Granted Patent B2

US 12,596,065 · App. 18/481,731 · Granted Apr 7, 2026

Inventors: Jilin Jay Zhang (Houston, TX); Hui-Hai Liu (Houston, TX)

Assignee: Saudi Arabian Oil Company

G01N15/088

Abstract

Claims (93)

1 . A method of determining one or more properties of a rock sample, comprising:

(i) performing a plurality of series of permeability measurements of a rock sample with a permeability test assembly to derive a plurality of permeability values, where:

each series of the plurality of series comprises a plurality of permeability measurements of the rock sample at a respective, constant differential pressure between a particular confining pressure and a particular pore pressure,

the particular confining pressure and the particular pore pressure increase with each permeability measurement within each series of the plurality of permeability measurements, and

the respective, constant differential pressure increases with each subsequent series of permeability measurements in the plurality of series of permeability measurements;

(ii) for each series of the plurality of series, performing a curve fit operation to determine a slope and an intercept of a curve associated with a selected Biot coefficient that is between 0 and 1, the permeability values of the series, and the particular pore pressures of the series to generate a plurality of slope values and a plurality of intercept values;

(iii) determining an effective stress coefficient of the rock sample based on the respective, constant differential pressures and the generated plurality of slope values and plurality of intercept values; and

(iv) determining an actual Biot coefficient of the rock sample based on the determined effective stress coefficient and the plurality of slope values.

2 . The method of claim 1 , wherein the particular pore pressure of a first series of the plurality of series is at least 1700 psi.

3 . The method of claim 1 , wherein the plurality of series comprise at least three series, and the plurality of permeability measurements comprise at least three permeability measurements.

4 . The method of claim 1 , wherein the selected Biot coefficient is at a lower boundary value of a predetermined range.

5 . The method of claim 1 , further comprising:

determining an effective stress differential between successive permeability measurements in a particular series of permeability measurements; and

adjusting at least one of the particular confining pressure or the particular pore pressure in the particular series based on the determined effective stress differential being negative.

6 . The method of claim 1 , further comprising:

adjusting at least one of the particular confining pressure or the particular pore pressure in a particular series to maintain a non-negative effective stress differential between successive permeability measurements in the particular series of permeability measurements.

7 . The method of claim 1 , wherein performing the curve fit operation comprises:

for each series of the plurality of series:

plotting a curve of ln(k) versus the particular pore pressures for the respective, constant differential pressure of the series, where k is the permeability value measured for each particular pore pressure for the respective, constant differential pressure of the series; and

determining the slope value and the intercept value from the plotted curve.

8 . The method of claim 1 , wherein determining the effective stress coefficient of the rock sample comprises:

plotting a curve of the plurality of intercept values versus the respective, constant differential pressures of the series; and

determining the effective stress coefficient of the rock sample based on the slope of the plotted curve.

9 . The method of claim 1 , wherein determining the actual Biot coefficient of the rock sample comprises:

for each series of the plurality of series, determining a Biot coefficient based on the determined effective stress coefficient and the slope value for the series; and

determining the actual Biot coefficient based on an average of the determined Biot coefficients.

10 . The method of claim 9 , further comprising:

determining a difference between the determined actual Biot coefficient and the selected Biot coefficient;

based on the difference exceeding a threshold value, determining another selected Biot coefficient; and

repeating (i)-(iv) with the another selected Biot coefficient.

11 . A system for determining one or more properties of a rock sample, comprising:

a permeability test assembly configured to perform a plurality of series of permeability measurements of a rock sample to derive a plurality of permeability values, where:

each series of the plurality of series comprises a plurality of permeability measurements of the rock sample at a respective, constant differential pressure between a particular confining pressure and a particular pore pressure,

the particular confining pressure and the particular pore pressure increase with each permeability measurement within each series of the plurality of permeability measurements, and

the respective, constant differential pressure increases with each subsequent series of permeability measurements in the plurality of series of permeability measurements; and

a control system configured to perform operations comprising:

identifying the plurality of permeability values, the respective, constant differential pressure for each series, the particular confining pressures, and the particular pore pressures from the permeability test assembly;

for each series of the plurality of series, performing a curve fit operation to determine a slope and an intercept of a curve associated with a selected Biot coefficient that is between 0 and 1, the permeability values of the series, and the particular pore pressures of the series to generate a plurality of slope values and a plurality of intercept values;

determining an effective stress coefficient of the rock sample based on the respective, constant differential pressure and the generated plurality of slope values and plurality of intercept values; and

determining an actual Biot coefficient of the rock sample based on the determined effective stress coefficient and the plurality of slope values.

12 . The system of claim 11 , wherein the particular pore pressure of a first series of the plurality of series is at least 1700 psi.

13 . The system of claim 11 , wherein the plurality of series comprise at least three series, and the plurality of permeability measurements comprise at least three permeability measurements.

14 . The system of claim 11 , wherein the selected Biot coefficient is between 0.7 and 1.

15 . The system of claim 11 , wherein the operations further comprise determining an effective stress differential between successive permeability measurements in a particular series of permeability measurements, and the permeability test assembly is configured to adjust at least one of the particular confining pressure or the particular pore pressure in the particular series based on the determined effective stress differential being negative.

16 . The system of claim 11 , wherein the permeability test assembly is configured to adjust at least one of the particular confining pressure or the particular pore pressure in a particular series to maintain a non-negative effective stress differential between successive permeability measurements in the particular series of permeability measurements.

17 . The system of claim 11 , wherein the operation of performing the curve fit operation comprises:

for each series of the plurality of series:

plotting a curve of ln (k) versus the particular pore pressures for the respective, constant differential pressure of the series, where k is the permeability value measured for each particular pore pressure for the respective, constant differential pressure of the series; and

determining the slope value and the intercept value from the plotted curve.

18 . The system of claim 11 , wherein the operation of determining the effective stress coefficient of the rock sample comprises:

plotting a curve of the plurality of intercept values versus the respective, constant differential pressures of the series; and

determining the effective stress coefficient of the rock sample based on the slope of the plotted curve.

19 . The system of claim 11 , wherein the operation of determining the actual Biot coefficient of the rock sample comprises:

for each series of the plurality of series, determining a Biot coefficient based on the determined effective stress coefficient and the slope value for the series; and

determining the actual Biot coefficient based on an average of the determined Biot coefficients.

20 . The system of claim 19 , wherein the operations further comprise:

determining a difference between the determined actual Biot coefficient and the selected Biot coefficient; and

based on the difference exceeding a threshold value, determining another selected Biot coefficient.

21 . The system of claim 20 , wherein the operations further comprise:

identifying another plurality of permeability values, another respective, constant differential pressure for another plurality of series, another set of particular confining pressures, and another set of particular pore pressures from the permeability test assembly;

for each series of the another plurality of series, performing a curve fit operation to determine a slope and an intercept of a curve associated with the another selected Biot coefficient, the another plurality of permeability values of the another plurality of series, and the another set of particular pore pressures of the series to generate another plurality of slope values and another plurality of intercept values;

determining another effective stress coefficient of the rock sample based on the another respective, constant differential pressure and the generated another plurality of slope values and plurality of intercept values; and

determining another actual Biot coefficient of the rock sample based on the determined another effective stress coefficient and the another plurality of slope values.

22 . A computer-implemented method for determining one or more properties of a rock sample, comprising:

identifying, with one or more hardware processors, information from a plurality of series of permeability measurements of a rock sample taken by a permeability test assembly, the information comprising a plurality of permeability values, with each series of the plurality of series comprising a set of permeability measurements of the rock sample at a respective, constant differential pressure between a particular confining pressure and a particular pore pressure, with the particular confining pressure and the particular pore pressure increasing with each permeability measurement within each series of the plurality of permeability measurements, and the respective, constant differential pressure increases with each subsequent series of permeability measurements in the plurality of series of permeability measurements;

for each series of the plurality of series, performing, with the one or more hardware processors, a curve fit operation to determine a slope and an intercept of a curve associated with a selected Biot coefficient that is between 0 and 1, the permeability values of the series, and the particular pore pressures of the series to generate a plurality of slope values and a plurality of intercept values;

determining, with the one or more hardware processors, an effective stress coefficient of the rock sample based on the respective, constant differential pressure and the generated plurality of slope values and plurality of intercept values; and

determining, with the one an actual Biot coefficient of the rock sample based on the determined effective stress coefficient and the plurality of slope values.

23 . The computer-implemented method of claim 22 , wherein the particular pore pressure of a first series of the plurality of series is at least 1700 psi.

24 . The computer-implemented method of claim 22 , wherein the plurality of series comprise at least three series, and the plurality of permeability measurements comprise at least three permeability measurements.

25 . The computer-implemented method of claim 22 , wherein the selected Biot coefficient is between 0.7 and 1.

26 . The computer-implemented method of claim 22 , further comprising:

determining, with the one or more hardware processors, an effective stress differential between successive permeability measurements in a particular series of permeability measurements; and

providing, with the one or more hardware processors, an indication to adjust at least one of the particular confining pressure or the particular pore pressure in the particular series based on the determined effective stress differential being negative.

27 . The computer-implemented method of claim 22 , further comprising providing, with the one or more hardware processors, an indication to adjust at least one of the particular confining pressure or the particular pore pressure in a particular series to maintain a non-negative effective stress differential between successive permeability measurements in the particular series of permeability measurements.

28 . The computer-implemented method of claim 22 , wherein performing the curve fit operation comprises:

for each series of the plurality of series:

plotting, with the one or more hardware processors, a curve of ln (k) versus the particular pore pressures for the respective, constant differential pressure of the series, where k is the permeability value measured for each particular pore pressure for the respective, constant differential pressure of the series; and

determining, with the one or more hardware processors, the slope value and the intercept value from the plotted curve.

29 . The computer-implemented method of claim 22 , wherein determining the effective stress coefficient of the rock sample comprises:

plotting, with the one or more hardware processors, a curve of the plurality of intercept values versus the respective, constant differential pressures of the series; and

determining, with the one or more hardware processors, the effective stress coefficient of the rock sample based on the slope of the plotted curve.

30 . The computer-implemented method of claim 22 , wherein determining the actual Biot coefficient of the rock sample comprises:

for each series of the plurality of series, determining, with the one or more hardware processors, a Biot coefficient based on the determined effective stress coefficient and the slope value for the series; and

determining, with the one or more hardware processors, the actual Biot coefficient based on an average of the determined Biot coefficients.

31 . The computer-implemented method of claim 30 , further comprising:

determining, with the one or more hardware processors, a difference between the determined actual Biot coefficient and the selected Biot coefficient; and

based on the difference exceeding a threshold value, determining, with the one or more hardware processors, another selected Biot coefficient.

32 . The computer-implemented method of claim 31 , further comprising:

identifying, with the one or more hardware processors, additional information from the permeability test assembly, the additional information comprising another plurality of permeability values, another respective, constant differential pressure for another plurality of series, another set of particular confining pressures, and another set of particular pore pressures from the permeability test assembly;

for each series of the another plurality of series, performing, with the one or more hardware processors, a curve fit operation to determine a slope and an intercept of a curve associated with the another selected Biot coefficient, the another plurality of permeability values of the another plurality of series, and the another set of particular pore pressures of the series to generate another plurality of slope values and another plurality of intercept values;

determining, with the one or more hardware processors, another effective stress coefficient of the rock sample based on the another respective, constant differential pressure and the generated another plurality of slope values and plurality of intercept values; and

determining, with the one or more hardware processors, another actual Biot coefficient of the rock sample based on the determined another effective stress coefficient and the another plurality of slope values.

Assignments (3)

Continuity (1)

References Cited (10)