Batch reactors optimal temperatures

This temperature dependency is exploited in optimal control problems of batch reactor where optimal temperature profile is obtained by either maximizing conversion, yield, profit, or minimizing batch time for the reaction. One of the earliest works on optimal control of batch reactor was presented by Denbigh[25] where he maximized the yield. The review paper by Srinivasan et al.[26] describes various optimization and optimal control problems in batch processing and provides examples of semi-batch and fed-batch reactor optimal control. 

Biocatalysts in nature tend to be optimized to perform best in aqueous environments, at neutral pH, temperatures below 40 °C, and at low osmotic pressure. These conditions are sometimes in conflict with the need of the chemist or process engineer to optimize a reaction with respect to space-time yield or high product concentration in order to facilitate downstream processing. Furthermore, enzymes and whole cells are often inhibited by products or substrates. This might be overcome by the use of continuously operated stirred tank reactors, fed-batch reactors, or reactors with in situ product removal [14, 15]. The addition of organic solvents to increase the solubility of substrates and/or products is a common practice [16]. 

This chapter treats the effects of temperature on the three types of ideal reactors batch, piston flow, and continuous-flow stirred tank. Three major questions in reactor design are addressed. What is the optimal temperature for a reaction How can this temperature be achieved or at least approximated in practice How can results from the laboratory or pilot plant be scaled up ... 

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 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. 

Optimization sequence (experimental data, arbitrary units) Runs 1 and 2 are initial experiments. From run 3 to run 6 the amounts of A, B, G, and feed rate of G are fixed. These constraints are relaxed for runs 7 and 8. (Reprinted from Marchal-Brassely et al. (1992), Optimal operation of a semi-batch reactor by self-adaptive models for temperature and feed profiles . Copyright (1992), with permission from Elsevier Science). 

TEMPERATURE OPTIMIZATION OF BATCH REACTOR CONSECUTIVE AND PARALLEL REACTION SEQUENCE... 

Operating conditions. Optimization variables such as batch cycle time and total amount of reactants have fixed values for a given batch reactor system. However, variables such as temperature, pressure, feed addition rates and product takeoff rates are dynamic variables that change through the batch cycle time. The values of these variables form a profile for each variable across the batch cycle time. 

Example 14.1 Consider again the chlorination reaction in Example 7.3. This was examined as a continuous process. Now assume it is carried out in batch or semibatch mode. The same reactor model will be used as in Example 7.3. The liquid feed of butanoic acid is 13.3 kmol. The butanoic acid and chlorine addition rates and the temperature profile need to be optimized simultaneously through the batch, and the batch time optimized. The reaction takes place isobarically at 10 bar. The upper and lower temperature bounds are 50°C and 150°C respectively. Assume the reactor vessel to be perfectly mixed and assume that the batch operation can be modeled as a series of mixed-flow reactors. The objective is to maximize the fractional yield of a-monochlorobutanoic acid with respect to butanoic acid. Specialized software is required to perform the calculations, in this case using simulated annealing3. 

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. 

The catalyst/substrate ratio is 1.5 mol% for the supported ionic liquid phase (SILP) catalyst, 3 mol% for the impregnated catalyst and 2 mol% for the homogeneous reaction aRuns 1 -4 are consecutive experiments with the same catalyst in a stirred batch reactor. bDimeric Cr (salen) catalyst impregnated on silica cHomogeneous reaction at 0-2 OC optimized for product selectivity dHomogeneous reaction at room temperature optimized for product selectivity... 

Determination of die process parameters that ensure a permissible temperature profile and optimal solidification path is based on the general principles of the theory of batch reactors formulated in Section 2.7. Let us illustrate this approach with the example of solidification of a urethane-based compound for use as a coating.176... 

This is the most common mode of addition. For safety or selectivity critical reactions, it is important to guarantee the feed rate by a control system. Here instruments such as orifice, volumetric pumps, control valves, and more sophisticated systems based on weight (of the reactor and/or of the feed tank) are commonly used. The feed rate is an essential parameter in the design of a semi-batch reactor. It may affect the chemical selectivity, and certainly affects the temperature control, the safety, and of course the economy of the process. The effect of feed rate on heat release rate and accumulation is shown in the example of an irreversible second-order reaction in Figure 7.8. The measurements made in a reaction calorimeter show the effect of three different feed rates on the heat release rate and on the accumulation of non-converted reactant computed on the basis of the thermal conversion. For such a case, the feed rate may be adapted to both safety constraints the maximum heat release rate must be lower than the cooling capacity of the industrial reactor and the maximum accumulation should remain below the maximum allowed accumulation with respect to MTSR. Thus, reaction calorimetry is a powerful tool for optimizing the feed rate for scale-up purposes [3, 11]. 

The method proposed for improving the batch operation can be divided into two phases on-line modification of the reactor temperature trajectory and on-line tracking of the desired temperature trajectory. The first phase involves determining an optimal temperature set point profile by solving the on-line dynamic optimization problem and will be described in this section. The other phase involves designing a nonlinear model-based controller to track the obtained temperature set point and will be presented in the next section. 

As a batch reactor is utilized for the production of a wide variety of high value products, an optimization of batch operating conditions, e.g. temperature, operating time, etc. is... 

In this type of problem, the objective is to compute the optimal temperature policy maximizing the amount of a desired product concentration for a given fixed batch time subject to bounds on the reactor temperature. The problem can be written mathematically as... 

N. Aziz, M.A. Hussain, I.M. Mujtaba, Performance of different types of controllers in tracking optimal temperature profiles in batch reactors, Comp. Chem. Eng. 24 (2000) 1069-1075. 

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. 

If consecutive reactions are conducted in a batch reactor, the optimization of the process includes finding the optimum time to stop the batch and determining the optimum temperature. To illustrate the issues, we take the simple reactions... 

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