Stationary States in a Nonisothermal Continuous Stirred-Tank Reactor

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This Demonstration analyzes the single-step reaction in a nonisothermal continuous well-stirred tank reactor (CSTR) where
is the heat of reaction. The rate of reaction is first order in the concentration of species
, so that
, and the rate constant has an Arrhenius temperature dependence:
. Heat is removed from the reactor using a cooling coil that has an overall heat transfer coefficient
and surface area
. The Demonstration shows the complex steady states (expressed as plots of temperature
versus
, and conversion fraction
versus
) that can occur in the reactor as the residence time
and the heat transfer parameter
are varied. The possibilities include a unique steady state and multiple steady states, as well as the birth and death of an isola (or island), which is a region in the solution space described by a closed loop.
Contributed by: Brian G. Higgins and Housam Binous (February 2012)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The dynamics of the nonadiabatic CSTR are described by the following mass and energy balances [1]:
,
,
subject to the initial conditions ,
.
[1] P. G. Gray and S. K. Scott, Chemical Oscillations and Instabilities: Non-linear Chemical Kinetics, Oxford: Claredon Press, 1994.
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