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, υ_o = 0.025 ft³/s

Conversion in first reactor, X_A1 = 0.65

Volume of first reactor, V₁ = 2 ft³

Volume of second reactor, V₂ = 3 ft³

Temperature, T = 298.15 °K

1. Residence time, t_m1 = V₁/υ_o = 2/0.025 = 80 s

2. kτ_m (Equation 1.69, first order CSTR at constant density):

1. k = 1.857/t_m1 = 1.857/80 = 0.023 s

2. C_A1 = C_Ao(1 - X₁) = (2.55 ´ 10^-3)(1 - 0.65) = 8.932 ´ 10^-4 lbmol/ft³

3. Residence time, τ_m2 = V₂/υ₁ = 3/0.025 = 120 s

4. Conversion, X_A2 (Equation 1.69):

5. Concentration from second reactor, C_A2

C_A2 = C_A1(1 - X_A2) = (8.932 ´ 10^-4)(1 - 0.736) = 2.359 ´ 10^-4 lbmol/ft³

6. Overall conversion, X_T

X_T = (C_Ao - C_A2)/C_Ao = (2.55 ´ 10^-3 - 2.359 ´ 10^-4)/2.55 ´ 10^-3 = 0.908