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Three-dimensional (3D) printing is capable of transforming intricate digital models into tangible objects, allowing geoscientists to replicate the geometry of 3D pore networks of sedimentary rocks. We provide a refined method for building scalable pore-network models ("proxies") using stereolithography 3D printing that can be used in repeated flow experiments (e.g., core flooding, permeametry, porosimetry). Typically, this workflow involves two steps, model design and 3D printing. In this study, we explore how the addition of post-processing and validation can reduce uncertainty in the 3D-printed proxy accuracy (difference of proxy geometry from the digital model). Post-processing is a multi-step cleaning of porous proxies involving pressurized ethanol flushing and oven drying. Proxies are validated by: (1) helium porosimetry and (2) digital measurements of porosity from thin-section images of 3D-printed proxies. 3D printer resolution was determined by measuring the smallest open channel in 3D-printed "gap test" wafers. This resolution (400 µm) was insufficient to build porosity of Fontainebleau sandstone (∼13%) from computed tomography data at the sample's natural scale, so proxies were printed at 15-, 23-, and 30-fold magnifications to validate the workflow. Helium porosities of the 3D-printed proxies differed from digital calculations by up to 7% points. Results improved after pressurized flushing with ethanol (e.g., porosity difference reduced to ∼1% point), though uncertainties remain regarding the nature of sub-micron "artifact" pores imparted by the 3D printing process. This study shows the benefits of including post-processing and validation in any workflow to produce porous rock proxies.

The relationship between porosity and permeability in limestones is a fundamental constitutive equation in subsurface fluid flow modelling, and is essential in quantifying a range of geological processes. For a given porosity, the permeability of limestones varies over a range of up to five orders of magnitude. Permeability of a given rock sample depends on the total amount of pore space, characterized by porosity, as well as how the pore space is distributed within the rock, which can be expressed as a probability density function of pore sizes. We investigate in this study whether the information about pore-size distribution can be sufficiently captured by the bulk petrographical properties extracted from thin sections. We demonstrate that most of the uncertainty can be explained by variations in texture, which is defined by the mud content (mass fraction of particles less than 0.06 mm in diameter). Using mud content as a quantitative texture descriptor, we used multivariable regression and neural network models to predict permeability from porosity. For a given porosity, inclusion of mud content reduces the uncertainty in permeability prediction from five to two orders of magnitude.

Summary Diagenetic effects in carbonate rocks can enhance or occlude depositional pore space. Reliable identification of porosity-enhancing diagenetic features (e.g., vugs and fractures) is essential for petrophysical characterization of reservoir properties (e.g., porosity and permeability), construction of geological and reservoir models, reserve estimation, and production forecasting. Challenges remain in characterizing these diagenetic features from well logs as they are often mixed with variations in mineral and fluid concentrations. Herein, we explore a data-driven approach that is based on a comprehensive well log data set from the Arbuckle Formation in Kansas to classify vuggy facies in carbonate rocks. The available well log data include conventional logs (gamma ray (GRTC), resistivity (RT), neutron/density porosity (NPHI/RHOB), photoelectric factor (PE), and acoustic slowness) and nuclear magnetic resonance (NMR) transverse relaxation time (T2) logs. We parameterized the measured T2 distribution using a multimodal lognormal Gaussian density function and combined the resulting Gaussian parameters with conventional logs as inputs into three supervised machine learning (ML) algorithms; namely, support vector machine (SVM), random forest (RF), and artificial neural network (ANN). The facies labeling data used in this study were based on visual examination of vug sizes from core samples, which include five classes; namely, nonvuggy, pinpoint-size, centimeter-size, fist-size, and super-vuggy. In total, 80% of the data set was used as the training set, and a fivefold cross validation was used for hyperparameter tuning. We conducted a detailed comparison of the above three ML algorithms on the basis of different combinations of features. The highest classification accuracy achieved on the holdout testing set is 84% using SVM on a combination of conventional logs and selected NMR Gaussian parameters as inputs. In general, inclusion of conventional log data improves the prediction accuracy compared with using NMR data alone. Feature selection improves the performance for SVM and ANN but is not recommended for RF.

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