Optimization - Batch Reactors

L. L. Simon, M. Introvigne, U. Fischer, K. Hungerbuhler, (2008), Batch reactor optimization under liquid swelling safety constraint, Chemical Engineering Science, 63, 770. 

Batch reactor optimization (Luyben, 1996) is a common issue in chemical engineering. One very typical problem is finding the residence time for isothermal batch reactors that maximizes/minimizes the conversion of an intermediate compound. 

Part One 0.0619 Standard batch reactor. Optimized for reaction time. 

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. 

Spreadsheet Applications. The types of appHcations handled with spreadsheets are a microcosm of the types of problems and situations handled with fuU-blown appHcation programs that are mn on microcomputers, minis, and mainframes and include engineering computations, process simulation, equipment design and rating, process optimization, reactor kinetics—design, cost estimation, feedback control, data analysis, and unsteady-state simulation (eg, batch distillation optimization). 

Because of the differences in primary and secondaiy metabolism, a reactor may have a dual-stage fed-batch system. In other words, fed-batch operation optimizes growth with little or no product formation. When sufficient biomass has accumulated, a different fed-batch protocol comes into play. 

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]. 

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. 

The reactions are still most often carried out in batch and semi-batch reactors, which implies that time-dependent, dynamic models are required to obtain a realistic description of the process. Diffusion and reaction in porous catalyst layers play a central role. The ultimate goal of the modehng based on the principles of chemical reaction engineering is the intensification of the process by maximizing the yields and selectivities of the desired products and optimizing the conditions for mass transfer. 

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

Suppose we perform an organic synthesis in a batch reactor where the desired molecule is the intermediate and not the end product. It is then very important that we know how long we should let the reaction run to obtain the highest yield of the intermediate. Setting the differential d[I]/dt in Eq. (99) equal to zero and substituting Eq. (102) into Eq. (99) we find the time, at which the maximum is reached - and by inserting Wx in Eq. (102) the corresponding optimal concentration of the intermediate ... 

Most accidents in the chemical and related industries occur in batch processing. Therefore, in Chapter 5 much attention is paid to theoretical analysis and experimental techniques for assessing hazards when scaling up a process. Reaction calorimetry, which has become a routine technique to scale up chemical reactors safely, is discussed in much detail. This technique has been proven to be very successful also in the identification of kinetic models suitable for reactor optimization and scale-up. 

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... 

Thus, the design equations for a batch reactor for the optimization of a temporal superstructure can be based on differential or algebraic equations. 

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. 

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. 

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. 

The hydrolysis of methyl acetate (A) in dilute aqueous solution to form methanol (B) and acetic acid (C) is to take place in a batch reactor operating isothermally. The reaction is reversible, pseudo-first-order with respect to acetate in the forward direction (kf = 1.82 X 10-4 s-1), and first-order with respect to each product species in the reverse direction (kr = 4.49 X10-4 L mol-1 S l). The feed contains only A in water, at a concentration of 0.050 mol L-1. Determine the size of the reactor required, if the rate of product formation is to be 100 mol h-1 on a continuing basis, the down-time per batch is 30 min, and the optimal fractional conversion (i.e., that which maximizes production) is obtained in each cycle. 

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