Conversion according to Tanks in Series Model

Reaction in a non-ideal reactor represented by tank in series model. 

Taking the steady-state balance of reactant A for the fth CSTR we 

Starting with the value of Caq, Equations 3.311 can be solved recursively to calculate 

In this equation, the numbers of ideal CSTRs, N is the parameter of the tanks in series model. This parameter N is estimated using the E-curve, obtained from the tracer experiment conducted on the reaction vessel. As a special case, consider a first-order reaction (n = 1). Substituting n = 1 in Equation 3.311 and solving the equation recursively for i = 1, 2,3. n, we get 

Equations 3.315 and 3.316 define the lower and upper limits, respectively, on the fractional conversion x, achievable in a non-ideal reactor represented by tanks in series model, that is, the fractional conversion for a first-order reaction in a non-ideal reactor represented by tanks in series model is always higher than the conversion in an ideal CSTR, and lower than the conversion in an ideal PFR with space time x being the same in all the reactors. 

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