Q: What is the tanks-in-series (TIS) model?

The tanks-in-series model represents non-ideal mixing by cascading N ideal CSTRs in series. N=1 gives an ideal CSTR, while N→∞ approaches plug flow. The step-tracer RTD is F(θ) = 1 − e^(−Nθ)·Σ(Nθ)^i/i! (i=0 to N−1). In practice, the N parameter is fitted from tracer experiments to account for dead zones and bypass.

Question 1

What is the power number Np in a stirred tank?

Accepted Answer

The power number Np is a dimensionless measure of agitator power: P = Np × ρ × N³ × d⁵. In the turbulent regime, Np is constant — approximately 5.0 for a Rushton turbine, 0.35 for a marine propeller, and 1.3 for a pitched-blade turbine. Fully turbulent conditions are reached when the mixing Reynolds number Re_m = ρNd²/μ exceeds roughly 10⁴.

Question 2

How is CSTR conversion calculated for a first-order reaction?

Accepted Answer

For the reaction A→B with first-order kinetics, the CSTR design equation gives conversion X = kτ/(1+kτ), where k is the rate constant (1/s) and τ = V/Q is the mean residence time (s). A CSTR always achieves lower conversion than a plug-flow reactor (PFR) of the same volume at the same residence time.

Question 3

What correlation is used for mixing time?

Accepted Answer

In the turbulent regime, the dimensionless blend time correlation N·t_m ≈ 5.9 (D/d)² is widely used, where D is tank diameter and d is impeller diameter. Larger D/d ratios require longer mixing times. In the laminar regime (Re_m < 10) the product N·t_m scales as Re_m⁻¹.

Question 4

What is the tanks-in-series (TIS) model?

Accepted Answer

The tanks-in-series model represents non-ideal mixing by cascading N ideal CSTRs in series. N=1 gives an ideal CSTR, while N→∞ approaches plug flow. The step-tracer RTD is F(θ) = 1 − e^(−Nθ)·Σ(Nθ)^i/i! (i=0 to N−1). In practice, the N parameter is fitted from tracer experiments to account for dead zones and bypass.

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