Geostatistical simulations of the full 3D block hydraulic conductivity tensor considering inner local-scale variability

Abstract

In regional hydrostratigraphic systems, heterogeneities in hydraulic conductivity (K) play a central role for flow velocities and contaminant transport modelling. Typical field measurements of K usually only represent one or at most a few local hydrofacies of a single hydrostratigraphic unit (HSU). At the regional scale, numerous HSUs exist, each showing a range of K-measurements spanning several orders of magnitude. For realistic numerical modelling, an intermediate scale, i.e. at the block scale, is required between the local and regional scales. Each HSU block must therefore be equipped with an equivalent 3D conductivity tensor that accounts for the connectivity of hydrofacies and conductivity variations at the local scale. We propose a four-step approach: 1- local-scale simulation of K for each HSU, 2- upscaling of local (quasi-point) realizations into the full 3D block K-tensors using a block by block finite element flow simulator, 3- definition of the block K-tensor spatial covariance, and 4- direct simulation of block K-tensors at the regional scale. This approach was applied for regional groundwater flow modelling on a complex 3D deterministic model, the Innisfil Creek watershed, Ontario, Canada. The K database was built using 1,086 transmissivity measurements extracted from public wells, 32 HSU borehole samples for laboratory permeability tests and 1,694 grain size analyses from high-resolution sampling of 15 boreholes located in the study area. The latter were used to characterize local-scale variability of K. A non-conditional turning bands method was used to simulate the local-scale scalar K fields. Block 3D hydraulic conductivity tensors were obtained by upscaling the local-scale simulation to the block scale using the Saltflow finite element flow simulator. Analysis of the upscaled K-tensor components revealed a clear control of principal components with strong correlations between them. The K-tensors showed correlation ranges of a few to several blocks depending of the HSU. The tensor covariance of the principal components was combined in a linear model of coregionalisation to simulate a series of block K-tensor fields within a fixed hydrostratigraphic model. Groundwater flow simulated using the ensemble K field was compared to a deterministic flow field using a single calibrated K-tensor per HSU. The uncalibrated fields simulated with the K tensor showed a match to available hydraulic head data which was comparable to the match of the calibrated deterministic model. The impact of K-tensor uncertainty on a typical flow simulation response was assessed and proved non-negligible. The approach can easily be applied to include uncertainty of the hydrostratigraphic model itself to obtain a better assessment of the complete uncertainty on the flow model.