Tubing leak is a burst load case, where the unknown is the internal pressure profile of the casing / tubing.
Summary
This load case is used in connection with production- and injection- operations, and represents a surface pressure on top of a completion fluid due to a tubing leak.
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Inputs
The following inputs define the tubing leak load case
The true vertical depth (TVD) along the wellbore as a function of measured depth. Alternatively, the wellbore described by a set of survey stations, with complete information about measured depth and inclination.
The true vertical depth / TVD of
The hanger of the tubing, TVDhanger.
The shoe of the tubing, TVDshoe.
The packer depth, TVDpacker.
The perforation depth, TVDperforation.
The pore pressure profile from hanger to influx depth.
The packer fluid density, ρpacker .
The temperature at the perforation depth, Tperforation .
The gas gravity, sggas .
Calculation
The internal pressure profile of the casing / tubing is calculated as follows
1. Calculate the pore pressure at perforation depth, pp, perforation.
2. Calculate the gas density at perforation depth from gas gravity, using Sutton correlations, ρgas, perforation .
3. Calculate the pressure at the hanger
phanger=pp, perforation−ρgas, perforationg(TVDperforation−TVDhanger) (1) where g is the gravitational constant.
4. The internal pressure of the tubing depends on where the packer- and perforation- depth are related to each other and the shoe of the tubing. Explicitly, parametrize the tubing by TVD
a) If TVDshoe≤TVDpacker≤TVDperforation , or if TVDshoe≤TVDperforation≤TVDpacker , then
pi=phanger+ρpackerg(TVD−TVDhanger) (2) b. If TVDpacker≤TVDshoe≤TVDperforation , then from hanger to packer
pi=phanger+ρpackerg(TVD−TVDhanger), (3) and from packer to shoe
pi=pperforation−ρgas, perforationg(TVDperforation−TVD). (4) c. If TVDpacker≤TVDperforation≤TVDshoe , then from hanger to packer
pi=phanger+ρpackerg(TVD−TVDhanger) (5) from packer to perforation
pi=pperforation−ρgas, perforationg(TVDperforation−TVD) (6) and finally, from perforation to shoe
pi=pperforation+ρpackerg(TVD−TVDperforation) (7) d. If a=b , then from hanger to perforation
pi=phanger+ρpackerg(TVD−TVDhanger)(8) and from perforation to shoe
pi=pperforation+ρpackerg(TVD−TVDperforation). (9) e. The last scenario, TVDperforation≤TVDpacker≤TVDshoe , is physically impossible.
References
[1] Curtis H. Whitson and Michael R. Brule ́. Phase behavior, volume 20 of Henry L. Doherty series. SPE Monograph series, 2000.
[2] Sutton, R.P.: “Compressibility Factors for High-Molecular Weight Reservoir Gases,” paper SPE 14265 presented at the 1985 SPE Annual, Technical Conference and Exhibition, Las Vegas, Nevada, 22–25 September.
