Collaborative Research: Solute Transport in Multimodal, Heterogeneous Geological Formations Combining Sedimentologic and Engineering Approaches

我们将开发一个分层空间随机函数（HSRF）模型，该模型代表颗粒含水层系统中由边界面定义的渗透率、沉积结构和沉积单元。在最小的尺度上，相被定义为单峰渗透率的区域，如果存在，则是与层状有共同朝向的跨层集。相将由一个连续的随机变量表示，该变量具有各向异性相关性，由层理和/或跨层集的方向控制。相组合，例如填满单个通道的相组合，将由一个指示随机变量和相关的过渡概率表示，这些过渡概率表示每个相的比例、几何形状和并置。复杂的相组合，如并置河道充填、沙洲增生和河道带沉积中的河岸上组合，由一个更高层次的指示随机变量表示，其过渡概率代表了组合的比例、几何形状和并置。所有三个层次的连续变量和指示变量将在一个单一的HSRF模型中进行数学表示，该模型适合于与溶质扩展的解析表达式集成。HSRF模型不同于现有的模型和方法，因为它可以捕获复杂的非高斯空间分布，并且可以结合解释沉积学来约束地质统计模型。通过实地研究和模型气质的结合，我们试图解决以下问题：(1)颗粒介质中渗透率的分布和(2)溶质扩散。(1)与渗透率分布有关的问题：o具有三个层次的HSRF模型是否捕获了渗透率和沉积结构的各个方面，这对理解典型羽流尺度上溶质扩散很重要？o任何一个层级的属性与另一个层级的属性是否相关？o HSRF模型能否用于改进未知位置渗透率的条件估计？o在开发地质统计模型时，是否可以利用高通量通量模型作为整合地质/沉积学软数据的框架？(2)与溶质扩散有关的问题：o三个层次对纵向和横向溶质扩散的相对贡献是什么？o随着渗透率的单变量统计量和空间相关性在相界上的差异越来越大，溶质扩散矩在什么时候受到显著影响？在什么条件下可以忽略任何层次的表示？o在什么条件下，多模态异质性中的输运可以用有效的羽流尺度相关参数来模拟？为了回答这些问题，我们正在开展一项跨学科的合作项目，涉及加州大学伯克利分校和赖特州立大学的研究人员。与赖特州立大学过去由uri资助的项目一样，该项目将为本科生提供研究经验。

0001125Ritzi We will develop a hierarchical spatial random function (HSRF) model that represents permeability, sedimentary structures, and sedimentary units defined by bounding surfaces in granular aquifer systems. At the smallest scale, facies are defined as regions of unimodal permeability and, if present, of cross-strata sets with common orientation to the laminae. Facies will be represented by a continuous random variable having anisotropic correlation controlled by bedding and/or the orientation of cross-strata sets. Assemblages of facies, such as the combination of facies filling a single channel, will be represented by an indicator random variable and associated transition probabilities which represent the proportions, geometries, and juxtapositioning of each facies. A complex of facies assemblages, such as juxtaposed channel fill, bar accretion, and overbank assemblages within channel belt deposits, is represented by a higher-tier indicator random variable with transition probabilities representing the proportions, geometries, and juxtapositioning of the assemblages. The continuous and indicator variables of all three levels will be mathematically expressed in a single HSRF model suitable for integration with analytical expressions for solute spreading. The HSRF model departs from current models and approaches in that it can capture complex, non-Gaussian spatial distributions and can incorporate interpretive sedimentology to constrain the geostatistical models. In combined field studies and model temperament, we seek to address the following questions relating to (1) the distribution of permeability in granular media and (2) solute spreading. (1) Questions relating to distribution of permeability: o Does the HSRF model, with its three hierarchical levels, capture the aspects of permeability and sedimentary structure important for understanding solute spreading at the scale of typical plumes? o Are the attributes of any one hierarchical level correlated with those of another level? o Can the HSRF model be used to improve the conditional estimation of permeability at unknown locations? o Can the HSRF model be used as a framework for incorporating geological/sedimentological soft data as geostatisticl models are developed? (2) Questions related to solute spreading: o What are the relative contributions of the three hierarchical levels to both longitudinal and lateral solute spreading? o As the univariate statististics and the spatial correlation of permeability become increasingly different across facies boundaries, at what point are the moments of solute spreading significantly affected? o Under what conditions can representation of any of the hierarchical levels be ignored? o Under what conditions can transport in a multimodal heterogeneity be modeled with effective, plume-scale-dependent parameters? To answer these questions, we are conducting a collaborative, interdisciplinary project involving investigators at both the University of California, Berkeley, and Wright State University. As in past URI-funded projects at Wright State University, the project will provide research experiences for undergraduates.