Abstract: A method for analyzing a rock sample includes segmenting a digital image volume corresponding to the rock sample, to associate voxels in the digital image volume with pore space or solid material. A distance transform is applied to each pore space voxel. The distance transform assigns a distance value to the pore space voxel specifying distance from the pore space voxel to a solid material voxel. Drainage is numerically simulated by, for a pore space, selecting each distance value assigned to a pore space voxel that is greater than a predetermined threshold value to represent a radius of a sphere of a non-wetting fluid introduced into the pore space. The sphere is centered at the pore space voxel corresponding to the distance value. The digital image volume is numerically analyzed to characterize a material property of the rock sample at a non-wetting fluid saturation produced by the drainage.

Abstract: Methods and systems for estimating conductivity of clay mineral systems, and for applying the estimates in larger-scale analysis. Conductivity of the clay may be estimated by constructing a molecular model of an anhydrous charge-neutral clay, and then assigning a charge density by substitution of ions in the model of the clay structure. Counterions are inserted for charge neutrality, and water molecules are added to the model to reflect a selected level of hydration. Following assignment of force-field coefficients, molecular dynamics simulation provides data from which diffusion coefficients can be estimated. Application of the Nernst-Einstein relationship to the diffusion coefficients of the counterions provides the ion conductivity of the clay system. This conductivity can be used to derive a formation factor, and can be applied in direct numerical simulation analysis.

Abstract: A method for analyzing a rock sample includes segmenting a digital image volume corresponding to the rock sample, to associate voxels in the digital image volume with pore space or solid material. A distance transform is applied to each pore space voxel. The distance transform assigns a distance value to the pore space voxel specifying distance from the pore space voxel to a solid material voxel. Drainage is numerically simulated by, for a pore space, selecting each distance value assigned to a pore space voxel that is greater than a predetermined threshold value to represent a radius of a sphere of a non-wetting fluid introduced into the pore space. The sphere is centered at the pore space voxel corresponding to the distance value. The digital image volume is numerically analyzed to characterize a material property of the rock sample at a non-wetting fluid saturation produced by the drainage.

Abstract: A sample preparation apparatus and method of preparing a rock sample using such an apparatus, as useful in connection with the digital numerical simulation of properties of the rock. The disclosed apparatus includes a fixably mounted diamond wire cutter. Three linear translation stages are coupled to a specimen holder. One of the translation stages moves the specimen in a direction parallel to the plane of the cutting wire. The other two translation stages move the specimen in different directions from one another, and when actuated together, advance the specimen into the wire for short distances in a direction out of the plane of the cutting wire. Short piecewise linear cuts are made in the specimen, to provide a sample of the desired shape with a small cross-section.

Abstract: Methods and systems for estimating conductivity of clay mineral systems, and for applying the estimates in larger-scale analysis. Conductivity of the clay may be estimated by constructing a molecular model of an anhydrous charge-neutral clay, and then assigning a charge density by substitution of ions in the model of the clay structure. Counterions are inserted for charge neutrality, and water molecules are added to the model to reflect a selected level of hydration. Following assignment of force-field coefficients, molecular dynamics simulation provides data from which diffusion coefficients can be estimated. Application of the Nernst-Einstein relationship to the diffusion coefficients of the counterions provides the ion conductivity of the clay system. This conductivity can be used to derive a formation factor, and can be applied in direct numerical simulation analysis.

Abstract: A testing system for performing image based direct numerical simulation to characterize petrophysical properties of a rock sample under the simulated deformation condition, for example as representative of subsurface conditions. A digital image volume corresponding to x-ray tomographic images of a rock sample is segmented into its significant elastic phases, such as pore space, clay fraction, grain contacts and mineral type, and overlaid with an unstructured finite element mesh. A simulated deformation is applied to the segmented image volume, and the resulting deformed unstructured mesh is numerically analyzed, for example by way of direct numerical simulation, to determine the desired petrophysical properties.

Abstract: A sample preparation apparatus and method of preparing a rock sample using such an apparatus, as useful in connection with the digital numerical simulation of properties of the rock. The disclosed apparatus includes a fixably mounted diamond wire cutter. Three linear translation stages are coupled to a specimen holder. One of the translation stages moves the specimen in a direction parallel to the plane of the cutting wire. The other two translation stages move the specimen in different directions from one another, and when actuated together, advance the specimen into the wire for short distances in a direction out of the plane of the cutting wire. Short piecewise linear cuts are made in the specimen, to provide a sample of the desired shape with a small cross-section.

Abstract: A sample preparation apparatus and method of preparing a rock sample using such an apparatus, as useful in connection with the digital numerical simulation of properties of the rock. The disclosed apparatus includes a fixably mounted diamond wire cutter. Three linear translation stages are coupled to a specimen holder. One of the translation stages moves the specimen in a direction parallel to the plane of the cutting wire. The other two translation stages move the specimen in different directions from one another, and when actuated together, advance the specimen into the wire for short distances in a direction out of the plane of the cutting wire. Short piecewise linear cuts are made in the specimen, to provide a sample of the desired shape with a small cross-section.

Abstract: A sample preparation apparatus and method of preparing a rock sample using such an apparatus, as useful in connection with the digital numerical simulation of properties of the rock. The disclosed apparatus includes a fixably mounted diamond wire cutter. Three linear translation stages are coupled to a specimen holder. One of the translation stages moves the specimen in a direction parallel to the plane of the cutting wire. The other two translation stages move the specimen in different directions from one another, and when actuated together, advance the specimen into the wire for short distances in a direction out of the plane of the cutting wire. Short piecewise linear cuts are made in the specimen, to provide a sample of the desired shape with a small cross-section.

Abstract: A testing system for analyzing a 3D digital volume of a material sample. The testing system defines several test volume sizes with each test volume size including a different numbers of voxels, defining the size of portions of the 3D digital volume to analyze. For each test volume size, the testing system acquires two adjacent portions of 3D digital volume at the test volume size currently being analyzed. The testing system calculates a material property value for the two adjacent portions of the 3D digital volume, and a difference value between the two adjacent portions of the 3D digital volume. The process is repeated over the different test volume sizes. The testing system calculates mean difference values for the different test volume sizes, from which it determines a representative elementary volume.

Abstract: A testing system for performing image based direct numerical simulation to characterize petrophysical properties of a rock sample under the simulated deformation condition, for example as representative of subsurface conditions. A digital image volume corresponding to x-ray tomographic images of a rock sample is segmented into its significant elastic phases, such as pore space, clay fraction, grain contacts and mineral type, and overlaid with an unstructured finite element mesh. A simulated deformation is applied to the segmented image volume, and the resulting deformed unstructured mesh is numerically analyzed, for example by way of direct numerical simulation, to determine the desired petrophysical properties.

Abstract: A testing system for analyzing a 3D digital volume of a material sample. The testing system defines several test volume sizes with each test volume size including a different numbers of voxels, defining the size of portions of the 3D digital volume to analyze. For each test volume size, the testing system acquires two adjacent portions of 3D digital volume at the test volume size currently being analyzed. The testing system calculates a material property value for the two adjacent portions of the 3D digital volume, and a difference value between the two adjacent portions of the 3D digital volume. The process is repeated over the different test volume sizes. The testing system calculates mean difference values for the different test volume sizes, from which it determines a representative elementary volume.

Abstract: A testing system can analyze a 3D digital volume of a material sample. The testing system can define several test volumes with each test volume including a different numbers of voxels. The test volumes can define the size of portions of the 3D digital volume to analyze. For each test volume, the testing system can acquire two adjacent portions of 3D digital volume that are the size of the test volume currently being analyzed. The testing system can calculate a petrophysical property value for the two adjacent portions of the 3D digital volume and can calculate the difference value between the two adjacent portions of the 3D digital volume. The testing system can repeat the process for the different test volumes. The testing system can plot the mean difference values for the different test volumes. The testing system can analyze the plot to determine a representative elementary volume that meets a predefined difference value.