PCP-GAN: Property-Constrained Pore-scale image reconstruction via conditional Generative Adversarial Networks

TL;DR

This work addresses the challenge of generating representative pore-scale images under scarce data and strong geological heterogeneity. It introduces PCP-GAN, a multi-conditional GAN conditioned on porosity and depth to produce color-coded RGB thin-section images that preserve pore-network morphology. Automated porosity labeling via an enhanced U-Net, coupled with a unified training strategy, yields high porosity control ($R^2=0.95$; $MAE\approx0.01$–$0.02$) and robust preservation of average pore radius, specific surface area, and tortuosity across four carbonate depths. Crucially, generated images demonstrate superior representativeness compared with real sub-images, achieving dual-constraint deviations of $1.9\%$–$11.3\%$ versus $36.4\%$–$578\%$ for real samples, thereby enabling more accurate digital rock representations for carbon storage, geothermal energy, and groundwater applications.

Abstract

Obtaining truly representative pore-scale images that match bulk formation properties remains a fundamental challenge in subsurface characterization, as natural spatial heterogeneity causes extracted sub-images to deviate significantly from core-measured values. This challenge is compounded by data scarcity, where physical samples are only available at sparse well locations. This study presents a multi-conditional Generative Adversarial Network (cGAN) framework that generates representative pore-scale images with precisely controlled properties, addressing both the representativeness challenge and data availability constraints. The framework was trained on thin section samples from four depths (1879.50-1943.50 m) of a carbonate formation, simultaneously conditioning on porosity values and depth parameters within a single unified model. This approach captures both universal pore network principles and depth-specific geological characteristics, from grainstone fabrics with interparticle-intercrystalline porosity to crystalline textures with anhydrite inclusions. The model achieved exceptional porosity control (R^2=0.95) across all formations with mean absolute errors of 0.0099-0.0197. Morphological validation confirmed preservation of critical pore network characteristics including average pore radius, specific surface area, and tortuosity, with statistical differences remaining within acceptable geological tolerances. Most significantly, generated images demonstrated superior representativeness with dual-constraint errors of 1.9-11.3% compared to 36.4-578% for randomly extracted real sub-images. This capability provides transformative tools for subsurface characterization, particularly valuable for carbon storage, geothermal energy, and groundwater management applications where knowing the representative morphology of the pore space is critical for implementing digital rock physics.

Figures (17)

• Figure 1: Examples of thin-section images (768×516 pixels) from the carbonate formation from different core samples: (a) Sample 1 (1879.50 m), (b) Sample 2 (1881.90 m), (c) Sample 3 (1918.50 m), and (d) Sample 4 (1943.50 m). Blue areas represent porous regions visualized by blue-dyed epoxy resin, with each image demonstrating the characteristic pore structure variability at different depths.
• Figure 2: Representative Elementary Volume (REV) analysis demonstrating porosity standard deviation analysis showing variability reduction with increasing sub-image size for four carbonate samples, with the established threshold ($\sigma = 0.06$) for maintaining adequate variability in cGAN training. The selected 480$\times$480 pixel size (red dashed line) optimizes both statistical representativeness and porosity diversity essential for effective conditional generation.
• Figure 3: Distribution of sub-images across sample and porosity class combinations: (a) Initial unbalanced distribution showing significant variations in sub-image counts across different porosity classes within each sample, and (b) Balanced distribution after data augmentation, with each viable porosity class containing exactly 160 images per class.
• Figure 4: Visualization of extracted sub-images (480$\times$480 pixels) across different samples and porosity classes. Each row represents a different sample in the carbonate formation (Sample 1 to Sample 4), while columns represent porosity classes (0-9).
• Figure 5: Schematic architecture of a standard Generative Adversarial Network (GAN) showing the adversarial training process. The generator network transforms random noise vectors (z) into synthetic porous media images, while the discriminator network evaluates both real training images and generator-produced fake images to distinguish their authenticity.