Method for estimating effective atomic number and bulk density of rock samples using dual energy X-ray computed tomographic imaging
A method for estimating effective atomic number and bulk density of objects, such as rock samples or well cores, using X-ray computed tomographic imaging techniques is provided. The method effectively compensates for errors in the interpretation of CT scan data and produces bulk densities which have lower residual error compared to actual bulk densities and produces bulk density—effective atomic number trends which are consistent with physical observations.
1. A method for estimating the bulk density of at least one target object comprising:
i. utilizing a scan of reference objects with known bulk density and calibration objects with known bulk density and effective atomic number,
ii. obtaining a functional relationship between bulk density error and effective atomic number using scan values from the reference objects and the calibration objects,
iii. utilizing a scan of the target object and the calibration objects,
iv. obtaining uncorrected density and effective atomic number for the target object,
v. obtaining bulk density corrections using the functional relationship between bulk density error and effective atomic number from the reference objects, and the effective atomic number for the target object, and
vi. obtaining the corrected bulk density using the bulk density corrections.
2. The method of claim 1 , wherein the target object is a porous body.
3. The method of claim 1 , wherein the target object is a rock sample or a well core.
4. The method of claim 1 , wherein the reference objects are two or more reference objects and the calibration objects are three or more calibration objects.
5. The method of claim 4 , wherein said two or more reference objects are rock samples, well core samples, partial well core samples, or other objects having a known bulk density.
6. The method of claim 4 , wherein said three or more calibration objects have a different effective atomic number and/or bulk density from each other.
7. The method of claim 4 , wherein at least one of the three or more calibration objects comprise a liquid.
8. The method of claim 4 , wherein at least one of the three or more calibration objects comprise a solid.
9. The method of claim 4 , wherein at least one of said three or more calibration objects is a mineral material, a polymer material, or an aqueous solution.
10. The method of claim 4 , wherein said calibration objects are quartz, Teflon, and water.
11. The method of claim 1 , wherein said target object is a solid.
12. The method of claim 1 , wherein the target object is a liquid or comprises a liquid.
13. The method of claim 1 , wherein said target object is obtained from a drilling site, proposed drilling site, subterranean site, or above-ground site.
14. The method of claim 1 , wherein said scans are a CT scan.
15. The method of claim 1 , wherein said scans are a dual-energy X-ray CT scan.
16. The method of claim 1 , wherein said scans are accomplished with a scanner, wherein said scanner moves to scan the target object, reference objects, and calibration objects.
17. The method of claim 1 , wherein said scans are accomplished with a stationary scanner, wherein the target object, reference objects, and calibration objects move through the stationary scanner.
18. The method of claim 1 , wherein said reference objects and/or target object are located on a tray.
19. The method of claim 18 , wherein said calibration objects are attached or otherwise held in place by said tray.
20. The method of claim 1 , wherein said calibration objects are located adjacent to the reference objects and/or target object.
21. The method of claim 1 , wherein said calibration objects are in contact with the target object and/or at least one reference object.
22. The method of claim 1 , wherein said calibration objects are located adjacent to the reference objects and/or target object, but not in contact with the reference objects or target object.
23. The method of claim 1 , wherein said calibration objects are equally spaced around said reference objects or said target object.
24. The method of claim 1 , wherein said reference objects and said target object are scanned in the same scan.
25. The method of claim 1 , wherein said reference objects and said target object are scanned in series.
26. The method of claim 1 , wherein said reference objects and said target object are scanned separately.
27. The method of claim 1 , wherein said calibration objects have sufficient voxels in each cross-section of each calibration object for efficient averaging of the scanned values.
28. The method of claim 1 , wherein each calibration object has 300 voxels or more per section that is scanned.
29. The method of claim 1 , wherein each calibration object has 400 voxels to 1,000 voxels per section that is scanned.
30. The method of claim 1 , wherein said calibration objects are circular or semi-circular.
31. The method of claim 1 , wherein each calibration object varies in shape and/or size from each other.
32. The method of claim 1 , wherein said calibration objects have a uniform size and shape with respect to each other.
33. The method of claim 1 , wherein said calibration objects have a sufficient length such that each calibration object is always part of any scan of said reference objects or said target object.
34. The method of claim 1 , wherein each of said calibration objects avoid elements having a ratio of atomic weight to atomic number of greater than 2.1.
35. The method of claim 1 , wherein each of said calibration objects are homogeneous at a level of resolution of said scan.
36. The method of claim 1 , wherein each of said calibration objects are homogeneous at a level of resolution of 0.2 mm or less.
37. The method of claim 1 , wherein the same calibration objects are used during the scanning of the reference objects and target object.
38. The method of claim 1 , wherein the reference objects have a similar or same cross-section in size and shape to said target object.
39. The method of claim 1 , wherein said reference objects are circular or semi-circular.
40. The method of claim 1 , wherein steps i. and iii. can be performed in any order.
41. The method of claim 1 , wherein said uncorrected density and/or effective atomic number is based upon an average per slice of said scan of the target object.
42. The method of claim 1 , wherein the corrected bulk density is based upon an average per slice of said scan in view of said bulk density corrections.
43. The method of claim 1 , wherein said uncorrected density and/or effective atomic number is based upon an average of entire scan of the target object.
44. The method of claim 1 , wherein the corrected bulk density is based upon an average of entire scan in view of said bulk density corrections.
45. The method of claim 1 , wherein obtaining a functional relationship between bulk density error and effective atomic number using scan values from the reference objects and the calibration objects comprises
i. scanning the reference objects and calibration objects in a X-ray CT scanner, and
ii. recording the high and low CT values from the X-ray CT scans, and
iii. averaging the high and low CT values in each X-Y plane of the reference objects and calibration objects, and
iv. using the known bulk density and effective atomic number of the calibration objects and their respective CT values to calculate a functional relationship between bulk density error and effective atomic number.
46. The method of claim 1 , wherein the obtaining bulk density corrections using the functional relationship between bulk density error and effective atomic number from the reference objects, and the effective atomic number for the target object comprises an absolute bulk density correction and/or relative bulk density correction.
47. The method of claim 1 , wherein the obtaining corrected bulk density using the bulk density corrections comprises applying absolute bulk density correction and/or relative bulk density correction.
48. A method for estimating the bulk density of a target object comprising:
i. obtaining measurements of bulk density and effective atomic number from a set of objects including two or more reference objects with known bulk density;
ii. expressing an error of the reference objects' bulk density obtained from the measurement in step i as a function of the effective atomic number of said reference objects;
iii. obtaining measurements of bulk density and effective atomic number from the target object with unknown bulk density;
iv. predict the error of the target object's bulk density obtained from the measurement in step iii using the effective atomic number of the target object obtained in step iii and bulk density error function obtained in step ii;
v. adjusting the value of target object's bulk density obtained from the measurement in step iii by the value of the error predicted in step iv.
49. The method of claim 48 , wherein said reference objects are rock samples, well core samples, or partial well core samples.
50. The method of claim 48 , wherein the measurements of the bulk density and the atomic number from the reference objects in step i are performed by scanning the reference objects and interpreting the values produced by the scanning.