Dual control of flow field heterogeneity and immobile porosity on non-Fickian transport in Berea sandstone

• Published in: Water resources research 2015-10, Vol.51 (10), p.8273-8293
• Main Authors: Gjetvaj, Filip, Russian, Anna, Gouze, Philippe, Dentz, Marco
• Format: Article
• Language: English
• Subjects: Advection; anomalous transport; Coefficients; continuous time random walk; Diffusion; Diffusion coefficient; Diffusion coefficients; Dye dispersion; Earth Sciences; Economic models; Environmental Sciences; Flow control; flow field heterogeneity; Geophysics; Global Changes; Heterogeneity; Macroporosity; Mass transfer; Microporosity; Modelling; multirate mass transfer; pore scale modeling; Pore size; Porosity; Random variables; Random walk; Resolution; Sandstone; Sciences of the Universe; Sedimentary rocks; Sensitivity analysis; Tortuosity; Transport
• ISSN: 0043-1397; 1944-7973
• DOI: 10.1002/2015WR017645

Both 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 ( ϕθ) 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 ϕθ, 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. Key Points: We simulate pore‐scale flow and anomalous transport in Berea sandstone We show that both flow heterogeneity and diffusion in immobile domain control BTC shape We upscale successfully the 3‐D transport behavior by a new 1‐D effective CTRW model