Fractional Conversion of a Reactant

Fractional conversion of a reactant, /A for reactant A, say, is the ratio of the amount of A reacted at some point (time or position) to the amount introduced into the system, and is a measure of consumption of the reactant. It is defined in equation 2.2-3 for a batch system, and in equation 2.3-5 for a flow system. The definition is the same whether the system is simple or complex. 

In complex systems, fA is not a unique parameter for following the course of a reaction, unlike in simple systems. For both kinetics and reactor considerations (Chapter 18), this means that rate laws and design equations cannot be uniquely expressed in terms of /A, and are usually written in terms of molar concentrations, or molar flow rates or extents of reaction. Nevertheless, fA may still be used to characterize the overall reaction extent with respect to reactant A. 

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It is often convenient to work with fractional conversion of a reactant species. Let i = A, a reactant, then... 

Analogous to the batch reactor, a fractional conversion of a reactant A can be defined as ... 

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. 

Chemical reactions do not take place instantaneously, and indeed often proceed rather slowly. In such cases, it is not practical to design the reactor for complete conversion of the limiting reactant instead, the reactor effluent emerges with some of the limiting reactant still present and is then usually subjected to a separation process to remove the unconverted reactant from the product. The separated reactant is then recycled to the reactor inlet. The fractional conversion of a reactant is the ratio... 

The fractional conversion of a reactant is the ratio of amount reacted to amount fed. The fractional conversions of different reactants are generally different unless the reactants are fed in stoichiometric proportion. 

The fraction conversion/is an intensive measure of the progress of a reaction. It is a variable that is simply related to the extent of reaction. The fraction conversion of a reactant Aj in a closed system in which only a single reaction is occurring is given by... 

The variable that describes composition in Eqn. (3-5) is Nu the total moles of species i . It sometimes is more convenient to work problems in terms of either the extent of reaction or the fractional conversion of a reactant, usually the limiting reactant. Extent of reaction is very convenient for problems where more than one reaction takes place. Fractional conversion is convenient for single-reaction problems, hut can he a source of confusion in problems that involve multiple reactions. The use of all three compositional variables, moles (or molar flow rates), fractional conversion, and extent of reaction, wiU be illustrated in this chapter, and in Chapter 4. 

For a single reaction, it frequently is convenient to write Eqn. (3-16) in terms of either extent of reaction or fractional conversion of a reactant. If i is a reactant, say A,... 

Only the concentrations of reactants and products appear in the final rate equation. The concentrations of active centers were eliminated in Step 3. All of the concentrations in the final rate equation are related through stoichiometry. For a single reaction, each concentration in the rate equation can be expressed in terms of one stoichiometric variable, e.g., extent of reaction, fractional conversion of a reactant, or the concentration of a single species, e.g., the concentration of the limiting reactant. 

The fractional conversion of a reactant in a differential PFR can be kept low (typically less than 10%) by operating the reactor at a very low space time tq. For a heterogeneous catalyst, tq (= W /vq) can be made low by using a very small amount of catalyst This can be an advantage when experimental catalysts are being studied, as the amoimt of catalyst available may be limited. 

In previous chapters, we used the fractional conversion of a reactant to measure the progress of a single reaction. Reactant conversion still is a valid concept, even when more than one reaction takes place. However, the conversion of a single reactant is not sufficient to describe the progress of more than one reaction, and is not sufficient to define the complete... 

The fractional conversion of a given reactant, Xa, is defined for a batch system as... 

For a simple A -t- B —> C reaction in a continuous stirred-tank reactor, as shown in Fig. 5.134, in terms of fraction conversion of the reactant A, the balance... 

Equation 2.2-2 may appear in various forms, if nA is related to other quantities (by normalization), as follows (1) If A is the limiting reactant, it may be convenient to normalize nA in terms of /A, the fractional conversion of A, defined by ... 

For a reaction represented by A - products, in which the rate, ( — rA), is proportional to cA, with a proportionality constant kA, show that the time (t) required to achieve a specified fractional conversion of A (/A) is independent of the initial concentration of reactant cAo. Assume reaction occurs in a constant-volume batch reactor. 

For a constant-density system, several simplifications result. First, regardless of the type of reactor, the fractional conversion of limiting reactant, say fA, can be expressed in terms of molar concentration, cA ... 

The aqueous second order reaction, 2A 2B, has the specific rate k = 1.0 liter/mol-hr and the initial concentration Ca0= 1 mol/liter. Downtime is 1 hr/batch. Cost of fresh reactant is 100/batch and the value of the product is 200xa/batch, where xa is the fractional conversion of A. What is the daily profit for each of these modes of operation ... 

In terms of the initial reactant ratio M = Cr(/Cao fractional conversion of A, this can be written as... 

When the density varies, we need to find another variable to express the progress of a reaction. Earlier we defined the fractional conversion X for a single reaction, and in this chapter we defined the conversion of a reactant species for reactant A and Xj for reaction j. For the conversion in a reaction we need a different variable, and we shall use Xj (bold type), with the index i describing the reaction. We will first work our series and parallel reactions with these variables and then consider a variable-density problem. 

Diagrams such as Fig. 6.3, which show the dependence of the stationary-state composition on a particular parameter, are known as bifurcation diagrams. It is customary, when trying to judge the efficiency of various processes for instance, to discuss the extent of reaction rather than the concentration of the reactant. The former is the fractional conversion of A into products and is given by the difference between the inflow concentration of A and its stationary-state value, i.e. how much A has reacted, divided by the original (inflow) concentration. For the extent of reaction we use the symbol y, and under stationary-state conditions... 

The basic equation for a tubular reactor is obtained by applying the general material balance, equation 1.12, with the plug flow assumptions. In steady state operation, which is usually the aim, the Rate of accumulation term (4) is zero. The material balance is taken with respect to a reactant A over a differential element of volume 8V, (Fig. 1.14). The fractional conversion of A in the mixture entering the element is aA and leaving it is (aA + SaA). If FA is the feed rate of A into the reactor (moles per unit time) the material balance over 8V, gives ... 

Assuming that the contents of the tank are well mixed, aAr is also the fractional conversion of the reactant A in tank r. 

Conversion of a Reactant. The conversion of a reactant A (XA) is the fraction of reactant A converted/transformed to products. 

While the individual reaction rates are the variables that, can be affected in a reacting system, we often express the performance of the reactor in terms of measures derived from the rates. Conversion and yield are such quantities. Conversion refers to the fractional consumption of a reactant in the reactor feed, whereas yield refers to the amount of product made relative to the amount of a key reactant fed to the reactor. In recycle systems the per-pass conversion of the various reactants is a relevant measure. It depends upon the rate of reaction for the specific component but also on the reactor feed. The per-pass conversion of an excess reactant is less than that of a limiting reactant. For example, the per-pass conversion of ethylene in a typical vinyl acetate reactor is only 7 percent whereas the per-pass conversion of oxygen is 36 percent. In Chap. 2 we discussed the plantwide control implications of incomplete conversion. 

It is desired to double the capacity of the existing plant by processing twice the feed of reactant A while maintaining the same fractional conversion of A to B in the reactor. How much larger a reactor, in terms of catalyst weight, would be required if all other operating variables are held constant You may use the Thoenes-Kramers correlation for mass transfer coefficients in a packed bed. Describe the effects of the flow rate, temperature, particle size at conversion. 

Figure 4.2-3 Fractional conversion of solid reactant as a function of dimensionless time for homogeneous model with zero-order solid kinetics sphere). 

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