larger catalyst particles were used. Citral was used as a model molecule. The intrinsic kinetics was determined with crushed catalyst particles at and at pressures ranging from 10 to 40 bar. A kinetic model was proposed and successfully fitted to the experimental data. In order to elucidate the influence of internal diffusion on the selectivity and activity in complex reactions, citral hydrogenation was performed with larger catalyst pellets, in a pressurized autoclave equipped with a catalyst basket. As expected, the activity decreased with increasing catalyst particle size. The product distribution was shifted from the primary hydrogenation product (citronellal) to the fully hydrogenated end product (3,7-dimethyloctanol) as the catalyst particle size was increased. The concentrations of the secondary hydrogenation products were minor throughout the experiment. A complete reaction-diffusion model was developed for large pellets and complex reactions systems.     

Analytical expression for the non-isothermal effectiveness factor: the nth-order reaction in a slab geometry

The problem of calculating the effectiveness factor for a porous slab of catalyst pellet under non-isothermal conditions has been revisited. An exact formal analytical solution was obtained for a nth-order (integer n?0), exothermic and irreversible chemical reaction. Numerical calculations where performed, and an analytical formula was obtained for the very fast reaction limit. In addition, a fairly simple formula, which was called the low beta approximation, was developed and tested to be valid for low values of the thermicity group β?0.1.     

Benzene selective hydrogenation over supported Ni (nano-) particles catalysts: Catalytic and kinetics studies

This report aims to reduce the benzene in a mixture of benzene and toluene as a model reaction using catalytic hydrogenation. In this research, we developed a series of catalysts with different supports such as Ni/HMS, Ni/HZSM-5, Ni/HZSM5-HMS, Ni/Al_2O_3 and Ni/SiO_2. Kinetic of this reaction was investigated under various hydrogen and benzene pressures. For more study, two kinetic models have also been selected and tested to describe the kinetics for this reaction. Both used models, the power law and Langmuir–Hinshelwood, provided a good fit toward the experimental data and allowed to determine the kinetic parameters. Among these catalysts, Ni/Al_2O_3 showed the maximum benzene conversion(99.19%) at 130 °C for benzene hydrogenation. The lowest toluene conversion was observed for Ni/SiO_2. Furthermore, this catalyst presented high selectivity to benzene(75.26%)at 130 °C. The catalytic performance(activity, selectivity and stability) and kinetics evaluations were shown that the Ni/SiO_2 is an effective catalyst to hydrogenate benzene. It seems that the surface properties particularly pore size are effective parameter compared to other factors such as acidity and metal dispersion in this process.     

Aqueous route for mesoporous metal oxides using inorganic metal source and their applications

In this paper, we report a synthetic route for mesoporous metal oxides from inorganic metal sources in aqueous media. This synthesis route offers a versatile, low cost and environmental friendly method to produce mesoporous metal oxides that have very high surface areas. As an example, the synthesis of iron oxide is described in detail. Synthesis conditions including aging time, aging temperature and amount of urea were varied to find the optimal synthesis conditions. We found that recycling the Cetyltrimethylammonium Bromide (CTAB) template is possible when the amount of urea is reduced to stoichiometric. The mesoporous metal oxides made under these conditions are self assemblies of leaf-like single crystal sub-units with randomly distributed mesopores embedded into the crystals. As a result of the crystalline nature, these mesoporous metal oxides have high thermal stabilities and their applications as gas sensors and CO disproportionation catalysts indicate promising aspects of these materials.     

PBT结晶速度方程及其应用

用 DSC法研究聚对苯二甲酸丁二酯 ( PBT)的结晶动力学 ,分别在 468.15 ,471.15 ,473.15 K的等温条件下进行了 PBT等温结晶实验 ,从 PBT等温结晶曲线和等速降温结晶曲线得到在不同温度条件下的结晶动力学数学模型。运用模型对不同 PBT试样进行分析 ,能较好地解释不同品质 PBT的结晶行为     

Catalytic Carbon Gasification: Review of Observed Kinetics and Proposed Mechanisms or Models - Highlighting Carbon Bulk Diffusion

Carbon gasification is an important reaction in industrial processes, energy generation processes, and diesel soot reduction. The observed kinetics are briefly reviewed, both in non porous and porous materials. The cases of combustion of graphite, coal, char, coke and diesel fuel soot are compared. A review of the proposed mechanisms is done with an emphasis in carbon bulk diffusion, using Fick's Law to articulate the carbon bulk diffusion step with the other steps. The relevance of the Hedvall effect and the Tammann temperature in transition metals is addressed, including a discussion about the relation between mechanistic models and phenomenological models.     

Use of stirred batch reactors for the assessment of adsorption constants in porous solid catalysts with simultaneous diffusion and reaction. Theoretical analysis

A simple, pseudo-equilibrium model was derived for a catalytic system with a first order chemical reaction and simultaneous diffusive and adsorptive processes, in order to assess the corresponding kinetics and Henry law's-type adsorption parameters. Solutions from this model were compared to exact solutions from a more detailed, general model. It was shown that under most of the experimental conditions used in stirred batch reactors and the usual model considerations, it is only possible to assess apparent adsorption parameters. Also, we observed that a stable relationship between the concentrations in the gas and solid phases is reached. The error produced in assuming that the apparent adsorption constant is the real one was calculated to be very important. The value of the apparent adsorption constant depends on various system properties and experimental conditions, such as the Thiele modulus, the amount of catalyst and the contact time. The ratio between the apparent and real adsorption constants was shown to be the transient effectiveness factor at any moment. This ratio reaches a maximum value for the pseudo-equilibrium state, that is always larger than the steady-state effectiveness factor, becoming closer as long as the system's adsorption capacity decreases. The analysis determines the operative conditions to reduce the parametric correlation. Also a criterion for the applicability of usual approximations in the assessment of kinetics and equilibrium adsorption parameters in porous solid catalysts by means of pulse injection methods is established.     

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.     

Electrocatalytic dechlorination of a PCB congener at a palladized granular-graphite-packed electrode: Reaction equilibrium and mechanism

Our previous study on the electrocatalytic dechlorination of 2-chlorobiphenyl at a Pd-loaded granular graphite-packed electrode demonstrated that the process did not follow the first-order kinetics. The rate constant varied with the applied potential at the beginning, but later became irrelevant to the potential. The electrocatalytic kinetic was investigated in this study, in which several experiments were conducted to dechlorinate 2-chlorobiphenyl using a Pd-loaded granular graphite-packed electrode at different potentials and in methanol–water solutions. Analysis of the experimental results reveals that the electrocatalytic process had reached equilibrium in these experiments. The apparent equilibrium constants, as well as the rate constants for the overall forward and backward reactions, were related to the applied potential. These relationships follow the Tafel equation, but the apparent charge transfer coefficients are very small values. The potential dependence of the overall rate constants suggests a reaction mechanism in which the electrocatalytic reaction is the rate-determining step. The influence of methanol on (together with the potential dependence of) the overall rate constants and the apparent equilibrium constant suggests a Langmuir–Hinshelwood mechanism.     

Using H-titanate nanofiber catalysts for water disinfection: Understanding and modelling of the inactivation kinetics and mechanisms

The H-titanate nanofiber catalyst (TNC), which has a favourable morphological structure for mass transfer and energy access, was proven as a promising alternate titanium dioxide (TiO₂) carrier for photo-inactivation of a sewage isolated E. coli strain (ATCC 11775). This study revealed that the TNC loading is a key process parameter that radically influenced the photo-inactivation of bacteria in an annular slurry photoreactor (ASP) system. Variation in the TNC loadings was found to have a considerable impact on the dissolved oxygen (DO) concentration profiles and subsequently, on the photo-inactivation rates of bacteria in the ASP system. The photo-inactivation reaction in the ASP system was found to exhibit three different bacterial inactivation regimes of shoulder, log-linear and tailing. Resultant photo-inactivation kinetics data was evaluated using both empirical and mechanistic bacterial inactivation models. The modified Hom model was found to be the best empirical model that can represent the sigmoid-type bacterial inactivation pattern. An interesting correlation between the TNC loadings and DO concentration profiles was also established. From the correlation, it was found necessary to integrate a DO limiting reactant term in the newly proposed mechanistic Langmuir–Hinshelwood model to describe the bacterial inactivation mechanisms under two different TNC loading conditions of sub-optimal and optimal, respectively.     

Modeling for the catalytic coupling reaction of carbon monoxide to diethyl oxalate in fixed-bed reactors: Reactor model and its applications

A two-dimensional (2D) pseudo-homogeneous reactor model was developed to simulate the performance of fixed-bed reactors for catalytic coupling reaction of carbon monoxide to diethyl oxalate. Reactor modeling was performed using a comprehensive numerical model consisting of two-dimensional coupled material and energy balance equations. A power law kinetic model was applied for simulating the catalytic coupling reaction with considering one main-reaction and two side-reactions. The validity of the reactor model was tested against the measured data from different-scale demonstration processes and satisfactory agreements between the model prediction and measured results were obtained. Furthermore, detailed numerical simulations were performed to investigate the effect of major operation parameters on the reactor behavior of fixed bed for catalytic coupling reaction of carbon monoxide to diethyl oxalate, and the result shows that the coolant temperature is the most sensitive parameter.     

Asymptotically exact driving force approximation for intraparticle mass transfer rate in diffusion and adsorption processes: nonlinear isotherm systems with macropore diffusion control

An asymptotically exact nonlinear driving force model of intra-particle mass-transfer rate for nonlinear isotherm systems with macropore diffusion control is presented. The obtained expression is compared with the solutions of the Fickian diffusion and adsorption model and excellent accuracy over the entire time (fractional uptake) domain is demonstrated. In the case of an irreversible isotherm the model reduces to the equations resulting from the shrinking core model a fact that guarantees its accuracy for highly nonlinear systems. The high accuracy of the model is further demonstrated by comparison with experimental data under various operational conditions.     

Efficient numerical integration of stiff differential equations in polymerisation reaction engineering: Computational aspects and applications

The modelling of the full molecular weight distribution in addition polymerisation gives rise to very large dimension (10³–10⁶) systems of ordinary differential equations, often exhibiting serious stiffness issues. This article summarises a methodology recently implemented by our group, in which the QSSA is applied on the fast dynamic species in order to reduce the stiffness, and then the remaining equations are solved by computationally inexpensive explicit algorithms (such as Euler). Specific features of the methodology are illustrated by application to the academically and industrially relevant systems of controlled radical polymerisation (RAFT and NMP cases) and coordination catalysis polymerisation. © 2012 Canadian Society for Chemical Engineering     

Simple three parameter equations for correlating liquid phase compositions in subcritical and supercritical systems

Two Chrastil type expressions have been developed to model the solubility of supercritical fluids/gases in liquids. The three parameter expressions proposed correlates the solubility as a function of temperature, pressure and density. The equation can also be used to check the self-consistency of the experimental data of liquid phase compositions for supercritical fluid–liquid equilibria. Fifty three different binary systems (carbon-dioxide + liquid) with around 2700 data points encompassing a wide range of compounds like esters, alcohols, carboxylic acids and ionic liquids were successfully modeled for a wide range of temperatures and pressures. Besides the test for self-consistency, based on the data at one temperature, the model can be used to predict the solubility of supercritical fluids in liquids at different temperatures.     

Zeolite-based materials for novel catalytic applications: Opportunities, perspectives and open problems

Zeolites and related materials (including a wide range of microporous and mesoporous materials with ordered pore structure) have been one of the areas in the field of materials and catalysis with the largest impact on science, technology and industrial processes. We discuss here some recent developments in this field, with particular references how to tailor and design zeolite and related material properties to control/enhance the catalytic performances. Four main topics have been addressed. (i) The recent progress and perspectives in the field of tailored syntheses, with selected examples showing the trend and prospects to develop new structures, control the location of active sites, and the crystal size and morphology, including nanoarchitecture of the final catalysts. (ii) The development and prospects of two-dimensional zeolites presenting an extended view/concept of zeolite structures integrating the classical 3D frameworks and the various lamellar forms. (iii) The progresses in the design and synthesis of hierarchical zeolites, with discussion on the still existing challenges related to the synthesis, characterization and catalytic application. (iv) Novel opportunities and needs in terms of zeolite multifunctional design for catalytic applications, with a discussion of the critical issues related to the use in the field of fine chemicals, organic industrial syntheses and biorefinery, and the prospects for the use in two novel challenging areas of the direct conversion of CO₂ to light olefins and methane to methanol.