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8 September, 10:03

For the following conditions determine whether a CMFR or a PFR is more efficient in removing a reactive compound from the waste stream under steady-state conditions with a first-order reaction: reactor volume = 280 m3, flow rate = 14 m3 · day-1, and reaction rate coefficient = 0.05 day-1.

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  1. 8 September, 10:08
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    The PFR is more efficient in the removal of the reactive compound as it has the higher conversion ratio.

    Xₚբᵣ = 0.632

    X꜀ₘբᵣ = 0.5

    Xₚբᵣ > X꜀ₘբᵣ

    Explanation:

    From the reaction rate coefficient, it is evident the reaction is a first order reaction

    Performance equation for a CMFR for a first order reaction is

    kτ = (X) / (1 - X)

    k = reaction rate constant = 0.05 / day

    τ = Time constant or holding time = V/F₀

    V = volume of reactor = 280 m³

    F₀ = Flowrate into the reactor = 14 m³/day

    X = conversion

    k (V/F₀) = (X) / (1 - X)

    0.05 * (280/14) = X / (1 - X)

    1 = X / (1 - X)

    X = 1 - X

    2X = 1

    X = 1/2 = 0.5

    For the PFR

    Performance equation for a first order reaction is given by

    kτ = In [1 / (1 - X) ]

    The parameters are the same as above,

    0.05 * (280/14) = In (1 / (1-X)

    1 = In (1 / (1-X))

    e = 1 / (1 - X)

    2.718 = 1 / (1 - X)

    1 - X = 1/2.718

    1 - X = 0.3679

    X = 1 - 0.3679

    X = 0.632

    The PFR is evidently more efficient in the removal of the reactive compound as it has the higher conversion ratio.
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