F1.6 CSTRs Formulas

Continuously Stirred Tank Flow Reactor: If a reaction is carried out in a stirred tank flow reactor its design equation is given as follows:

Simplified solutions are provided below for constant pressure operations.

Zero order reaction: -r_A = k

First order reaction: -r_A = kC_A

Second order reaction: -r_A = kC_A²

Third order reaction: -r_A = kC_A³

Second order reaction: -r_A = kC_AC_B

Third order reaction: -r_A = kC_A²C_B

Third order reaction: -r_A = kC_AC_B²

Third order reaction: -r_A = kC_AC_BC_C

Continuously Stirred Tank Flow Reactor, Constant Volume

Zero order reaction: -r_A = k

First order reaction: -r_A = kC_A

Second order reaction: -r_A = kC_A²

Third order reaction: -r_A = kC_A³

Second order reaction: -r_A = kC_AC_B

Third order reaction: -r_A = kC_A²C_B

Third order reaction: -r_A = kC_AC_B²

Third order reaction: -r_A = kC_AC_BC_C

Reactors in Series: Sometimes one can save money by using more reactors. Their arrangement can produce different levels of conversion.

(a) If a reaction is first order and is conducted in CSTRs, then volumetric flow rate entering the second reactor can be found through Equation 1.16 as

and for the second reactor

and the design equation for second reactor is

and exit concentration from second reactor is

and the overall conversion, X_At, is given by

(b) If the reaction is conducted under constant volume conditions and residence time in all CSTRs is the same, then the overall conversion for n reactors can be found as follows.

Obtain the information k, τ_m, and X_A or the single reactor and then incorporate this information to obtain the overall conversion or reactor size as follows.

(c) If a second order reaction is conducted in a constant volume mixed reactor, then design equation is

which can solved for conversion. It is noted that this is a quadratic equation.

And overall conversion can be found to be