Probabilistic Grain-Size and Grain-Shape Distributions of 3D Sediment Volumes Using 2D and 1D Observations: Insights from Digital-Grain Models

Size and shape distributions of sedimentary particles are critical for interpreting depositional processes and play a key role in the geomechanical behavior and reservoir quality of sedimentary rocks. For loose particles, generating accurate grain-size distributions is straightforward, but grain size is often measured in 2D for ancient sedimentary rocks. Previous studies have provided useful mathematical, statistical, and stereological approaches to estimating true (i.e., 3D) grain-size distribution from 2D cross-sections. However, these studies mostly assume spherical or ellipsoidal grains and thus are not appropriate for particles with more complex shapes, such as encountered in skeletal carbonates, and lithoclast-rich breccias.

This study utilizes digital-grain models to develop a methodology for predicting 3D grain-size distribution from 2D outcrop and 1D borehole data. Grains with simple and complex shapes are created using Blender software and mixed into monodisperse and polydisperse models with known size and shape sorting. We use Python to segment these models and generate thousands of random 1D sections and 2D slices to generate grain-size and -shape data. These data are then compared to the known 3D size-shape distributions to formulate probabilistic 1D/2D to 3D scaling relationships and correction equations. Finally, we use these relationships to aid in the interpretation of vertical and lateral patterns of particle size-shape distributions observed in deep-water carbonate breccias from outcrops of the Permian Bell Canyon Formation, West Texas. These quantified results can be leveraged to predict depositional processes and geomechanical properties of similar deposits (e.g., in Pricaspian and Permian Basins) where complex-shape particle deposits are found.