IGW-NET Visualization - Effects of Interacting Heterogeneity

Parameter	Case 1	Case 2	Case 3	Case 4
Geometric mean hydraulic conductivity, K_g (m/day)	10	10	10	10
ln K variance	2.0	2.0	2.0	2.0
Correlation scale, λ (m)	2	2	2	2
Mean porosity, n_m	0.25	0.25	0.25	0.25
Coefficient of variation – n and K	NA	0.27	0.25	0.10 (ln n variance)
Correlation – n and K	NA	Positive	Negative	None
White noise, w	NA	0	0	0
Local pore-scale dispersivity	0	0	0	0
Head difference (m)	1	1	1	1
Size of model (m)	200 x 50	200 x 50	200 x 50	200 x 50
Covariance function	NA	Exponential	Exponential	Exponential
Approximate initial plume size (m)	10	10	10	10
Grid	401 x 407	401 x 407	401 x 407	401 x 407
Cell size, Δx (m)	0.5 x 0.5	0.5 x 0.5	0.5 x 0.5	0.5 x 0.5
Time step, Δt (days)	1	1	1	1
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 (Kg) of K, correlation scale, variance and covariance. The geometric mean, ln K and correlation scale are constant for all cases. The covariance function for all cases is exponential. The covariance function for cases 2, 3 and 4 is exponential. The interactions between n and K are characterized by a coefficient of variation and the type of correlation. 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 (To download, right click and select "Save Link As" )

INTERACTIONS BETWEEN CONDUCTIVITY AND POROSITY HETEROGENEITIES

Problem Statement

This video demonstrates the impact of interactions between conductivity and porosity heterogeneities 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 1.3.

Key Observations

The following observations can be made from the video:

Interaction between conductivity ( K ) and porosity ( n ) heterogeneities has a significant impact on plume spreading.
In most situations n is positively correlated with K , which results in less plume spreading compared to when there is no heterogeneity in n .
When n is negatively correlated with K , plume spreading is greater compared to when there is no heterogeneity in n .
When n and K are independent of each other, plume spreading is less than case 1, although in general, this might not be the case.

Additional Observations

Case 1: Even though K varies continuously over space, n remains constant throughout the field. This is not a commonly encountered situation. In the absence of sufficient data, n is assumed to be constant throughout the field.

Case 2: In a more common situation, n interacts positively with K . When n increases, the seepage velocity decreases. The seepage velocity is given by q/n , where q is the Darcy velocity. When n increases, the seepage velocity decreases, resulting in less plume spreading. Hence, the plume spreads lesser than in case 1.

Case 3: In this case, n interacts negatively with K . This means that n decreases when K increases. This relatively uncommon situation results in enhanced spreading of the plume. The eventual size of the plume is greater in comparison to case 1.

Case 4: When n varies with no relationship to K , velocity variability is random. The plume spreading is dependent on ln n realization.

Giving n a single value ignores the variability, resulting in increasing or reducing plume spreading. The video shows that the effect on plume spreading is significant.

The video shows only the variation of K over space. The variation of n over space is shown below. Notice that, even though the cases look very different from each other, the head contours are the same. The head is dependent only on K . Since the ln K realization is the same for all cases, the head contours are identical.