This paper summarises the results of a benchmark study that compares a number of mathematical and numerical models applied to specific problems in the context of carbon dioxide (CO 2 ) storage in geologic formations. The processes modelled comprise ad-H. Class (B) · A. Ebigbo · R. Helmig · M. Darcis · B. Flemisch vective multi-phase flow, compositional effects due to dissolution of CO 2 into the ambient brine and nonisothermal effects due to temperature gradients and the Joule-Thompson effect. The problems deal with leakage through a leaky well, methane recovery enhanced P. Audigane BRGM, French Geological Survey, 410 Comput Geosci (2009) 13:409-434 by CO 2 injection and a reservoir-scale injection scenario into a heterogeneous formation. We give a description of the benchmark problems then briefly introduce the participating codes and finally present and discuss the results of the benchmark study.

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Convection-enhanced drug delivery is a technique where a therapeutic agent is infused under positive pressure directly into the brain tissue. For predicting the final concentration distribution and optimizing infusion rate and catheter placement, numerical models can be of great help. However, despite advances in modeling this process, often the infused agent does not reach the targeted region prescribed in the modeling phase. In this study, patient-specific brain structure and parameters, obtained from diffusion tensor imaging (DTI), are implemented in a numerical model which describes the flow and transport in an elastic deformable matrix. To our knowledge, this is the first time that information from DTI is used in a numerical model which includes both transport of a therapeutic agent and tissue deformation. Fractional anisotropy (FA) is used to distinguish between gray and white matter and tortuosity to differentiate between inside and outside the brain tissue. One voxel in the DT-image is represented by one element of the numerical grid. The DT-images were in addition used to determine the orientation of the white matter fiber tracts and calibrate permeability and diffusion coefficients found in the literature. Values chosen for the porosity and Lamé parameters are also based on those found in the literature. Given realistic literature values, the calibration of the permeability and diffusion tensors are shown to be successful. Our result shows that preferential flow occur in direction of the white matter fiber tracts. The current model assumes linear deformation, corresponding to small porosity changes.