Off-Shore Natural Gas An image of an off-shore natural gas well is shown. In normal operation natural gas flows from beneath the ocean floor upward through the pipes of the production rig and then through pipes leading to shore facilities. Occassionally valves are closed such the the gas flow is stopped. The "stopped flow" condition is our interest.

The schematic sketch (below right) shows the basic "stopped flow" configuration along with some representative average densities of the substances involved. Also some reference points have been added to the sketch. Use the information provided to calculae the approximate reading of the gage located at the well head, "D."

♦  The procedure will be to write the hydrostatic equation.

i) The pressure at point A, the surface of the sea, is atmospheric. The pressure at A' (closely below A but in sea water) is also atmospheric since pressure change across a flat gas/liquid interface is zero.

ii)The pressure at B is greater than at A' by a 2200 foot column of sea water. This is also the pressure at B' above and across the water/gas interface. The point is located in gas and has the same pressure as B.

iii) Natural gas fills the well pipe. At C, the substance is gas. The pressure at C is the pressure inside the gage. Point D is in atmospheric air, outside and directly beside the gage.

Now construct an equation containing the gage reading, GR. Begin at point A where the pressure is known to be one atmosphere.

p_atm = p_A

At B (in sea water) the pressure is greater than at A by the amount of pressure added by a column of sea water 2200 feet in height. The pressure in the gas also equals, p_B

p_atm + ρ_{sea water} g (2200ft) = p_B

The point C is directly above B. Pressure, starting at B will decrease steadily with positions above B. The pressure at C is:

p_atm + ρ_{sea water} g (2200ft) - ρ_gas,avg g (2320ft) = p_C

The point D is the ambient pressure outside of the gage. The gage reading tells us the difference in pressure, p_inside- p_outside. Thus if we subtract the gage reading (GR) from p_C we get p_D.

p_atm + ρ_{sea water} g (2200ft) - ρ_gas,avg g (2320ft) - GR = p_D

p_atm + ρ_{sea water} g (2200ft) 

- ρ_gas,avg  g (2320ft) - GR +  ρ_air g (120ft) = p_atm

Now we have one equation and one unknown. Subtract p_atm from both sides. Put numbers into the equation.

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