Pseudohomogeneous reactor model

The microreactor was described by the most simple mathematical model the onedimensional pseudohomogeneous reactor model. The different rate expressions were tested for use by calculation. The initial value problem... 

In this section, a two-dimensional, pseudohomogeneous reactor model will be developed neglecting heat- and mass-transfer limitations between the bulk phase and catalyst particles, as well as inside the catalyst pellets. The two-dimensional formulation presented takes advantage of the cylindrical reactor geometry shown in Fig. 5.11. 

The fit between simulation (using a pseudohomogeneous reactor model) and experiment is shown in Fig. 20. The fit seems to be rather good however it should be mentioned that and h had to be optimized simultaneously with the kinetic parameters, which is not surprising regarding the results shown in Fig. 11. Values for these... 

In the case of the pseudohomogeneous reactor model given by eq. (1), we consider as a model output variable, g, the maximum temperature value along the reactor, v. In this case we talk about a normalized objective sensitivity S(v ), where the model input parameter can be any of the five independent parameters in eq.(l), i.e.

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In this chapter, we develop some guidelines regarding choice of reactor and operating conditions for reaction networks of the types introduced in Chapter 5. These involve features of reversible, parallel, and series reactions. We first consider these features separately in turn, and then in some combinations. The necessary aspects of reaction kinetics for these systems are developed in Chapter 5, together with stoichiometric analysis and variables, such as yield and fractional yield or selectivity, describing product distribution. We continue to consider only ideal reactor models and homogeneous or pseudohomogeneous systems. 

In this chapter, we first cite examples of catalyzed two-phase reactions. We then consider types of reactors from the point of view of modes of operation and general design considerations. Following introduction of general aspects of reactor models, we focus on the simplest of these for pseudohomogeneous and heterogeneous reactor models, and conclude with a brief discussion of one-dimensional and two-dimensional models. 

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 one-dimensional pseudohomogeneous plug flow reactor model assuming isothermality was used to simulate experimental results. The continuity and kinetic expressions used were as follows ... 

If the catalyst is dispersed throughout the pellet, then internal diffusion of the species within the pores of the pellet, along with simultaneous reaction(s) must be accounted for if the prevailing Thiele modulus > 1. This aspect gives rise to the effectiveness factor" problem, to which a significant amount of effort, summarized by Aris ( ), has been devoted in the literature. It is important to realize that if the catalyst pellet effectiveness factor is different from unity, then the packed-bed reactor model must be a heterogeneous model it cannot be a pseudohomogeneous model. 

Assuming a pseudohomogeneous two-dimensional reactor model with plug flow of fluid and constant properties, calculate the axial concentration and temperature profiles at several radial positions along the axis of a single tube. Use the following property/parameter values (Doraiswamy, 2001) ... 

In most investigations concerning the reactor modelling, simple pseudohomogeneous (t = 1) reactor models were used. The effect of external and internal mass and heat transfer resistances on the effectiveness factors using realistic complex reaction network has not been widely investigated. The simple linear kinetics proposed by... 

All these steps can influence the overall reaction rate. The reactor models of Chapter 9 are used to predict the bulk, gas phase concentrations of reactants and products at point (r, z) in the reactor. They directly model only steps 1 and 9, and the effects of steps 2-8 are lumped into the pseudohomogeneous rate expression 5 (a,, ...), where a, Z ,... are the bulk, gas phase concentrations. The overall reaction mechanism is complex, and the rate expression is necessarily empirical. Heterogeneous catalysis remains an experimental science. The techniques of this chapter are useful to interpret experimental results. Their predictive value is limited. 

Reactor models accounting for radial porosity profile were compared with models using the averaged bed-porosity value. Isothermal conditions were applied in order to rule out thermal effects on the concentration profiles. To check the need for two-dimensional models the results were compared with that obtained by using the pseudohomogeneous one-dimensional reactor model (Eqs. (5.1)-(5.4)). 

The Ideal Single-Stage, Constant-Volume Continuous Stirred Tank Reactor, CSTR (Pseudohomogeneous L-Phase Reactor Model)... 

The pseudohomogeneous biofilm model, given in Equs. 6.116 and 6.121, can be readily adapted to quantify the behavior of a rotating biological disk reactor. The setup of a similar balance equation for S using Monod-type kinetics yields for the case of rds kinetics... 

A pseudohomogeneous, two-dimensional reactor model for MRs consists of the total gas—phase continuity and Navier—Stokes equations, augmented with gas—phase component mass balances and the overall energy balance. 

In the phenomenological approach an attempt is made to isolate the various phenomena that affect the apparent reaction and to establish the appropriate correlations for each of them (assuming separable mechanisms). An example is the reactor models in which it is assumed that the reaction is pseudohomogeneous and the phases are in plug flow. For a first-order reaction one may write [113]... 

Parameters and Reactor Characteristics for the Pseudohomogeneous Unidimensional Catalytic Reactor Model... 

The first eight chapters of this book treat homogeneous reactions. Chapter 9 provides models for packed-bed reactors, but the reaction kinetics are pseudohomogeneous so that the rate expressions are based on fluid-phase concentrations. There is a good reason for this. Fluid-phase concentrations are what can be measured. The fluid-phase concentrations at the outlet are what can be sold. 

Chapter 10 begins a more detailed treatment of heterogeneous reactors. This chapter continues the use of pseudohomogeneous models for steady-state, packed-bed reactors, but derives expressions for the reaction rate that reflect the underlying kinetics of surface-catalyzed reactions. The kinetic models are site-competition models that apply to a variety of catalytic systems, including the enzymatic reactions treated in Chapter 12. Here in Chapter 10, the example system is a solid-catalyzed gas reaction that is typical of the traditional chemical industry. A few important examples are listed here ... 

A well-defined bed of particles does not exist in the fast-fluidization regime. Instead, the particles are distributed more or less uniformly throughout the reactor. The two-phase model does not apply. Typically, the cracking reactor is described with a pseudohomogeneous, axial dispersion model. The maximum contact time in such a reactor is quite limited because of the low catalyst densities and high gas velocities that prevail in a fast-fluidized or transport-line reactor. Thus, the reaction must be fast, or low conversions must be acceptable. Also, the catalyst must be quite robust to minimize particle attrition. 

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