Question about Joule-Thomson effect and Gulf blowout

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marzolian
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A friend who never studied engineering but is very curious sent me a blog entry, claiming that the methane being discharged from the BP blowout was cold enough to freeze seawater. I think someone is confusing water freezing with hydrate formation.

But I started wondering: What approach would you follow if you wanted to see how cold the methane would get, if it was flowing through an orifice and allowed to expand?

This does not represent a practical approach to solving that or any other real-life problem. But assume the following:

1. Homogeneous flow (methane only, no oil or other gases).

2. All pressure drop occurs at the wellhead. Ignore the resistance inside the well.

3. The pressure upstream of the restriction is the same as the downhole formation pressure, possibly 16,000 psi.

4. Initial downhole gas temperature is probably between 300 and 400 degrees F, assume 350 when it reaches the wellhead.

5. The methane flows adiabatically through the wellhead, and expands to the water pressure (approximately 2200 psi). (This is a significant assumption, because the pressure at the bottom of the riser / top of BOP stack is undoubtedly higher)

What would be the temperature of the methane, before it mixes with the seawater?

I know that Joule-Thomson is involved, but bear with me, it's been 25 years since I studied this subject and I haven't worked with it since then.

Can anyone give a back-of-the-envelope answer?

Steve Marzuola
Houston, Texas
 
on Phys.org
Don't forget that at 5000 foot depths you'd have a significant change in expansion rate as well. I officially deem this problem unsolvable by us mere mortals.

I will consult Google calculator.