Method for determining rock physics relationships using computer tomographic images thereof
A method for estimating a relationship between physical properties of a porous material from a sample thereof includes making a three dimensional tomographic image of the sample of the material. The image is segmented into pixels each representing pore space or rock grains. The image is divided into sub-volumes. A porosity is estimated for each sub-volume. At least one petrophysical parameter is modeled from the image of each sub-volume. A relationship between the porosity and the at least one modeled petrophysical parameter is determined by, e.g., a best-fit statistical method. The relationship and the modeled petrophysical parameter for each sub-volume are stored in a computer or displayed.
1. A method for estimating a relationship between physical properties 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 mineral grain;
subdividing the image into sub-volumes;
estimating a porosity for each sub-volume from the image thereof;
modeling at least one petrophysical parameter from the image of each sub-volume;
determining a relationship between the porosity and the modeled petrophysical parameter using the estimated porosity and the modeled petrophysical parameter from a plurality of the sub volumes; and
at least one of storing and displaying the relationship and the modeled petrophysical parameter, wherein the relationship is determined by statistical best fit.
2. The method of claim 1 wherein the tomographic image comprises a value of gray scale allocated to each of a plurality of pixels in the image.
3. The method of claim 2 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 pore space or rock grain for each pixel meeting threshold criteria for each of the pore space and rock grain thresholds, respectively;
(c) interrogating pixels adjacent to each 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.
4. The method of claim 3 wherein the determining initial gray scale thresholds comprises histogram analysis of the tomographic image.
5. The method of claim 3 wherein the allocating interrogated adjacent pixels comprises determining a difference between a gray scale value and a gray scale value of the adjacent pixel in the seed, and allocating the interrogated pixel to the seed if the difference falls below a selected threshold.
6. The method of claim 5 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.
7. The method of claim 1 wherein the material comprises a rock formation.
8. The method of claim 7 wherein the at least one petrophysical parameter comprises permeability.
9. The method of claim 8 wherein permeability is estimated using the Lattice-Boltzmann approximation.
10. The method of claim 7 wherein the at least one petrophysical parameter comprises electrical resistivity formation factor.
11. The method of claim 7 wherein the at least one petrophysical parameter comprises at least one of elastic modulus, bulk modulus and shear modulus.