Obtaining ethylene from ethane usually involves a thermal cracking unit which is a plug flow reactor.

The ethane enters the PFR where a furnace is used to hear the ethane to a very high temperature which causes the ethane to react. The reactions are as follows:

where



The material balance can be written as

Accumulation = Flow in - Flow out + Generation

A mole balance can be written for a cross-section of the tubular plug flow reactor and the following differential equations are derived



Since the reaction is taking place while being heated by a furnace, the isothermal assumption is no longer valid. Allowing the moles and temperature to change and using the heat transfer relationship



the final equations for calculation are