<p>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 property-matching challenges and data availability constraints. The framework was trained on thin section samples from four depths (1879.50 m to 1943.50 m) of a carbonate formation, simultaneously conditioning on porosity values and depth parameters within a single model. Unlike previous approaches requiring separate models for different formations, the framework processes RGB thin section images that preserve critical mineralogical information (anhydrite-dolomite differentiation, grain boundaries, interparticle-intraparticle porosity distinctions) lost in conventional grayscale or binarized representations. 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 strong porosity control (R<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$^2$</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>2</mn> </mmultiscripts> </math></EquationSource> </InlineEquation> = 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, consistent with geological authenticity. Two-point correlation (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$S_2$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>) analysis further confirmed that the generated images preserve the spatial continuity and characteristic length scales of natural pore networks rather than reproducing porosity in a spatially incoherent manner, and both porosity control and reconstruction accuracy remained consistent across the range of imaging resolutions tested (1.8–3.0 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>m/pixel). When validated against core sample properties, generated images demonstrated higher property fidelity with dual-constraint errors (combined porosity-permeability deviations) of 1.9–12.4% compared to 37.5–713.6% for randomly extracted real sub-images, showing tighter clustering around target porosity-permeability values. This capability to generate geologically authentic images that better match bulk formation properties than traditional sampling provides practical tools for subsurface characterization, particularly valuable for modeling processes in carbon storage, geothermal energy, and groundwater management, where knowing the characteristic morphology of the pore space is critical for implementing digital rock physics.</p>

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

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2026年7月8日

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Ali Sadeghkhani,
Brandon Bennett,
Masoud Babaei,
Arash Rabbani

摘要

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 property-matching challenges and data availability constraints. The framework was trained on thin section samples from four depths (1879.50 m to 1943.50 m) of a carbonate formation, simultaneously conditioning on porosity values and depth parameters within a single model. Unlike previous approaches requiring separate models for different formations, the framework processes RGB thin section images that preserve critical mineralogical information (anhydrite-dolomite differentiation, grain boundaries, interparticle-intraparticle porosity distinctions) lost in conventional grayscale or binarized representations. 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 strong porosity control (R $^2$ $^{2}$ = 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, consistent with geological authenticity. Two-point correlation ( $S_2$ $S_{2}$ ) analysis further confirmed that the generated images preserve the spatial continuity and characteristic length scales of natural pore networks rather than reproducing porosity in a spatially incoherent manner, and both porosity control and reconstruction accuracy remained consistent across the range of imaging resolutions tested (1.8–3.0 $\mu $ $μ$ m/pixel). When validated against core sample properties, generated images demonstrated higher property fidelity with dual-constraint errors (combined porosity-permeability deviations) of 1.9–12.4% compared to 37.5–713.6% for randomly extracted real sub-images, showing tighter clustering around target porosity-permeability values. This capability to generate geologically authentic images that better match bulk formation properties than traditional sampling provides practical tools for subsurface characterization, particularly valuable for modeling processes in carbon storage, geothermal energy, and groundwater management, where knowing the characteristic morphology of the pore space is critical for implementing digital rock physics.