IGW-NET Visualization - Effects of Multiscale Heterogeneity

Parameter	Case 1	Case 2	Case 3
Geometric mean hydraulic conductivity, K _g (m/day)	10	10	10
ln K variance (for all scales)	1.0	1.0	1.0
Scale 1 Correlation scale, λ (m)	500	500	500
Scale 2 Correlation scale, λ (m)	-	100	100
Scale 3 Correlation scale, λ (m)	-	-	10
Porosity, n	0.3	0.3	0.3
Local pore-scale dispersivity	0	0	0
Head difference (m)	1	1	1
Size of model (m)	2000 x 500	2000 x 500	2000 x 500
Covariance function	Gaussian	Gaussian	Gaussian
Approximate initial plume size (m)	100	100	100
Grid	801 x 201	801 x 201	801 x 201
Cell size, Δx (m)	2.5 x 2.5	2.5 x 2.5	2.5 x 2.5
Time step, Δt(days)	100	100	100
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 geometric mean and ln K variance are constant for all cases. The first scale of heterogeneity is common to all cases, and has a correlation scale of 500 m. The second scale of heterogeneity is applicable only to cases 2 and 3, and has a correlation scale of 100 m. The third scale of heterogeneity is applicable only to cases 2 and 3, and has a correlation scale of 10 m. The covariance function for all cases is Gaussian. 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. The time step, Δt , is selected such that a particle of the plume travels a distance that is less than λ in one time step. Download model - 1 (To download, right click and select "Save Link As" ) Download model - 2 Download model - 3

EFFECTS OF MULTIPLE SCALES OF HETEROGENEITY

Problem Statement

This video demonstrates the effects of multiple scales of heterogeneity, in the absence of pore-scale dispersion, on the spreading of a conservative solute plume. The modeling domain consists of constant head boundaries on the left and right extremes, and no-flow boundaries at the top and bottom. Details are provided in Table 4.1.

Key Observations

The following observations can be made from the video:

Multiple scales of heterogeneity have a drastic impact on plume spreading.
In case 1, the scale of heterogeneity is much larger than the initial size of the plume. As a result, the plume does not encounter all the heterogeneity, and hence does not spread greatly.
In case 2, two large scales of heterogeneity are modeled, the smallest scale of heterogeneity is larger than the initial size of the plume. Plume spreading is enhanced in comparison to case 1, though not significantly, because the plume does not encounter all of the heterogeneity.
In case 3, three scales of heterogeneity are modeled, plume spreading is considerably enhanced. Since the smallest scale of heterogeneity is smaller than the initial size of the plume, the plume encounters all the heterogeneity and hence the spreading is increased.
Mean plume displacement, for this particular realization, increased as more scales of heterogeneity were modeled.

Additional Observations

Case 1: The correlation scale of heterogeneity is 500 m, which is much larger than the initial size of the plume; therefore the plume does not spread greatly. In such cases, the ln K realization is an important factor that controls plume migration.

Case 2: The correlation scales of heterogeneity in the first and second scales are 500 m and 100 m respectively. The initial size of the plume is of the order of 100 m. The plume does not exhibit detailed fingers and tails. However, in comparison to case 1, spreading is increased. The mean plume displacement is greater than in case 1, because the plume encounters more preferential paths (high velocity channels).

Case 3: The correlation scales of heterogeneity in the first, second and third scales are 500 m, 100 m, and 10 m respectively. The third scale is smaller than the initial size of the plume; most of the heterogeneity is encountered, and thus plume spreading is greatly enhanced. The mean displacement is greater than in cases 1 and 2, because the plume encounters more preferential paths (high velocity channels).

A comparison of the three cases shows that increasing the number of scales of heterogeneity increases plume spreading. Eliminating smaller scales of heterogeneity from the model underestimates plume spreading. Incorporating smaller scales requires higher-resolution data, which is costly, and perhaps infeasible. When only larger scales are modeled, the detailed structure of the aquifer represented by the smaller scales of heterogeneity is averaged. In this process of averaging, considerable amount of detail is lost. These details are critical, and make a huge difference in the prediction of plume spreading.