Example 1.11 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 volume 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.
Solution:
Volumetric flow rate entering first reactor, υo = 0.025 ft3/s
Conversion in first reactor, XA1 = 0.65
Volume of first reactor, V1 = 2 ft3
Volume of second reactor, V2 = 3 ft3
Temperature, T = 298.15 °K
. Residence time, tm1 = V1/υo = 2/0.025 = 80 s
. kτm (Equation 1.69, first order CSTR at constant density):
. k = 1.857/tm1 = 1.857/80 = 0.023 s
. CA1 = CAo(1 - X1) = (2.55 ´ 10-3)(1 - 0.65) = 8.932 ´ 10-4 lbmol/ft3
. Residence time, τm2 = V2/υ1 = 3/0.025 = 120 s
. Conversion, XA2 (Equation 1.69):
. Concentration from second reactor, CA2
CA2 = CA1(1 - XA2) = (8.932 ´ 10-4)(1 - 0.736) = 2.359 ´ 10-4 lbmol/ft3
. Overall conversion, XT
XT = (CAo - CA2)/CAo = (2.55 ´ 10-3 - 2.359 ´ 10-4)/2.55 ´ 10-3 = 0.908