Digital rock analysis systems and methods that reliably predict a porosity-permeability trend

1. A method that comprises:

scanning a sample using an electron microscope to obtain an image of the sample;

processing the image to derive a three-dimensional pore/matrix model;

measuring, by a processor, a distribution of porosity-related parameter variation for the pore/matrix model as a function of subvolume size;

measuring, by the processor, a pore connectivity-related parameter for the pore/matrix model as a function of subvolume size;

determining, by a processor, a reachable porosity for subvolumes in the model where the distribution of porosity-related parameter variation of the subvolumes is below a variation threshold and the pore connectivity-related parameter of the subvolumes is below a connectivity threshold;

adjusting, by the processor, either or both of the variation threshold or the connectivity threshold to determine the subvolumes offering a maximum reachable porosity;

determining, by the processor, porosity and permeability values associated with the determined subvolumes; and

displaying said permeability values as a function of porosity.

2. The method of claim 1 , further comprising determining an integral scale based at least in part on said distribution of porosity-related parameter variation as a function of subvolume size.

3. The method of claim 2 , further comprising determining a percolation scale based at least in part on the connectivity-related parameter as a function of subvolume size.

4. The method of claim 1 , further comprising determining, by the processor, porosities possessed by the subvolumes and selecting, by the processor, a subvolume size offering a maximum reachable porosity range from the determined porosities by determining that at least one of an integral scale or a percolation scale are to the same size as a dimension of the pore/matrix model.

5. The method of claim 1 , wherein the sample is a physical rock sample.

6. The method of claim 1 , wherein measuring the distribution of porosity-related parameter variation for the pore/matrix model as a function of the size of the subvolume further comprises wherein the porosity-related parameter variation comprises a standard deviation of porosity of slices of the subvolume and the slices are divided perpendicular to a flow direction of the subvolumes.

7. The method of claim 6 , further comprising measuring a distribution of standard deviation of pore surface to volume ratio.

8. The method of claim 1 , wherein said determining a reachable porosity for subvolumes includes:

screening out subvolumes having porosity-related parameter variation above the variation threshold;

screening out subvolumes having a connectivity-related parameter value above the connectivity threshold.

9. The method of claim 8 , wherein the variation threshold screens subvolumes having variation in an upper ⅗ths of the distribution.

10. The method of claim 8 , wherein the connectivity threshold screens subvolumes having more than 10% disconnected porosity.

11. A system for analyzing a sample, comprising:

an electron microscope operable to produce an image of the sample;

a memory having software; and

one or more processors coupled to the memory to execute the software, the software causing the one or more processors to:

derive a three-dimensional pore/matrix model from the image;

measure a distribution of porosity-related parameter variation for the pore/matrix model as a function of subvolume size;

measure a pore connectivity-related parameter for the pore/matrix model as a function of subvolume size;

determining a reachable porosity for subvolumes in the model where the distribution of porosity-related parameter variation of the subvolumes is below a variation threshold and the pore connectivity-related parameter of the subvolumes is below a connectivity threshold;

adjusting either or both of the variation threshold or the connectivity threshold to determine the subvolumes offering a maximum reachable porosity; and

determining porosity and permeability values associated with the determined subvolumes.

12. The system of claim 11 , wherein the software further causes the one or more processors to determine an integral scale based at least in part on said distribution of porosity-related parameter variation as a function of subvolume size.

13. The system of claim 12 , wherein the software further causes the one or more processors to determine a percolation scale based at least in part on the connectivity-related parameter as a function of subvolume size.

14. The system of claim 11 , further comprising determining, by the processor, porosities possessed by the subvolumes and selecting a subvolume size offering a maximum reachable porosity range from the determined porosities by determining that at least one of an integral scale or a percolation scale are the same size to a dimension of the pore/matrix model.

15. The system of claim 11 , wherein the sample is a physical rock sample.

16. The system of claim 11 , wherein the distribution of porosity-related parameter variation is a distribution of standard deviation of porosity.

17. The system of claim 16 , wherein the software further causes the one or more processors to measure a distribution of standard deviation of pore surface to volume ratio.

18. The system of claim 11 , wherein as part of said determining a reachable porosity for subvolumes, the software causes the one or more processors to:

screen out subvolumes having porosity-related parameter variation above a given variation threshold;

screen out subvolumes having a connectivity-related parameter value above a given connectivity threshold.

19. The system of claim 18 , wherein the variation threshold screens subvolumes having variation in an upper ⅗ths of the distribution.

20. The system of claim 18 , wherein the connectivity threshold screens subvolumes having more than 10% disconnected porosity.