Reactor equal-sized

Thus the problem involves the two independent variables, time t and length Z. The distance variable can be eliminated by finite-differencing the reactor length into N equal-sized segments of length AZ such that N AZ equals L, where L is the total reactor length. 

The boundary conditions are satisfied by Cq = 1 for a step change in feed concentration at the inlet, and by the condition that at the outlet C n+i = C n, which sets the concentration gradient to zero. The reactor is divided into 8 equal-sized segments. 

As Levenspiel points out, the optimum size ratio is generally dependent on the form of the reaction rate expression and on the conversion task specified. For first-order kinetics (either irreversible or reversible with first-order kinetics in both directions) equal-sized reactors should be used. For orders above unity the smaller reactor should precede the larger for orders between zero and unity the larger reactor should precede the smaller. Szepe and Levenspiel (14) have presented charts showing the optimum size ratio for a cascade of two reactors as a function of the conversion level for various reaction orders. Their results indicate that the minimum in the total volume requirement is an extremely shallow one. For example, for a simple... 

For the case of multiple equal-sized reactors in series, the problem of determining the reactor sizes necessary to achieve a specified degree of... 

We wish to determine the effect of using a cascade of two CSTR s that differ in size on the volume requirements for the reactor network. In Illustration 8.8 we saw that for reactors of equal size the total volume requirement was 6.72 m3. If the same feed composition and flow... 

For a first-order reaction, we showed that for a cascade composed of equal-sized reactors, equation 8.3.42 governed the effluent composition from the nth reactor. 

Comparison of performance of a series of N equal-size CSTR reactors with a plug flow reactor for the first-order reaction... 

In Section 11.1.3.2 we considered a model of reactor performance in which the actual reactor is simulated by a cascade of equal-sized continuous stirred tank reactors operating in series. We indicated how the residence time distribution function can be used to determine the number of tanks that best model the tracer measurement data. Once this parameter has been determined, the techniques discussed in Section 8.3.2 can be used to determine the effluent conversion level. 

The model of a reactor consists of two equal sized CSTRs joined by a PFR whose residence time equals that of the combined CSTRs. A second order... 

The model of a reactor consists of two equal sized CSTRs joined by a PFR whose residence time equals that of the combined CSTRs. A second order reaction with kC0t = 2 is to be studied by the maximum mixedness mechanism. More details of this problem are in problem P5.04.09 where the RTD is developed as... 

CN+i = CN, which sets the concentration gradient to zero. The reactor is divided into equal-sized segments. 

The reactor length is divided into equal-sized sections, whose number, Nelem, can be varied. The model equations are written in dimensionless form. 

Finite-differencing the dimensionless length of the reactor (Z = l) into N equal-sized segments of length AZ, such that N AZ = L, gives for segment n... 

Gibilaro [49] has considered a recycle model of the form of eqn. (60) where Gj (s) and G2(s) are general series combinations of PFR and equal size CSTR reactors and he gives sixteen references to published work involving more restricted forms of Gj (s) and G2 is). With an infinite choice over the forms of G (s) and G2(s) and the magnitude of R, the recycle model is seen to be the most flexible of all flow-mixing models. The performance of each specific form of Gj (s) as a potential reactor must be investigated individually in practice, the model is often reduced to a pure PFR element... 

Equal-Size Mixed Flow Reactors in Series... 

Let us now quantitatively evaluate the behavior of a series of N equal-size mixed flow reactors. Density changes will be assumed to be negligible hence 8 = 0 and r = T. As a rule, with mixed flow reactors it is more convenient to develop the necessary equations in terms of concentrations rather than fractional conversions therefore, we use this approach. The nomenclature used is shown in Fig. 6.4 with subscript i referring to the ith vessel. 

Figure 6.4 Notation for a system of N equal-size mixed reactors in series.

Now the space-time t (or mean residence time t) is the same in all the equal-size reactors of volume V,. Therefore,... 

The optimum size ratio for two mixed flow reactors in series is found in general to be dependent on the kinetics of the reaction and on the conversion level. For the special case of first-order reactions equal-size reactors are best for reaction orders n > 1 the smaller reactor should come first for n < 1 the larger should come first (see Problem 6.3). However, Szepe and Levenspiel (1964) show that the advantage of the minimum size system over the equal-size system is quite small, only a few percent at most. Hence, overall economic consideration would nearly always recommend using equal-size units. 

Reactant A (A R, C o = 26 mol/m ) passes in steady flow through four equal-size mixed flow reactors in series (r otai = 2 min). When steady state is achieved the concentration of A is found to be 11, 5, 2, 1 mol/m in the four units. For this reaction, what must be so as to reduce from... 

Scheme Q D, and E, From Fig. 12.1 the exit age distribution function for the two equal-size plug-mixed flow reactor system is...

For a series of equal-sized backmix reactors the exit age distribution function is... 

Table 11.2 Dimensionless total holding times for optimal and equal-sized mixed reactors, for a =0.01 and two values of k.

Table 11.2 gives the total holding times for two values of K, both for a series of CSTRs with minimal total volume and for a series of equal-sized mixed reactors. Total holding times for equal-sized mixed reactors have been calculated using a zero finding routine. The last value in Table 11.2 is the dimensionless holding time for a PFR reactor with Michaelis-Menten kinetics, calculated by means of the following equation ... 

An important observation from Table 11.2 is the considerable difference going from one to two or more CSTRs. For the conditions studied, there is only a minor difference (less than 10%) between the total holding time for optimal and equal-sized mixed reactors. Even in extreme cases, i.e., for very low values of k and this difference remains relatively small (37% for n=3, k=10 and df=10 ). 

Furthermore, it can be shown that, in the limiting cases of first-order kinetics [Equation (11.35) also holds for this case] and zero-order kinetics, the equal and optimal sizes are exactly the same. As shown, the optimal holding times can be calculated very simply by means of Equation (11.40) and the sum of these can thus be used as a good approximation for the total holding time of equal-sized CSTRs. This makes Equation (11.31) an even more valuable tool for design equations. The restrictions are imposed by the assumption that the biocatalytic activity is constant in the reactors. Especially in the case of soluble enzymes, for which ordinary Michaelis-Menten kinetics in particular apply, special measures have to be taken. Continuous supply of relatively stable enzyme to the first tank in the series is a possibility, though in general expensive. A more attractive alternative is the application of a series of membrane reactors. 

After some manipulation this gives =1, showing that the two reactors should be of equal size. If, however, a fixed total volume is considered and the ratio s is varied to find the effect on a2, the maximum value of a2 is found by setting ... 

For the vinyl acetate system at 0.06 mol/1 of emulsifier in the feed, the process identification technique of Brantley (10) was used to find the conversion response of the third equal-sized reactor in the train to changes in feed rate of initiator to that reactor ... 

On the basis of the considered macroscopic flow pattern, the dominant circulation flows (/ c and Fc/2) subdivide the reactor into three parallel levels, where each level is then divided into Nc/3 equally sized compartments of equal volume Vc = Vr/Nc. Every compartment is modeled as a nonstationary ideal continuous stirred tank reactor, with a main inlet and outlet flow, which connects the given compartment with adjacent compartments on the same level, and secondary exchange flow rates accounting for the turbulent mixing with adjacent compartments laying on the upper and/or lower level (Fig. 7.3). 

For N equal size mixed flow reactors in series, a general equation for the exit concentration CAN is... 

Consider a series of continuous flow stirred tank reactors of equal size with inlet and exit conversions as X0 and XN. The intermediate optimal conversions Xu X2, X3. .. Xt. .. XN t can be determined, which will minimize the overall reactor size. Levenspiel [1] has shown... 

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