CSTRs in Parallel

Since the reactors are of equal size, operate at the same temperature, and have identical feed rates, the conversion will be the same for each reactor  

The volume of each individual reactor. V . is related to the total volume. K of all the reactors by the equation 

A similar relationship exists for the total molar flow rate, which is equally divided  

Substituting these values into Equation (4-12) yields 

Com ersioti for ranks in parallel. Is rhis result surprising  

In Section 15.4 for PFRs operated in parallel, it is noted (point (3)) that when exit streams are combined, they should be at the same state for example, they should have the same composition. The same applies to CSTRs operated in parallel. In the following example, it is shown that this leads to the most efficient operation. 

For a given throughput (q0), the maximum rate of production is obtained if cA at M is 

The result contained in equation 17.2-1 is that the feed should be split in the same ratio as the sizes of the tanks. An implication of this result is that the space times in the two tanks should be equal  

That is, the two exit streams are at the same composition before being mixed at M. 

With the feed divided as in equation (17.2-1), the two tanks act together the same as one tank of volume V= Vj + V2. There is thus no inherent performance advantage of multiple CSTRs in parallel, but there may be increased operating flexibility. 

You probably are suspicious that this configuration is not very practical. We have already learned that the performance of two CSTRs in sraies is better than the performance of a single CSTR with the same total volume. Is thrae any reason to believe that two CSTRs in parallel will praform better than a single CSTR with the same total volume  

Let s tackle this question by analyzing a simplified version of the above configuration. Suppose that the feed is split into two equal streams, so that Fao(1) = Fao(2) = Fao/2. Considerthe case where both reactors are operated at the same temperature and with the same feed concentrations, and where the kinetics are normal. If the avera conversion x is fixed, will the total reactor volume be lower if the two reactors each have the same volume, or will the total volume be lower if the two reactors have different volumes  

Let reactor 1 be smaller than reactor 2, i.e., V V2. Since both reactors have the same molar inlet flow rate of A (Fao/2), the fractional conversion of A in the stream leaving reactor 1 willbelowerthantheconversionleavingreactor2,i.e., jca,i xa,2-The conversion of A in the combined effluent is x, and the molar feed rate of A to each reactor is the same. Therefore, if A = jc — xa,i, then xa,2 = A -H x. 

The area of the rectangle bounded by solid lines, i.e., (1/—rA(x)) x x, is the value of V/(Fao/2), where Vis the volume required to produce a conversion of x when the molar flow rate of A to the reactor is Fao/2. The area of the lower unfilled r on is Vi / (Fao/2). Thaefore, the area of flie lower L-shaped region, with diagonals running Atom upper left to lowerri t, is the difference between V/(Fao/2) and Vi/(FAo/2),i.e.,2 (V Ao) — (Vi ao) -This area is directly proportional to the diffoence (V — Vi). It is the volume savings associated with the smaller reactor, operating at a conversion xa,i, compared to a reactor wifli a volume of V, operating with the same feed rate (Fao/2), but at a hi er conversion x. 

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Figure 17.2 Flow diagram for CSTRs in parallel in Example 17-3...

For CSTRs in parallel with the feed split as for optimal performance, the fact that two (or more) reactors behave the same as one CSTR of the same total volume means that the RTD is also the same in each case. Here, we consider the RTD for CSTRs in series, as in a multistage CSTR (Section 14.4). In the following example, the RTD is obtained for two tanks in series. The general case of N tanks in series is considered in Chapter... 

A reactor is made up of three zones. Zone 1 is a CSTR in parallel with a PFR that is zone 2, and both are in series with zone 3 that is another PFR. The fraction of the flow going to the CSTR is a. Find the response functions E(tr) and F(tr). 

I. G. Farbenindustrie in Germany implemented such a concept to produce polystyrene commercially in the 1930s. Two CSTRs in parallel followed by a plug flow reactor were used in their process. During World War II, Union Carbide applied for a patent (US Patent 2496653, 1950) for a continuous polystyrene process. Their process consisted of three cascade CSTR reactors followed by a plug flow reactor. The temperature in the three CSTR reactors is 100, 115-120 and 140 °C, respectively. The conversion at the outflow of the third CSTR reactor is around 85 %. The temperature in the plug flow reactor is between 210 and 215 °C. The final conversion at the plug flow reactor was claimed to be 97 %. 

CSTRs in Parallel. We now consider the case in which equal-sized reactors are placed in parallel rather than in series, and the feed is distributed equally among each of the reactors (Figure 4-5). A balance on any reactor, say i, gives... 

CSTRs in parallel. For two 800-gal CSTRs arranged in parallel with 7.67 ftVmin (Vo/2) fed to each reactor, the conversion achieved can be calculated from... 

Two equal-sized CSTRs in series will give a higher conversion than two CSTRs in parallel of the same size when the reaction order is greater than zero. 

Figure 14-14 Combinations of ideal reactors used to model real PFRs. (a) two PFRs in parallel (b) PFR and CSTR in parallel.

P14-1b Make up and solve an original problem. The guidelines are given in Problem P4-1. However, make up a problem in reverse by first choosing a model system such as a CSTR in parallel with a CSTR and PFR [with the PFR modeled as four small CSTRs in series Figure P14-l(a)] or a CSTR with recycle and bypass [Figure P14-l(b)]. Write tracer mass balances and use an ODE solver to predict the effluent concentrations. In fact, you could build up an arsenal cf tracer curves for different model systems to compare against real reactor RTD data. In this way you could deduce which model best describes the real reactor. 

The model in Fig 14-14b is PFR and CSTR in parallel. The exit age distribution for the eSTR is a negative gradient curve, intcmipted by the distinct exit age distribution pulse of the PFR. The CSTR will always provide a fraction of eflluenc which has been inside the reactor for less than time t, which incicases with time. But when (he effluent exits the PFR at a specified time after zero, this increased effluent is superimposed upon F9t) of the CSTR. giving a combined F(t). 

Two CSTRs in parallel. The volume of each reactor is 5 L and the volumetric flow rate in each reactor is 5 L/min. 

System C consists of a PFR and CSTR in parallel. By increasing the ratio of CSTR feed rate to PFR feed rate, the degree of mixing is increased. By increasing the ratio of PFR feed rate to CSTR feed rate, dead space (regions that are not well mixed) in a CSTR can be simulated. 

Figure 4-11 Graphical representation of the design equations for two CSTRs in parallel.

For two CSTRs in parallel, with the same feed to each reactor, the required total volume is greater if the CSTRs have different volumes and operate at different conversions than if the two CSTRs have the same volume and operate at the same conversion. 

This analysis confirms that operating two CSTRs in series would give a better performance than operating the same reactors in parallel. In fact, it is difficult to imagine a situation where one would deliberately choose to operate two CSTRs in parallel. 

PFRs or CSTRs in parallel have, at best, the same performance as a single CSTR or PFR, respectively. 

The existence of two CSTRs in parallel is easier to detect, and analysis of the E t) data is easier, if ln[E(t)] is plotted against time. If the values of x for the two reactors are sufficiently different, the value of (//r) x E t) for the reactor with the smaller value of t will he much greater than ( //t) x E t) for the reactor with the larger value, at short times. The converse will be true at long times. 

The information in the table below was obtained for a vessel with a constant-density fluid flowing through it at steady state. It is has been suggested fliat the vessel can be modeled as two CSTRs in parallel, each with a different space time. Determine the best values of the unknown parameters in this model and compare the model with the values in the table. 

A nonlinear regression was then performed in an EXCEL spreadsheet using SOLVER, beginning with these estimates.The resulting values of ti, x, and f were 10 min, 49 min, and 0.80. These values were then used to calculate E t). A comparison of the E(t) data from the table above with the calculated values of E(t) from the CSTRs in parallel compartment model are shown in the following table. The fit of the model to the data is excellent. 

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