Optimal Conversion

Consider the case of a single reaction with a large chemical equilibrium constant such that it is possible to obtain a complete conversion. However, the optimal conversion may not be complete conversion. Instead, an economic balance between a high reactor section cost at high conversion and a high separation section cost at low conversion determines the optimum. Unfortunately, a heuristic for the optimal conversion is not available because it depends on many factors. This subject is considered in more detail in Chapter 8 on reactor-separator-recycle networks. 

Heuristic 9 Separate liquid mixtures using d tillation, stripping, enhanced 

Heuristic 10 Attempt to condense or partially condense vapor mixtures with cooling water or a refrigerant. Then, use Heuristic 9. 

Heuristic 11 Separate vapor mixtures using partial condensation, cryogenic distillation, absorption, adsorption, membrane separation and/or desublimation. The selection among these alternatives is considered in Chapter 7. 

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In Fig. 8.3, the only cost forcing the optimal conversion hack from high values is that of the reactor. Hence, for such simple reaction systems, a high optimal conversion would he expected. This was the reason in Chap. 2 that an initial value of reactor conversion of 0.95 was chosen for simple reaction systems. 

Objective Function This is the quantity for which a minimax is sought. For a complete manufacturing plant, it is related closely to the economy of the plant. Subsidiary problems may be to optimize conversion, production, selectivity, energy consumption, and so on in terms of temperature, pressure, catalyst, or other pertinent variables. 

The significance of the coupling of micro- and macrorelaxations for resonance phenomena observed in catalytic systems under forced periodic operation (cycling) (15) implies that the wave-front analysis of transients of this kind can eventually suggest a more effective strategy in seeking the optimal conversion and selectivity. Finally the existence of certain surface structures and complexes could be established, if the transients of the surface intermediates will be followed e.g. by infrared spectroscopy (see e.g. (16, 17)). 

However, the real breakthrough came with the drastically facilitated preparation of 1-cyclopropylcyclopropanol (15) from methyl cyclopropanecarboxylate (19) applying the transformation of an alkoxycarbonyl group into a cyclopropanol fragment with ethylmagnesium bromide in the presence of Ti(zPrO)4 as developed by Kulinkovich et al. [13]. The optimized conversion of the alcohol 15 to the bromide 16 and its dehydrobromination makes the alkene 1 available in synthetically useful quantities of 40 -55 g within one week (Scheme 3) [ 14]. This sequence is also applicable to prepare substituted, especially spirocyclopropane-annelated, bicyclopropylidenes [ 14a]. 

The time for optimized conversion has been determined by GLC for all olefins. It is crucial for all reactions to be stopped at optimum conversion, because slow decomposition of the allylic product occurs during the reaction. To obtain optimum yields one should follow the reaction by GLC. Optimized conversion is defined as allylic acetate/allylic acetate plus remaining olefin. 

All feeds require an optimized catalyst for the optimal conversion to lighter and more valuable products. This insight has always concerned FCC professionals. Even with vacuum gas oil as feed the optimization problem was evident. Wear and Mott used a MAT reactor to optimize the zeolite to matrix surface area ratio (ZSA/MSA) for a vacuum gas oil catalyst [4]. The naphtha yield increased with increasing ZSA/ MSA ratio, while the coke and dry gas yields decreased. This investigation showed that the optimization of the catalyst indeed was necessary and was very profitable even when vacuum gas oil was used as feed to the catalytic cracker. 

In a similar fashion, palladium-catalyzed alkoxycarbonylation of 54 was effective in producing pyrimdine esters 55 <99T405>. It was noted that dppf along with the use of the alcohols as solvents (rather than solely as reagents) was required for optimal conversion. 

Typically, viscous materials transfer energy poorly. With conventional con-ductively heated vessels, thermal decomposition on the walls can occur at the same time as incomplete reaction towards the center of the sample. Such substantial thermal gradients can afford sub-optimal conversions. That in turn leads to loss of product and renders product isolation difficult. Furthermore, at high temperatures, heat losses with conductive heating increase and the efficiency declines. With microwave systems, these problems are not as pronounced and in some cases, even the heating efficiency can increase with temperature. 

Consider a series of continuous flow stirred tank reactors of equal size with inlet and exit conversions as X0 and XN. The intermediate optimal conversions Xu X2, X3. .. Xt. .. XN t can be determined, which will minimize the overall reactor size. Levenspiel [1] has shown... 

Figu re 2.13 Optimal conversion at different levels of the process synthesis by the hiearchical approach. 

Figure 2.13 illustrates the variation of the economic potential during flowsheet synthesis at different stages as a function of the dominant variable, reactor conversion. EPmin is necessary to ensure the economic viability of the process. At the input/output level EP2 sets the upper limit of the reactor conversion. On the other hand, the lower bound is set at the reactor/separation/recycle level by EP3, which accounts for the cost of reactor and recycles, and eventually of the separations. In this way, the range of optimal conversion can be determined. This problem may be handled conveniently by means of standard optimization capabilities of simulation packages, as demonstrated by the case study of a HDA plant [3]. 

Rapid solids mixing ensures uniform bed temperature, and therefore optimal conversion. 

Optimal conversion to 1,4-hexadiene is favoured by a large excess of ethanol over RhCla. 3-Methyl-1,4-pentadiene and 2,4-hexadiene are also formed in low yields. Butadiene and ethylene are used in excess to restrict isomerization to 2, 4-hexadiene as they compete with the product (1,4-hexadiene) for the coordination sites involved. 

The influence of acyl donor concentration in the IL/SC-CO2 medium was exploited in order to achieve higher enantiopure yield (Figure 8.7) at 313.15 K and 16MPa. The highest conversion was achieved at the same substrate composition as in SC-CO2, namely vinyl acetate/1-phenylethanol molar ratio of 9/1. No (S)-1-phenylethanol conversion was detected at all tested conditions, which means an enantiomeric excess for products evaluated higher than 99.9%. Optimal conversion, achieved after five hours of reaction, was 47.2% and enantiomeric excess for reactants was 89.5%. The conversion could be maximized with higher amount of biocatalyst in the reaction mixture. As expected, after five hours of bioconversion, approximately complete conversion 49.9% of (R)-1-phenylethanol into the enantiopure (R)-l-phenylethyl acetate was achieved. Enantiomeric excess for reactants was 99.3%. 

Catalyst Characteristic channel dimension d (mm) Selectivity at optimum HCN Optimal conversion /HCN ... 

Since chemical and field enhancement are sensitive to a number of variables, including substrate material, particle size and shape, laser wavelength, and the nature of the adsorbate-substrate interaction (including those requiring active adsorption sites), there is wide latitude in how a given substrate may be designed and optimized. Conversely, the observed enhancement can vary by orders of magnitude if the important substrate variables are not adequately controlled. Examples of SERS substrates that have been proposed for chemical analysis... 

In the reaction process shown in Fig. P2.84, fresh ethane and chlorine gas and recycled ethane are combined and fed into the reactor. A test shows that if 100% excess chlorine is mixed with ethane, a single-pass optimal conversion of 60% results, and of the ethane that reacts, all is converted to products and none goes into undesired products. Calculate ... 

As clearly indicated in Figure 6, the benzene selectivity can reach 100% when the conversion of cumene is less than 5 % at Cp =5, while the maximum benzene selectivity at Cp = 50 can only achieve 92%. However, this does not provide a clear picture of which catalyst to feed ration to be chosen from, neither the optimal conversion level, nor the status of the equilibrium catalyst. 

A similar lack of clarity pervades other areas concerning the relationship between the catalytic performance and fundamental properties of the catalysts. Wakabayashl et al. (10) reported that the optimized conversion of propylene to acrolein (>7%) over alumina-supported tin-antimony oxide (3 1) was dependent on the sintering temperature of the catalyst and was maximized after heating at 10(X)°C for 3 hr. Further work (22) showed that both electrical conductivity and surface area were maximized in the material containing 3% antimony and a close association between acrolein production and solid solution formation was suggested. 

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