Copyright, Texaco, 1990
Polyethylene is made from ethane, which is found in natural gas. Natural gas is found deep under the surface of the earth, usually in pockets of crud oil. Before the process of making polyethylene can begin, the oil must be pumped up to the surface, and the natural gas must be separated from the oil. Several difficult engineering problems arise when transporting natural gas to the surface.
Copyright, British Petroleum, 1996
Deep within the earth, the crude oil is at a higher pressure than at the surface. This means that as the oil is pumped upwards, some of it converts from a liquid to a vapor. Knowing exactly what vapor/liquid fraction will exist during the pumping process is a difficult problem. The liquid/vapor equilibrium problem can be solved, but they involve complex calculations.
While the oil is being pumped to the surface, it is travelling through a packed bed (the ground). There are lengthy mass and momentum transport equations for flow through a packed bed. These equations also must be solved to be able to pump the oil up to the surface.
If you would like to see these equations, click here: