Modelling and Simulation of 4D GeoPET Measurements with COMSOL Multiphysics 4.2a

Our GeoPET-method allows the 4D monitoring of (reactive) transport processes in geological material on laboratory scale (Gründig et al., 2007; Kulenkampff et al., 2008; Richter et al., 2005) by quantitative imaging of tracer concentrations. Recently we have conducted a long-term 22Na+ in-diffusion experiment in an Opalinus clay drill core over aperiod of 7 months. We modelled this experiment with COMSOL Multiphysics ® 4.2a (3D convection-diffusion equation, PDE mode, PARDISO solver) for reproducing the observed spatiotemporal concentration distribution data with the following underlying equation for this anisotropie diffusion and adsorption:

8Ci ( ) 8q
cßt = \l Dc . \lCi P8t
-c [-] porosity, ci[moVm3] 22Na+concentration, D e [m2/s] tensor of the effective diffusion constant for 22Na+ in Opalinus clay, P [kg/m3 ] bulk density and 8q/8t sink term for considering the sorption. By importing GeoPET images from various time steps and applying the Optirnization Module (least square fit applying the LevenbcrgMarquardt algorithrn) to these images we efficiently deterrnined hest fit values e.g. of the diffusion tensor. Cornbined with the parameter sweep operation the sensitivity analysis is performed in parallel and covers the range of literature values for porosity and Kd values for 22Na+sorption on Opalinus cIay.
The experimental data could be reproduced quite weIl, but the obtained parameter values for diffusion parallel and normal to the bedding are slightly larger than reported in Gimmi and Kosakowski (2011). This is coherent with our observations of an emerging gas bubble in the central borehole tracer reservoir: Soil moisture tension in the partly unsaturated clay must have significantly influenccd thc transport regime by an additional advective component.
We suggest COMSOL Multiphysics ® is a powerful tool for the inverse modelling of timedependent, multidimensional experimental data as obtained by GeoPET.
References.
Gründig, M. et a1., 2007. Tomographie radiotraeer studies ofthe spatial distribution ofheterogeneous geoehemieal transport proeesses. Appl. Geochem., 22: 2334-2343.
Kulenkampff, J. et al., 2008. Evaluation ofpositron emission tomography for visualisation ofmigration proeesses in geomaterials. Phys. Chern. Earth, 33: 937-942.
Richter, M. et al., 2005. Positron Emission Tomography for modelling of geochmical transport processes in clay. Radiochirn. Acta, 93: 643-651.
Gimmi, T. & Kosakowski, G. 2011. How mobile are sorbed eations in clay and clay rocks? Environ. Sei. Techn., 45:1443-1449