Methods and systems for determining gas permeability of a subsurface formation
Methods and systems for determining permeability, as a function of pore pressure, and porosity of a subsurface formation. The method includes positioning a sample in a sample assembly comprising of a gas and a pressure gauge, inside a pressure vessel comprising gas or liquid and a pressure gauge, measuring a first gas pressure, p i , of the sample inside the pressure vessel, applying a second gas pressure, p o , to the pressure vessel, the second gas pressure being greater than the first gas pressure, measuring a third gas pressure, p, at time, t, at location, x, from the inlet of sample inside the pressure vessel, determining a total gas mass per unit volume of the subsurface formation, m, and determining the permeability, k, of the subsurface formation as a function of pore pressure based at least in part on the first gas pressure, the second pressure, the third gas pressure, and the gas density, with a single test run.
1. A transient flow method for determining gas permeability of a subsurface formation, comprising:
acquiring a sample of the subsurface formation;
positioning the sample in a pressure vessel comprising a fluid and a pressure gauge;
equilibrating the sample at a predetermined first pore gas pressure, p i ;
applying a predetermined constant second pore gas pressure, p o , to an inlet of the sample, the second pore gas pressure being greater than the first pore gas pressure;
measuring a third pore gas pressure, p, as a function of time, t, at location, x, along the axis of the sample in the pressure vessel, wherein the location, x, is at a predetermined distance from the inlet of the sample;
in a computer, determining a gas density or total gas mass per unit volume of the subsurface formation, m; and
in the computer, determining the gas permeability of the subsurface formation as a function of pore pressure, k(p), based at least in part on the first pore gas pressure, the second pore gas pressure, the third pore gas pressure as a function of time, and the gas density as a function of pore pressure, with a single test run.
2. The method of claim 1 , wherein the subsurface formation comprises at least one of shale, limestone, and sandstone.
3. A transient flow method for determining gas permeability of a subsurface formation, comprising:
acquiring a sample of the subsurface formation;
positioning the sample in a pressure vessel comprising a fluid and a pressure gauge;
equilibrating the sample at a predetermined first pore gas pressure, p i ;
applying a predetermined constant second pore gas pressure, p o , to an inlet of the sample, the second pore gas pressure being greater than the first pore gas pressure;
measuring a third pore gas pressure, p, as a function of time, t, at location, x, along the axis of the sample in the pressure vessel, wherein the location, x, is at a predetermined distance from the inlet of the sample;
in a computer, determining a gas density or total gas mass per unit volume of the subsurface formation, m;
in the computer, determining the gas permeability of the subsurface formation as a function of pore pressure, k(p), based at least in part on the first pore gas pressure, the second pore gas pressure, the third pore gas pressure as a function of time, and the gas density as a function of pore pressure, with a single test run; and
determining a transport parameter of the subsurface formation, D(p), using a first formula:
D
(
p
)
=
-
∫
p
i
p
λ
2
dm
dp
dp
dp
d
λ
where λ is an independent variable calculated using the formula λ=xt −1/2 ; and
determining gas permeability k of the subsurface formation from D(p) using
D
(
p
)
=
k
ρ
μ
where μ stands for gas viscosity, and ρ for gas density.
4. The method of claim 3 , further comprising:
determining the total gas mass per unit volume of the subsurface formation, m, using a second formula:
m =ϕρ+(1−ϕ)ρ a
where Φ is porosity of the subsurface formation, ρ is gas density of the gas, and ρ a is adsorbed gas mass per unit volume of the subsurface formation.
5. The method of claim 4 , further comprising:
determining the porosity Φ of the subsurface formation using a third formula:
ϕ
=
B
-
A
∫
p
i
p
0
λ
d
ρ
a
dp
dp
A
∫
p
i
p
0
λ
d
(
ρ
-
ρ
a
)
dp
dp
where A is a cross-sectional area of the sample, and B is a slope of a curve of the cumulative gas flow into the sample at x=0 versus t 1/2 .
6. The method of claim 5 , further comprising:
determining the slope of the curve, B, using a fourth formula:
B
=
A
∫
p
i
p
0
λ
dm
dp
dp
.