Denbigh reactions problem

The curves in Fig. 4-12 are helpful in choosing a reactor size appropriate for producing a specified product distribution. For example, if the objective is to make the maximum amount of trimer (P3), the reactor volume should be such that d is about 13 sec. This problem does not allow for destruction of active polymer P by termination reactions. This is often the case and leads to a more symmetrical distribution of molecular weights. Denbigh has considered this and siriiilar polymerization problems. 

The problem of a heterogeneous chemical reaction can be treated as follows (Denbigh. 1971, p. 159ff) A chemical reaction can be represented in a general way by the expression... 

There are only three independent chemical reactions among these five reactions [see Problem 8.9(c)] This is easily demonstrated using Denbigh s method (cf. Sec. 8.3) we start by writing the reactions... 

I did my PhD looking at a reaction and its kinetics. As a result of this, I became interested in chemical reactor theory. I remember, in particular, the excellent books of Denbigh and Levenspiel. Both of them talked about the aforementioned problem and documented some heuristics to help industrialists to come up with some solutions. However, it was recognized that these heuristics were sometimes contradictory. 

The aim of Denbigh s volume is to develop the general theory of equilibrium, including its statistical treatment, with problems to illustrate numerous practical applications. It is assumed that the student is already very familiar with the concepts of temperature and heat and that he already has some knowledge of thermodynamics. It is recognized that thermodynamics needs to be studied several times over at advancing levels. Part I presents a traditional development of the subject. Part II presents reaction and phase equilibria, and Part III develops statistical thermodynamics. 

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. 

In the general case of nonisothermal shrinking-core systems controlled both by chemical reaction and diffusion, the thermal effect of the reaction may bring about multiple steady states and instability due to sudden transition of rate-controlling steps during the reaction. The problem of thermal instability in noncatalytic gas-solid reactions was first pointed out by Cannon and Denbigh [37] and has been discussed by Shen and Smith [23] and Wen and coworkers [38, 39]. 

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