Dynamics of Counter-Current Cooled CSTRs

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This Demonstration illustrates the dynamics of a system composed of two CSTRs in series with counter-current cooling in which a first-order reversible exothermic chemical reaction takes place. The system of two identical CSTRs is governed by six dimensionless differential equations [1]:








where represents dimensionless time, is the dimensionless concentration of reactant , and and stand for the dimensionless temperatures of the reactor and cooling fluid, respectively. The following parameters are also dimensionless: , , and for the Damköhler number, the activation energy, and the heat transfer coefficient; , , and stand for the adiabatic temperature rise, the ratio of heat capacity of the reactor flow rate to the coolant flow rate, and the ratio of the heat capacity of the coolant volume to the reactor volume; and is the inlet coolant temperature. The system of equations is solved with


and initial values


In this high-dimensional nonlinear system, the entanglement of input and output between the two reactors leads to chaotic behavior. As , the Damköhler number of the first reactor, is increased, the trajectories change from oscillations leading to a steady state to periodic, then chaotic oscillations, and again to oscillations leading to a steady state.


Contributed by: Clay Gruesbeck (September 2013)
Open content licensed under CC BY-NC-SA




[1] K. S. Chang and R. Aris, "Chaotic Dynamics of Counter Currently Cooled CSTRs," Latin American Applied Research, 18, 1988 pp. 1–30.

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