In view of increasing evidence for migration in some of the shale plays (since it has become common practice, should we still call it unconventional?), I wanted to try to estimate the migration rates in the shales, using he Eagle Ford as an example.
Darcy's law states that at 1 Darcy (D) permeability, a fluid with 1 centipoise (cP) viscosity will flow 1 centimeter per second under a pressure gradient of 1 atmosphere (14.7 psi) per centimeter. That translates to about a rate of 0.000073 ft/sec at a gradient of 1 psi/ft.
At typical reservoir conditions, gas viscosity is around 0.01 cP, and the permeability of the shales are known to range between 1 nano darcy (nD) to 10 micro darcies (μD) or more. At hydrostatic conditions, the buoyancy gradient for typical gas (static water gradient is 0.43 psi/ft and 0.13 psi/ft for gas) is 0.3 psi/ft. There are about 3.16 x10 13 seconds in a million years. The Eagle Ford dips at about 30 meters per kilometer, meaning the lateral buoyancy gradient is about 0.009 psi/ft. Given all these, gas migration rate up dip along a 1 μD permeability zone would be
Migration rates (ft/my) = (0.000073*0.009) (psi/ft) x 10-6 D x 3.16x1013 (sec/my) / 0.01 cP = 2082 ft/my (635 m/my) **.
The gas window part of the Eagle ford is quite over pressured, and the pressure gradient may be around 5000 psi over 50 km (=0.1 psi/ft, or about 10 times higher than the buoyancy gradient) which can result in 10 times the above migration rate. Higher rates would be possible in zones if the permeability is 10 μD or higher. The Eagle ford has been generating gas for more than 10 million years so this could add up to fairly long distance migration. Imagine what would happen in the Permian basin where the source rock was mature since 200 million years ago.
Since the incline (dip) is (30 m/km) and the permeability anisotropy (kx/kv) is is at least 100 to 1000 times, the process still favors lateral migration rates by 3 to 30 times. Perhaps lateral migration in the shales is more common than we have thought?
This could also partly explain some of the higher than expected GORs we see at relatively low maturity. Some of the gas condensates may have migrated up dip to mix with the oil. Since oil viscosity is 100 times that of gas, and a one third in buoyancy gradient - so it would migrate 300 times slower. The vast difference in migration rates in the oil window and the gas window creates a super sized natural dynamic trap. The difference in over pressure gradients may also provide additional help in this regard.
** note an earlier version of this post had a mistake in conversion that resulted in much higher rates. Thanks to Andrew for finding the mistake!
Darcy's law states that at 1 Darcy (D) permeability, a fluid with 1 centipoise (cP) viscosity will flow 1 centimeter per second under a pressure gradient of 1 atmosphere (14.7 psi) per centimeter. That translates to about a rate of 0.000073 ft/sec at a gradient of 1 psi/ft.
At typical reservoir conditions, gas viscosity is around 0.01 cP, and the permeability of the shales are known to range between 1 nano darcy (nD) to 10 micro darcies (μD) or more. At hydrostatic conditions, the buoyancy gradient for typical gas (static water gradient is 0.43 psi/ft and 0.13 psi/ft for gas) is 0.3 psi/ft. There are about 3.16 x10 13 seconds in a million years. The Eagle Ford dips at about 30 meters per kilometer, meaning the lateral buoyancy gradient is about 0.009 psi/ft. Given all these, gas migration rate up dip along a 1 μD permeability zone would be
Migration rates (ft/my) = (0.000073*0.009) (psi/ft) x 10-6 D x 3.16x1013 (sec/my) / 0.01 cP = 2082 ft/my (635 m/my) **.
The gas window part of the Eagle ford is quite over pressured, and the pressure gradient may be around 5000 psi over 50 km (=0.1 psi/ft, or about 10 times higher than the buoyancy gradient) which can result in 10 times the above migration rate. Higher rates would be possible in zones if the permeability is 10 μD or higher. The Eagle ford has been generating gas for more than 10 million years so this could add up to fairly long distance migration. Imagine what would happen in the Permian basin where the source rock was mature since 200 million years ago.
Since the incline (dip) is (30 m/km) and the permeability anisotropy (kx/kv) is is at least 100 to 1000 times, the process still favors lateral migration rates by 3 to 30 times. Perhaps lateral migration in the shales is more common than we have thought?
This could also partly explain some of the higher than expected GORs we see at relatively low maturity. Some of the gas condensates may have migrated up dip to mix with the oil. Since oil viscosity is 100 times that of gas, and a one third in buoyancy gradient - so it would migrate 300 times slower. The vast difference in migration rates in the oil window and the gas window creates a super sized natural dynamic trap. The difference in over pressure gradients may also provide additional help in this regard.
** note an earlier version of this post had a mistake in conversion that resulted in much higher rates. Thanks to Andrew for finding the mistake!
That's a nice little calculation that others can try for themselves--a good way to look at this problem.
ReplyDeleteAre there any implications in your post for the behavior of oil and gas migrating from conventional kitchens to traps? Most of us were brought up to believe that long-distance migration is a first-expelled-first-trapped proposition. This seems to be supported by observations that accumulations close to the kitchen usually comprise more mature fluids (gassier) while fluid accumulations far away from the kitchen are lower maturity (oilier). Is there any reason to re-think this paradigm?
Thanks for the comment. I would say no, the natural sequence of oil vs gas we observe is not caused by migration rates, but the fill-spill/leak system and the maturity spread between the kitchen and the up dip. The heterogeneity of geological system usually does not allow a simple race of the two. Even the shales, these are rate limiting "baffles" that prevent gas from completely taking over the oil. There seems enough up dip migration in the Eagle Ford to cause higher than expected GORs at a given maturity. In another shale play, where the inter-beds are sandier, gas may have even formed a "gas cap" up dip with high gas production rates, but oil is produced from below and down dip. My simple calculations is meant to bring migration into the shale conversation - Nature is more complex and interesting.
ReplyDeleteI might add that the "gas cap" behavior is only possible in uplifted areas where the pressure is bellow bubble point.
ReplyDeleteHi, I'm interesting in your comment regarding the rate of oil migration being 300times slower,, would that be simply 635m/ma divided by 300 for in effect 2.11m/my?
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