12.6.1 Energy Balance for Multiple Reactions in Plug-Flow Reactors
In this section we give the energy balance for multiple reactions. We begin by recalling the energy balance for a single reaction taking place in a PFR, which is given by Equation 12-5,
When we have multiple reactions occurring, we have to account for the heat of reaction in each reaction. For q multiple reactions taking place in the PFR where there are m species, it is easily shown that Equation (12-5) can be generalized to
Energy balance for multiple reactions
The heat of reaction for reaction i must be referenced to the same species in the rate, rij, by which ΔHRxij is multiplied, that is,
where the subscript j refers to the species, the subscript i refers to the particular reaction, q is the number of independent reactions, and m is the number of species. We are going to let
and
Qr = Ua(T – Ta)
Then Equation (12-35) becomes
Equation (12-37) represents a nice compact form of the energy balance for multiple reactions.
Consider the following reaction sequence carried out in a PFR:
Reaction 1: 
Reaction 2: 
The PFR energy balance becomes
One of the major goals of this text is that the reader will be able to solve multiple reactions with heat effects, and this section shows how!
