Reaction yield, like selectivity, has two definitions: one based on the ratio of reaction rates and one based on the ratio of molar flow rates. In the first case, the yield at a point can be defined as the ratio of the reaction rate of a given product to the reaction rate of the key reactant A, usually the basis of calculation. This yield is referred to as the instantaneous yield YD.
The overall yield is based on molar flow rates , and defined as the ratio of moles of product formed at the end of the reaction to the number of moles of the key reactant, A, that have been consumed.
For a batch system:
For a flow system:
As with selectivity, the instantaneous yield and the overall yield are identical for a CSTR (i.e., ). From an economic standpoint, the overall selectivities, , and yields, , are important in determining profits, while the instantaneous selectivities give insights in choosing reactors and reaction schemes that will help maximize the profit. There often is a conflict between selectivity and conversion because you want to make as much as possible of your desired product (D) and at the same time minimize the undesired product (U). However, in many instances, the greater the conversion you achieve, not only do you make more D, but you also form more U.
The multiple reaction algorithm can be applied to parallel reactions, series reactions, complex reactions, and independent reactions. The availability of software packages (ODE solvers) makes it much easier to solve problems using moles Nj or molar flow rates Fj rather than conversion. For liquid systems, concentration is usually the preferred variable used in the mole balance equations.
The mole balances for the various types of reactors we have been studying are shown in Table 8-1. The resulting coupled differential mole balance equations can be easily solved using an ODE solver. In fact, this section has been developed to take advantage of the vast number of computational techniques now available on personal computers (e.g., Polymath).
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