Multiscale permeability parameterization in geologic cores is key for quantifying multiphase flow and conservative, reactive, and colloidal transport processes in geologic systems. Despite its importance in controlling flow and transport processes, permeability measurement methods often suffer from low spatial resolution, high computational cost, or lack of generalizability. This study leverages positron emission tomography (PET) experimental data to record time-lapse radiotracer concentration distributions at millimeter-scale resolution in geologic cores. Through iterative forward simulations, an Ensemble Kalman Filter (EnKF) is employed to assimilate the input transport data and an ensemble of possible permeability distributions to determine the corresponding three-dimensional permeability map for a given geologic core sample. A second approach, specifically a convolutional neural network (CNN) with new hierarchical modifications, is also used for permeability inversion. This data-driven CNN eliminates the need for numerically defining and iteratively running a forward operator once the training is completed. The EnKF and CNN methods are separately evaluated for permeability inversion with a combination of synthetically generated data and PET imaging data. Inverted 3-D sub-core scale permeability maps are used to parameterize forward numerical models for direct comparison with the PET measurements for accuracy evaluation on experimental data. The trained CNN produces more robust inversion results with orders of magnitude improvement in computational efficiency compared with the EnKF. Finally, we propose an improved EnKF inversion workflow where the initial ensemble is generated by adding perturbations to the CNN permeability map prediction. The results indicate that the hybrid EnKF-CNN workflow achieves improvements in inversion accuracy in nearly all core samples but at the expense of computational efficiency relative to the CNN alone. Overall, this combination of experimental, numerical, and deep-learning methodologies considerably advances the speed and reliability of 3-D multiscale permeability characterization in geologic core samples.

地质岩心的多尺度渗透率参数化是量化地质系统中多相流以及保守、反应和胶体传输过程的关键。尽管渗透率测量方法在控制流动和传输过程中很重要，但它经常受到空间分辨率低、计算成本高或缺乏通用性的困扰。这项研究利用正电子发射断层扫描(PET) 实验数据来记录地质岩心中毫米级分辨率的延时放射性示踪剂浓度分布。通过迭代正向模拟，采用集合卡尔曼滤波器（EnKF）来同化输入传输数据和可能的渗透率分布的集合，以确定给定地质岩心样本的相应三维渗透率图。第二种方法，特别是具有新的分层修改的卷积神经网络（CNN），也用于渗透率反演。这种数据驱动的 CNN 无需在训练完成后对前向算子进行数值定义和迭代运行。结合综合生成的数据和 PET 成像数据，分别评估 EnKF 和 CNN 方法的渗透率反演。倒置 3-D 子岩心比例渗透率图用于参数化正向数值模型，以便与 PET 测量直接比较，从而对实验数据进行准确性评估。与 EnKF 相比，经过训练的 CNN 可以产生更稳健的反演结果，计算效率提高了几个数量级。最后，我们提出了一种改进的 EnKF 反演工作流程，其中通过向 CNN 渗透率图预测添加扰动来生成初始集合。结果表明，混合 EnKF-CNN 工作流程几乎在所有岩心样本中都实现了反演精度的提高，但相对于单独的 CNN 而言，以牺牲计算效率为代价。总体而言，这种实验、数值和深度学习方法的结合大大提高了地质岩心样本中 3D 多尺度渗透率表征的速度和可靠性。