Multiscale Digital Rock Analysis for Complex Rocks

Full scale, microscopically resolved tomographies of sandstone and carbonate rocks augmented by experimental porosity and permeability values

We report a dataset containing full-scale, 3D images of rock plugs augmented by petrophysical lab characterization data for application in digital rock and capillary network analysis. Specifically, we have acquired microscopically resolved tomography datasets of 18 cylindrical sandstone and carbonate rock samples having lengths of 25.4 mm and diameters of 9.5 mm. Based on the micro-tomography data, we have computed porosity-values for each imaged rock sample. For validating the computed porosity values with a complementary lab method, we have measured porosity for each rock sample by using standard petrophysical characterization techniques. Overall, the tomography-based porosity values agree with the measurement results obtained from the lab, with values ranging from 8% to 30%. In addition, we provide for each rock sample the experimental permeabilities, with values ranging from 0.4 mD to above 5D. This dataset will be essential for establishing, benchmarking, and referencing the relation between porosity and permeability of reservoir rock at pore scale.

A Closed-Form Equation for Capillary Pressure in Porous Media for All Wettabilities

A saturation–capillary pressure relationship is proposed that is applicable for all wettabilities, including mixed-wet and oil-wet or hydrophobic media. This formulation is more flexible than existing correlations that only match water-wet data, while also allowing saturation to be written as a closed-form function of capillary pressure: we can determine capillary pressure explicitly from saturation, and vice versa. We propose $$P_{{\text{c}}} = A + B\tan \left( {\frac{\pi }{2} - \pi S_{e}^{C} } \right)\,{\text{for}}\,0 \le S_{{\text{e}}} \le 1,$$ P c = A + B tan π 2 - π S e C for 0 ≤ S e ≤ 1 , where $$S_{{\text{e}}}$$ S e is the normalized saturation. A indicates the wettability: $$A>0$$ A > 0 is a water-wet medium, $$A<0$$ A < 0 is hydrophobic while small A suggests mixed wettability. B represents the average curvature and pore-size distribution which can be much lower in mixed-wet compared to water-wet media with the same pore structure if the menisci are approximately minimal surfaces. C is an exponent that controls the inflection point in the capillary pressure and the asymptotic behaviour near end points. We match the model accurately to 29 datasets in the literature for water-wet, mixed-wet and hydrophobic media, including rocks, soils, bead and sand packs and fibrous materials with over four orders of magnitude difference in permeability and porosities from 20% to nearly 90%. We apply Leverett J-function scaling to make the expression for capillary pressure dimensionless and discuss the behaviour of analytical solutions for spontaneous imbibition.

Automatic segmentation tool for 3D digital rocks by deep learning

Obtaining an accurate segmentation of images obtained by computed microtomography (micro-CT) techniques is a non-trivial process due to the wide range of noise types and artifacts present in these images. Current methodologies are often time-consuming, sensitive to noise and artifacts, and require skilled people to give accurate results. Motivated by the rapid advancement of deep learning-based segmentation techniques in recent years, we have developed a tool that aims to fully automate the segmentation process in one step, without the need for any extra image processing steps such as noise filtering or artifact removal. To get a general model, we train our network using a dataset made of high-quality three-dimensional micro-CT images from different scanners, rock types, and resolutions. In addition, we use a domain-specific augmented training pipeline with various types of noise, synthetic artifacts, and image transformation/distortion. For validation, we use a synthetic dataset to measure accuracy and analyze noise/artifact sensitivity. The results show a robust and accurate segmentation performance for the most common types of noises present in real micro-CT images. We also compared the segmentation of our method and five expert users, using commercial and open software packages on real rock images. We found that most of the current tools fail to reduce the impact of local and global noises and artifacts. We quantified the variation on human-assisted segmentation results in terms of physical properties and observed a large variation. In comparison, the new method is more robust to local noises and artifacts, outperforming the human segmentation and giving consistent results. Finally, we compared the porosity of our model segmented images with experimental porosity measured in the laboratory for ten different untrained samples, finding very encouraging results.