The experimental determination of transport properties of low permeability clay rocks, especially of relative permeabilities and capillary pressure curves for water and gas, is a very challenging issue, in particular at high water saturation (very low gas permeability resulting in long equilibration times) and for gaseous hydrogen (due to the high pressures involved and the resulting explosion risk). Navier-Stokes equations are solved inside a porous medium on the pore scale, so as to derive the absolute and relative (two-phase-flow) permeabilities. For this purpose microtomography data of Opalinus clay samples acquired in the Mont Terri Ventilation Experiment are used to visualize the pore space in 3D at a micrometric scale (porosity size .0.7 mm). The corresponding percolating porosity is mainly composed of micrometric cracks parallel to the bedding and attributed to shrinkage. Two-phase flow is calculated in the percolating cracks by an immiscible Lattice Boltzmann (LBM) code. In addition, some validation results of the LBM model for three-phase systems (liquid-gas-solid) are presented. © The Geological Society of London 2014.