Stochastic modelling of aquifer heterogeneity and hydraulic conductivity field distribution: implications for solute transport modelling

Flow and solute transport in groundwater are primarily controlled by the hydraulic conductivity (K) field. Variations in the K field greatly influence subsurface flow rates and solute migration and dispersion. Due to the importance of aquifer heterogeneity, several approaches have been proposed in the literature for modelling K field spatial distribution based on borehole data. In this work, we evaluate two methods to generate spatial realisations of the K field of a heterogeneous aquifer. Results are analysed in terms of the connectivity of high-K cells, and solute transport results are compared and discussed.  

The methodology consists of three main steps. First, borehole PSD data are used to characterise hydrofacies and generate 3D stochastic realisations of those hydrofacies using the Markov-Chain/Transition Probability approach (MC/TP). Resultant realisations are used to fill a 3D grid. Then, two methods are used to generate hydraulic conductivity fields by assigning a K value to each cell on those grids: (1) using the geometric mean of each hydrofacies (GMEAN) and (2) using a value sampled from the KDE probability functions of each hydrofacies (KDE). Two different porosity scenarios are considered (high porosity, HP; and low porosity, LP). Finally, solute transport estimates were computed using MODFLOW and MT3DMS.

Connectivity analysis of the stochastic realisations shows a higher degree of connectivity of high-K cells on the GMEAN mode than in the KDE. The latter leads to overall higher average K values, but also to slower flow regions with lower K values than the GMEAN.

Solute transport runs result in slower travel times and lower peak concentrations on the KDE realisations than in the GMEAN case. Breakthrough curves at different observation points show that, when concentrations fall after peaking (for a time-limited input pulse), both GMEAN and KDE curves tend to converge. The field-scale longitudinal dispersivity implied from the ensemble probability plumes is similar between the two K field realisation approaches modelled, but the vertical dispersivity is higher in the KDE realisations. The high porosity scenario shows higher dispersivities and considerably longer travel times.

Results show that, for the same porosity scenario, contaminant plumes behave similarly for the KDE and GMEAN approaches at longer times and distances from the source. This suggests that, on the studied site, the small-scale heterogeneity has a reduced effect on the on the long term, field scale macrodispersivity and solute transport behaviour.