# Continuously Stirred Tank Reactor problem

Continuously Stirred Tank Reactor problem | |
---|---|

State dimension: | 1 |

Differential states: | 4 |

Continuous control functions: | 2 |

Interior point equalities: | 2 |

The Continuously Stirred Tank Reactor problem considers a chemical reaction that produces cyclopenthenol while using up cyclepentadiene "by an acid-catalyzed electrophilic hydration in aqueous solution", an exothermal reaction which needs to be cooled. This problem can e.g. be found in [Diehl2001]**Author: ** *M. Diehl***School: ** *Universit\"at Heidelberg***Title: ** *Real-Time Optimization for Large Scale Nonlinear Processes***Url: ** *http://www.ub.uni-heidelberg.de/archiv/1659/***Year: ** *2001*

.

The inflow into the tank contains only cyclopentadiene (substance ) with temperature and the flow rate can be controlled. The outflow rate is the same as the inflow rate to keep the liquid level in the tank constant. "The outflow contains a remainder of cyclopentadiene, the wanted product cyclepentenol (substance ) and two unwated by-products, cyclopentanediol (substance ) and dicyclopentadiene (substance ) with concentrations ." The latter two are not tracked in the problem as the substances are not of use. The reaction scheme is given as:

where the reaction rates are a function of the reactor temperature via an Arrhenius law

"The temperature in the cooling jacket is held down by an external heat exchanger whose heat removal rate can be controlled."

## Mathematical formulation

The problem is given by

where the various values are given in the Parameters section.

## Parameters

These fixed values are used within the model.

Name | Symbol | Value | Unit |

Arrhenius coefficient | |||

Arrhenius coefficient | |||

Arrhenius coefficient | |||

Arrhenius coefficient | [-] | ||

Arrhenius coefficient | [-] | ||

Arrhenius coefficient | [-] | ||

Reaction enthalpy | |||

Reaction enthalpy | |||

Reaction enthalpy | |||

Solution density | |||

Capacity of aqueous solution | |||

Heat transfer coefficient for cooling jacket | |||

Reactor surface area | |||

Reactor volume | |||

Coolant mass | |||

Capacity of coolant solution | |||

Starting concentration of subs. | |||

Inflow temperature |

## Reference solution

"The result of a steady state optimization of the yield with respect to the design parameter (feed temperature) and the two controls yields the steady stae and controls" and .

## Source Code

Model descriptions are available in