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.

翻译：获取与整体地层属性匹配的真正具有代表性的孔隙尺度图像，仍然是地下表征中的一个根本性挑战，因为天然的空间非均质性导致提取的子图像与岩心测量值显著偏离。数据稀缺性加剧了这一挑战，物理样本仅存在于稀疏的井位。本研究提出了一种多条件生成对抗网络（cGAN）框架，该框架生成具有精确控制属性的代表性孔隙尺度图像，同时解决了代表性和数据可用性限制这两大难题。该框架在碳酸盐岩地层四个深度（1879.50-1943.50 m）的薄片样本上进行训练，在单个统一模型中同时对孔隙度值和深度参数进行条件约束。这种方法捕获了通用的孔隙网络原理和特定深度的地质特征，从具有粒间-晶间孔隙的颗粒岩结构到含有硬石膏包裹体的结晶结构。该模型在所有地层中实现了卓越的孔隙度控制（R^2=0.95），平均绝对误差为0.0099-0.0197。形态学验证证实了关键孔隙网络特征（包括平均孔隙半径、比表面积和迂曲度）的保持，其统计差异保持在可接受的地质容差范围内。最重要的是，生成的图像表现出卓越的代表性，其双约束误差为1.9-11.3%，而随机提取的真实子图像的误差为36.4-578%。这种能力为地下表征提供了变革性工具，对于碳封存、地热能和水资源管理等应用尤其有价值，在这些应用中，了解孔隙空间的代表性形态对于实施数字岩石物理至关重要。