Sensitivity of a Plug Flow Reactor to Model Parameters

Download the CDF file to view the simulation using the free 
Wolfram CDF player.
Gas-phase series reactions (A → B → C) take place in a non-isothermal plug flow reactor (PFR). Both reactions are first order. In this Demonstration you vary seven of the parameters used in the model and two of the feed conditions (temperature and flow rate) over relatively narrow ranges of values. Changing the feed temperature and flow rate shows how sensitive the reaction is to the feed conditions. You can vary each parameter and feed condition a maximum of ±10% as a way to illustrate the sensitivity of the model to the values of the parameters (parametric sensitivity) and what effects inaccuracies in their values have on the reactor conditions calculated. Since parameters used in a reactor simulation are not always known accurately, performing a parametric sensitivity analysis can be valuable.
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)).