UNIVERSAL SCALING OF HYDRAULIC CONDUCTIVITIES AND DISPERSIVITIES IN GEOLOGIC MEDIA
UNIVERSAL SCALING OF HYDRAULIC CONDUCTIVITIES AND DISPERSIVITIES IN GEOLOGIC MEDIA
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DOI：
10.1029/wr026i008p01749
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发表时间：
1990-08-01
影响因子：
5.4
通讯作者：
NEUMAN, SP
中科院分区：
文献类型：
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作者：
NEUMAN, SP
对色散随规模增大的观测结果提供了一种解释。假设来自各种水文地质环境的表观纵向色散数据表示具有相互不相关增量的测井水力导电性场的连续层次结构，每个场都有自己的指数自协方差，相关的积分尺度和方差随着尺度的幂次而增加。从理论上证明了这种层次结构可以形成齐次增量的自相似随机场。不管潜在的假设是否有效，人们都可以用一种与最近齐质介质中非菲克和菲克色散的准线性理论相一致的方式来解释表观色散，该理论支持了自相似层次的概念。该层次结构具有半变分函数γ(s;) cs½（其中为常数）和分形维数E+ 0.75（其中为感兴趣的拓扑维数）。这可以看作是一个普遍的标度规则，由于局部影响，包括存在离散的自然标度，其中测井水力传导率在统计上是均匀的，因此会出现较大的偏差。由于这种均匀性充其量是在尺度谱的窄频带上间歇性发生的局部现象，人们必须质疑将介质性质与代表性基本体积联系起来以及在相对较窄的尺度间隔上依赖菲克模型的效用。多孔介质和裂缝介质似乎在流动和输运方面都遵循相同的理想尺度规则，这就提出了一个问题，即在这两种介质之间通常所作的许多区分的有效性。最后，数据表明，通过对水力测量进行校准来调节输运模型具有从层次中过滤掉大尺度模式的效果。
An interpretation is offered for the observation that dispersivities increase with scale. Apparent longitudinal dispersivity data from a variety of hydrogeologic settings are assumed to represent a continuous hierarchy of log hydraulic conductivity fields with mutually uncorrelated increments, each field having its own exponential autocovariance, associated integral scale, and variance that increases as a power of scale. Such a hierarchy is shown theoretically to form a self‐similar random field with homogeneous increments. Regardless of whether or not the underlying assumption is valid, one can justify interpreting the apparent dispersivities in a manner consistent with a recent quasi‐linear theory of non‐Fickian and Fickian dispersion in homogeneous media which supports the notion of a self‐similar hierarchy a posteriori. The hierarchy is revealed to possess a semivariogram γ(s;) ≊cs½, wherecis a constant, and a fractal dimensionD≊E+ 0.75, whereEis the topological dimension of interest. This can be viewed as a universal scaling rule about which large deviations occur due to local influences including the existence of discrete natural scales at which log hydraulic conductivity is statistically homogeneous. As such homogeneity is at best a local phenomenon occurring intermittently over narrow bands of the scale spectrum, one must question the utility of associating medium properties with representative elementary volumes and relying on Fickian models of dispersion over more than relatively narrow scale intervals. Porous and fractured media appear to follow the same idealized scaling rule for both flow and transport, raising a question about the validity of many distinctions commonly drawn between such media. Finally, the data suggest that conditioning transport models through calibration against hydraulic measurements has the effect of filtering out large‐scale modes from the hierarchy.