4.2 Ideal Reactor Arrangement Principles

Definition of Fractional Conversion at a Point ‘\(i\)’ in the Series of Reactors

It is customary to define the fractional conversion of the limiting reactant (\(A\)) as follows in case of reactors connected in series: \[X_{Ai}=\frac{\text{Total moles of $A$ reacted up to point `$i$'}}{\text{Moles fed to the first reactor in series}}\] Consider three ideal flow reactors connected in series as follows:


By the above definition of fractional conversion, note that, \[\begin{align*} F_{Ai} &= F_{A0}-F_{A0} X_{Ai}=F_{A0}(1-X_{Ai}) \\ X_{A1} &= \text{Conversion achieved in MFR1} \\ X_{A2} &= \text{Conversion (for the first two reactors) achieved in MFR1 and PFR} \\ X_{A3} &= \text{Conversion (overall for all the three reactors) achieved in MFR1, PFR and MFR2}\end{align*}\] However, one can always do the material balance around any reactor in the series, by carefully accounting for the limits of conversion, in order to calculate the conversion achieved in that particular reactor: \[\begin{align*} \frac{V_{\text{MFR1}}}{F_{A0}} &=\frac{X_{A1}}{-r_{A _{\text{MFR1}}}} \\ \frac{V_{\text{PFR}}}{F_{A0}} &=\int_{X_{A1}}^{X_{A2}} \frac{dX_A}{-r_A} \\ \frac{V_{\text{MFR2}}}{F_{A0}} &=\frac{X_{A3}-X_{A2}}{-r_{A_{\text{MFR2}}}}\end{align*}\]