Optimization of a Batch Reactor

Batch reactor optimization (Luyben, 1990) is a common issue in chemical engineering. One very typical problem is finding the residence time for isothermal batch reactors that marimizes/minimizes the conversion of an intermediate compound. 

As is the case here and in other problem, the goal is to calculate the value of the independent variable t for which the dependent variables y is optimal during the integration of ODE/DAE systems. 

If the function to be optimized is unimodal, an object from the BzzMinimiza-tionMono class may be used. This class can be combined with classes used for the integration of differential systems based on multivalue algorithms (see Vol. 4 -Buzzi-Eerraris and Manenti, in press). The objects from these classes automatically change the integration step and the order of the algorithm as well by adapting them to the problem s features and certain specific requirements. 

Suppose that the following reaction takes place (Edgar and Himmelblau, 2001) in a perfectly mixed batch reactor 

Our objective is to calculate the residence time that maximizes the concentration of the component B, Y2-The program is 

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Optimization of a Batch Polymerization Reactor at the Final Stage of Conversion... 

Thus, the design of a batch reactor can be based on the optimization of a temporal superstructure. Given a simulation model with a mathematical formulation, the next step is to determine the optimal values for the control variables of a batch reaction system. 

In this chapter, we first consider uses of batch reactors, and their advantages and disadvantages compared with continuous-flow reactors. After considering what the essential features of process design are, we then develop design or performance equations for both isothermal and nonisothermal operation. The latter requires the energy balance, in addition to the material balance. We continue with an example of optimal performance of a batch reactor, and conclude with a discussion of semibatch and semi-continuous operation. We restrict attention to simple systems, deferring treatment of complex systems to Chapter 18. 

The performance of a batch reactor may be optimized in various ways. Here, we consider the case of choosing the cycle time, tc, equation 12.3-5, to maximize the rate of production of a product. For simplicity, we assume constant density and temperature. 

FIGURE 18 Structure of the optimal control of a batch reactor. 

Studies in optimization-V The bang-bang control of a batch reactor (with N. Blakemore). Chem. Eng. ScL 17, 591-598 (1962). 

The adaptive control of a batch reactor-II Optimal path control (with H.H.-Y. Chien). Automatica 2, 59-71 (1964). 

One aspect of optimizing the operation of a batch reactor is establishing the temperature such that the selectivity is as high as possible. If the activation energies of the two reactions are different, changing temperature shifts the ratio of the rates. 

Batch processes present challenging control problems due to the time-varying nature of operation. Chylla and Haase [4] present a detailed example of a batch reactor problem in the polymer products industry. This reactor has an overall heat transfer coefficient that decreases from batch to batch due to fouling of the heat transfer surface inside the reactor. Bonvin [5] discusses a number of important topics in batch processing, including safety, product quality, and scale-up. He notes that the frequent repetition of batch runs enables the results from previous runs to be used to optimize the operation of subsequent ones. 

This paper presents an on-line model based level control of a batch reactor with reaction rate uncertainties. The analyzed chemical batch process is catalyzed by a catalyst which decomposes in the reactor therefore it is fed several times during the batch. The chemical reaction produces a vapour phase by-product which causes level change in the system. The on-line control method is based on the shrinking horizon optimal control methodology based on the detailed model of the process. The results demonstrate that the on-line optimization based control strategy provides good control performance despite the disturbances. 

This work presents the on-line level control of a batch reactor. The on-line strategy is required to accommodate the reaction rate disturbances which arise due to catalyst dosing uncertainties (catalyst mass and feeding time). It is concluded that the implemented shrinking horizon on-line optimization strategy is able to calculate the optimal temperature profile without causing swelling or sub-optimal operation. Additionally, it is concluded that, for this process, a closed-loop formulation of the model predictive controller is needed where an output feedback controller ensures the level is controlled within the discretization intervals. 

We shall recapitulate the governing equations in the next section and discuss the economic operation in the one following. The results on optimal control are essentially a reinterpretation of the optimal design for the tubular reactor. We shall not attempt a full derivation but hope that the qualitative description will be sufficiently convincing. The isothermal operation of a batch reactor is completely covered by the discussion in Chap. 5 of the integration of the rate equations at constant temperature. The simplest form of nonisothermal operation occurs when the reactor is insulated and the reaction follows an adiabatic path the behavior of the reactor is then entirely similar to that discussed in Chap. 8. 

Kachhap, R. and Guria, C. (2005). Multi-objective optimization of a batch copoly (ethylene-polyoxyethylene terephthalate) reactor using different adaptations of nondominated sorting genetic algorithm, Macromol. Theor. SimuL, 14, pp. 358-373. 

Optimization of (semi)batch reactor operation will include considerations of reaction time versus conversion, reaction time versus monomer recovery cosh and the potential for variations in polymerization temperature within a batch to achieve desired product quality, and hence end-use properties. Open-loop trajectories may be determined for the addition of monomers and/or initiators. Temperature programming is often done to develop polymer of unique properties. The semibatch addition of the more reactive monomer in copolymerization is often carried out to develop a product with a uniform or gradient CCD. In pulsion polymerization, programmed addition of monomer, comonomer, initiator. 

Another problem that arises in batch operations is the question. What is the optimal time to run a particular operation For exanple, consider the sinple case of a batch reactor producing a product via a first-order, irreversible reaction. The conversion of product follows a single e q)onential relationship, as shown in Figure 14.11. 

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. 

In this paper we present a meaningful analysis of the operation of a batch polymerization reactor in its final stages (i.e. high conversion levels) where MWD broadening is relatively unimportant. The ultimate objective is to minimize the residual monomer concentration as fast as possible, using the time-optimal problem formulation. Isothermal as well as nonisothermal policies are derived based on a mathematical model that also takes depropagation into account. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and time is studied. 

In this paper we formulated and solved the time optimal problem for a batch reactor in its final stage for isothermal and nonisothermal policies. The effect of initiator concentration, initiator half-life and activation energy on optimum temperature and optimum time was studied. It was shown that the optimum isothermal policy was influenced by two factors the equilibrium monomer concentration, and the dead end polymerization caused by the depletion of the initiator. When values determine optimum temperature, a faster initiator or higher initiator concentration should be used to reduce reaction time. 

Model-based optimization of a sequencing batch reactor for advanced biological wastewater treatment... 

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