Fixed bed catalytic reactors models

A generalized method to predict the deviations of the different types of fixed-bed catalytic reactor models with respect to an heterogeneous two-dimensional model is presented. Very good agreement with numerically calculated errors is found. The differences in the responses between the one and two-dimensional versions of each type of model are analyzed. The conditions in which the different types of models should be used are discussed. 

DUARTE AND LEMCOFF Fixed-Bed Catalytic Reactor Models... 

BALANCE EQUATIONS FOR THE FIXED BED CATALYTIC REACTOR MODELS... 

Balance equations, fixed-bed catalytic reactor models, 252... 

The gas solid fixed bed catalytic reactor models can also be classified broadly into continuum models and cell (or discrete) models. This chapter concentrates on the continuum model since they are the more widely used in the steady state modelling, simulation and optimization of these types of reactors. Cell models are more widely used in the dynamic simulation of these reactors, a subject which is beyond the scope of this book. Of course in principle, there is nothing that prevents the used of cell models for steady state simulation nor is there anything in principle that prevents the use of continuum models in dynamic simulation. 

Fixed-bed reactors are used for testing commercial catalysts of larger particle sizes and to collect data for scale-up (validation of mathematical models, studying the influence of transport processes on overall reactor performance, etc.). Catalyst particles with a size ranging from 1 to 10 mm are tested using reactors of 20 to 100 mm ID. The reactor diameter can be decreased if the catalyst is diluted by fine inert particles the ratio of the reactor diameter to the size of catalyst particles then can be decreased to 3 1 (instead of the 10 to 20 recommended for fixed-bed catalytic reactors). This leads to a lower consumption of reactants. Very important for proper operation of fixed-bed reactors, both in cocurrent and countercurrent mode, is a uniform distribution of both phases over the entire cross-section of the reactor. If this is not the case, reactor performance will be significantly falsified by flow maldistribution. 

The One-Dimensional Pseudo Homogeneous Model of Fixed Bed Reactors. The design of tubular fixed bed catalytic reactors has generally been based on a one-dimensional model that assumes that species concentrations and fluid temperature vary only in the axial direction. Heat transfer between the reacting fluid and the reactor walls is considered by presuming that all of the resistance is contained within a very thin boundary layer next to the wall and by using a heat transfer coefficient based on the temperature difference between the fluid and the wall. Per unit area of the tube... 

Elnashaie, S.S.E.H., and S.S. Elshishini (1993), Modelling, Simulation and Optimization of Industrial Fixed Bed Catalytic Reactors, Gordon and Breach, New York. 

Our treatment of Chemical Reaction Engineering begins in Chapters 1 and 2 and continues in Chapters 11-24. After an introduction (Chapter 11) surveying the field, the next five Chapters (12-16) are devoted to performance and design characteristics of four ideal reactor models (batch, CSTR, plug-flow, and laminar-flow), and to the characteristics of various types of ideal flow involved in continuous-flow reactors. Chapter 17 deals with comparisons and combinations of ideal reactors. Chapter 18 deals with ideal reactors for complex (multireaction) systems. Chapters 19 and 20 treat nonideal flow and reactor considerations taking this into account. Chapters 21-24 provide an introduction to reactors for multiphase systems, including fixed-bed catalytic reactors, fluidized-bed reactors, and reactors for gas-solid and gas-liquid reactions. 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Kjaer (K9) gives a very comprehensive study of concentration and temperature profiles in fixed-bed catalytic reactors. Both theoretical and experimental work is reported for a phthallic anhydride reactor and various types of ammonia converters. Fair agreement was obtained, but due to the lack of sufficiently accurate thermodynamic and kinetic data, definite conclusions as to the suitability of the dispersed plug flow model could not be reached. However, the results seemed to indicate that the... 

Froment, G. F., Design of fixed-bed catalytic reactors based on effective transport models. Chem. Eng. Sci. 17, 849 (1962). (VC)... 

If the radial diffusion or radial eddy transport mechanisms considered above are insufficient to smear out any radial concentration differences, then the simple dispersed plug-flow model becomes inadequate to describe the system. It is then necessary to develop a mathematical model for simultaneous radial and axial dispersion incorporating both radial and axial dispersion coefficients. This is especially important for fixed bed catalytic reactors and packed beds generally (see Volume 2, Chapter 4). 

In the process, ethylbenzene is dehydrogenated to styrene in a fixed-bed catalytic reactor. The feed stream is preheated and mixed with superheated steam before being injected into the reactor at a temperature above 490°C. The steam serves as a dilutant and decokes the catalyst, thereby extending its life. The steam also supplies the necessary heat for the endothermic dehydrogenation reaction. For our model we have chosen six reactions to represent the plant data. 

The differential equations (7.164), (7.165), (7.166), and (7.168) form a pseudohomogene-ous model of the fixed-bed catalytic reactor. More accurately, in this pseudohomogeneous model, the effectiveness factors rji are assumed to be constantly equal to 1 and thus they can be included within the rates of reaction ki. Such a model is not very rigorous. Because it includes the effects of diffusion and conduction empirically in the catalyst pellet, it cannot be used reliably for other units. 

A dynamic model for on-line estimation and control of a fixed bed catalytic reactor must be based on a thorough experimental program. It must be able to predict the measured experimental effects of the variation of key variables such as jacket temperature, feed flow rate, composition and temperature on the dynamic behaviour of the reactor this, in turn, requires the knowledge of the kinetic and "effective" transport parameters involved in the model. 

The development of mathematical models for the simulation of non-adiabatic fixed-bed catalytic reactors has received considerable attention. In previous work, we have analyzed the two-dimensional and one-dimensional versions of the models (1, 2) which, in turn, were classified as (I) pseudohomogeneous, (II) heterogeneous, but conceptually wrong, and (III) heterogeneous, written in the correct way (Table I). Model equations are in the Appendix. 

There were basically two approaches, which were used in the past for HDT process development studies using catalyst in the commercially applied size and shape. The first one, which was followed 30-40 yr ago in various industrial research and development centers, was to test the commercial catalyst in large pilot plants. The second approach was to use a smaller pilot plant and simulate the data generated in these units, applying a suitable hydrodynamic model to predict the performance of a commercial unit. These are generally known as small-scale TBRs. Because of the presence of a liquid phase, the problems in these small TBRs are more complex as compared to those present in other small-scale fixed-bed catalytic reactors handling only vapor phases. 

In Chap. 4 the plug-flow model was used as a basis for designing homogeneous tubular ow reactors. The equation employed to calculate the conversion in the effluent stream was either Eq. (3-13) or Eq. (4-5). The same equations and the same calculational procedure may be used for fixed-bed catalytic reactors, provided that plug-flow behavior is a vahd assumption. AH that is necessary is to replace the homogeneous rate of reaction in those equations with the global rate for the catalytic reaction. 

One- and two-dimensional models of fixed-bed reactors are compared for a numerical case in G. F. Froment, Current Design Status, Fixed-bed Catalytic Reactors, Ind. Eng. Chem., 59, 18 (1967). 

Volume 7 MODELLING, SIMULATION AND OPTIMIZATION OF INDUSTRIAL FIXED BED CATALYTIC REACTORS by S.S.E.H. Elnashaie and S.S. Elshishini... 

MODELLING, SIMULATION AND OPTIMIZATION OF INDUSTRIAL FIXED BED CATALYTIC REACTORS... 

The book is written in the spirit of bringing to chemical engineers in both academia and industry a comprehensive text for the development of reliable mathematical models for industrial fixed bed catalytic reactors from the first step of surface phenomena to the final stage of putting the verified model into a user friendly software package with... 

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