Statistical and Stochastic Analyses of Hydraulic Conductivity and Particle‐Size in a Fluvial Sand

Abstract

An untilled medium‐grained fluvial sand near Socorro, N. Mex., was sampled in horizontal and vertical transects to study the statistical and stochastic properties of particle‐size parameters and saturated hydraulic conductivity. Hydraulic conductivity is log‐normally distributed, whereas the 10% finer, median, and geometric mean particle sizes are normally distributed. The strongest correlation between hydraulic conductivity and particle‐size distribution parameters is that of the log of hydraulic conductivity with the 10% finer particle size. Stochastic analyses using the autocorrelation function and spectrum indicate that the log of hydraulic conductivity and particle size are characterized by dissimilar spatial correlation structures in the vertical directions. In general, particle size is more structured, regular, and predictable and shows a close similarity with the stratigraphy as observed in the field. On the other hand, hydraulic conductivity in the vertical direction may best be modeled as a simple random variable. Variogram and kriging analyses indicate that both hydraulic conductivity and particle size are relatively isotropic in the horizontal plane and that marked similarities in spatial structure exist in this plane. The spatial distribution of saturated hydraulic conductivity in the horizontal plane is estimated reasonably well using the empirical relationship between particle size and conductivity along with the kriged estimates of the 10% finer particle size.

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

“…Farthing et al [22] presented results for di↵erent porous media scenarios by using di↵erent types of sands. It has been shown [11,29,48] that although the permeability values can exhibit large spatial variations, these variations are not entirely random but spatially correlated. Previously, such fields have been modelled using a log-normal distribution assumption [39].…”

Simulation of transport in three‐dimensional heterogeneous unsaturated soils with upscaled dispersion coefficients

“…In line with field studies [e.g., Byers and Stephans, 1983;Sudicky, 1986, Russo et al, 1997, axisymmetric anisotropy is adopted for C pp (x), i.e., I pv = I p1 and I ph = I p2 = I p3 are the characteristic length scales of p( x ) in the vertical (longitudinal) direction, and in the horizontal plane, respectively. The values of s p 2 for the various soil parameters of (14) were adopted from the Bet Dagan trench [Russo and Bouton, 1992] and are summarized in Table 1; the correlation length scales of the various parameters of (14) were assumed as equal to those of logK s , adopted from Russo et al [1997], i.e., I ph = I h = 0.8 m and I pv = I v = 0.2 m. Mean values of the soil parameters of (14) representing coarse-textured sandy and fine-textured clayey soils were adopted from Mishra et al [1989] and are summarized in Table 1.…”

Stochastic modelling of groundwater flow and solute transport in aquifers

“…However, recent analyses of hydraulic conductivity data (Bakr, 1976;Byers and Stephens, 1983;and Hoeksema and Kitanidis, 1985) showed that although the hydraulic conductivity values vary significantly in space, the variation is not entirely random, but correlated in space. Such a correlated nature implies that the parameter values are not statistically independent in space and they must be treated as a stochastic process, instead of a single random variable.…”