Pseudohomogeneous rates

However, the intrinsic pseudohomogeneous rate used in Equation (10.39) is not identical to the rate determined from the CSTR measurements since the catalyst density will be different. The correction procedure is... 

The intrinsic pseudohomogeneous rate as determined using the CSTR is... 

Example 10.10 Suppose the reaction in Example 10.9 is first order. Determine the pseudohomogeneous rate constant, the rate constant based on catalyst mass, and the rate constant based on catalyst surface area. 

Solution Since = —kuout for a CSTR, the rates in the previous example are just divided by the appropriate exit concentrations to obtain k. The ordinary, gas-phase concentration is used for the pseudohomogeneous rate ... 

It is more common to specify not the catalyst surface area per unit volume of pellet (we frequently have a problem in deterrnining the pellet volume and e), but rather its area per unit weight of catalyst. We then measure its rate per weight of catalyst r (units of molesAveight time) rather than its rate per unit area of catalyst r". The pseudohomogeneous rate r is now... 

Thus we can in general write for the pseudohomogeneous rate of a catalytic reaction in a reactor with porous catalyst pellets... 

We now can begin to see how we choose catalyst parameters in a catalytic reactor if we want the pseudohomogeneous rate to be as high as possible. We write the general expression for a catalytic reaction rate as... 

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

As with catalytic reactions, our task is to develop pseudohomogeneous rate expressions to insert into the relevant mass-balance equations. For ary multiphase reactor where reaction occurs at the interface between phases, the reactions are pritnarily surface reactions (rate r ), and we have to find these expressions as functions of concentrations and rate and transport coefficients and then convert them into pseudohomogeneous expressions,... 

Here, R, is the pseudohomogeneous rate of production or disappearance of species / per unit volume which in the general case of a network of multiple reactions may be the result of M different chemical transformations. Therefore,... 

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. 

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. 

As discussed in Chapter 7, this form can provide a good fit of the data if the reaction is not too close to equilibrium. However, most reaction engineers prefer a mechanistically based rate expression. This section describes how to obtain plausible functional forms for based on simple models of the surface reactions and on the observation that all the rates in steps 2-8 must be equal at steady state. Thus the rate of transfer across the film resistance equals the rate of diffusion into a pore equals the rate of adsorption equals the rate of reaction equals the rate of desorption and so on. This rate is the pseudohomogeneous rate used in steps 1 and 9. 

SOLUTION The catalyst charge is unchanged. If the reaction is truly heterogeneous and there are no mass transfer resistances, the rate of reaction of the component should be unchanged. More specifically, the pseudohomogeneous rate for the CSTR will change since the... 

To calculate the mass of the catalyst, we use the PFR model, assuming a pseudohomogeneous rate and without axial or radial dispersion effects. Thus ... 

While pseudohomogeneous rates of biokinetics follow the equation for [kgm h i]... 

Pseudokinetic phenomena become evident only when process kinetic analysis is carried out with mathematical models. Most bioprocesses are basically heterogeneous systems. Generally, pseudohomogeneous rates measured in L phase analyses are used, because they are thought to reflect directly the intrinsic reaction rate of metabolism in the solid phase (biomass). Even under steady-state conditions, however, this assumption is not necessarily valid. 

The final equations for the solution of this interacting system are sometimes given in the form of the pseudohomogeneous rate Equ. 6.121, substituting for the factor (/cl2 % s) the rate constant for biological reaction multiplied with the effectiveness factor rjj. (cf. Equ. 4.51)... 

Note again that the concentrations c,- are given in moles per unit void volume, while the pseudohomogeneous rates /), defined by Eq.(2.1.26), are given in moles per unit total volume per unit time. Eq.(2.1.32) is a simplified form of the energy equation. It is a heat conduction equation with a chemical reaction source term and partly neglects the variation with temperature of the enthalpies. 

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