Catalytic reactors performance equations

Under steady-state conditions in a plug-flow tubular reactor, the onedimensional mass transfer equation for reactant A can be integrated rather easily to predict reactor performance. Equation (22-1) was derived for a control volume that is differentially thick in all coordinate directions. Consequently, mass transfer rate processes due to convection and diffusion occur, at most, in three coordinate directions and the mass balance is described by a partial differential equation. Current research in computational fluid dynamics applied to fixed-bed reactors seeks a better understanding of the flow phenomena by modeling the catalytic pellets where they are, instead of averaging or homogenizing... 

Extensions of the Simple Performance Equations. There are numerous applications of catalytic reactions where the fraction of solids / varies with height z in the reactor (see Fig. 18.10). 

Any type of reactor with known contacting pattern may be used to explore the kinetics of catalytic reactions. Since only one fluid phase is present in these reactions, the rates can be found as with homogeneous reactions. The only special precaution to observe is to make sure that the performance equation used is dimensionally correct and that its terms are carefully and precisely defined. 

The equations are also coupled by the mass transfer coefficient This is the standard mass transfer problem we encountered with catalytic reactions. As with catalytic reactors, processes are very often limited by mass transfer so that the kinetics become unimportant in predicting performance. 

The kinetic modelling of complex multiphase catalytic reactions needs a careful consideration of various complexities of adsorption and desorption of reactants and products. In such cases the kinetic model developed based on the initial rate data may not be adequate to explain the integral batch reactor performance. Hence it was thought appropriate to use mainly the integral rate data for developing a suitable kinetic model. Different rate equations were derived based on various Langumir-Hinshelwood mechanisms and a few of them are given below. 

If there is only one chemical reaction on the internal catalytic surface, then vai = — 1 and subscript j is not required for all quantities that are specific to the yth chemical reaction. When the mass transfer Peclet number which accounts for interpellet axial dispersion in packed beds is large, residence-time distribution effects are insignificant and axial diffusion can be neglected in the plug-flow mass balance given by equation (22-11). Under these conditions, reactor performance can be predicted from a simplified one-dimensional model. The differential design equation is... 

Reactor performance is established by calculating the molar density of reactant A from a steady-state mass balance that accounts for axial convection and transverse diffusion. Chemical reaction only occurs on the well-defined catalytic surface which bounds fluid flow in the regular polygon channel. Hence, depletion of reactant A due to chemical reaction appears in the boundary conditions, but not in the mass balance which applies volumetrically throughout the homogeneous flow channel. The mass transfer equation for duct reactors is written in vector form ... 

The kinetics of catalytic reactions can be explored using any type of reactor with known contacting pattern. The only prereqisite to observe is to apply the correct performance equation. Usually the extent of conversion of gas passing in steady flow through a batch or solids is measured. In turn we discuss the experimental devices ... 

In this chapter, the Navier-Stokes equations have been solved in the actual 3D geometry of the reactor, thereby exploiting the full potential of the new approach, and detailed surface kinetics (Visconti et al., 2013) was implemented in the model with two main implications. On a more fundamental level, it demonstrates the power of the CAT-PP approach proposed here, which allows us to perform simulations of complex catalytic reactors characterized by nonideal flow fields, in which multistep reactions take place. On a more applied level, it allows us to assess the extent of the nonidealities of the simulated operando FTIR reaction cell, which is commercially available and is used by many research groups worldwide. This is extremely relevant especially for researchers who ivant to use the cell to collect quantitative information, since it will allow the verification of whether the cell is an ideal reactor or not. This latter hypothesis has been exploited, for example, by Visconti et al. (2013) to develop the first comprehensive and physically consistent spectrokinetic model for NOx storage... 

Transport Criteria in PBRs In laboratory catalytic reactors, basic problems are related to scaling down in order to eliminate all diffusional gradients so that the reactor performance reflects chemical phenomena only [24, 25]. Evaluation of catalyst performance, kinetic modeling, and hence reactor scale-up depend on data that show the steady-state chemical activity and selectivity correctly. The criteria to be satisfied for achieving this goal are defined both at the reactor scale (macroscale) and at the catalyst particle scale (microscale). External and internal transport effects existing around and within catalyst particles distort intrinsic chemical data, and catalyst evaluation based on such data can mislead the decision to be made on an industrial catalyst or generate irrelevant data and felse rate equations in a kinetic study. The elimination of microscale transport effects from experiments on intrinsic kinetics is discussed in detail in Sections 2.3 and 2.4 of this chapter. 

Although the Orcutt model is simple, it does allow us to explore the effects of operating conditions, reaction rate and degree of interphase mass transfer on performance of a fluidized bed as a gas-phase catalytic reactor. Figure 7.20 shows the variation of conversion with reaction rate (expressed as fcHmf(l — p/U)) with excess gas velocity (expressed as jS) calculated using Equation (7.65) for a first-order reaction. 

Abstract In this chapter, an exothermic catalytic reaction process is simulated by using computational mass transfer (CMT) models as presented in Chap. 3. The difference between the simulation in this chapter from those in Chaps. 4,5, and 6 is that chemical reaction is involved. The source term in the species conservation equation represents not only the mass transferred from one phase to the other, but also the mass created or depleted by a chemical reaction. Thus, the application of the CMT model is extended to simulating the chemical reactor. The simulation is carried out on a wall-cooled catalytic reactor for the synthesis of vinyl acetate from acetic acid and acetylene by using both c — Sc model and Reynolds mass flux model. The simulated axial concentration and temperature distributions are in agreement with the experimental measurement. As the distribution of lx shows dissimilarity with Dj and the Sci or Pri are thus varying throughout the reactor. The anisotropic axial and radial turbulent mass transfer diffusivities are predicted where the wavy shape of axial diffusivity D, along the radial direction indicates the important influence of catalysis porosity distribution on the performance of a reactor. 

There is a general trend toward structured packings and monoliths, particularly in demanding applications such as automotive catalytic converters. In principle, the steady-state performance of such reactors can be modeled using Equations (9.1) and (9.3). However, the parameter estimates in Figures 9.1 and 9.2 and Equations (9.6)-(9.7) were developed for random packings, and even the boundary condition of Equation (9.4) may be inappropriate for monoliths or structured packings. Also, at least for automotive catalytic converters. 

The regression for integral kinetic analysis is generally non-linear. Differential equations may include unobservable variables, which may produce some additional problems. For instance, heterogeneous catalytic models include concentrations of species inside particles, while these are not measured. The concentration distributions, however, can affect the overall performance of the catalyst/reactor. 

Hence the dimension ("the order") of the reaction is different, even in the simplest case, and hence a comparison of the two rate constants has little meaning. Comparisons of rates are meaningful only if the catalysts follow the same mechanism and if the product formation can be expressed by the same rate equation. In this instance we can talk about rate enhancements of catalysts relative to another. If an uncatalysed reaction and a catalysed one occur simultaneously in a system we may determine what part of the product is made via the catalytic route and what part isn t. In enzyme catalysis and enzyme mimics one often compares the k, of the uncatalysed reaction with k2 of the catalysed reaction if the mechanisms of the two reactions are the same this may be a useful comparison. A practical yardstick of catalyst performance in industry is the space-time-yield mentioned above, that is to say the yield of kg of product per reactor volume per unit of time (e.g. kg product/m3.h), assuming that other factors such as catalyst costs, including recycling, and work-up costs remain the same. 

At some point in most processes, a detailed model of performance is needed to evaluate the effects of changing feedstocks, added capacity needs, changing costs of materials and operations, etc. For this, we need to solve the complete equations with detailed chemistry and reactor flow patterns. This is a problem of solving the R simultaneous equations for S chemical species, as we have discussed. However, the real process is seldom isothermal, and the flow pattern involves partial mixing. Therefore, in formulating a complete simulation, we need to add many additional complexities to the ideas developed thus far. We will consider each of these complexities in successive chapters temperature variations in Chapters 5 and 6, catalytic processes in Chapter 7, and nonideal flow patterns in Chapter 8. In Chapter 8 we will return to the issue of detailed modeling of chemical reactors, which include all these effects. 

The space velocity for a given conversion is often used as a ready measure of the performance of a reactor. The use of equation 1.25 to calculate reaction time, as if for a batch reactor, is not to be recommended as normal practice it can be equated to VJv only if there is no change in volume. Further, the method of using reaction time is a blind alley in the sense that it has to be abandoned when the theory of tubular reactors is extended to take into account longitudinal and radial dispersion and other departures from the plug flow hypothesis which are important in the design of catalytic tubular reactors (Chapter 3, Section 3.6.1)... 

Takeuchi et al. 7 reported a membrane reactor as a reaction system that provides higher productivity and lower separation cost in chemical reaction processes. In this paper, packed bed catalytic membrane reactor with palladium membrane for SMR reaction has been discussed. The numerical model consists of a full set of partial differential equations derived from conservation of mass, momentum, heat, and chemical species, respectively, with chemical kinetics and appropriate boundary conditions for the problem. The solution of this system was obtained by computational fluid dynamics (CFD). To perform CFD calculations, a commercial solver FLUENT has been used, and the selective permeation through the membrane has been modeled by user-defined functions. The CFD simulation results exhibited the flow distribution in the reactor by inserting a membrane protection tube, in addition to the temperature and concentration distribution in the axial and radial directions in the reactor, as reported in the membrane reactor numerical simulation. On the basis of the simulation results, effects of the flow distribution, concentration polarization, and mass transfer in the packed bed have been evaluated to design a membrane reactor system. 

As a result of the high heat transfer performance, rapid heating and cooling of fluids in open reactor systems becomes possible. Reaction mixtures can be efficiently quenched to avoid consecutive decomposition of reactive intermediates in sequential reactions. A practical example is the direct catalytic dehydrogenation of methanol to formaldehyde at a temperature of about 700 °C (Equation (1)) [5-7] ... 

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