There is growing interest in using advanced imaging techniques to describe the complex pore-space of natural rocks at resolutions that allow for quantitative assessment of the flow and transport behaviors in these complex media. Here, we focus on representations of the complex pore-space obtained from X-ray microtomography and the subsequent use of such 'pore-scale' representations to characterize the overall porosity and permeability of the rock sample. Specifically, we analyze the impact of sub-resolution porosity on the macroscopic (Darcy scale) flow properties of the rock. The pore structure of a rock sample is obtained using high-resolution X-ray microtomography (3.16 3 µm 3 /voxel). Image analysis of the Berea sandstone sample indicates that about 2 % of the connected porosity lies below the resolution of the instrument. We employ a Darcy-Brinkman approach, in which a Darcy model is used for the sub-resolution porosity, and the Stokes equation is used to describe the flow in the fully resolved pore-space. We compare the Darcy-Brinkman numerical simulations with core flooding experiments, and we show that proper interpretation of the sub-resolution porosity can be essential in characterizing the overall permeability of natural porous media.

International audienceBoth flow field heterogeneity and mass transfer between mobile and immobile domains have been studied separately for explaining observed anomalous transport. Here we investigate non-Fickian transport using high-resolution 3-D X-ray microtomographic images of Berea sandstone containing microporous cement with pore size below the setup resolution. Transport is computed for a set of representative elementary volumes and results from advection and diffusion in the resolved macroporosity (mobile domain) and diffusion in the microporous phase (immobile domain) where the effective diffusion coefficient is calculated from the measured local porosity using a phenomenological model that includes a porosity threshold ( inline image) below which diffusion is null and the exponent n that characterizes tortuosity-porosity power-law relationship. We show that both flow field heterogeneity and microporosity trigger anomalous transport. Breakthrough curve (BTC) tailing is positively correlated to microporosity volume and mobile-immobile interface area. The sensitivity analysis showed that the BTC tailing increases with the value of inline image, due to the increase of the diffusion path tortuosity until the volume of the microporosity becomes negligible. Furthermore, increasing the value of n leads to an increase in the standard deviation of the distribution of effective diffusion coefficients, which in turn results in an increase of the BTC tailing. Finally, we propose a continuous time random walk upscaled model where the transition time is the sum of independently distributed random variables characterized by specific distributions. It allows modeling a 1-D equivalent macroscopic transport honoring both the control of the flow field heterogeneity and the multirate mass transfer between mobile and immobile domains