Optimum temperature progression

The following also diseusses autothermal reaetors, the eonversion of ammonia, and finally, the optimum-temperature progression, with derived equations for reversible exothermie reaetions for whieh profiles are not readily available. 

The following derives equations for the optimum temperature progression for the four types of reaetions previously deseribed at eonstant density. Figures 6-28, 6-29, 6-30, and 6-31 show that the r - T - profile for an exothermie reaetion is unimodal. Therefore, the optimum temperature T p is obtained by performing a partial differentiation of (-r ) with respeet to temperature T at a eonstant eonversion and equating this to zero. That is. 

Consider the solution of Equation 6-170 for eaeh of the four types of rate expressions to determine the optimum temperature progression at any given fraetional eonversion X. ... 

Equation 6-173 suggests that for every value of X, there is a eorresponding temperature T p on the optimum temperature progression OTP. ki... 

Optimum temperature progression for a first order reversible reaction A o R... 

Using the kinetic parameters in Type 1 reaction at = 0.5, the optimum temperature progression is... 

The Microsoft Excel Spreadsheet (OPTIMUM63.xls) was used to evaluate T p for varying values of X. Table 6-12 gives the results of the spreadsheet calculation, and Figure 6-34 illustrates the profile of Tgp( against X, showing that the optimum temperature progression decreases as the fractional conversion increases. 

Omoleye, J. A., Adesina, A. A., and Udegbunam, E. O., Optimal design of nonisothermal reactors Derivation of equations for the rate-temperature conversion profile and the optimum temperature progression for a general class of reversible reactions, Chem. Eng. Comm., Vol. 79, pp. 95-107, 1989. 

The various types of reaetors employed in the proeessing of fluids in the ehemieal proeess industries (CPI) were reviewed in Chapter 4. Design equations were also derived (Chapters 5 and 6) for ideal reaetors, namely the eontinuous flow stirred tank reaetor (CFSTR), bateh, and plug flow under isothermal and non-isothermal eonditions, whieh established equilibrium eonversions for reversible reaetions and optimum temperature progressions of industrial reaetions. 

The optimum temperature progression to use in this sequence is a high temperature to start followed by lower temperatures where the concentration of species R is high and then increasing temperatures when the concentration of species S becomes appreciable. Levenspiel (13) has summarized the results of several analyses of the optimum temperature level and progression to be used for several general reaction schemes. 

We follow a three-step procedure First, we must find how equilibrium composition, rate of reaction, and product distribution are affected by changes in operating temperatures and pressures. This will allow us to determine the optimum temperature progression, and it is this that we strive to approximate with a real design. Second, chemical reactions are usually accompanied by heat effects, and we must know how these will change the temperature of the reacting mixture. With this information we are able to propose a number of favorable reactor and heat exchange systems—those which closely approach the optimum. Finally, economic considerations will select one of these favorable systems as the best. 

The optimum temperature progression in any type of reactor is as follows At any composition, it will always be at the temperature where the rate is a maximum. The locus of maximum rates is found by examining the r(F, C) curves of Fig. 9.4 Fig. 9.5 shows this progression. 

For the optimum temperature progression in a plug flow reactor in Example... 

Qualitatively find the optimum temperature progression to maximize Q for the reaction scheme... 

The optimum temperature progression at T = Topt from Equation 6-177 is... 

At T = Topt and rearranging Equation 6-181, the optimum temperature progression Topt is... 

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