Supplement of A field evidence model: how to predict transport in heterogeneous aquifers at low investigation level

Abstract. Aquifer heterogeneity in combination with data scarcity is a major challenge for reliable solute transport prediction. Velocity fluctuations cause non-regular plume shapes with potentially long-tailing and/or fast-travelling mass fractions. High monitoring cost and a shortage of simple concepts have limited the incorporation of heterogeneity into many field transport models up to now. We present an easily applicable hierarchical conceptualization strategy for hydraulic conductivity to integrate aquifer heterogeneity into quantitative flow and transport modelling. The modular approach combines large-scale deterministic structures with random substructures. Depending on the modelling aim, the required structural complexity can be adapted. The same holds for the amount of monitoring data. The conductivity model is constructed step-wise following field evidence from observations, seeking a balance between model complexity and available field data. The starting point is a structure of deterministic blocks, derived from head profiles and pumping tests. Then, subscale heterogeneity in the form of random binary inclusions is introduced to each block. Structural parameters can be determined, for example, from flowmeter measurements or hydraulic profiling. As proof of concept, we implemented a predictive transport model for the heterogeneous MADE site. The proposed hierarchical aquifer structure reproduces the plume development of the MADE-1 transport experiment without calibration. Thus, classical advection–dispersion equation (ADE) models are able to describe highly skewed tracer plumes by incorporating deterministic contrasts and effects of connectivity in a stochastic way without using uni-modal heterogeneity models with high variances. The reliance of the conceptual model on few observations makes it appealing for a goal-oriented site-specific transport analysis of less well investigated heterogeneous sites.


Overview on field data at MADE site Table 1 provides a list of subsurface investigation activities performed at the MADE site located on the Columbus Air Force Base, Mississippi. Monitoring campaigns at the nearby 1-Ha test site, e.g. Young [1995]; Herweijer [1997] are not included. Since the tracer injection site is not located within the support volume of the pumping test AT1, we consider additional data taken during tracer injection. Water levels were monitored manually in the injection wells and seven observation wells close to the source [Boggs et al., 1990]. A pressure head increase of more then 0.5 m up to 0.64 m was observed in all injection wells. Combining the head increase with the mean injection rate of Q in = 1.15e − 5 m 3 /s indicates an average conductivity ofK Z1 = 2e − 6 m/s in the source area.
Details on parametric uncertainty for binary structure A+B Figure 1: Mass distribution at T = 126 days for conductivity concept (A+B) for various input parameter combinations of inclusion structure: inclusion length I L , volume fraction of inclusions p, distance of zone interface x I to source location and mean conductivity K 1 of zone Z 1 (source area). Mass distribution for standard parameters in black. MADE experiment observations in red. Other parameters as the distance of the interface to the injection location x I , the volume fraction of inclusion p ( Figure 1) as well as the vertical inclusion length I v have minor effects, at least within the range tested. Similarly, the choice of sub-scale heterogeneity parameters is secondary since the inclusion structure dominates the mass distribution. We tested values up to σ 2 = 2 and found nearly no difference to the results of the standard setting for the conductivity concept (A+B+C).
In general, all parameter combinations within the value ranges determined for MADE show a similar mass distribution pattern. In this regard, the binary structure is very stable towards parametric uncertainty.

Details on flow and transport model settings
The

Details on model dimensionality
The model setup we present is 2D although in many applications of heterogeneous hydraulic conductivity it is well known that dimensionality (i.e. 2D vs. 3D) can make a significant difference Figure 2: Realization of a three dimensional binary inclusion structure with p = 15% inclusions and inclusion lengths I y = I x = 10 m, I z = 0.5 − 1 m. Black areas corresponds to low and white to high conductivity. Length is reduced to x = 60 m, source is located at in the flow and transport pattern [Zinn and Harvey, 2003;Jankovic et al., 2017].
To check the dimensionality effect, we performed simulations for a 3D conductivity conceptualizations with binary inclusion for the MADE transport experiment. Therefore, we generated a reduced set of realizations of binary inclusion, which now also expand in the transverse hori- We found almost no differences between 2D and 3D results of flow patterns and mass distribution pattern. We relate that to the conceptualization of the binary structure: Assuming horizontal isotropy, the inclusion lengths are identical in both horizontal directions. Thus, extending the binary structure in y-direction perpendicular to main flow is like combining many copies of the 2D cross section. The structural pattern does not change over the length of the horizontal inclusion I y , e.g. 5, 10 or even 20 m. Consequently, deviations of flow in the horizontal direction perpendicular to the head gradient are negligible. Thus, there is no real change in the flow pattern, in mean velocity and preferential flow between binary structures in 2D and 3D.
We relate the very light differences between 2D and 3D results to a slight increase of mean flow velocity due to a higher connectivity of inclusion in 3D. However, this is only relevant over a large domain and does hardly impact the local flow pattern in the area where transport takes place.
Dimensionality is important in (purely) log-normal random fields, where uniform flow through heterogeneous fields shows higher effective K values in 3D than 2D. Here, conductivity values change gradually in all directions. Thus, adding a third dimension perpendicular to the main flow direction allows to circumvent areas of low conductivity and thus increases the effective mean flow velocity. In the binary material, there are no gradual changes. A layer of low conductivity in horizontal direction extends in both horizontal directions, being an obstacle for the flow and not allowing to circumvent low-K regions by deviating from the main flow direction.
We like to stress, that when applying the proposed heterogeneity conceptualizations for modelling flow and transport in other application, it should be considered to setup the model in 3D. This is particular relevant when heterogeneity is dominated by a log-normal distribution (modules C). A reduction in complexity by using 2D models is warranted when conductivity conceptualizations is dominated by the binary structure (module B).