Tanks in Series Model

Levenspiel (Hfst. 14) p. 321 - 338

Tanks-inTanks-in-series model
Another model that is frequently used to simulate the behavior of actual reactor networks is a cascade of ideal CSTRs operating in series. series

Tanks-inTanks-in-series model

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The actual reactor is replaced by n identical stirred tank reactors whose total volume is the same as that of the actual reactor.
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Tanks-inTanks-in-series model
Model definition:

Tanks-inTanks-in-series model
Material balance – tank N:

t  t⋅E =   t 

N −1

NN t e − tN t ; t = N t i ; σ 2 = (N − 1)! N
2 1 t e −t t i ; t i = ; σ 2 = N t i ( N − 1)! N

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t  ti ⋅ E =    ti  θi = t = dimensionl ess time based on mean residence time per tank, t i ti t θ = = dimensionl ess time based on mean residence time in all N tanks, t t θ i = 1; θ = 1; θ i = Nθ
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N −1

Eθ = t ⋅ E = N Eθ i = t i ⋅ E =

( N θ )N −1 e − Nθ ; σ 2 = θ ( N − 1)! θ iN −1 e −θ i ; σ θ2i = N

1 N

(N − 1)!

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Tanks-inTanks-in-series model

Chemical conversion Tanks-inTanks-in-series model
1st order reaction in one tank:

CA 1 = C A0 1 + k t
1st order reaction in N tanks-in-series:

N=

t2

σ

2

CA 1 = C A0  k t  N 1 +   N  
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Number of tanks-in-series N → ∞, plug flow
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Class example
The concentration reading in the following table represents a continuous response to a pulse input. How many tanks in series is the reactor equivalent to?
Time t (min) 0 5 10 15 20 25 30 35 Tracer output concentration C(t) (g/L) 0 3 5 5 4 2 1 0
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From previous class example:

N=

t2

σ2

= 4.737 ≈ 5
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