Consider the Diels–Alder reaction between benzoquinone (B) and cyclopentadiene (C) which was discussed in Illustration 8.1. B + C → adduct If the reaction occurs in the liquid phase at 25°C, determine the reactor volume requirements for cascades of one and three identical CSTRs that operate at the

Question

Consider the Diels–Alder reaction between benzoquinone (B) and cyclopentadiene (C) which was discussed in Illustration 8.1.

[latex]B+C\rightarrow[/latex] adduct

If the reaction occurs in the liquid phase at [latex]25^{\circ}[/latex]C, determine the reactor volume requirements for cascades of one and three identical CSTRs that operate at the same temperature. The rate at which liquid feed is supplied is 0.278 [latex]m^{3}[/latex]/Ks. Use the graphical approach outlined previously. The following constraints are applicable: [latex]r=kC_{B}C_{C}[/latex] with k = 9.92 [latex]m^{3}/(Kmol\cdot Ks)[/latex]; [latex]C_{C0}=0.1\, Kmol/m^{3}[/latex]; [latex]C_{B0}=0.08\, Kmol/m^{3}[/latex]; conversion desired = 87.5%.

Accepted Answer

The graphical approach requires a plot of reaction rate versus the concentration of the limiting reagent (benzoquinone). To prepare this plot it is necessary to relate the two reactant concentrations to one another. From the initial concentrations and the stoichiometric coefficients.

[latex]C_{C}=C_{B}+0.02[/latex]

Thus,

[latex]r=kC_{B}(C_{B}+0.02)[/latex]

or at [latex]25^{\circ}[/latex]C,

[latex]r=9.92C_{B}^{2}+0.1984C_{B}[/latex] (A)

where the rate is expressed in kilomol/[latex](m^{3}\cdot Ks)[/latex] when concentrations are expressed in kilomol/[latex]m^{3}[/latex]. Equation (A) is presented in graphical form as curve M in Figure I8.7.

For 87.5% conversion the concentration of benzoquinone in the effluent from the last reactor in the cascade will be equal to (1-0.875)(0.08), or 0.010 Kmol/[latex]m^{3}[/latex].

For the case where the cascade consists of just a single reactor, only a single straight line of the form of equation (8.3.31) is involved in the graphical solution. One merely links the point on curve M corresponding to the effluent concentration of benzoquinone with the point on the abscissa corresponding to the feed concentration. The slope of this line is equal to [latex]-1/ au[/latex] or [latex]- u _{0}/V_{R}[/latex]. In the present instance the slope is equal to [latex](2.976-0) imes 10^{-3}/(0.01-0.08)[/latex] or -0.0425 [latex]Ks^{-1}[/latex]. Thus,

[latex]V_{R}=\frac{ u _{0}}{0.0425}=\frac{0.278}{0.0425}=6.54\, m^{3}[/latex]

For the case where the cascade consists of three identical reactors, a trial and-error approach is necessary to determine the reactor size required. One starts at the inlet concentration and draws a line linking this point on the abscissa with some point J on curve M. One then draws a straight line parallel to the first, but passing through the point on the abscissa corresponding to the benzoquinone concentration at point J. This straight line intersects curve M at some point K. One then repeats the procedure by drawing yet another parallel line through the point on the abscissa corresponding to the benzoquinone concentration at K. If the intersection of this straight line with curve M occurs at a reactant concentration of 0.010 [latex]kmol/m^{3}[/latex],the initial choice of slope was correct. If not, one must choose a new point J and repeat the procedure until such agreement is obtained. Figure I8.7 indicates the construction for this case. The slopes of the straight lines are equal to [latex](18.2-0) imes 10^{-3}/(0.034-0.08)[/latex] or -0.396 [latex]Ks^{-1}[/latex]. The volume of an individual CSTR is then 0.278/0.396 or 0.70 [latex]m^{3}[/latex], and the total volume of the three CSTRs is 2.1 [latex]m^{3}[/latex]. For the cascade the volume is reduced by more than a factor of 3 relative to that of a single CSTR. In Section 8.3.2.3 we shall see that large volume reductions are typical for use of cascades of CSTRs.

Question : Consider the Diels–Alder reaction between benzoquinone (B) a...