Multiple CSTR s

Analysis of CSTR Cascades under Nonsteady-State Conditions. In Section 8.3.1.4 the equations relevant to the analysis of the transient behavior of an individual CSTR were developed and discussed. It is relatively simple to extend the most general of these relations to the case of multiple CSTR s in series. For example, equations 8.3.15 to 8.3.21 may all be applied to any individual reactor in the cascade of stirred tank reactors, and these relations may be used to analyze the cascade in stepwise fashion. The difference in the analysis for the cascade, however, arises from the fact that more of the terms in the basic relations are likely to be time variant when applied to reactors beyond the first. For example, even though the feed to the first reactor may be time invariant during a period of nonsteady-state behavior in the cascade, the feed to the second reactor will vary with time as the first reactor strives to reach its steady-state condition. Similar considerations apply further downstream. However, since there is no effect of variations downstream on the performance of upstream CSTR s, one may start at the reactor where the disturbance is introduced and work downstream from that point. In our generalized notation, equation 8.3.20 becomes... 

It is possible to extend this treatment to the case of multiple CSTR s operating in series by adapting the procedure outlined by Denbigh and Turner (2). Let (ACA)U (ACA)2, and (ACA)h represent the changes in the concentration of species A that take place in tanks one, two, and i, respectively. 

After extracting the kinetic parameters, selected results for CO oxidation over were used to analyze the effect of non-uniform temperature and velocity distributions on the conversion of CO. In order to determine the optimum number of multiple CSTR s to capture the behavior of a PFR, the rate law of Oh and Carpenter (14) for the NO+CO reaction was used to model a monolith channel as a CSTR in series. The results indicated that it was sufficient to use 5 reactors in series to capture the performance of the PFR behavior in the NO+CO reaction The cells of a monolith reactor were taken as independent parallel reactors ignoring the mass transfer and diffusion through the ceramic pores. The axial and radial temperature and velocity profiles collected from the literature(4,5) are used to calculate the... 

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 reactor in the reactor-stripper process is larger than the first reactor in the 3-CSTR process and therefore has more heat transfer area. However, all the conversion occurs in this one reactor, so we would expect the heat transfer rate to be high. In fact, it is not high but is even lower than the heat transfer rate in the 1-CSTR process (1.78 x 106 kJ/s, as shown in Fig. 2.21). The reason for this unexpected result is the large recycle stream in the reactor-stripper process. We assume that its temperature is 322 K. The total flow into the reactor is 0.1591 krnol/s (the sum of the recycle 0.1241 kmol/s and the fresh feed is 0.03506 kmol/s), while the flow into the first reactor of the 3-CSTR process is just the fresh feed. Thus the larger sensible heat of the larger stream reduces the heat than must be transferred in the reactor. Note that the total heat of reaction for a 98% conversion is 2.395 x 106 kJ/s. The sensible heat of the large feed stream to the reactor in the reactor-stripper process is 1.398 x 106 kJ/s. In the 3-CSTR process (and in all the multiple CSTR processes) the sensible-heat term in the first reactor is only 0.616 x 106 kJ/s because the flowrate is smaller. 

The basic reactor choice is between a packed bed, stirred tank, or combinations thereof (with or without possibilities for enzyme retention by membranes or immobilization) and compartmentalization. The packed bed reactor can only handle immobilized enzyme(s) and operates in plug-flow mode (mixing only in the radial, rather than axial direction). For many enzymes their kinetics are such that operation in plug-flow hydrodynamic mode is favored. Hence, in cases where mixing is required (e.g., for pH control via addition of a neutralizing acid or alkali or addition of an inhibitory substrate), then the use of multiple CSTRs can be used (Figure 20.3). 

Escher, C. and Ross, J. (1983). Multiple ranges of flow rate with bistability and limit cycles for Schlogl s mechanism in a CSTR. J. Chem. Phys., 79, 3773-7. 

Gray, P. and Scott, S. K. (1985). Sustained oscillations and other exotic patterns of behavior in isothermal reactions. J. Phys. Chem., 89, 22-32. Lin, K. F. (1981). Multiplicity, stability and dynamics for isothermal autocatalytic reactions in CSTR. Chem. Eng. Sci., 36, 1447-52. 

As in Section 3.1 for the adiabatic CSTR problem, we again start with a generic MATLAB fzero.m based root finder to try to settle the issues of multiplicity in the nonadiabatic CSTR case. The MATLAB m file solveNadiabxy. m below finds the values for y (up to three values if a lies in the bifurcation region) that satisfy equation (3.12) for the given values of a, / , 7, Kc, and yc using MATLAB s root finder fzero. 

Compared to solveadiabxy. m for the adiabatic CSTR case in Section 3.1, the above MATLAB function solveNadiabxy. m depends on the two extra parameters Kc and yc that were defined following equation (3.9). It uses MATLAB s built-in root finder fzero.m. As explained in Section 3.1, such root-finding algorithms are not very reliable for finding multiple steady states near the borders of the multiplicity region. The reason - as pointed out earlier in Section 1.2 - is geometric the points of intersection of the linear and exponential parts of equations such as (3.16) are very shallow, and their values are very hard to pin down via either a Newton or a bisection method, especially near the bifurcation points. 

Our final MATLAB m file in this section rounds out our efforts just as Figure 3.10 did for the adiabatic CSTR problem. It uses the plotting routine for Figure 3.18 in conjunction with a MATLAB interpolator to mark and evaluate the (multiple) steady state(s) graphically for nonadiabatic, nonisothermal CSTR problems. 

Up to this point we have looked at a single CSTR and have pointed out some of this reactor s problems, particularly if high conversions are desired. Alternative flowsheets with multiple reactors are frequently used to reduce capital investment, improve yields and to reduce inventories of dangerous chemicals. 

Figure 7- Isothermal multiplicity for the emulsion polymerization of methyl methacrylate in a CSTR (20h). S = 0.03...

As discussed in Chapter 4, to describe the operation of a CSTR with multiple reactions, we have to write Eq. 8.1.1 for each independent chemical reaction. The solution of the design equations (the relationships between Z Js and t) provide the reaction operating curves and describe the reactor operation. To solve the design equations, we have to express the rates of the chemical reactions that take place in the reactor in terms of Z s and t. Below, we derive the auxiliary relations used in the design equations. 

Salnikov specifically reported multiple singular points and a limit cycle establishing the existence of oscillations in chemical reactions. Bilous and Amundson (1955) referred to Salnikov s (1948) paper as the first work where periodic phenomenon in reaction systems was discussed. They also indicated that a reaction A -> B in CSTR is irreversible, exothermic, and kinetically first order. Considering mass balance and heat balance equations it is known that at the steady states, the heat consumption... 

We divide the chapter into two parts Part 1 Mote Balances in Terms of Conversion, and Part 2 Mole Balances in Terms of Concentration, C,. and Molar Flow Rates, F,." In Pan 1, we will concentrate on batch reactors, CSTRs, and PFRs where conversion is the preferred measure of a reaction s progress for single reactions. In Part 2. we will analyze membrane reactors, the startup of a CSTR. and semibatch reactors, which are most easily analyzed using concentration and molar How rates as the variables rather than conversion. We will again use mole balances in terms of these variables (Q. f,) for multiple reactors in Chapter 6. 

Example S tl Multiple Reactions in a CSTR The elementary liquid-phase reactions... 

Closure. After completing this chapter, the reader should be able to appi the unsteady-state energy balance to CSTRs, semibatch and batch reactor The reader should be able to discuss reactor safety using two examples on a case study of an explosion and the other the use of the ARSST to hel prevent explosions. Included in the reader s discussion should be how t start up a reactor so as not to exceed the practical stability liniit. After reac ing these examples, the reader should be able to describe how to operat reactors in a safe maimer for both single and multiple reactions. 

Example 14. /. Multiple steady states and hysteresis in a nonisothermal continuous stirred-tank reactor (CSTR) [1,2]. In a CSTR, the curve for the temperature dependence of heat loss to the cooling coil is linear (loss proportional to temperature difference) while that for heat generation by the reaction is S-shaped (Arrhenius ex-... 

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