THE LAMINAR FLOW TUBULAR REACTOR WITH HOMOGENEOUS AND HETEROGENEOUS REACTIONS I. Integral Equations for Diverse Reaction Rate Regimes

Design equations for non-isothermal Laminar Flow Tubular Reactors (LFTRs) with homogeneous and heterogeneous - at the reactor wall - reactions with arbitrary kinetic equations have been satisfactorily treated transforming the original P.D.E. problem into a system of integral equations. The kernels of the integral operators are related to an eigenvalue problem which does not depend on the kinetic equations; this avoids repetitive computational effort in the treating of different reaction kinetics.

To render a more efficient numerical treatment and according to the governing reaction rate regime, modified expressions of the general solution were obtained was follows: (i) a solution with kernels depending only on the diffusion and convective times was obtained for a low reaction regime; (ii) another solution with kernels including the reaction lime, besides the diffusion and convective ones, was necessary for a fast reaction regime and (iii) the local quasi-steady-state approximation was obtained as limiting case of solution (ii) for a instantaneous reaction regime.     

THE LAMINAR FLOW TUBULAR REACTOR WITH HOMOGENEOUS AND HETEROGENEOUS REACTIONS I. Integral Equations for Diverse Reaction Rate Regimes

Design equations for non-isothermal Laminar Flow Tubular Reactors (LFTRs) with homogeneous and heterogeneous - at the reactor wall - reactions with arbitrary kinetic equations have been satisfactorily treated transforming the original P.D.E. problem into a system of integral equations. The kernels of the integral operators are related to an eigenvalue problem which does not depend on the kinetic equations; this avoids repetitive computational effort in the treating of different reaction kinetics.

To render a more efficient numerical treatment and according to the governing reaction rate regime, modified expressions of the general solution were obtained was follows: (i) a solution with kernels depending only on the diffusion and convective times was obtained for a low reaction regime; (ii) another solution with kernels including the reaction lime, besides the diffusion and convective ones, was necessary for a fast reaction regime and (iii) the local quasi-steady-state approximation was obtained as limiting case of solution (ii) for a instantaneous reaction regime.     

Acid–base transport model depicting the dynamic pH response of interfacial reactions

Acid–base transport is integral to many important interfacial reactions in various fields of chemistry, but its theoretical foundation is lacked. Herein, a common acid–base transport model is established owing to the success in deriving buffer transport equations. This model is applicable to most buffer systems by flexibly integrating the transport equations in terms of buffer components, and is verified through the model relationships of buffer transport limiting current by using hydrogen evolution reaction experiments. Based on model calculations, two diagram approaches are proposed to depict the dynamic pH response and aid buffer operation optimizations. The model and methods allow us to quantify the rate-limiting effect of acid–base transport on interfacial reactions and to precisely control the effect through medium regulations. Furthermore, the model has laid the foundation of dynamic pH effect on species transformation and process mechanism, which can be of wide interest in the chemistry encompassing interfacial reactions.     

Finite element solution for gas–solid reactions: Application to the moving boundary problems

Gas–solid reactions are very important in the chemical and metallurgical process industries. Several models described these reactions such as volume reaction model, grain model, and nucleation model. These models give two coupled partial differential equations (CPDEs). In this work an integral transformation and subsequent finite element method is used for solving the coupled partial differential equations of these reactions. In each mesh the Rayleigh–Ritz method is applied. Finally the results of this work are compared with the existing numerical solutions and experimental data successfully.     

The effect of liquid flow distribution on the behaviour of a trickle bed reactor

A mathematical model has been formulated of the effect of flow distribution of the liquid phase carrying a dissolved reactant on the progress of an nth order, irreversible, catalytic reaction with heat effects in an adiabatic trickle bed reactor. The model has been stated in terms of the density of irrigation, temperature and concentration of the reactant in the liquid, all treated as spatially distributed variables. Provisions have been made to account for the existence of the flow down the surface of the wall, which has no catalytic effect.Local concentration and temperature have been proven to be coupled by the invariant T + Uγc = γU. The same invariant governs also local concentration and temperature of the wall flow. Mathematically, the model is represented by a coupled set of nonlinear parabolic partial differential equations enabling concentration and temperature fields to be obtained for an arbitrary type of liquid distribution and intensity of the wall flow.Numerical solutions have been obtained by the finite-difference method simulating reactors irrigated by liquid distributors as central discs of different radii, or a central annulus, and strongly exothermic reactions with the reaction order ranging between 0.1 and 2. Numerical results have shown the effect of liquid distribution on the overall reaction conversion to be very complex. Optimum initial distribution varies depending on the reaction order as well as the required degree of conversion. In general, however, the entrance region flow pattern may play a significant role in affecting especially reactions exhibiting kinetics close to zero order (hydrogenations). The effect of the wall flow has been found unambigously adverse to reaching high conversions and of increasing importance for low order reactions.     

Kinetics of the photocatalytic total oxidation of different alkanes and alkenes on TiO2 powder

Although photocatalyzed total oxidation reaction of hydrocarbon species has been discussed in the literature, most of these studies were performed to obtain an appropriate reaction mechanism. Studies on the kinetics of this type of reaction are rare. Using titanium dioxide as the photo catalyst, the kinetics of the total oxidation of methane, ethane, ethene, as well as propene, have been investigated using a continuous‐stirred tank reactor. In the experiments, the hydrocarbon concentrations, the oxygen concentration, and the irradiation intensity were varied. The results obtained are evaluated on the basis of a kinetic model to derive rate equations which can be used for reactor design.     

Two-dimensional Simulation for Hydrogen/Air Combustion in a Monolith Reactor

Recent studies on hydrogen combustion were reviewed briefly. The laminar flow and combustion of premixed hydrogen/air mixture in a cylindrical channel of a monolith reactor with and without catalytic wall was numerically modeled by solving two-dimensional (2-D) Navier Stokes (N S) equations, energy equation, and species equations. Eight gas species and twenty reversible gas reactions were considered. The control volume technique and the SIMPLE algorithm were used to solve the partial differential equations. The streamlines of the flow field, temperature contours, the entrance length, and the concentration fields were computed. It is found that the entrance zone plays an important role on flow and temperature as well as species distribution. Therefore, the flow cannot be assumed either as fully developed or as plug flow. There is a small but strong thermal expansion zone between the wall and the entrance. Both diffusion and convection affect the heat and mass transfer processes in the expansion zone. Thus the equations of momentum, energy and species conservations should be used to describe hydrogen/air combustion in the monolith reactor. The hot-spot location and concentration field of the homogeneous combustion is strongly influenced by the inlet velocity and temperature, and the equivalence ratio. The catalytic combustion of premixed hydrogen/air mixture over platinum catalyst-coated wall in a cylindrical channel was also simulated.     

A new solution technique for fluid–solid reactions

Fluid–solid reactions are very important in the chemical and metallurgical process industries. Several models described these reactions such as volume reaction model, grain model, random pore model and nucleation model. These models give two nonlinear-coupled partial differential equations (CPDE). When the fluid concentration is high (for example in liquid–solid reactions), the fluid mass balance must be written as an unsteady equation. There is not any analytical or approximate solution for these equations, due to its complex CPDE. In this work, a new solution technique (quantized method) has been applied to these unsteady state CPDE. The results of this method (conversion–time profiles) have been compared with some existing numerical solutions with a good accuracy. Therefore, this method can be used for rapid estimation of kinetic parameters from experimental data.     

CFD modeling of slurry bubble column reactors for Fisher-Tropsch synthesis

Industrial bubble column reactors for Fischer-Tropsch (FT) synthesis include complex hydrodynamic, chemical and thermal interaction of three material phases: a population of gas bubbles of different sizes, a liquid phase and solid catalyst particles suspended in the liquid. In this paper, a CFD model of FT reactors has been developed, including variable gas bubble size, effects of the catalyst present in the liquid phase and chemical reactions, with the objective of predicting quantitative reactor performance information useful for design purposes. The model is based on a Eulerian multifluid formulation and includes two phases: liquid-catalyst slurry and syngas bubbles. The bubble size distribution is predicted using a Population Balance (PB) model. Experimentally observed strong influence of the catalyst particles concentration on the bubble size distribution is taken into account by including a catalyst particle induced modification of the turbulent dissipation rate in the liquid. A simple scaling modification to the dissipation rate is proposed to model this influence in the PB model. Additional mass conservation equations are introduced for chemical species associated with the gas and liquid phases. Heterogeneous and homogeneous reaction rates representing simplified FT synthesis are taken from the literature and incorporated in the model.Hydrodynamic effects have been validated against experimental results for laboratory scale bubble columns, including the influence of catalyst particles. Good agreement was observed on bubble size distribution and gas holdup for bubble columns operating in the bubble and churn turbulence regimes. Finally, the complete model including chemical species transport was applied to an industrial scale bubble column. Resulting hydrocarbon production rates were compared to predictions made by previously published one-dimensional semi-empirical models. As confirmed by the comparisons with available data, the modeling methodology proposed in this work represents the physics of FT reactors consistently, since the influence of chemical reactions, catalyst particles, bubble coalescence and breakup on the key bubble-fluid drag force and interfacial area effects are accounted for. However, heat transfer effects have not yet been considered. Inclusion of heat transfer should be the final step in the creation of a comprehensive FT CFD simulation methodology. A significant conclusion from the modeling results is that a highly localized FT reaction rate appears next to the gas injection region when the syngas flow rate is low. As the FT reaction is exothermal, it may lead to a highly concentrated heat release in the liquid. From the design perspective, the introduction of appropriate heat removal devices may be required.     

钛硅分子筛催化环已酮氨肟化反应动力学

An intrinsic kinetics of cyclohexanone ammoximation in the liquid phase over titanium silicate molecular sieves is investigated in an isothermal slurry reactor at different initial reactant concentrations, catalyst loading,and reaction temperature. The rate equations are developed by analyzing data of kinetic measurements. More than 10 side reactions were found. H202 decomposition reaction Inust be considered and other side reactions can be neglected in the kinetic modeling. The predicted values of reaction rates based on the kinetic models are almost consistent with experimental ones. The models have guidance to the selection of reactor types and they are useful to the design and operation of reactor used.     

Enhancement of catalytic reaction by pressure swing adsorption

A theoretical study of an adsorptive reactor which combines multibed pressure swing adsorption and chemical reaction is presented; such a reactor is referred to as a pressure swing reactor, or PSR. Studies have concentrated on an asymptotic case in which there is the ideal propagation of concentration waves within the reactor beds; the method of characteristics was employed in the solution of the governing PSR equations. The studies assessed the effects of operating conditions, and cycle configurations, on the PSR performance. Calculations indicate enhanced reactant conversion when compared to conventional steady state plug flow operation. In particular, for some reversible reactions, substantial improvements over equilibrium yields have been calculated. For example, for the dissociation reaction 2A B + C, and where B is the only adsorbing component, approximately two-fold improvements over the equilibrium yield of product B have been predicted. Such reaction enhancement can be attributed to the limitation of the backward reaction, which results from the separation of the product species B and C.

In addition to the method of characteristics, a cells-in-series method for the asymptotic case has been developed, and found to yield calculations consistent with the method of characteristics solutions. In a third numerical approach, the spatial discretisation technique of orthogonal collocation on finite elements was applied to the governing PSR equations, and the resulting system of ordinary differential equations solved by a standard integration algorithm. In this case, many of the simplifying model assumptions were relaxed, allowing, for example, the simulation of a non-isothermal PSR with finite mass transfer rates.

One practical significance of reaction enhancement by pressure swing adsorption is a lower temperature of operation than in a conventional reactor. This would lead to savings in the energy requirements of the reactor, and limit the rate and degree of catalyst deactivation due to coke deposition or sintering.     

The formation and destruction of NO in turbulent propane diffusion flames

This paper describes a study of the formation and destruction of NO in turbulent propane diffusion flames with recourse to both experiments and modelling. Detailed in-flame measurements of local mean gas species concentrations of O₂, CO, CO₂, unburnt hydrocarbons and NO_x and local mean gas temperature have been performed for three flames — two of them with the same Froude number and two with the same Reynolds number. These experimental data have been analysed with the aid of a mathematical model. For the NO calculations, three reaction schemes have been used: the Zeldovich reactions, an overall approximate prompt reaction, and a 27 reaction scheme, which includes the thermal NO and the prompt NO reactions and the NO to HCN recycle via fuel NO reactions. The main conclusions are that in the present flames: (1) the prompt NO (or Fenimore) mechanism is the dominant route for the NO formation; and (2) the reactions between NO and hydrocarbon radicals, recycling NO to HCN via the fuel NO reactions, play an important role in the global NO reduction.     

Solving partial differential equations of gas–solid reactions by orthogonal collocation

In this work the solution of the coupled partial differential equations for noncatalytic gas–solid reactions has been considered by orthogonal collocation. First of all, by an integral transformation and then by applying the orthogonal collocation method, these partial differential equations are converted to the ordinary differential equations. Then the equations are solved and the conversion–time profiles are obtained. The solution of the equations for volume reaction model, grain model and grain model with product layer resistance, modified grain model, random pore model, nucleation model and reaction of two gas with one solid has been presented in this work. The orthogonal collocation is a rapid method for solving of these equations and shows a good accuracy with respect to other solution techniques in the literature.     

Course of degradation and build‐up reactions in isotactic polypropylene during peroxide decomposition

In the investigation of the course of degradation and build‐up reactions during the decomposition of the tert‐butyl perbenzoate (TBPB) (at eight different concentrations) in isotactic polypropylene (iPP), it was found that, at the beginning of the peroxide decomposition at all investigated peroxide concentrations from 4.62–200 mmol/kg iPP, the degradation reactions of iPP prevailed. At the TBPB concentration of ≤37.0 mmol/kg iPP during the whole period of peroxide decomposition, degradation reactions leading to a lower of molecular mass of PP prevailed. But at higher peroxide concentrations of TBPB ≥74.4 mmol/kg iPP and at the later stage of peroxide decomposition, a predominance of the build‐up reactions, that is, an increase the molecular mass, was observed. The degradation and build‐up reactions were determined from the measurements of the melting‐flow indexes of the peroxide‐treated iPP samples. The reaction mechanism of the degradation and build‐up reactions in iPP is discussed. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 78: 886–893, 2000     

Simulation of Secondary Reformer in Industrial Ammonia Plant

In order to develop a reactor design model for the secondary reformer in the industrial ammonia plant, the effectiveness factor and convection heat transfer coefficient between gas and catalyst surface have been studied. The temperature and composition of inlet gas to the catalyst bed are predicted using the kinetic equations of 32 radical reactions. The effect of oxygen content in air on the product synthesis gas composition and the ratio of synthesis gas to nitrogen have been studied. The effectiveness factor has been calculated with the assumption that the steam methane reforming reaction is first order in methane partial pressure. The catalyst shape is assumed to be spherical with an equivalent volumetric diameter. The temperature and composition profiles along the axial distance are predicted using a one‐dimensional heterogeneous catalytic reaction model. The temperatures of both gas and catalyst surface decreased with the axial distance from the top of the bed, while the reactions took place. The temperature difference between gas and catalyst surface also decreased along the axial distance. The predicted temperature and composition by the proposed simulation method have been verified with the data from the industrial plant.     

Non-equilibrium effects on fast reactions in a heterogeneous batch reactor

Recent studies by the authors of the heterogeneous catalysis of fast binary reactions have taken a dynamical systems approach, assuming that fast enough reactions are confined to a manifold upon which surface equilibrium holds. This approximation makes substantial simplification possible, for instance in the case of a batch reactor, it allows a naturally sixth order system to be approximated by a two dimensional manifold for the dynamics of two modified Thiele moduli. Nevertheless, a proper assessment of how much faster must the velocity of surface reaction be than the velocity of mass transfer to the catalytic surface before the quasi-equilibrium on the surface holds should be made. In this paper, a theory for the systematic correction to infinitely fast reactions is made for large but finite velocity reactions. It is compared to full numerical solutions to the model equations. Recommendations about the regime of applicability of the quasi-equilibrium approximation are made. In general, the predictions of the quasi-equilibrium theory hold for ratios of mass transfer coefficients to reaction velocity ξ of less than 1/1000, with qualitative agreement in regimes of less than 1/100. The general trend, however, is that the stronger the kinetic asymmetry between the mass transfer coefficients of the reactants, the slower the reaction rate can be and still have the quasi-equilibrium theory hold. A perturbation analysis demonstrates that the quasi-equilibrium theory is a regular limit of the fast non-equilibrium theory. In the irreversible case, a matched asymptotic analysis gives the same prediction for the switch time from effective surface depletion of one reagent to the other as the quasi-equilibrium theory. Furthermore, it gives an estimate of the smoothing out of the transition zone with a temporal width of ξ^1/2. It should be noted that the continual drive for improved catalyst activities inevitably leads to mass transfer limited reactions, and thus this regime is not uncommon.     

ESTIMATION OF UPPER BOUNDS FOR THE RATES OF ENZYMATIC REACTIONS

A general methodology that allows the estimation of maximum rates of enzymatic reactions is described. For a typical mechanism of an enzymatic reaction, the rate is a function of kinetic parameters which are unknown but required to obey certain constraints. Specifically, the ratio of forward to backward rate constants must be consistent with the equilibrium constant, and the rate of each bimolecular reaction-step must be less than the rate of collision of the two reactant species. If additional information is available on the reaction rate, more constraints can be introduced. By maximizing the rate expression with respect to the kinetic parameters, subject to all applicable constraints, a first-principles upper bound is obtained for the reaction rate. If the reaction rate is actually known, the methodology can alternatively estimate an extremum for the concentration of the enzyme, a substrate, or a product. Simple thermodynamic arguments could also provide bounds for concentrations or the direction (but not the magnitude) of the rate, by examining only the overall transformation of reactants to products and completely ignoring the mechanism. The collision-limit treatment proposed here exploits basic internal characteristics of enzymatic reaction mechanisms to predict better bounds for the concentrations and the thermodynamically allowable maximum magnitude of the rate.     

Advanced Oxidation and Degradation of Vinyl Chloride in Water

A kinetic model has been developed for the degradation of organic pollutants, by considering both the decomposition of ozone molecules and the interaction between ozone and hydrogen peroxide in the formation of a hydroxyl radical, and the subsequent reactions. Rate equations were derived for the depletion of ozone and pollutants in the advanced oxidation processes (known as the peroxone oxidation). Experiments were carried out at 298 K in the pH range 3 to 11. Kinetic data obtained experimentally from the hydrogen peroxide‐ozone reaction and advanced oxidation of vinyl chloride were analyzed by using the proposed rate equations, indicating that the depletion rate of ozone increases with the concentrations of ozone, hydrogen peroxide, and hydroxyl ion, as predicted by the kinetic model.     

Transient solution of chemical vapor infiltration/deposition in a reactor

A chemical vapor infiltration/deposition (CVI/CVD) reactor used to manufacture carbon/carbon (C/C) composites aircraft brakes has been simulated numerically. This simulation accounts for a homogeneous gas reaction mechanism as well as a heterogeneous surface reaction mechanism that is coupled with hydrogen inhibition effect and a pore model. Non-Boussinesq (low Mach number) equations are used to predict fluid flow, heat transfer, and species concentrations inside the reactor and within the porous brakes. In addition, we use an efficient quasi-steady state integration procedure to predict porosity distribution at different infiltration times. Results showing the flow, temperature and concentration fields, as well as the deposition rate of the pyrolytic carbon and porosity change with time, are presented. Optimized operating conditions for pressure and temperature are obtained through a parametric study that consists of 16 different cases. Recommendations are presented for improving performance.