Selectivity instantaneous

The following details mathematical expressions for instantaneous (point or local) or overall (integral) selectivity in series and parallel reactions at constant density and isotliermal conditions. An instantaneous selectivity is defined as the ratio of the rate of formation of one product relative to the rate of formation of another product at any point in the system. The overall selectivity is the ratio of the amount of one product formed to the amount of some other product formed in the same period of time. 

It follows that one obtains maximum selectivity by choosing reaction conditions such that the ratio (rv/rw) always has its highest value. This ratio is often referred to as the instantaneous selectivity. 

In this case the order of the desired reaction is higher than that of the unwanted reaction so the exponent on the concentration is positive. The instantaneous selectivity is promoted by employing high concentrations of reactant. Consequently, batch or plug flow reactors are most appropriate from a selectivity viewpoint. 

Here SB,c is the instantaneous selectivity of the desired product B to unwanted product in this parallel reaction. 

If component B is the desired product and C is unwanted, the instantaneous selectivity of B relative to C is expressed as S from Equations 5-270 and 5-271 as... 

In developing mathematical expressions for selectivities, knowledge of the rate equations are required. This is because the instantaneous selectivity is defined in terms of the rate ratios. The parameters that affect the instantaneous and the overall selectivities are exactly the same as those influencing the reaction rates, namely, the concentration, temperature, activation energy, time of reaction (residence time in flow reactors), catalysts, and the fluid mechanics. 

Due to side reactions, in most of the experiments a higher octanol conversion than acid conversion is found. To investigate this phenomenon, an instantaneous selectivity is defined as the ratio of the rate of ester formation over the rate of 1-octanol-disappearance in one pass through the column ... 

As the selectivity depends on the concentrations of all compounds, the instantaneous selectivity is plotted over octanol inlet conversions to compare different experiments at similar concentrations. Figure 8.29 shows the Sinst for five different experiments where only the type of packing was varied. Two striking observations can be made. First, all data points for Sinst are on the same curve and second, this curve starts at around 75 96, runs through a maximum, then at ca. 50 % conversion level through a minimum followed by a second maximum and a final decay to ca. 50 % at very high inlet conversion levels. 

In order to understand the maxima and the minimum of the instantaneous selectivity Smstr it is useful to plot the predictions of the kinetic model as represented by the two rate Equations (1) and (2). In Fig. 8.31, the S m( expected from the kinetics is plotted depending on the fraction of water stripped from the liquid. All these curves start at around 75 %, increase to near-unity, and then show a sharp drop at high inlet conversion levels. Depending on the fraction of water stripped, the slope of the initial increase and onset of the final drop of Smst differ. 

If the conversion level increases, the reactant concentrations decrease. As the esterification is of first order in acid, but the etherification of second order in alcohol, the latter suffers more from low reactant concentrations. In consequence, the instantaneous selectivity increases with increasing conversion levels. 

The instantaneous selectivity SP is the ratio of the momentary rate of reactant conversion to P to the rate of reactant consumption ... 

Fractional conversion of a reactant is defined as the ratio of the amount consumed to that charged. In this book, the following definitions of yield, yield ratio, and selectivity are used The yield of a product is the ratio of the amount of reactant (or reactants) converted to the product to the total amount of reactant (or reactants) charged. The cumulative yield ratio of two products is the ratios of their yields. The instantaneous yield ratio is the ratio of the momentary rates of conversion to these products. The cumulative selectivity to a product is the ratio of the amount of reactant (or reactants) converted to that product to the amount consumed. The instantaneous selectivity is the ratio of the momentary rate of reactant conversion to the product to that of reactant consumption. Not used in this book is the extent of reaction, defined as the number of moles consumed or formed, divided by the stoichiometric coefficient of the respective participant. 

Derivation. The instantaneous selectivity to P (moles of A forming P per mole of A reacting) at given conversion level /A is... 

In a CSTR at steady state, the compositions of reactor content and effluent are the same, so that the cumulative selectivity SP (moles of A converted to P per mole of A reacted) equals the instantaneous selectivity Sr. In a batch reactor, eqn 5.32 describes the incremental fractional conversion of A to P at the respective conversion level ... 

When dealing with multiple reactions that lead to various products, issues of selectivity and yield arise. The instantaneous selectivity, s, is a function of the local conditions and is defined as the production rate of species i divided by the production rates of all products of interest ... 

Thus, the rate (i,e., instantaneous selectivity parameter of xylene relative to toluene is e "X... 

In this section we examine ways to maximize S, which is sometimes referred to as the instantaneous selectivity, for different reaction orders of the desired and undesired products. 

Similarly, the xylene yield based on reaetion rates is also zero. Consequently, we see that under these eonditions (Tpp,) the instantaneous selectivity and instantaneous yield, whieh are based on reactioji rates, are not very meaningful parameters and we must use the overall seleetivity 5xt and the overall yield, which are based on molar flow rates. The yield of xylene from mesitylene based on molar flow rates exiting the CSTR for t = 0.5 is... 

Selectivity tells us how one product is favored over another when we have multiple reactions. We can quantify the formation of D with respect to U by defining the selectivity and yield of the system. The instantaneous selectivity of D with respect to U is the ratio of the rate of formation of D to the rate of formation of U. 

Example 6 1 Comparing the Overall and Instantaneous Selectives, Sw foraCSTR... 

Consider the instantaneous selectivity for the two parallel reactions just discussed ... 

Consequently for a CSTR the overall and instantaneous selectivities are equal that is. 

Recall that for a CSTR the overall selectivity and yield are identical with the instantaneous selectivity and yield,... 

Straight forward problem to reinforce principles of how to choose reactor schemes to maximize the instantaneous selectivity for parallel reactions. 

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