For a CSTR

CSTR Reactions For a CSTR reaction, the quantities tij are molal flow rates. Per unit of time,... 

Conditions at steady state are determined by heat and material balances. Such balances for a CSTR can be put in the form. 

As can be seen for infinite recycle ratio where C = Cl, all reactions will occur at a constant C. The resulting expression is simply the basic material balance statement for a CSTR, divided here by the catalyst quantity of W. On the other side, for no recycle at all, the integrated expression reverts to the usual and well known expression of tubular reactors. The two small graphs at the bottom show that the results should be illustrated for the CSTR case differently than for tubular reactor results. In CSTRs, rates are measured directly and this must be plotted against the driving force of... 

The material balance function for a CSTR, m(C,T) is the transient material balance equation ... 

For the design of a CSTR with inhibition, consider the following rate is valid for a CSTR as a fermentation vessel. 

The Monod rate model is valid for a CSTR bioreactor with maximum specific growth rate of 0.5 li 1 and K, 2 g-1. What would be a suitable dilution rate at steady-state condition, where there is no cell death if initial substrate concentration is 50g-l-1 and yield of biomass on substrate is 100%. 

One of the most promising ways of dealing with conversion oscillations is the use of a small-particle latex seed in a feed stream so that particle nucleation does not occur in the CSTRs. Berens (3) used a seed produced in another reactor to achieve stable operation of a continuous PVC reactor. Gonzalez used a continuous tubular pre-reactor to generate the seed for a CSTR producing PMMA latex. 

Determine t and Ugut for a CSTR that approaches equilibrium within 5% that is. 

The design equations for a CSTR do not require that the reacting mixture has constant physical properties or that operating conditions such as temperature and pressure be the same for the inlet and outlet environments. It is required, however, that these variables be known. Pressure in a CSTR is usually determined or controlled independently of the extent of reaction. Temperatures can also be set arbitrarily in small, laboratory equipment because of excellent heat transfer at the small scale. It is sometimes possible to predetermine the temperature in industrial-scale reactors for example, if the heat of reaction is small or if the contents are boiling. This chapter considers the case where both Pout and Tout are known. Density and Q ut wiU not be known if they depend on composition. A steady-state material balance gives... 

There is one significant difference between batch and continuous-flow stirred tanks. The heat balance for a CSTR depends on the inlet temperature, and Tin can be adjusted to achieve a desired steady state. As discussed in Section 5.3.1, this can eliminate scaleup problems. 

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 ... 

Example 12.3 Suppose S P according to first-order, Michaelis-Menten kinetics. Find Sout for a CSTR. 

The case for a CSTR is similar. Under normal operating conditions, the solution in Example 12.3 will apply to free enzymes as well as to confined enzymes. Like the PFR case, unusual behavior will occur if kfis small or if the substrate is very dilute so Sj Ej . 

Since = 0, the steady-state cell balance for a CSTR is... 

Set the time derivatives in Example 12.6 to zero to find the steady-state design equations for a CSTR with a Michaelis-Menten reaction. An analytical solution is possible. Find the solution and compare it with the solution in Example 12.3. Under what conditions does the quasisteady solution in Example 12.3 become identical to the general solution in Example 12.6 ... 

The dimensionless variance has been used extensively, perhaps excessively, to characterize mixing. For piston flow, a = 0 and for a CSTR, a = l. Most turbulent flow systems have dimensionless variances that lie between zero and 1, and cr can then be used to fit a variety of residence time models as will be discussed in Section 15.2. The dimensionless variance is generally unsatisfactory for characterizing laminar flows where > 1 is normal in liquid systems. 

The Single CSTR. The washout function for a CSTR is found from its response to a negative step change in tracer concentration from Equation (15.1) ... 

Solution The limits you can calculate under part (a) correspond to the three apexes in Figure 15.14. The limits are 0.167 for a PFR (Equation (1.47)), 0.358 for a CSTR (Equation (1.52)), and 0.299 for a completely segregated stirred tank. The last limit was obtained by integrating Equation (15.48) in the form... 

Dynamic differential equation balances were written to calculate the molar concentration of each species in the reactor. These equations consist of inflow, outflow, accumulation, and reaction terms for a CSTR. If there are no outflow terms, the equations reduce to semibatch... 

This equation differs from that for the plug flow reactor (8.2.9) in that for a CSTR the rate is evaluated at effluent conditions and thus appears outside the integral. 

Unlike the situation in the PFR, there is always a simple relationship between the mean residence time and the reactor space time for a CSTR. Since one normally associates a liquid feed stream with these reactors, volumetric expansion effects are usually negligible (SA = 0). 

For a CSTR equal in volume to the tubular reactor, one moves along a line of constant kCB0T in Figure 8.16 in order to determine the conversions accomplished in cascades composed of different numbers of reactors but with the same overall space time. The intersection of the line/cCg0T = 19.6 and the curve for N = 1 gives fB = 0.80. 

If there is no volume change because of reaction, the design equation for a CSTR indicates that... 

Derive the F(t) curve for a CSTR by considering its response to a step change in the input tracer concentration. Let Wq and represent the weight fraction tracer in the feed before and... 

In Figure 4.4, similar to Figure 4.3, cA/cAo is plotted as a function of MAn. The behavior is similar in both figures, but the values of cA/cAo for a CSTR are higher than those for a BR or PFR (except for n = 0, where they are the same). This is an important characteristic in comparing these types of reactors (Chapter 17). Another difference is that cAlcAo approaches 0 asymptotically for all values of n > 0, and not just for n 1, as in Figure 4.3. 

We derive the kinetics consequences for this scheme for reaction in a constant-volume batch reactor, the results also being applicable to a PFR for a constant-density system. The results for a CSTR differ from this, and are explored in Example 18-4. 

Repeat part (b) of Example 8-2 for a CSTR, and comment on the result. 

Backmix flow (BMF) is the flow model for a CSTR, and is described in Section 2.3.1. BMF implies perfect mixing and, hence, uniform fluid properties throughout the vessel. It also implies a continuous distribution of residence times. The stepwise or discontinuous change in properties across the point of entry, and the continuity of property behavior across the exit are illustrated in Figure 2.3. 

In this chapter, we develop the basis for design and performance analysis for a CSTR (continuous stirred-tank reactor). The general features of a CSTR are outlined in Section 2.3.1, and are illustrated schematically in Figure 2.3 for both a single-stage CSTR and a two-stage CSTR. The essential features, as applied to complete dispersion at the microscopic level, i.e., nonsegregated flow, are recapitulated as follows ... 

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