Solute transport in crystalline rocks at Äspö — II: Blind predictions, inverse modelling and lessons learnt from test STT1

Based on the results from detailed structural and petrological characterisation and on up-scaled laboratory values for sorption and diffusion, blind predictions were made for the STT1 dipole tracer test performed in the Swedish A¨ spo¨ Hard Rock Laboratory. The tracers used were nonsorbing, such as uranine and tritiated water, weakly sorbing 22Na+, 85Sr2 +, 47Ca2 +and more strongly sorbing 86Rb+, 133Ba2 +, 137Cs+. Our model consists of two parts: (1) a flow part based on a 2D-streamtube formalism accounting for the natural background flow field and with an underlying homogeneous and isotropic transmissivity field and (2) a transport part in terms of the dual porosity medium approach which is linked to the flow part by the flow porosity. The calibration of the model was done using the data from one single uranine breakthrough (PDT3). The study clearly showed that matrix diffusion into a highly porous material, fault gouge, had to be included in our model evidenced by the characteristic shape of the breakthrough curve and in line with geological observations. After the disclosure of the measurements, it turned out that, in spite of the simplicity of our model, the prediction for the nonsorbing and weakly sorbing tracers was fairly good. The blind prediction for the more strongly sorbing tracers was in general less accurate. The reason for the good predictions is deemed to be the result of the choice of a model structure strongly based on geological observation. The breakthrough curves were inversely modelled to determine in situ values for the transport parameters and to draw consequences on the model structure applied. For good fits, only one additional fracture family in contact with cataclasite had to be taken into account, but no new transport mechanisms had to be invoked. The in situ values for the effective diffusion coefficient for fault gouge are a factor of 2–15 larger than the laboratory data. For cataclasite, both data sets have values comparable to laboratory data. The extracted Kd values for the weakly sorbing tracers are larger than Swedish laboratory data by a factor of 25–60, but agree within a factor of 3–5 for the more strongly sorbing nuclides. The reason for the inconsistency concerning Kds is the use of fresh granite in the laboratory studies, whereas tracers in the field experiments interact only with fracture fault gouge and to a lesser extent with cataclasite both being mineralogically very different (e.g. clay-bearing) from the intact wall rock.

Transport of volatile chlorinated hydrocarbons in unsaturated aggregated media

Transport of volatile hydrocarbons in soils is largely controlled by interactions of vapours with the liquid and solid phase. Sorption on solids of gaseous or dissolved comPounds may be important. Since the contact time between a chemical and a specific sorption site can be rather short, kinetic or mass-transfer resistance effects may be relevant. An existing mathematical model describing advection and diffusion in the gas phase and diffusional transport from the gaseous phase into an intra-aggregate water phase is modified to include linear kinetic sorption on ps-solid and water-solid interfaces. The model accounts for kinetic mass transfer between all three phases in a soil. The solution of the Laplace-transformed equations is inverted numerically. We performed transient column experiments with 1,1,2-Trichloroethane, Trichloroethylene, and Tetrachloroethylene using air-dry solid and water-saturated porous glass beads. The breakthrough curves were calculated based on independently estimated parameters. The model calculations agree well with experimental data. The different transport behaviour of the three compounds in our system primarily depends on Henry's constants.

Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.