Method for determining permeability of rock formation using computer tomograpic images thereof
A method for estimating permeability 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. The components of a permeability tensor are determined by conducting simulations. Principal permeability values and directions are then calculated. The permeability properties are stored in a computer or displayed.
1. A method for estimating permeability 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 rock grain to form a segmented image;
determining components of a permeability tensor through use of the segmented image;
calculating principal permeability values using the components of the permeability tensor;
calculating permeability directions using the components of the permeability tensor;
and at least one of storing and displaying the permeability values and permeability directions,
wherein the tomographic image comprises a value of gray scale allocated to each of a plurality of pixels in the image.
2. The method of claim 1 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.
3. The method of claim 2 wherein the determining initial gray scale thresholds comprises histogram analysis of the tomographic image.
4. The method of claim 2 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.
5. The method of claim 4 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.
6. The method of claim 1 wherein the porous material comprises a rock formation.
7. The method of claim 1 wherein the step of determining components of a permeability tensor further comprises conducting a numerical simulation.
8. The method of claim 7 wherein the step of determining components of a permeability tensor further comprises evaluating the results of the numerical simulation using a volumetric flux equation.
9. The method of claim 7 wherein the step of determining components of a permeability tensor further comprises
digitally subdividing the original segmented image at an angle to obtain a subsample of different orientation; and
performing simulations on the subsample.
10. The method of claim 9 wherein the step of determining components of a permeability tensor further comprises re-indexing the sample image.