当前位置: X-MOL 学术Phys. Rev. Appl. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Solving Multiphysics, Multiparameter, Multimodal Inverse Problems: An Application to NMR Relaxation in Porous Media
Physical Review Applied ( IF 4.6 ) Pub Date : 2021-05-03 , DOI: 10.1103/physrevapplied.15.054003
Rupeng Li , Igor Shikhov , Christoph H. Arns

A general and robust Bayesian optimization framework for the extraction of intrinsic physical properties from an integration of pore-scale forward modeling and experimental measurements of macroscopic system responses is developed. The efficiency of the scheme, which utilizes Gaussian process regression, enables the simultaneous extraction of multiple intrinsic physical properties with a minimal number of function evaluations. Here it is applied to nuclear magnetic resonance (NMR) relaxation responses, paving the way for inverse problem approaches to digital rock physics given its general nature. NMR relaxation responses of fluids in porous media may be described by sums of multiexponential decays resulting in a relaxation time distribution. The shape of this distribution is dependent on intrinsic physical system properties, but also effects like diffusion coupling between different relaxation regimes in heterogeneous porous materials. Forward models based on high-resolution images are employed to naturally incorporate structural heterogeneity and diffusive motion without limiting assumptions. Extracting the required multiple intrinsic parameters of the system poses an ill-conditioned multiphysics multiparameter inverse problem where multiple scales are covered by the underlying microstructure. Exploration of the multidimensional search space given an expensive cost function makes an efficient solution strategy mandatory. We propose a workflow to match experimental measurements with simulations via Bayesian optimization, with special attention paid to the multimodal nature of the topography of the objective function using solution space partitioning. A multimodal search strategy using state-of-the-art evolutionary algorithms and gradient-based optimization algorithms guarantees that the multimodal nature is captured. The workflow is demonstrated on T2 relaxation responses of Bentheimer sandstone, extracting three physical parameters simultaneously: the surface relaxivity of quartz grains, the effective transverse relaxation time, and the effective diffusion coefficient in clay regions. Multiple mathematically sound and physically plausible solutions corresponding to global minimum and multiple local minima of the objective function are identified within a limited number of function evaluations. Importantly, the shape of the experimental T2 distribution is recovered almost perfectly, enabling the use of classical interpretation techniques and local analysis of responses based on numerical simulation.

中文翻译:

解决多物理场,多参数,多峰反问题:多孔介质中NMR弛豫的应用

开发了一个通用且鲁棒的贝叶斯优化框架,用于从孔隙尺度正演模型和宏观系统响应的实验测量的集成中提取固有物理特性。该方案利用高斯过程回归的效率使得能够以最少数量的功能评估同时提取多个内在的物理特性。这里将其应用于核磁共振(NMR)弛豫响应,鉴于其一般性质,为数字岩石物理学的反问题方法铺平了道路。多孔介质中流体的NMR弛豫响应可以通过导致弛豫时间分布的多指数衰减之和来描述。这种分布的形状取决于固有的物理系统属性,而且还产生了异质多孔材料中不同弛豫范围之间的扩散耦合效应。采用基于高分辨率图像的正向模型可以自然地纳入结构异质性和扩散运动,而无需进行任何假设。提取系统所需的多个内在参数会带来一个病态的多物理场多参数逆问题,其中多个尺度被底层的微结构覆盖。给定昂贵的成本函数,对多维搜索空间的探索使有效的解决方案策略成为强制性的。我们提出了一种工作流程,以通过贝叶斯优化将实验测量结果与模拟结果进行匹配,并特别注意使用解决方案空间划分的目标函数形貌的多峰性质。使用最新的进化算法和基于梯度的优化算法的多峰搜索策略可确保捕获多峰性质。工作流程在上进行了演示Ť2个Bentheimer砂岩的弛豫响应,同时提取三个物理参数:石英颗粒的表面弛豫度,有效横向弛豫时间和黏土区域中的有效扩散系数。在有限数量的功能评估中,确定了与目标函数的全局最小值和多个局部最小值相对应的多个数学上合理且在物理上可行的解决方案。重要的是,实验的形状Ť2个 分布几乎可以完美恢复,从而可以使用经典解释技术和基于数值模拟的响应本地分析。
更新日期:2021-05-03
down
wechat
bug