CSTR mass balance

Note that this problem is even easier than for a batch reactor because for the CSTR we just have to solve an algebraic equation rather than a differential equation For second-order kinetics, r = kC, the CSTR mass-balance equation becomes... 

We took the 4- sign on the square root term for second-order kinetics because the other root would give a negative concentration, which is physically unreasonable. This is true for any reaction with nth-order kinetics in an isothermal reactor There is only one real root of the isothermal CSTR mass-balance polynomial in the physically reasonable range of compositions. We will later find solutions of similar equations where multiple roots are found in physically possible compositions. These are true multiple steady states that have important consequences, especially for stirred reactors. However, for the nth-order reaction in an isothermal CSTR there is only one physically significant root (0 < Ca < Cao) to the CSTR equation for a given T. ... 

Returning to the CSTR mass-balance equation for species A, we obtain... 

Now the mass density varies with conversion because 1 mole of A is converted into 2 moles of C when the reaction system goes to completion. Therefore, we cannot use the CSTR mass-balance equations, Cjo — Cj = X to use the variable-... 

For a CSTR we solve the transient CSTR mass-balance equation because we want the time dependence of a pulse injection without reactiou The transient CSTR equation on a species of concentration C is... 

Calculate the conversion of A B, r = kC in two CSTRs using the residence time distribution and compare the result with that obtained by integrating the CSTR mass balances. Repeat this problem for zeroth-order kinetics. 

However, when we examine the CSTR mass balance, we see that the pseudo-Steady-state approximation is indeed that the concentration be small or that [CH3CO ]/t = 0. Thus by examining the CSTR version of the mass-balance equations, we are led to the pseudo-steady-state approximation naturally. This is expressly because the CSTR mass-balance equations are developed assuming steady state so that the pseudo-steady-state approximation in fact implies simply that an intermediate species is in steady state and its concentration is small. 

The CSTR mass-balance equations for these species are... 

However with stirring and coalescence and breakup, both effects tend to mix the contents of the bubbles or drops, and this situation should be handled using the CSTR mass balance equation. As you might expect, for a real drop or bubble reactor the residence time distribution might not be given accurately by either of these limits, and it might be necessary to measure the RDT to correctly describe the flow pattern in the discontinuous phase. 

Combining this with the conventional CSTR mass balance gives uCo... 

Based on the kinetic mechanism and using the parameter values, one can analyze the continuous stirred tank reactor (CSTR) as well as the dispersed plug flow reactor (PFR) in which the reaction between ethylene and cyclopentadiene takes place. The steady state mass balance equations maybe expressed by using the usual notation as follows ... 

The mass balance of a continuous flow stirred-tank reactor (CSTR) with a first-order chemical reaction is very similar to the problem in Section 2.8.1 (p. 2-20). We just need to add the chemical reaction term. The balance written for the reactant A will appear as ... 

Thus, for known kinetics and a specified residence time distribution, we can predict the fractional conversion of reactant which the system of Fig. 9 would achieve. Recall, however, that this performance is also expected from any other system with the same E(t) no matter what detailed mixing process gave rise to that RTD. Equation (34) therefore applies to all reactor systems when first-order reactions take place therein. In the following example, we apply this equation to the design of the ideal CSTR and PFR reactors discussed in Chap. 2. The predicted conversion is, of course, identical to that which would be derived from conventional mass balance equations. 

The flow-mixing transfer functions Gi(s) and G2(s) can be chosen to represent any desired parallel or series combinations of PFRs and CSTRs or other more complex elements. Making a mass balance at the entry flowmixing point... 

Consider a CSTR of constant volume V, operated in the steady state, with a volumetric throughflow Q in which a first-order reaction, with rate coefficient k, is occurring. The inlet concentration of the reacting species is Ca and the outlet concentration is Ca. Writing the conventional mass balance for a CSTR... 

With these approximations we write the steady-state mass balance on species j in the CSTR as... 

This will be the most used forni of the mass-balance equation in the CSTR in this book. Students should either memorize this equation or preferably be able to derive it from an integral mass balance on the reactor. This equation requires three major assumptions ... 

For the CSTR we begin with the mass-balance equation we derived before we substitute for concentration... 

This expression can be inserted into the CSTR and PFTR mass-balance equations to yield... 

For first-order kinetics with equal-volume CSTR reactors (and therefore for all TS equal), the mass balances on species A become... 

For a PFTR followed by a CSTR we solve each reactor mass balance sequentially to find Ca2(Cao t). For first-order kinetics this gives... 

In this chapter we consider the performance of isothermal batch and continuous reactors with multiple reactions. Recall that for a single reaction the single differential equation describing the mass balance for batch or PETR was always separable and the algebraic equation for the CSTR was a simple polynomial. In contrast to single-reaction systems, the mathematics of solving for performance rapidly becomes so complex that analytical solutions are not possible. We will first consider simple multiple-reaction systems where analytical solutions are possible. Then we will discuss more complex systems where we can only obtain numerical solutions. 

Next we consider parallel first-order irreversible reactions in a CSTR. The mass-balance equations with Cbo Cco are... 

All these arguments require a single reactant A on which to base the calculation of selectivity. For more complex situations we can stiU determine how the selectivity varies with conversion in PFTR and CSTR, but calculation of the selectivity requires complete solution of the mass-balance equations. 

In a CSTR the mass balances on the three species become... 

For the CSTR we have S algebraic species mass-balance equations. We can eliminate S R of these to obtain R irreducible algebraic polynomials in R of the S species which we... 

We first derive the energy balance in a CSTR. For the mass balance in a constant-density reactor we wrote an integral balance on the rate of change of the number of moles Nj of species j in the reactor to obtain... 

The last term is not present in the mass balance (unless the reactor leaks), but heat can be carried in and out not only with flow but also by heat transfer through the walls. An enthalpy balance on the contents of this CSTR gives... 

For a single reaction in a steady-state CSTR the mass-balance equation on reactant A and temperature T give the equations... 

For the adiabatic reactor we have a unique relation between T and conversion. We can therefore solve for T and eliminate it from the mass-balance equation. For the CSTR the mass-balance equation for a single first-order irreversible reaction... 

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