Mole balances CSTRs

The CSTR model, on the other hand, is based on a stirred vessel with continuous inflow and outflow (see Fig. 1.2). The principal assumption made when deriving the model is that the vessel is stirred vigorously enough to eliminate all concentration gradients inside the reactor (i.e., the assumption of well stirred). The outlet concentrations will then be identical to the reactor concentrations, and a simple mole balance yields the CSTR model equation ... 

It is useful to examine the consequences of a closed ion source on kinetics measurements. We approach this with a simple mathematical model from which it is possible to make quantitative estimates of the distortion of concentration-time curves due to the ion source residence time. The ion source pressure is normally low enough that flow through it is in the Knudsen regime where all collisions are with the walls, backmixing is complete, and the source can be treated as a continuous stirred tank reactor (CSTR). The isothermal mole balance with a first-order reaction occurring in the source can be written as... 

We are going to formulate the mole balance equation in a CSTR operating at steady state, where nothing changes with time. This means that there is no accumulation inside the reactor and that the inlet, as well as outlet streams are at steady state. Following the general equation the mole balance for a component i in a CSTR is... 

Let us write the mole balance equation for the reactant in the /-th CSTR ... 

Constant density implies that the volumetric flow rate from reactor to reactor is constant. The relationships listed in Table 7.4 apply to any number of CSTRs in series. The subscript, n, refers to the reactor number and also to the number of the entering stream. The subscript, n + 1, refers to the number of the leaving stream. Equations 7.4.1 to 7.4.3, are the mole balance for reactant A, the energy equation, and the rate equation. 

The mole balance can now be conpleted for one CSTR. The inlet molar flow rate for propylene oxide is calculated above. The inlet molar flow rate of methanol,... 

Table 7.1.2 Mole Balance for a CSTR Producing Propylene Glycol ...

P1-6a What is the difference between the rate of reaction for a homogeneous system, —ta, and the rate of reaction for a heterogeneous system, — ri Use the mole balance to derive an equation analogous to Equation (1-6) for a fluidized CSTR containing catalyst particles in terms of the catalyst weight, IV, and other appropriate terms. 

A mole balance on species A for the CSTR in the middle gives... 

These are the forms [Note In many calculations the CSTR mole balance (Fao -r y) will be i... 

L s calculate the CSTR volume necessary to achieve 40% conversion. The mole balance is... 

To obtain a plot of heat generated, G(T), as a function of temperature, we must solve for X as a function of T using the CSTR mole balance, the rate law, and stoichiometry. For example, for a first-order liquid-phase reaction, the CSTR mole balance becomes... 

Liquid Phase. For liquid-phase reactions in which there is no volume change, concentration is the preferred variable. The mole balances are shown in Table 4-5 in terms of concentration for the four reactor types we have been discussing. We see from Table 4-5 that we have only to specify the parameter values for the system (CAo,Uo,etc.) and for the rate law (i.e., ifcyv. .3) to solve the coupled ordiaaiy differential equations for either PFR, PBR, or batch reactors or to solve the coupled algebraic equations for a CSTR. 

The startup of a fixed volume CSTR under iscrthennal conditions is rare, but it does occur occasionally. Here we want to determine the time necessary to reach steady-state operation. We begin with the general mole balance equation applied to Figure 4-13a ... 

In a similar fashion one can solve the combined CSTR mole balances and rate laws, that is,... 

In many instances the ACp T-Tg) term in the denominator of Equation (8-49) is negligible with respect to the term, so that a plot of X vs. T will usually be linear, as shown in Figure 8-3. To remind us that the conversion in this plot was obtained from the energy balance rather than the mole balance it is given the subscript EP (i.e., Zgs) in Figure 8-3. Equation (8-49) applies to a CSTR, PER, PER, and also to a batch (as will be shown in Chapter 9). For g = 0 and Ws = 0, Equation (8-49) gives us the explicit relationship between X and T needed to be used in conjunction with the mole balance to solve reaction engineering problems as discussed in Section 8.1. 

Note that equations analogous to Equation (8-71) for G(T) can be derived for other reaction orders and for reversible reactions simply by solving the CSTR mole balance for X. For example, for the second-order liquid-phase reaction... 

Both CSTR energy and mole balances are of the form... 

For a packed-bed reactor, the approach is quite similar to that described for a CSTR. For a first-order reaction, the combined mole balance and rate law is... 

Again, consider first the CSTR followed ly the plug-flow section (Figure El 3-4.1). A mole balance on the CSTR section gives... 

Combining the CSTR mole balance, the rate law, and stoichiometry, we have... 

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