Method for digitally characterizing the permeability of rock

1. A method for estimating the permeability of rock, comprising:

obtaining a three-dimensional image of a rock wherein the image is comprised of a plurality of voxels and the image has a resolution;

processing the three-dimensional image of the rock to segment the image by selecting each voxel of the image to represent either pore space in the rock or solid material in the rock;

estimating an image permeability of the rock from the segmented three-dimensional image of the rock;

deriving a non-wetting liquid capillary pressure curve from the segmented three-dimensional image of the rock;

determining one or more permeability correction factors from the segmented three-dimensional image and the non-wetting liquid capillary pressure curve; and

applying the one or more permeability correction factors to the image permeability of the rock to obtain a corrected permeability of the rock.

2. The method of claim 1 , wherein the three-dimensional image of the rock is obtained by x-ray computer tomography.

3. The method of claim 1 , wherein the rock is obtained from a hydrocarbon-bearing formation comprised of sandstone, carbonate, shale and combinations thereof.

4. The method of claim 1 , wherein the non-wetting liquid is mercury or Wood's metal.

5. The method of claim 1 , wherein the image permeability of the rock is estimated by computation in a permeability simulation method utilizing the segmented three-dimensional image of the rock.

6. The method of claim 1 , wherein the one or more permeability correction factors comprises a permeability image resolution correction factor that is determined from an image entry pore throat size, as determined from the non-wetting liquid capillary pressure curve, voxel size, as determined from the image resolution, and a predicted measured entry pore throat size to voxel size ratio.

7. The method of claim 1 , wherein the one or more permeability correction factors comprises a permeability image field of view correction factor that is determined from the non-wetting liquid capillary pressure curve, the voxel size in the image, the number of voxels along an axis extending the length, width, or height of the image, and a corrected image porosity estimated from the segmented three-dimensional image of the rock and the non-wetting liquid capillary pressure curve.

8. The method of claim 1 , wherein the non-wetting liquid capillary pressure curve is derived from the segmented three-dimensional image of the rock at pressures of up to an image-limited pressure, where the image-limited pressure is the minimum pressure that can be applied on the non-wetting liquid to overcome the capillary pressure of the narrowest pore throat distinguishable from the segmented three-dimensional image of the rock.

9. The method of claim 1 , wherein the one or more permeability correction factors comprises a pore geometric factor is determined from the non-wetting liquid capillary pressure curve by plotting a best fit curve to the non-wetting liquid capillary pressure curve and determining the pore geometric factor from the shape of the curve.

10. The method of claim 1 wherein the one or more permeability correction factors comprises a pore throat resolution parameter is determined by determining a pore throat size of pores entered by the non-wetting liquid at an entry pressure from the non-wetting liquid capillary pressure curve and calculating a ratio between the pore throat size of pores entered by the non-wetting liquid at the entry pressure and the resolution of the image.

11. The method of claim 1 , wherein the three-dimensional image is obtained from a cloud-based tool adapted to store and process 2D projection images from a pore-scaling imaging technology.

12. A backpropagation-enabled method for estimating the permeability of rock from a three-dimensional image of rock, comprising the steps of:

obtaining a three-dimensional image of rock, the three-dimensional image having a resolution;

applying a backpropagation-enabled trained model to segment the three-dimensional image of rock;

estimating an image permeability of the rock from the segmented image;

deriving a non-wetting liquid capillary pressure curve from the segmented image;

determining one of more permeability correction factors from the non-wetting liquid capillary pressure curve and the resolution; and

applying the one or more permeability correction factors to the image permeability of the rock to obtain a corrected permeability of the rock.

13. The method of claim 12 , wherein the trained model is produced by:

providing a training set of images of rock;

segmenting the images of rock into a plurality of labeled voxels, the plurality of labeled voxels representing pore spaces and solid material in the rock; and

using the labeled voxels to train a model via backpropagation.

14. The method of claim 13 , wherein the training set of images is obtained from a cloud-based tool adapted to store and process 2D projection images from a pore-scaling imaging technology.

15. The method of claim 12 , wherein the non-wetting liquid capillary pressure curve is derived from the segmented image at pressures of up to an image-limited pressure, where the image-limited pressure is the minimum pressure that can be applied on the non-wetting liquid to overcome the capillary pressure of the narrowest pore throat distinguishable from the segmented image of the rock.

16. The method of claim 12 , wherein the three-dimensional image is obtained from a cloud-based tool adapted to store and process 2D projection images from a pore-scaling imaging technology.