Example 1.12: A first order reaction proceeds in a back-mixed reactor. Reactant A is fed at a rate of 0.025 ft3/s to a reactor operating under constant pressure conditions at 25 °C. A conversion of 65% results when a reactor volume is 2.0 ft3. If another reactor having volume 3.0 ft3 is added in series, estimate the conversion of A. The reaction proceeds as follows:
Solution
Volumetric flow rate, υ = 0.025 ft3/s
Conversion in first reactor, XA1 = 0.65
Volume of first reactor, V1 = 2 ft3
Volume of first reactor, V2 = 3 ft3
Initial concentration, CAo = 2.55 ´ 10-3 lbmol/ft3
Residence time in first reactor, tm1 = V1/υo = 2/0.025 = 80 s
kτm1 (Equation 1.61, First order variable volume CSTR):
Reaction rate constant, k1 = 3.064/tm1 = 3.064/80 = 0.038 s-1
Concentration of reactant A exiting first reactor, CA1 (Equation 1.9)
Concentration of product Q exiting first reactor, CQ1 (Equation 1.12)
Volumetric flow rate exiting first reactor, υ1 (Equation)
Residence time in second reactor, τm2 (Equation)
Fractional volume change for second reactor, ε1
XA2 can be obtained from rearrangement of (Equation 1.61)
and plugging in the appropriate values
Concentration of A exiting second reactor, CA2
Overall conversion, XAT