Tanks-in-Series TIS Reactor Model

A material balance for A around the ith tank of volume Vi in the N-tank series (all tanks of equal size), in the case of unsteady-state behavior of a variable-density system, 

For unsteady-state operation, equation 20.1-1 constitutes a set of N ordinary differential equations that must be solved simultaneously (usually numerically) to obtain the time-dependent concentration within each tank. For a constant-density system, dnAl/dr is replaced by Vt dcAi/dr. We focus on steady-state operation in this chapter. 

The first-order, liquid-phase reaction of lidocaine (A) to monoethylglycinexylidide (MEGX) is conducted in a reactor (the liver) with arbitrary flow conditions that is to be modeled by the TIS reactor model with N tanks. Derive an expression for c, the steady-state outlet concentration from the Nth tank, in terms of system parameters. 

The system parameters are the feed concentration, cAo, the rate constant in the rate law, (—rA) = kAcA, the mean-residence time, t, and N. Equation 20.1-4 for this case is 

As N °°, this result becomes identical with that for a PFR 

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