The governing equation for the temperature force on tubing that is latched into a packer is 207ATs(Tf-Ta). It's found on Guidebook page 6 DTC 9.
ATs is merely the area of the x-section; for example 9.60 - 7.01 = 2.59 in^2. Get these numbers from the given problem, or from a packer handbook.
The temperature difference is confusing. Start with the average temperature for the well at start (Ta); easy enough to calculate (surface + bottom hole)/2. In this case, assume 145 deg F.
However, the Tf is confusing. This is the average temperature of the string when cooled to the maximum condition while injecting. It is dependent on the fluid temperature plus the injection rate & duration. Just roll with whatever a problem gives you; if given "final pumping conditions", use that. In this case let's assume 100 deg F.
Working the numbers it's 207(2.59)(100 - 145) = -24.1 Mlbf.
Note the negative sign reflects an "up" force (highlighted in the Guidebook variable box).
Super helpful, thanks!! The Ta and Tf always got me
ReplyDeleteMe too! In reality, this should be done on a computer; these back-of-the-envelope calcs are just for the PE exam (or a quick check in real life). But I've updated the GB to show the expanded definition of Tf.
DeleteNote the negative sign reflects an "up" force
ReplyDeleteSo here "up" force means compression?
"down" force means tension?