A 3D Permeability Prediction Model for Multicomponent Carbonate Rocks: Multisoft-Threshold Transformer-UNet

Summary Carbonate rocks exhibit highly complex pore systems and multicomponent mineral compositions, and the coupled effects of mineralogy and pore geometry strongly influence fluid flow at the microscopic scale. However, laboratory permeability measurements on carbonate cores (e.g., steady-state coreflooding) are time-consuming and costly, which limits throughput for routine characterization. In practice, the 3D mineral components and pore structure can be obtained once via automated mineral imaging Quantitative Evaluation of Minerals by Scanning Electron Microscopy (QEMSCAN®)/scanning electron microscopy-energy-dispersive X-ray spectroscopy, suggesting a data-driven alternative: Given known multicomponent digital rocks, directly predict the coreflood permeability to reduce repeated experimental testing. Traditional experimental and numerical methods struggle to capture these multicomponent interactions, leading to limited accuracy in permeability prediction. Recent machine learning approaches have shown promise, but most overlook multicomponent mineralogy and long-range 3D structure in carbonate rocks, which limits their accuracy of permeability prediction. To address these gaps, we introduce soft-threshold attention-enhanced transformer-UNet (STAE-UNet) to address these issues by (i) embedding a lightweight transformer in the decoder to efficiently capture global spatial dependencies during upsampling, (ii) incorporating a multisoft-threshold attention mechanism for sparsity-aware denoising and enhancement of component-pore interfaces, and (iii) performing component-aware multichannel representation and fusion. (UNet is a convolutional encoder–decoder with skip connections.) The model is trained on 667 3D multicomponent digital rock samples (256³ voxels) constructed from QEMSCAN mineral imaging of carbonate reservoirs. STAE-UNet embeds a transformer module in the decoder to capture long-range dependencies during feature upsampling and introduces a multisoft-threshold attention mechanism that adaptively suppresses redundant voxels while enhancing critical pore-mineral connectivity. In comparative experiments, STAE-UNet achieved a coefficient of determination (R2) = 0.94 and mean absolute error (MAE) = 0.057, significantly outperforming the lattice Boltzmann method (LBM; R2 = 0.75, MAE = 0.119) and the finite volume method (FVM; R2 = 0.68, MAE = 0.135). Ablation studies further confirmed that the transformer and soft-threshold attention independently improve accuracy, with combined use yielding the best results. These findings demonstrate that explicitly modeling multicomponent structures with STAE-UNet provides a more accurate data-driven framework for permeability prediction in carbonate reservoirs on the evaluated data set, offering a practical and cost-effective complement to laboratory testing and physics-based simulations where labeled data are available and providing new insights into pore-scale flow mechanisms. These results demonstrate a targeted improvement to the machine learning framework for 3D multicomponent digital rocks—better leveraging global dependencies and component-aware features for lower-error permeability prediction on this data set where labeled data are available.