Systems and methods to determine permeability of rock under anisotropic stress
Methods and systems are disclosed. The methods may include determining a first sequence of permeabilities by subjecting a rock sample to a first sequence of confining stress, axial stress, pore pressure (CSASPP) triplets and determining a first rock parameter using the first sequence of permeabilities, the first sequence of CSASPP triplets, and a first permeability model. The methods may further include determining a second sequence of permeabilities by subjecting the rock sample to a second sequence of CSASPP triplets and determining a second rock parameter using the second sequence of permeabilities, the second sequence of CSASPP triplets, and the first permeability model. The method may still further include determining an in situ permeability for an in situ rock based on an initial permeability, a second stress sensitivity parameter, a first stress sensitivity parameter, a confining stress value, axial stress values, a pore pressure value, and a second permeability model.
1. A method comprising:
obtaining, from a subterranean region of interest, a rock sample having a rock type;
determining a first sequence of permeabilities by subjecting the rock sample, using a permeability system, to a first sequence of confining stress, axial stress, pore pressure (CSASPP) triplets, wherein the first sequence of CSASPP triplets comprises a constant confining stress;
determining a first rock parameter using the first sequence of permeabilities, the first sequence of CSASPP triplets, and a first permeability model, wherein the first permeability model comprises a first stress model, wherein the first stress model comprises a first stress sensitivity parameter;
determining a second sequence of permeabilities by subjecting the rock sample, using the permeability system, to a second sequence of CSASPP triplets, wherein the second sequence of CSASPP triplets comprises a constant axial stress;
determining a second rock parameter using the second sequence of permeabilities, the second sequence of CSASPP triplets, and the first permeability model;
determining the first stress sensitivity parameter based, at least in part, on the first rock parameter and the second rock parameter;
determining, using a computer processor, an initial permeability and a second stress sensitivity parameter based, at least in part, on the first sequence of CSASPP triplets, the first sequence of permeabilities, the second sequence of CSASPP triplets, the second sequence of permeabilities, the first stress sensitivity parameter, and the first permeability model;
obtaining an in situ confining stress value, in situ axial stress values, and an in situ pore pressure value for an in situ rock in the subterranean region of interest, wherein the in situ rock is of the rock type; and
determining an in situ permeability for the in situ rock based, at least in part, on the initial permeability, the second stress sensitivity parameter, the first stress sensitivity parameter, the in situ confining stress value, the in situ axial stress values, the in situ pore pressure value, and a second permeability model, wherein the second permeability model comprises a second stress model.
2. The method of claim 1 , wherein the rock sample comprises source rock.
3. The method of claim 1 , wherein the rock type comprises shale.
4. The method of claim 1 , further comprising:
determining a hydrocarbon production rate based, at least in part, on the in situ permeability; and
determining a production management plan based, at least in part, on the hydrocarbon production rate.
5. The method of claim 4 , further comprising stimulating a well within the subterranean region of interest based, at least in part, on the production management plan.
6. The method of claim 1 , wherein obtaining the rock sample further comprises:
cutting the rock sample;
drying the rock sample; and
pre-stressing the rock sample.
7. The method of claim 1 , wherein a pore pressure among the first sequence of CSASPP triplets is selected to minimize Knudsen diffusion.
8. The method of claim 7 , wherein the pore pressure is greater than 17 megapascals.
9. The method of claim 1 , wherein the first rock parameter comprises the first stress sensitivity parameter.
10. The method of claim 1 , wherein determining the first sequence of permeabilities comprises a pressure pulse decay method.
11. The method of claim 10 , wherein the pressure pulse decay method comprises:
obtaining a permeability-pressure model;
subjecting a test sample to a CSASPP triplet;
generating a pressure pulse;
determining a test sample pressure differential in the test sample as a function of time due to the pressure pulse; and
determining a permeability by fitting, in part, the test sample pressure differential as the function of time to the permeability-pressure model.
12. The method of claim 1 , wherein the first stress sensitivity parameter comprises a ratio of the first rock parameter and a summation of the first rock parameter and the second rock parameter.
13. A system comprising:
a permeability system configured to subject a rock sample, from a subterranean region of interest, having a rock type to a first sequence of confining stress, axial stress, pore pressure (CSASPP) triplets and a second sequence of CSASPP triplets; and
a computer system configured to:
determine a first sequence of permeabilities following the rock sample being subjected to the first sequence of CSASPP triplets using the permeability system, wherein the first sequence of CSASPP triplets comprises a constant confining stress,
determine a first rock parameter using the first sequence of permeabilities, the first sequence of CSASPP triplets, and a first permeability model, wherein the first permeability model comprises a first stress model, wherein the first stress model comprises a first stress sensitivity parameter,
determine a second sequence of permeabilities following the rock sample being subjected to the second sequence of CSASPP triplets using the permeability system, wherein the second sequence of CSASPP triplets comprises a constant axial stress,
determine a second rock parameter using the second sequence of permeabilities, the second sequence of CSASPP triplets, and the first permeability model,
determine the first stress sensitivity parameter based, at least in part, on the first rock parameter and the second rock parameter,
determine an initial permeability and a second stress sensitivity parameter based, at least in part, on the first sequence of CSASPP triplets, the first sequence of permeabilities, the second sequence of CSASPP triplets, the second sequence of permeabilities, the first stress sensitivity parameter, and the first permeability model,
receive an in situ confining stress value, in situ axial stress values, and an in situ pore pressure value for an in situ rock in the subterranean region of interest, wherein the in situ rock is of the rock type, and
determine an in situ permeability for the in situ rock based, at least in part, on the initial permeability, the second stress sensitivity parameter, the first stress sensitivity parameter, the in situ confining stress value, the in situ axial stress values, the in situ pore pressure value, and a second permeability model, wherein the second permeability model comprises a second stress model.
14. The system of claim 13 , wherein the computer system is further configured to determine a hydrocarbon production rate based, at least in part, on the in situ permeability.
15. The system of claim 14 , further comprising production management software configured to determine a production management plan based, at least in part, on the hydrocarbon production rate.
16. The system of claim 13 , further comprising a rock sample extraction tool configured to obtain the rock sample from the subterranean region of interest.
17. The system of claim 16 , wherein the rock sample extraction tool comprises a coring system.
18. The system of claim 13 , wherein the permeability system comprises:
a jacket for housing the rock sample;
a pressure generator configured to apply the confining stress to the rock sample;
an actuator configured to apply the axial stress to the rock sample; and
a gas pump configured to apply the pore pressure to the rock sample, wherein the gas pump comprises:
an upstream reservoir, and
a downstream reservoir.
19. The system of claim 18 , wherein the gas pump houses helium.
20. The system of claim 18 , wherein the gas pump is configured to emit a pressure pulse.