CSTR mean residence time

The CSTR mean residence time is defined in terms of the inlet flow rate qm and the reactor volume Vest,- by... 

Continuous. stirred tank reactor (CSTR), with the effluent concentration the same as the uniform vessel concentration. With a mean residence time t = V /V, the material balance is... 

Frequently, stirred tanks are used with a continuous flow of material in on one side of the tank and with a continuous outflow from the other. A particular application is the use of the tank as a continuous stirred-tank reactor (CSTR). Inevitably, there will be a vety wide range of residence times for elements of fluid in the tank. Even if the mixing is so rapid that the contents of the tank are always virtually uniform in composition, some elements of fluid will almost immediately flow to the outlet point and others will continue circulating in the tank for a very long period before leaving. The mean residence time of fluid in the tank is given by ... 

Ideal CSTR (continuous stirred tank reactor) behavior is approached when the mean residence time is 5-10 times the length of time needed to achieve homogeneity, which is accomplished with 500-2000 revolutions of a properly designed stirrer. 

Example 1.6 Apply Equation (1.54) to calculate the mean residence time needed to achieve 90% conversion in a CSTR for (a) a first-order reaction, (b) a second-order reaction of the type A - - B — Products. The rate constant... 

Also assume that the pilot- and full-scale vessels will operate at the same temperature. This means that A(o-out,bout, . )and/i/2 will be the same for the two vessels and that Equation (1.49) will have the same solution for provided that 7 is held constant during scaleup. Scaling with a constant value for the mean residence time is standard practice for reactors. If the scaleup succeeds in maintaining the CSTR-like environment, the large and small reactors will behave identically with respect to the reaction. Constant residence time means that the system inventory, pV, should also scale as S. The inventory scaleup factor is defined as... 

Example 4.8 Find the yield for a first-order reaction in a composite reactor that consists of a CSTR followed by a piston flow reactor. Assume that the mean residence time is ij in the CSTR and ti in the piston flow reactor. 

Thus, the limit gives the same result as a piston flow reactor with mean residence time t. Putting tanks in series is one way to combine the advantages of CSTRs with the better yield of a PFR. In practice, good improvements in yield are possible for fairly small N. 

The results of Example 5.2 apply to a reactor with a fixed reaction time, i or thatch- Equation (5.5) shows that the optimal temperature in a CSTR decreases as the mean residence time increases. This is also true for a PFR or a batch reactor. There is no interior optimum with respect to reaction time for a single, reversible reaction. When Ef < Ef, the best yield is obtained in a large reactor operating at low temperature. Obviously, the kinetic model ceases to apply when the reactants freeze. More realistically, capital and operating costs impose constraints on the design. 

Example 5.7 A CSTR is commonly used for the bulk pol5anerization of styrene. Assume a mean residence time of 2 h, cold monomer feed (300 K), adiabatic operation UAgxt = ), and a pseudo-first-order reaction with rate constant... 

Suppose the following data on the iodination of ethane have been obtained at 603 K using a recirculating gas-phase reactor that closely approximates a CSTR. The indicated concentrations are partial pressures in atmospheres and the mean residence time is in seconds. 

The piston flow case assumes that the particles spend the same time in the reactor, i, even though the fluid phase is well mixed. This case resembles the mass transfer situation of piston flow in contact with a CSTR as considered in Section 11.1.4. The particles leave the reactor with size Ro — kf i. None will survive if f > Ro/k". Note that i is the mean residence time of the solid particles, not that of the fluid phase. 

The easiest reactor to analyze is a steady-state CSTR. Biochemists call it a chemostat because the chemistry within a CSTR is maintained in a static condition. Biochemists use the dilution rate to characterize the flow through a CSTR. The dilution rate is the reciprocal of the mean residence time. 

Example 12.8 The batch reactor in Example 12.7 has been converted to a CSTR. Determine its steady-state performance at a mean residence time of 4 h. Ignore product inhibition. 

Example 14.6 derives a rather remarkable result. Here is a way of gradually shutting down a CSTR while keeping a constant outlet composition. The derivation applies to an arbitrary SI a and can be extended to include multiple reactions and adiabatic reactions. It is been experimentally verified for a polymerization. It can be generalized to shut down a train of CSTRs in series. The reason it works is that the material in the tank always experiences the same mean residence time and residence time distribution as existed during the original steady state. Hence, it is called constant RTD control. It will cease to work in a real vessel when the liquid level drops below the agitator. 

A washout experiment is performed on a CSTR to measure its mean residence time. What is the effect of starting the experiment before the outlet concentration has fully reached Co Assume that the normalized output response is based on the outlet concentration measured at I = 0 so that the experimental washout function starts at 1.0. 

If the process is carried out in a stirred batch reactor (SBR) or in a plug-flow reactor (PFR) the final product will always be the mixture of both products, i.e. the selectivity will be less than one. Contrary to this, the selectivity in a continuous stirred-tank reactor (CSTR) can approach one. A selectivity equal to one, however, can only be achieved in an infinite time. In order to reach a high selectivity the mean residence time must be very long, and, consequently, the productivity of the reactor will be very low. A compromise must be made between selectivity and productivity. This is always a choice based upon economics. 

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). 

Calculate the mean residence time (t) and space time (t) for reaction in a CSTR for each of the following cases, and explain any difference between (f) and t ... 

Second, for a flow reactor, such as a CSTR, the mean residence time and space time are equal, since q = q0 ... 

Develop the E(t) profile for a 10-m laminar-flow reactor which has a maximum flow velocity of 0.40 m min-1. Consider t = 0.5 to 80 min. Compare the resulting profile with that for a reactor system consisting of a CSTR followed by a PFR in series, where the CSTR has the same mean residence time as the LFR and the PFR has a residence time of 25 min. Include in the comparison a plot of the two profiles on the same graph. 

Consider the entry of a small amount of fluid as tracer into the PFR at time t = 0. No tracer leaves the PFR until t = VPF/q0 = fPF, the mean residence time in the PFR, and hence no tracer leaves the two-vessel system, at the exit from the CSTR, during the period 0 sk fpF. As a result,... 

For exothermic, reversible reactions, the existence of a locus of maximum rates, as shown in Section 5.3.4, and illustrated in Figures 5.2(a) and 18.3, introduces the opportunity to optimize (minimize) the reactor volume or mean residence time for a specified throughput and fractional conversion of reactant. This is done by choice of an appropriate T (for a CSTR) or T profile (for a PFR) so that the rate is a maximum at each point. The mode of operation (e.g., adiabatic operation for a PFR) may not allow a faithful interpretation of this requirement. For illustration, we consider the optimization of both a CSTR and a PFR for the model reaction... 

For a CSTR, from Section 18.3.2, the mean residence time (equal to the space time... 

Consider the flow mixing through three identical ideal CSTRs in series. Each tank has a space time, r, or mean residence time, Mj, of 2 min. An idealised impulse of tracer is made in the inlet to the first tank what tracer response will be observed from the third tank ... 

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