Method for estimating material properties of porous media using computer tomographic images thereof
A method for estimating a physical property of a porous material from a sample of the material includes making a three dimensional tomographic image of the sample of the material, segmenting the image into pixels each representing pore space or rock grain, and estimating at least one physical property from the segmented image.
1. A method for estimating a physical property of a porous material from a sample thereof, comprising:
making a three dimensional tomographic image of the sample of the material;
segmenting the image into pixels each representing pore space or rock grain;
estimating at least one physical property from the segmented image; and
at least one of storing and displaying the estimated physical property, wherein the tomographic image comprises a value of gray scale allocated to each of a plurality of pixels in the image, and wherein the segmenting comprises:
(a) determining an initial gray scale threshold for each of pore space and rock grain;
(b) allocating each pixel in the image to a pore space seed or a rock grain seed for each pixel meeting threshold criteria for each of the pore space and rock grain thresholds, respectively;
(c) interrogating pixels adjacent to each pore space seed and rock grain seed;
(d) allocating the interrogated adjacent pixels previously not allocated to a seed to the pore space seed or the rock grain seed based on threshold criteria; and
(e) repeating (c) and (d) until substantially all pixels in the image are allocated to the rock grain or the pore space.
2. The method of claim 1 wherein the determining initial gray scale thresholds comprises histogram analysis of the tomographic image.
3. The method of claim 1 wherein the allocating interrogated adjacent pixels comprises determining a difference between a gray scale value assigned to said pore space seed or rock grain seed and a gray scale value of the pixels adjacent to each pore space seed and rock grain seed, and allocating the interrogated pixel to the seed if the difference falls below a selected threshold.
4. The method of claim 3 further comprising:
determining whether unallocated pixels exist in the image;
increasing the selected difference threshold; and
repeating the interrogating adjacent and allocating the interrogate pixels having gray scale values wherein the difference is below the increased difference threshold.
5. The method of claim 1 wherein the material comprises a rock formation.
6. The method of claim 5 wherein the at least one physical property comprises permeability.
7. The method of claim 6 wherein permeability is estimated using the Lattice-Boltzmann approximation.
8. The method of claim 5 wherein the at least one physical property comprises electrical resistivity formation factor.
9. The method of claim 5 wherein the at least one physical property comprises acoustic compressional velocity.
10. The method of claim 5 wherein the at least one physical property comprises acoustic shear velocity.
11. A method for analyzing subsurface rock formations during drilling of a wellbore through the formations, comprising:
obtaining a sample of the rock formations during the drilling of the wellbore;
making a three dimensional tomographic image of the sample;
segmenting the image into pixels each representing pore space or rock grain;
estimating at least one physical property from the segmented image; and at least one of storing and displaying the estimated physical property, wherein the segmenting comprises:
(a) determining an initial gray scale threshold for each of pore space and rock grain;
(b) allocating each pixel in the image to a pore space seed or a rock grain seed for each pixel meeting threshold criteria for each of the pore space and rock grain thresholds, respectively;
(c) interrogating pixels adjacent to each one space seed and rock grain seed;
(d) allocating the interrogated adjacent pixels previously not allocated to a seed to the pore space seed or the rock grain seed based on threshold criteria; and
(e) repeating (c) and (d) until substantially all pixels in the image are allocated to the rock grain or the pore space.
12. The method of claim 11 wherein the tomographic image comprises a value of gray scale allocated to each of a plurality of pixels in the image.
13. The method of claim 11 wherein the determining initial gray scale thresholds comprises histogram analysis of the tomographic image.
14. The method of claim 11 further comprising:
determining whether unallocated pixels exist in the image;
increasing the threshold criteria; and
repeating the interrogating adjacent and allocating the interrogate pixels having gray scale values to have a difference that is below the increased threshold criteria.
15. The method of claim 14 wherein the at least one physical property comprises permeability.
16. The method of claim 15 wherein permeability is estimated using the Lattice-Boltzmann approximation.
17. The method of claim 11 wherein the at least one physical property comprises electrical resistivity formation factor.
18. The method of claim 11 wherein the at least one physical property comprises acoustic compressional-wave velocity.
19. The method of claim 11 wherein the at least one physical property comprises acoustic shear-wave velocity.
20. The method of claim 11 wherein the at least one physical property comprises at least one of nuclear magnetic resonance relaxation time and a distribution thereof.