Paramater

"Truth"

Conductivity (m/day)

10

λ (m)

10

ln K variance

2.0

SIze of model (m)

100 x 75

Covariance function

Exponential

Grid

201 x 151

Cell size, Δx (m)

0.5 x 0.5

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, variance and covariance.
  • The cell size, Δx, is selected such that the correlation scale, λ, is resolved. Typically, Δx is at least 3 to 4 times smaller than the correlation scale.

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UNCONDITIONAL AND CONDITIONAL SIMULATIONS

 Problem Statement

This video demonstrates the effect of conditioning of data on the aquifer texture. The effect of extent of conditioning is also shown. Details are provided in Table 1.4.

 Key Observations

The following observations can be made from the video:

  • Unconditional simulations can predict the extent and texture of variability in the aquifer, but do not satisfy the data at the data points.
  • Conditional simulations can predict the extent and texture of variability in the aquifer, and also satisfy the data at the data points.
  • By increasing the number of data points, conditional simulations become increasingly better representations of “reality.”

 Additional Observations

Given a set of data for representing the variability in an aquifer, two methods can be used to represent the aquifer structure: a) Unconditional simulations, b) Conditional simulations. Unconditional simulations can predict the variability in an aquifer, but are not constrained by the data at the data points. On the other hand, conditional simulations can predict the variability, and are also constrained by the data. This makes conditional simulations a better representation of the “real” aquifer. Obviously, the effectiveness of conditional simulations increases by increasing the number of data points.