Chemical reactors attainable region

For chemical reactor networks, the attainable region concept was first defined by Horn (1964), who noted that... 

Attainable Region (/ / ) is a systematic geometric method for the synthesis of a complex chemical reactor network. The concept has been developed in the last 15 years, starting with the pioneering works of Glaser and Hildebrand (1987). The visit of the website www.wits.ac.za (University of Witwatersrand, South Africa) may serve both as introduction and update in this topic. 

Fig. 5.24. Attainable regions of the bottom products (gray) of a pervaporative reactor (left) at different relative membrane permeabilities (dashed line chemical equilibrium line at K — 5, Damkohler number Da — 0...

First, the focus is on chemical reactors in Chapter 6, in which reactor models are reviewed, followed by a discussion of configurations for heat transfer in exothermic and endothermic reactors. Then, attainable region analysis is introduced for the optimal design of reactor networks. 

This section describes the use of the attainable region (AR), which defines the achievable ohii-positions that may be obtained from a network of chemical reactors. This is analogous to die topic of feasible product compositions in distillation, presented in Section 7.5. The attainaUe region in composition space was introduced by Horn (1964), with more recent developnots and extensions by Glasser and co-workers (Glasser et al. 1987 Hildebrandt et al., 1990). 

This book is concerned with a field of study called attainable regions (ARs), which is a set of ideas intended to address a generalized problem, often encountered in chemical reactor and process design. Although the problem can become quite detailed if we allow it, the basic idea is simple to understand. This chapter serves to articulate the type of problems AR theory could help address. To gain a sense of the scientific discipline that we are interested in, many (but not all) of the problems we are concerned with can be represented by Figure 1.1. 

In Chapter 4, we discuss the role of three fundamental reactor types in attainable region (AR) theory. Many readers may already be familiar with these reactors, for they are common in chemical reaction engineering. A small, qualitative, summary of these reactors is provided in the following text. 

The material covered in this book is organized into two sections. It may be helpful to refer to Figure P.l for an overview of the organization of chapters. Section I (Chapters 1-5) focuses on the basics of attainable region (AR) theory. Importantly, this section introduces a different way of viewing chemical reactors and reactor networks. The examples discussed in Section I are of a simpler nature, with an emphasis on describing all problems in two dimensions only. Section I is best read in a sequential fashion. 

Quasi-kinetic models deal with processes that are controlled by mass transfer rates rather than by chemical reaction rates. These models assume nearly instantaneous attainment of equilibrium within the region of interest, so changes in the species distribution are controlled by the rate of transfer of substances into or out of that region. These models are constrained by continuity equations making them similar to the chemical reactors models in Chapter 4. 

Chemical Engineering Science, Vol.54, No.7, pp. 2535-2543, ISSN 0009-2509 Feinberg, M, Hildebrand, D. (1997). Optimal reactor design from a geometric viewpoint -1. Universal properties of the attainable region. Chemical Engineering Science, Vol.52, No.lO, pp. 1637-1665, ISSN 0009-2509... 

After this time so much has been done that there is no one place where even the work on reactors can be found in survey. The notion of attainable and nonattainable regions in chemical reaction technique has been elegantly treated in a paper of that title by F. Horn in the 1964 Chemical Reaction Engineering Symposium volume (p. 293) referred to above. 

Ultrafiltration of an enzyme solution through a UF membrane does not always result in gel layer formation. Unless a gel layer is formed, this immobilization technique cannot be used for flow systems lacking effective enzyme immobilization. In any event, soluble enzyme membrane reactors can be useful in order to perform kinetic analysis at high enzyme concentrations. Once steady state is attained, the theoretical model permits calculation of reaction rates in both regions. Once the layer is formed it behaves like a secondary membrane,34 capable of separating compounds of different molecular weight in the mixture as well as catalyzing a chemical reaction. 

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