Reactor optimization

Where there are large volumes of contaminated water under a small site, it is sometimes most convenient to treat the contaminant in a biological reactor at the surface. Considerable research has gone into reactor optimization for different situations and a variety of stirred reactors, fluidized-bed reactors, and trickling filters have been developed. Such reactors are usually much more efficient than in situ treatments, although correspondingly more expensive. 

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. 

Kinetic models developed for reactor scale-up are also suitable for reactor optimization. The development of detailed kinetic models accounting for all factors influencing process rates is a time-consuming task. Therefore, more empirical simplified models are often used for simulation and optimization of existing reactors. 

Objective function. The objective function for the reactor optimization is based on the difference between the value of the product gas (heating value and ammonia value) and the value of the feed gas (as a source of heat only) less the amortization of reactor capital costs. Other operating costs are omitted. As shown in Murase et al., the final consolidation of the objective function terms (corrected here) is... 

In order to illustrate this approach, we next consider the optimization of an ammonia synthesis reactor. Formulation of the reactor optimization problem includes the discretized modeling equations for a packed bed reactor, along with the set of knot placement constraints. The following case study illustrates how a differential-algebraic problem can be optimized efficiently using (27). In addition, suitable accuracy of the ODE model can be obtained at the optimum by directly enforcing error restrictions and adaptively adding elements. Finally, bounds on the continuous state profiles can be enforced directly in the optimization problem. 

D. C. Dyson, F. J. M. Horn, R. Jackson, and C. B. Schlesinger. Reactor optimization problems for reversible exothermic reactions. Canadian J. ofChem. Eng., 45 310,1967. 

Continuous emulsion polymerization processes are presently employed for large scale production of synthetic rubber latexes. Owing to the recent growth of the market for polymers in latex form, this process is becoming more and more important also in the production of a number of other synthetic latexes, and hence, the necessity of the knowledge of continuous emulsion polymerization kinetics has recently increased. Nevertheless/ the study of continuous emulsion polymerization kinetics hasf to datef received comparatively scant attention in contrast to batch kinetics/ and very little published work is available at present/ especially as to the reactor optimization of continuous emulsion polymerization processes. For the theoretical optimization of continuous emulsion polymerization reactors/ it is desirable to understand the kinetics of emulsion polymerization as deeply and quantitatively as possible. 

Software tools are applied in every step of process development. Tools for individual reactor simulations such as computational fluid dynamic simulations are not the topic in this chapter. These tools supply only numerical data for specific defined reactor geometry and defined specific process conditions. A change of parameter would demand a complete recalculation, which is often a very time-consuming process and not applicable to a parameter screening. Methods for reactor optimization by CFD are described in detail in the first volume of this series. Tools for process simulation allow the early selection of feasible process routes from a large... 

The membrane reactor has an additional degree of freedom allowing to optimize the amount of the product removed. This can be conveniently described by a dimensionless Peclet number which relates convective flow through the reactor to transport through the membrane [50]. For each Da number there exists an optimal Pe number maximizing the conversion. For a given membrane material the Pe number is directly related to the membrane thickness. Curve (b) in Fig. 12.12 represents the theoretical behavior of a membrane reactor optimized with respect to membrane thickness. For low Da numbers the membrane should be very thick in order to keep the reactants in the reactor, and in this respect the membrane reactor is identical to the conventional fixed-bed reactor. In contrast, for high Da numbers the membrane reactor should possess a very thin wall for... 

Because the physics of XRD requires strong compromises in the choice of the sample environment, it is not realistic to apply actual catalytic reaction conditions in these measurements. Unavoidably, some extrapolations have to be made to link experimental observations to the state of the functioning catalyst in a reactor optimized for performance in the sense of production of desired products. The gas flow and energy transport conditions, for example, must often be chosen to be different in the catalyst testing and in XRD experiments. The catalytic performance is often analyzed in terms of a model of the kinetics, and the results may be used to make a connection with the conditions of the XRD experiment. A discussion of the issues has been published (Schlogl and Baerns, 2004). 

This can be illustrated by a simple reactor optimization example. The size and cost of a reactor are proportional to residence time, which decreases as temperature is increased. The optimal temperature is usually a trade-off between reactor cost and the formation of byproducts in side reactions but if there were no side reactions, then the next constraint would be the maximum temperature allowed by the pressure vessel design code. More expensive alloys might allow for operation at higher temperatures. The variation of reactor cost with temperature will look something like Figure 1.8, where T, Tg, and Tc are the maximum temperatures allowed by the vessel design code for alloys A, B, and C, respectively. 

If there is minimal byproduct formation, then the reactor costs (volume, catalyst, heating, etc.) can be traded off against the costs of separating and recycling unconverted reagents to determine the optimal reactor conversion. More frequently, the selectivity of the most expensive feeds for the desired product is less than 100%, and byproduct costs must also be taken into account. The reactor optimization then requires a relationship between reactor conversion and selectivity, not just for the main product, but for all the byproducts that are formed in sufficient quantity to have an impact on process costs. 

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

Consider the first order series reaction taking place in a plug flow reactor. Optimize the length of the reactor to maximize the concentration of B in the outlet stream. Take initial conditions from problem 5. 

V.A. Papavassiliou, J.A. McHenry, E.W. Corcoran, H.W. Deckman and J.H. Meldon, High flux asymmetric catalytic membrane reactors. Optimization of operating conditions. Paper presented at the 1st International Workshop on Catalytic Membranes, September 1994, Lyon-Villeurbanne, France. 

The challenges to be overcome in emulsion polymerization reactor optimization and control include the following considerations ... 

The microscopic transport equations are often considered too complex for practical applications considering reactor optimization, scale-up and design. In engineering practice integral averages of the equations over one, two or three spatial directions are used reducing the model to that of an ideal reactor model type. 

Although considerable advances have been made both in understanding the basic aspects of slurry bubble column reactors (SBCR) and in developing rational design procedures, computational fluid dynamics (CFD) - assisted design methodology for reactor optimization is sparse. 

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