Adiabatic reactor, optimization

Figure 11.5.d-2 Definition of symbols used in multibed adiabatic reactor optimization by dynamic programming. 

Nonisothermal reactors with adiabatic beds. Optimization of the temperature profile described above assumes that heat can be added or removed wherever required and at whatever rate required so that the optimal temperature profile can be achieved. A superstructure can be set up to examine design options involving adiabatic reaction sections. Figure 7.12 shows a superstructure for a reactor with adiabatic sections912 that allows heat to be transferred indirectly or directly through intermediate feed injection. 

Studies in optimization-I The optimum design of adiabatic reactors with several beds. Chem. Eng. Sci., 12, 243-252 (1960). 

The optimal design of stagewise adiabatic reactors. Paper presented at the AIChE/ORSA Symposium on Optimization in Chemical Engineering, New York, 1960. 

J. Caha, V. Hlavacek, M. Kubicek, and M. Marek. Study of the optimization of chemical engineering equipment. Numerical solution of the optimization of an adiabatic reactor. Inter. Chem. Eng., 13 466, 1973. 

A contour plot given in Figure 5.17 shows how TAC varies in a two-stage adiabatic reactor system with interstage cooling. The reactant ratio yRA/yRB is fixed at unity in this figure, so there are two design optimization variables, the inlet temperatures of the two reactors 7) and T2-... 

Narasimhan. G. "Optimization of Adiabatic Reactor Sequence with Heat Exchanger Cooling, Br. Chem. Eng. 14, 1402 (1969). 

R. Aris, On Optimal Adiabatic Reactors of Combined Types, ibid., 40, 87 (1962). 

The conventional MTBE synthesis consists of a reaction of isobutene and methanol over an acidic sulfonated cation-exchange catalyst. This reaction is highly selective, equilibrium-limited, and exothermic in nature. Several types of industrial reactors such as tubular reactors, adiabatic reactors with recycle, and catalytic distillation configurations have been utilized to cany out the MTBE synthesis reaction. The factors considered in the optimal design of a MTBE unit include the following items [52]. 

The optimal catalyst distribution problem was studied in an adiabatic reactor (Ogunye and Ray, 197la,b). The optimal initial distribution of catalyst activity along the axis of a tubular fixed-bed reactor was examined for a class of reactivation-deactivation problems by Gryaert and Crowe (1976). A general set of simultaneous reactions was considered, quasi steady state approximation was used, and the decay of the catalyst expressed as a function of temperature, concentration and catalyst activity. The influence of various initial catalyst activity distributions upon the reactor performance was also considered. 

There is no reason to suppose that the temperature profile in an adiabatic reactor is the best possible profile. Finding the best temperature profile is a problem in functional optimization. 

Figure 6.2b displays the temperature profile for a 100-zone case that is a tour de force for the optimization routine. The results took less than 20 min of computing time, but the difference in bout between the 10- and 100-zone cases is negligible. These multizone designs give bout = 3.61 compared to 3.59 for the best adiabatic reactor with t = 0.8 h, but multizone reactors would be very expensive to build. Problems 6.11-6.13 suggest practical approaches to achieving a desirable temperature profile. 

Oxidation of SO2 into SO3 is a classic example of exothermic reversible reaction. Optimal temperature regime for such a reaction requires starting at as high temperatures as a catalyst can handle, then the temperature decrease along with progressing conversion of a reactant. It is traditionally performed in multi-bed adiabatic reactors with intermediate cooling. Temperature profile in an RFR (Fig. 4) has lower temperatures at both ends of the catalyst bed, suggesting that an RFR would perform close to the theoretical optimum. 

A very convenient diagram for visualizing the problem of optimizing a multibed adiabatic reactor is the conversion versus temperature plot already encountered in Sec. 11.3, and drawn in Fig. 11.5.d-l for the SO oxidation based on the rate equation of Collina, Corbetta, and Cappelli [113] with an effectiveness factor of 1. (For further reading on this subject see [114] and [115].) This equation is... 

Consider now two steps, the last two of the multibed adiabatic reactor. From Bellman s maximum principle it follows that the optimal policy of bed 1 is preserved. This time X2 and Ti have to be chosen in an optimal way to arrive at... 

Figure II.5.d-3 Optimal reaction paths in a multibed adiabatic reactor according to dynamic programming.

The above discussion was based on a graphical representation. In reality the computations are performed on a computer and the Xj, Tj, Xj, and Tj are stored. The above has been applied to a three-bed adiabatic reactor for SO2 oxidation, using Collina, Corbetta, and Cappelli s [113] rate equation. The pressure is considered constant. There are no AT and Ap over the film surrounding the catalyst. Also, to simplify the treatment the effectiveness factor is considered to be one in this illustrative example. The objective function to be optimized consists of two parts ... 

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