Conditional Diffusion Models With Integrated Porosity Fusion for 3D Digital Rock Reconstruction

The characterization of subsurface rock pore structures is critical to studying fluid seepage laws in reservoirs. However, drilling core samples downhole is very expensive. Traditional digital rock reconstruction methods also struggle to replicate intricate pore geometries while controlling for properties such as porosity. In this study, we propose a method for generating three- dimensional digital rock samples with controlled porosity using a conditional Denoising Diffusion Probabilistic Models (DDPM) enhanced by feature modulation. The diffusion model architecture is modified by integrating feature modulation at each network layer, which conditions the model on target porosity values to ensure generated samples adhere to specified porosity levels. Specifically, we implemented feature modulation within a three-dimensional U-Net architecture, which functions as the noise estimation model in the diffusion framework. This setup allows the model to effectively capture the complex spatial features of pore structures. The model is trained on a dataset comprising high- resolution micro-CT scans of real rock samples to learn the intricate relationship between porosity and pore morphology. In the forward diffusion process, Gaussian noise is progressively added to the input data over multiple timesteps, thereby transforming it into a noise distribution. During the reverse diffusion process, the model reconstructs realistic pore structures from pure noise by leveraging learned noise estimations conditioned on the target porosity. The reconstructed digital rocks were evaluated by comparing their porosity, pore space structure, connectivity, and pore throat coordination numbers with those of the original core samples. The results exhibit a high consistency, confirming that the conditional DDPM accurately reproduces the pore structure complexity of natural rocks. Additionally, multiple digital rock samples were generated, and the mean values and standard deviations of pore structure parameters were quantified. The minimal variation across these samples further validates the robustness of the trained generative model. Our approach integrates higher-order statistical features from real rock images with precise porosity control through feature modulation, enabling the generation of high-quality 3D digital rock samples. These samples not only replicate the complex pore structures of natural rocks but also strictly adhere to user-defined porosity targets. The ability to generate multiple samples with controlled properties provides a robust foundation for pore-scale fluid flow simulations and uncertainty quantification in reservoir modeling.