# Sensitivity of a Plug Flow Reactor to Model Parameters

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Plots of temperature and molar flow rates versus reactor volume are shown for gas-phase reactions in a non-isothermal, plug flow reactor (PFR). Both reactions are first order and only is fed to the reactor. Use the sliders to vary the inlet molar flow rate, feed temperature and seven model parameters (a maximum of 10%) to see how sensitive the temperature and molar flow rates are to values used in the reactor model (parametric sensitivity). Since parameters used in a reactor model are not always known accurately, doing a parametric sensitivity analysis could identify potential problems.

Contributed by: Rachael L. Baumann (August 2013)
Additional contributions by: John L. Falconer and Nick Bongiardina
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA

## Details

The rate laws for these reactions are:

,

,

,

,

,

where is the rate of reaction (), is the rate constant (), is reaction temperature (K), and are the concentrations of and (), the subscript refers to the inlet, , and are the molar flow rates of , and (mol/s) and is the total molar flow rate (mol/s).

The rate constants are calculated from the pre-exponential factors which are solved at :

,

,

where is a pre-exponential factor (1/s), is the rate constant at 380 K, is activation energy (kJ/mol) and is the ideal gas constant (kJ/(mol K)),

Mole and energy balances are done around the reactor:

,

,

,

,

where is volume (), is the heat transfer coefficient times heat transfer area per volume (kJ/(m s K)), is the coolant temperature (K), is heat of reaction (kJ/mol), and , and are the heat capacities of , and (kJ/(mol K)).

The screencast video [1] explains how to use this Demonstration.

Reference

[1] Sensitivity of a Plug Flow Reactor to Model Parameters [Video]. (Mar 29, 2017) www.colorado.edu/learncheme/kinetics/SensitivityOfPFRtoModelParameters.html.

## Permanent Citation

Rachael L. Baumann

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