Pseudohomogeneous system

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. 

Figure 4.9(a) and (b) illustrate the system behavior at a total pressure of 15 atm and 8 atm, respectively. As can be seen from the location of the PSPS, this system has similar features as the ideal system example 1 which has an elhpse-shaped PSPS (see Fig. 4.2(a)), as discussed above. Due to the boiling sequence of the reaction components, the PSPS is fully located outside the physically relevant composition space and, as a consequence, no reactive azeotrope can appear. It is worth noting that inside the phase-splitting region, the PSPS of the real heterogeneous system and the PSPS of the pseudohomogeneous system are different However, this does not affect the feasible top and bottom products of a fully reactive distillation column. 

Strictly gas-phase CSTRs are rare. Two-phase, gas-liquid CSTRs are common and are treated in Chapter 11. Two-phase, gas-solid CSTRs are fairly common. When the solid is a catalyst, the use of pseudohomogeneous kinetics allows these two-phase systems to be treated as though only the fluid phase were present. All concentration measurements are made in the gas phase, and the rate expression is fitted to the gas-phase concentrations. This section outlines the method for fitting pseudo-homogeneous kinetics using measurements made in a CSTR. A more general treatment is given in Chapter 10. 

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 ... 

In previous chapters, we deal with simple systems in which the stoichiometry and kinetics can each be represented by a single equation. In this chapter we deal with complex systems, which require more than one equation, and this introduces the additional features of product distribution and reaction network. Product distribution is not uniquely determined by a single stoichiometric equation, but depends on the reactor type, as well as on the relative rates of two or more simultaneous processes, which form a reaction network. From the point of view of kinetics, we must follow the course of reaction with respect to more than one species in order to determine values of more than one rate constant. We continue to consider only systems in which reaction occurs in a single phase. This includes some catalytic reactions, which, for our purpose in this chapter, may be treated as pseudohomogeneous. Some development is done with those famous fictitious species A, B, C, etc. to illustrate some features as simply as possible, but real systems are introduced to explore details of product distribution and reaction networks involving more than one reaction step. 

In Section 21.5, the treatment is based on the pseudohomogeneous assumption for the catalyst + fluid system (Section 21.4). In this section, we consider the local gradients in concentration and temperature that may exist both within a catalyst particle and in the surrounding gas film. The system is then heterogeneous. We retain the assumptions of... 

We want the pseudohomogeneous rate as a function of the parameters in the system,... 

In our original system of partial differential equations, to obtain a pseudohomogeneous model the two energy balances can be combined by eliminating the term (Usg/Vb)(Ts — Tg), that describes the heat transfer between the solid and the gas. If the gas and solid temperatures are assumed to be equal (Ts = Tg)19 and the homogeneous gas/solid temperature is defined as T, the combined energy balance for the gas and solid becomes... 

Various aspects of the effect of process scale-up on the safety of batch reactors have been discussed by Gygax [7], who presents methods to assess thermal runaway. Shukla and Pushpavanam [8] present parametric sensitivy and safety results for three exothermic systems modeled using pseudohomogenous rate expressions from the literature. Caygill et al. [9] identify the common factors that cause a reduction in performance on scale-up. They present results of a survey of pharmaceutical and fine chemicals companies indicating that problems with mixing and heat transfer are commonly experienced with large-scale reactors. 

Packed-bed reactors are discussed qualitatively, particularly with respect to their models. Features of the two basic types of models, the pseudohomogene-ous and the heterogeneous models, are outlined. Additional issues — such as catalyst deactivation steady state multiplicity, stability, and complex transients and parametric sensitivity — which assume importance in specific reaction systems are also briefly discussed. 

The influence of activity changes on the dynamic behavior of nonisotherma pseudohomogeneous CSTR and axial dispersion tubular reactor (ADTR) with first order catalytic reaction and reversible deactivation due to adsorption and desorption of a poison or inert compound is considered. The mathematical models of these systems are described by systems of differential equations with a small time parameter. Therefor the singular perturbation methods is used to study several features of their behavior. Its limitations are discussed and other, more general methods are developed. 

A set of simultaneous PDEs (ODEs if the pellets are spherical) must be solved to estimate the extent of reaction and conversion occurring within a single pellet. These local values are then substituted into Equations 9.1 and 9.3 so that we need to solve a set of PDEs that are embedded within a set of PDEs. The resulting system truly reflects the complexity of heterogeneous reactors, but practical solutions rarely go to this complexity. Most industrial reactors are designed on the basis of pseudohomogeneous models as in Equations 9.1 and 9.3, and the local catalyst behavior is described by the effectiveness factor defined in Chapter 10. 

A recycle reactor containing 101 g of catalyst is used in an experimental study. The catalyst is packed into a segment of the reactor having a volume of 125 cm. The recycle lines and pump have an additional volume of 150 cm. The particle density of the catalyst is 1.12 g cm , its internal void fraction is 0.505, and its surface area is 400 m g . A gas mixture is fed to the system at 150 cm s . The inlet concentration of reactant A is 1.6 mol m . The outlet concentration of reactant A is 0.4 mol m . Determine the intrinsic pseudohomogeneous reaction rate, the rate per unit mass of catalyst, and the rate per unit surface area of catalyst. The reaction isA- - Psov.4 = —1. 

The process is described by an one-dimensional, pseudohomogeneous, non-steady state dispersion model for an adiabatic fixed bed reactor. The kinetics are modelled by a re-versibll reaction system where each reaction step follows a power law with a reaction order of one in the gas and in the solid component. The temperature dependency of the reaction rate constant follows the Arrhenius law. The equilibrium constant is set to be independent of temperature. 

The kinetics of octanoic acid esterification by t-butanol catalyzed by the macroretic-ular, sulfonylated ion-exchange resin, Amberlite-15, in a batch reactor was measured [37]. The effect of the catalyst amount, temperature and concentration of alcohol, water and butyl octanoate was investigated. Experimental data suggested that the solvated sulfo groups are bonded with the alcohol-water matrix. It was assumed that the examined reaction system included the heterogeneous reaction catalyzed by nonionized sulfo groups as well as the pseudohomogeneous reaction catalyzed by solvated protons. 

The pseudohomogeneous chemical equilibrium (PCE) for the cyclohexanol reaction system is illustrated in Fig. 5.21a and the non-reactive isobaric L-L phase diagram is plotted in Fig. 5.21b. The rafSnate phase is very dose to the pure water vertex (see enlarged view in the right block). The two L-L envelopes intersect the PCE at two points x = (0.3466, 0.1840) and x = (0.0003, 0.9969). The two parts of the PCE outside the L-L region and the so called unique reactive liquid-liquid tie line [19] comprise the heterogeneous chemical equilibrium line (HCE), which is the bold line in Fig. 5.21b. 

Fig. 5.22. Residue curve maps for heterogeneously catalyzed cyclohexanol synthesis at p — 0.1 MPa a-c) pseudohomogeneous liquid system, d-f) heterogeneous liquid system ([19], reprinted from Chem. Eng. Sci., Vol 57, Qi, Kolah and Sundmacher, Pages 163-178, Copyright 2002, with permission from Elsevier Science)...

For the heterogeneous liquid system, the reaction was assumed to take place in both liquid phases. When we compare the RCMs at the same Da for the pseudohomogeneous and heterogeneous systems, again we can find that the properties (including the reactive azeotrope) of the RCMs outside the L-L region are identical. But they are distinct inside the L-L region because of their different chemical equilibrium curves (compare Fig. 5.21). 

If this reaction were to occur only in the aqueous bulk, the film has no role to play, the entire system is pseudohomogeneous, and a true kinetic analysis as outlined earlier is possible. If mass transfer effects are present between the pseudophases, the analysis outlined before for such systems would apply. However, if reaction occurs in the film, two situations can arise (1) reaction occurs only in the micelles present in the film and not in the rest of the film, and (2) reaction occurs in both the micellar and aqueous phases in the film. The analysis of both the situations is very similar to that for microphase action described in Chapter 23. 

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