A Single CSTR

This equation applies to a single CSTR or to the first reactor of CSTRs connected in scries. 

CSTR Rdationstiip between space lime and conversion for a first-order liquid-phase reaclion 

Let s consider a first-order irreversible reaction for which the rate law is 

For liquid-phase reactions, there is no volume change during the course of the reaction, so we can use Equation (3-29) to relate concentration and conversion. 

Wc can combine mole balance Equation (4-7). the rate law and concentration. Equation (3-29) to obtain 

We can combine the mole balance Equation (5-7), the rate law, and concentration Equation (4-12) to obtain 

CSTR relationship between space time and conversion for a firsl-ordcr liquid-pha.sc reaction 

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Since the syrup solids increase generally stepwise while proceeding from one compartment to the next, and the contents of each compartment are boiling under constant pressure, the temperature in each succeeding compartment increases. It is claimed that the linear flow behavior provided by the reactor staging results in more favorable rubber phase morphology than would be the case if the second reactor were operated as a single CSTR. 

Compare this result with that for a single, ideal reactor having the same input concentration, throughput, and total volume. Specifically, compare the outlet concentration of the composite reactor with that from a single CSTR having a... 

Thus, the combination reactor gives intermediate performance. The fraction unreacted from the composite reactor will be lower than that from a single CSTR with F = q + F2 but higher than that from a single PFR with F = Fi + F2. 

Thus, aout/cim = 0.432 for the series combination. A single CSTR with twice the volume has ki ajn = 1. Equation (4.16) gives Uoutlam =0.5 so that the composite reactor with two tanks in series gives the higher conversion. 

Thus, a single CSTR requires 144.6 times the volume of a single PFR, and the inefficiency of using a CSTR to achieve high conversions is dramatically illustrated. The volume disadvantage drops fairly quickly when CSTRs are put in series, but the economic disadvantage remains great. Cost consequences are explored in Problems 4.19 and 4.20. 

Example 6.2 Cost-out a process that uses a single CSTR for the reaction. Solution The reactor design equations are very simple ... 

Simple evaluation of a single CSTR using a binary search... 

The results for a single CSTR operating at 7 , = 400K and F=10m are shown below ... 

TABLE 6.2 Results of a Comprehensive Search for the Case of a Single CSTR... 

Example 6.7 Determine optimal reactor volumes and operating temperatures for the three ideal reactors a single CSTR, an isothermal PER, and an adiabatic PER. 

The stability of a first-order exothermic reaction A—>B, in a single CSTR with jacket cooling has been studied by Seborg (1971), and the usefulness of simulations for this type of investigation has been emphasised by Luus (1972). The influence of sinusoidal, feed-temperature variations is corrected by simple... 

For a single continuous reactor, the model predicted the expected oscillatory behaviour. The oscillations disappeared when a seeded feed stream was used. Figure 5c shows a single CSTR behaviour when different start-up conditions are applied. The solid line corresponds to the reactor starting up full of water. The expected overshoot, when the reactor starts full of the emulsion recipe, is correctly predicted by the model and furthermore the model numerical predictions (conversion — 25%, diameter - 1500 A) are in a reasonable range. 

It is readily apparent that equation 8.3.21 reduces to the basic design equation (equation 8.3.7) when steady-state conditions prevail. Under the presumptions that CA in undergoes a step change at time zero and that the system is isothermal, equation 8.3.21 has been solved for various reaction rate expressions. In the case of first-order reactions, solutions are available for both multiple identical CSTR s in series and individual CSTR s (12). In the case of a first-order irreversible reaction in a single CSTR, equation 8.3.21 becomes... 

The total volume of the two reactors is 6.72 m3, which is considerably less than half that required if only a single CSTR is employed. 

What degree of conversion would be obtained in a single CSTR equal in size to the tubular reactor ... 

The material balance on a single CSTR operating at steady state may be represented by ... 

Illustration 10.8 indicates how one determines the optimum temperature at which a single CSTR should be operated. 

ILLUSTRATION 10.8 DETERMINATION OF OPTIMUM TEMPERATURE FOR OPERATION OF A SINGLE CSTR IN WHICH A REVERSIBLE EXOTHERMIC REACTION IS BEING CARRIEb OUT... 

The relative response of a single CSTR to an ideal pulse input may be obtained by taking the time derivative of equation 11.1.13. 

A single CSTR of volume V is to be replaced in an emergency by three tanks of volumes V/2, 3V/8, and y/8. If the same performance with a given reaction and throughput is to be achieved, how should the tanks be arranged, and how should the total volumetric throughput... 

To develop E(B) for two CSTRs in series, we use a slightly different, but equivalent, method from that used for a single CSTR in Section 13.4.1.1. Thus, consider a small amount (moles) of tracer M, nMo = F,dt, where Ft is the total steady-state molar flow rate, added to the first vessel at time 0. The initial concentration of M is cMo = nMo/(V/2). We develop a material balance for M around each tank to determine the time-dependent outlet concentration of M from the second vessel, cM2(l). 

As indicated in the problem statement, E(t) is based upon two cases a single CSTR, and two CSTRs in series. The respective E(t) expressions are ... 

Table 20.2 gives the results obtained for the two cases, with E(t) based upon a single CSTR, and upon two CSTRs in series. 

Current operation achieves 90% of equilibrium conversion in a single CSTR. The single unit is to be replaced by two units with the same total residence time. Find the proportions of the two stages that will give the highest conversion. At equilibrium,... 

The family of curves represented by eqn. (46) is shown in Fig. 11 and the mean and variance of both the E(f) and E(0) RTDs are as indicated in Table 5. When N assumes the value of 0, the model represents a system with complete bypassing, whilst with N equal to unity, the model reduces to a single CSTR. As N continues to increase, the spread of the E 0) curves reduces and the curve maxima, which occur when 0 = 1 —(1/N), move towards the mean value of unity. When N tends to infinity, E(0) is a dirac delta function at 0 = 1, this being the RTD of an ideal PER. The maximum value of E(0), the time at which it occurs, or any other appropriate curve property, enables the parameter N to be chosen so that the model adequately describes an experimental RTD which has been expressed in terms of dimensionless time see, for example. Sect. 66 of ref. 26 for appropriate relationships. 

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