Question #231006

"An infinite equal size mixed flow reactors connected in series will give same performance as a single plug flow reactor" Justify.

Expert's answer

The mixed reactor is always bigger than the plug flow reactor for any given job, and all positive reaction commands. The volume-to-volume ratio rises as response order rises. When the conversion is minimal, flow type has only a little impact on reactor performance. At high conversion, the performance ratio rises extremely quickly; as a result, a good depiction of the flow becomes critical in this range of conversion. The fluctuation in density throughout the reaction affects the design, although it is usually secondary to the variance inflow type.

Consider a Plug Flow Reactors in Series

N plug flow reactors

X_1, X_2, . . . , X_N

The fractional conversion of component A leaving reactor 1, 2, . . . , N

For the ith reactor

\frac{V_i}{F_0}= \int_{X_{i-1}}^{X_i} \frac{dX}{-r}

For several reactors with a total volume of V

\frac{V}{F_o}= \sum^N_{i=1} \frac{V_i}{F_o}= \frac{V_1+V_2+...+V_0}{F_o}\\ =\int_{X_{0=0}}^{X_1} \frac{dX}{-r}+\int_{X_{1}}^{X_2} \frac{dX}{-r}+...+\int_{X_{N-1}}^{X_N} \frac{dX}{-r}=\int_{0}^{X_N} \frac{dX}{-r}

N plug flow reactors in series with a total volume V gives the same conversion as

a single plug flow reactor of volume V

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