A large set of experimental solute tracer breakthrough data (corresponding to more than 350 individual tracer breakthrough curves) in eight granular filter materials, were used to investigate the links between solute dispersivity and the shape of the pore velocity—relative pore area distributions for the materials. Solute dispersivity values and the shape of the pore velocity—relative pore area distributions were determined by fitting the breakthrough data to the advection–dispersion equation and to the stream tube modeling (STM), respectively. For the STM calculations, stream tube diameter and average stream tube flow rate were allowed to vary between individual stream tubes. Shape parameters e.g., mean, coefficient of variation, skewness and excess kurtosis for the STM-based pore velocity—relative pore area distributions were subsequently calculated. Comparisons between dispersivity and shape parameter values showed strong correlation between dispersivity, coefficient of variation, skewness and excess kurtosis. These results also indicated a universal relationship between dispersivity, skewness and excess kurtosis across all materials and breakthrough curves. This relationship will assist in modelling of experimental data which cannot be characterized by a single or a limited number of pore velocities but require continuous pore velocity distributions. Results further indicated, that the shape of the observed pore velocity—relative pore area distributions could be well approximated by a log-normal distribution.

使用八种颗粒过滤材料中的大量实验溶质示踪剂突破数据（对应于350多个示踪剂突破曲线），研究了溶质分散性与孔隙速度形状之间的联系-相对孔隙面积分布。溶质的弥散度值和孔隙速度的形状（相对孔隙面积分布）分别通过将突破数据与对流扩散方程和流管模型（STM）拟合来确定。对于STM计算，允许在单个流管之间改变流管直径和平均流管流速。形状参数，例如均值，变异系数，随后计算了基于STM的孔隙速度的偏斜度和过量峰度-相对孔隙面积分布。分散度和形状参数值之间的比较表明，分散度，变异系数，偏度和过量峰度之间具有很强的相关性。这些结果还表明在所有材料和突破曲线上的分散性，偏度和过量峰度之间存在普遍关系。这种关系将有助于对实验数据进行建模，这些数据不能用单个或有限数量的孔隙速度来表征，而需要连续的孔隙速度分布。结果进一步表明，观测到的孔隙速度的形状（相对孔隙面积分布）可以通过对数正态分布很好地近似。分散度和形状参数值之间的比较表明，分散度，变异系数，偏度和过量峰度之间具有很强的相关性。这些结果还表明在所有材料和突破曲线上的分散性，偏度和过量峰度之间存在普遍关系。这种关系将有助于对实验数据进行建模，这些数据不能用单个或有限数量的孔隙速度来表征，而需要连续的孔隙速度分布。结果进一步表明，观测到的孔隙速度的形状（相对孔隙面积分布）可以通过对数正态分布很好地近似。分散度和形状参数值之间的比较表明，分散度，变异系数，偏度和过量峰度之间具有很强的相关性。这些结果还表明在所有材料和突破曲线上的分散性，偏度和过量峰度之间存在普遍关系。这种关系将有助于对无法通过单个或有限数量的孔隙速度表征但需要连续孔隙速度分布的实验数据进行建模。结果进一步表明，观测到的孔隙速度的形状（相对孔隙面积分布）可以通过对数正态分布很好地近似。所有材料和突破曲线的偏斜和过度峰度。这种关系将有助于对无法通过单个或有限数量的孔隙速度表征但需要连续孔隙速度分布的实验数据进行建模。结果进一步表明，观测到的孔隙速度的形状（相对孔隙面积分布）可以通过对数正态分布很好地近似。所有材料和突破曲线的偏斜和过度峰度。这种关系将有助于对实验数据进行建模，这些数据不能用单个或有限数量的孔隙速度来表征，而需要连续的孔隙速度分布。结果进一步表明，观测到的孔隙速度的形状（相对孔隙面积分布）可以通过对数正态分布很好地近似。