**Parametric Sensitivity of Plug Flow Reactor with Heat Exchange**

This Demonstration plots the temperature and molar flow rate of the reactant as a function of distance down a plug flow reactor for an exothermic, gas-phase reaction. The reactor has heat exchange through the walls. Vary the feed temperature, activation energy for the reaction, and total molar flow rate with the sliders. Thermal runaway occurs at certain conditions and it is a sensitive function (parametric sensitivity) of the feed temperature and the activation energy.
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**Details**

This is a model of the partial oxidation of o-xylene in a large excess of oxygen in a 1.5 m long plug flow reactor.

The first-order rate expression:

where ρ is rate of reaction (mol/[m

^{3}s]), k is the pre-exponential factor in the rate constant (1/s), E_{a}is the activation energy (kJ/mol) R_{2}is the ideal gas constant (kJ/[mol K]), T is the absolute temperature in the reactor (K), P is pressure (atm), R is the ideal gas constant ([atm m^{3}]/[mol K]), F_{x}is the molar flow rate of the reactant o-xylene (kmol/s), and F_{tot}is the total molar flow rate of the feed (kmol/s).Mole balance as a function of length:

where z is the distance down the PFR (m), A = πr

^{2}is the cross-sectional area of the PFR (m

^{2}), and r is the PFR radius (m).

Energy balance as a function of length:

where β and γ are simplification terms, T

_{a}is the temperature of the heat transfer fluid surrounding the reactor (K), ΔH is the heat of reaction (kJ/kmol), m is the mass flow rate (kg/s), C

_{Pm}is the mass heat capacity of gas in the reactor (kJ/[kg K]), and U is the overall heat transfer coefficient (kJ/[m

^{2}s K]).

At the PFR inlet (z=0) T = T

_{f}and F_{x}=y_{x,f}F_{tot}, where T_{f}is the feed temperature (K) and y_{x,f}is the mole fraction of reactant in the feed.