# Continuous Stirred Tank Reactor (CSTR)

** Category:** Chemical Engineering

** Demonstrates:** Differential equations; Dynamic simulation

## Problem Description

A chemical reaction A → B takes place in a continuous stirred tank reactor (CSTR). The reactor is heated by a heating jacket containing a fluid at a constant temperature.

Calculate the changes in concentration and temperature over time inside the reactor when the first-order reaction takes place. The reaction rate is defined by:

r = ke |

where r is the reaction rate [mol/cm^{3}.s]; T is the temperature [K]; and C is the concentration of the
reactant in the liquid [mol/cm^{3}]. The density of the reactant is assumed
to be constant regardless of temperature. Other parameters and operating conditions are as follows:

Volume of reactor | V = 2000 cm^{3} |

Feed rate | F = 10 cm^{3}/s |

Rate constant of reaction | k = 7.86 x 10^{12} l/s |

Activation energy | E = 22500 cal/mol |

Gas constant | E = 1.987 cal/mol.K |

Density of reactant | ρ = 1 g/cm^{3} |

Specific heat of reactant | C_{p} = 1 cal/g.K |

Heat of reaction | ΔH = -10000 cal/mol |

Heat transfer coefficient * Area | UA = 1.356 cal/s.K |

Temperature of heat transfer medium | T_{w} = 350 K |

Temperature of feed | T_{0} = 300 K |

Concentration of feed | C_{0} = 5.0 x 10^{-6} mol/cm^{3} |

The following equations will be used:

Material and Heat Balances:

V(dC/dt) = FC |

Initial Conditions:

t = 0 : C = C |

The EQUATRAN source text for this problem is:

/* Continuous Stirred Tank Reactor (CSTR) */ |

Enter the lines above into a new source text window, then click the Run button. No further input is required, so the results will be displayed imediately.

/* Continuous Stirred Tank Reactor (CSTR) */ |

A graph can be displayed to show the variation in the reactor conditions over time. Click the Graph icon on the toolbar, select Time as the X value, Temperature as Y1 and Concentration as Y2, the click Ok.

The EQUATRAN file for this example can be downloaded from the link below: