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, X_A1 = 0.65

Volume of first reactor, V₁ = 2 ft³

Volume of first reactor, V₂ = 3 ft³

Initial concentration, C_Ao = 2.55 ´ 10^-3 lbmol/ft³

$ Residence time in first reactor, t_m1 = V₁/υ_o = 2/0.025 = 80 s

$ kτ_m1 (Equation 1.61, First order variable volume CSTR):

$ Reaction rate constant, k₁ = 3.064/t_m1 = 3.064/80 = 0.038 s^-1

$ Concentration of reactant A exiting first reactor, C_A1 (Equation 1.9)

Concentration of product Q exiting first reactor, C_Q1 (Equation 1.12)

$ Volumetric flow rate exiting first reactor, υ₁ (Equation)

$ Residence time in second reactor, τ_m2 (Equation)

$ Fractional volume change for second reactor, ε₁

$ X_A2 can be obtained from rearrangement of (Equation 1.61)

and plugging in the appropriate values

$ Concentration of A exiting second reactor, C_A2

$ Overall conversion, X_AT