Geometric mean hydraulic conductivity K g (cm/sec)

9.75 x 10 -3

ln K variance

0.38

Correlation scale, λx (m)

2.8

Correlation scale, λz (m)

0.12

Size of model (m)

19 x 1.75

Grid

761 x 71

Cell size, Δx (m)

0.025 x 0.025

The model parameters and inputs are explained below:

  • The ln K field is a normally distributed random field. Therefore, there is an equal probability of the plume encountering a ‘low' K zone or a ‘high' K zone.
  • The heterogeneous conductivity field is uniquely characterized by the following set of statistical parameters: geometric mean ( K g ) of K , correlation scale, ln K variance and covariance.
  • The geometric mean, ln K variance, and correlation scale is constant for all cases.
  • The covariance function for all realizations is exponential.
  • The cell size, D x , is selected such that the correlation scale, l , is resolved; typically, D x is at least 3 to 4 times smaller than the correlation scale.

Source: Sudicky, E. A., A natural gradient experiment on solute transport in a sand aquifer: Spatial variability of hydraulic conductivity and its role in the dispersion process, Water Resources Research, 22(13), 2069-2082, 1986.

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BORDEN AQUIFER, CROSS-SECTION A-A

 Problem Statement

This video demonstrates the multiple realizations for the statistical parameters of the Borden aquifer, Canada ( Sudicky , 1986). Details are provided in Tables 2.1.1.

 Key Observations

The following observations can be made from the video:

  • A random field is characterized by a set of statistical parameters, such as mean, variance and correlation scale.
  • Multiple realizations of the Borden aquifer data share the same “texture” as the data.
  • In spite of having the same structure, each realization is different from other realizations.
  • An infinite number of realizations exist that satisfy the same statistical parameters; hence, uniquely characterizing aquifer structure with limited data is impossible.
  • All the realizations statistically represent the truth. None of them can deterministically represent the truth.

 Additional Observations

Any aquifer can be statistically represented using a mean, ln K variance and a correlation scale. A brief description of these parameters is given below:

  • Mean – Is the geometric mean of the data, which represents the average conditions that exist in the aquifer
  • Correlation scale – Is a measure of the spatial distance across which the aquifer properties are supposed to be correlated. This parameter can be different in all three directions making the aquifer anisotropic. However, in most cases, the horizontal correlation scales ( λ x and λy) are assumed to be constant. Vertical correlation scale (λz) is in general smaller than the horizontal correlation scales. Correlation scales give an idea about the “texture” or “pattern” of variability.
  • Variance – Is a measure of how variable the aquifer properties are with respect to the mean. A higher variance means higher variability of aquifer properties and vice versa.

The Borden aquifer is a test site, which generated a large amount of hydraulic conductivity data with extremely fine resolution. Using this data, Sudicky (1986) performed a statistical analysis to obtain the mean, variance and correlation scale for this site. Given these parameters, it is possible to create a random field that statistically represents the Borden aquifer.