Integrated global random walk model for reactive transport in groundwater adapted to measurement spatio-temporal scales
Final Report Abstract
Upscaling reactive transport in subsurface hydrological systems aims at obtaining models that can account for small scale processes in predicting the fate of contaminants at larger scales and in designing remediation strategies. Solutions proposed so far are based on volume averages or on homogenization approaches to spatial upscaling. However, it has been argued that small-scale temporal fluctuations of reacting species concentrations, in conditions of locally varying effects of advection and diffusion, propagate from local to larger spatial scales and at least an implicit temporal averaging must also be included in upscaling reactive transport. Moreover, since real measurements are not only associated to a support volume but also span a finite time interval, the measurement time scale has to be explicitly taken into account when comparing models and experiments. The integrated global random walk model proposed in the project simulates the global random walk in saturated/unsaturated velocity fields of the actual number of molecules involved in reactions. The fine-grained solution, representative for the local Darcy scale, is given by the mol fractions of the number of molecules. On the other side, the evolution of the system of particles undergoing advective and rändom wälk displäcements provides ä “microscopicäl” description of the physical system. Coarse grained space-time averages on the microscopical description define almost everywhere continuous fields obeying partial differential equations similar to the local balance equations of the fluid dynamics. Theoretical relations expressing the flow velocity and the intrinsic diffusion coefficient as averages over the microscopical description have been used to check the consistency of the numerical space-time upscaling approach. The space-time upscaling approach has been illustrated by solving a couple of onedimensional reactive transport problems. The results indicate that the traditional volume average may be a good approximation of the space-time average for processes characterized by slow variations in time, e.g., reactions in homogeneous systems or observations of the biodegradation process in heterogeneous aquifers made far away from the contaminant source. Instead, if the biodegradation reaction takes place in non-steady flows through partially saturated soils, the two averages may be dramatically different almost everywhere in the space-time computational domain and the volume average is no longer an acceptable representation of the measured concentrations. Since the support volume and the time interval of the averaging procedure can be taken as representative for field or laboratory measurements, the coarse grained space-time upscaling approach offers the perspective of explicitly relating the upscaled concentrations to the spatiotemporal scales of interest.
Publications
- 2019. Diffusion in Random Fields. Applications to Transport in Groundwater. Birkhäuser / Springer
Suciu, N.
(See online at https://doi.org/10.1007/978-3-030-15081-5) - 2020. Global Random Walk Solutions for Flow and Transport in Porous Media, in: Numerical Mathematics and Advanced Applicätions ENUMATH 2019, European Conference, Egmond aa Zee, The Netherlands, September 30 - October 4
Suciu, N.
(See online at https://doi.org/10.1007/978-3-030-55874-1_93) - 2020. Numerical benchmark study for flow in heterogeneous aquifers. Advances in Water Resources, 138, 103558
Alecsa, C.D., Boros, I., Frank, F., Nechita, M., Knabner, P., Prechtel, A., Rupp, A., Suciu, N.
(See online at https://doi.org/10.1016/j.advwatres.2020.103558) - 2021. Space-time upscaling of reactive transport in porous media
Suciu, N., Radu, F.A.
- Global random walk solvers for fully coupled flow and transport in saturated/unsaturated porous media, 2021, Advances in Water Resources 152,103935
Suciu, N, Iliano, D., Prectel, A., Radu, F.A.
(See online at https://doi.org/10.1016/j.advwatres.2021.103935)
