Partial Reversibility of Dispersion in Heterogeneous Porous Media

• Applicant: Professor Dr.-Ing. Olaf A. Cirpka
• Subject Area: Hydrogeology, Hydrology, Limnology, Urban Water Management, Water Chemistry, Integrated Water Resources Management ; Fluid Mechanics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 506393436

Solute transport in heterogeneous porous media has been the topic of intensive research in the last four decades. It is well established that solute spreading, measuring the increasing irregularity of solute plumes, differs from solute mixing, quantifying the mass exchange of a solute plume with its surrounding. The former precedes the latter, but only the latter facilitates mixing-controlled reactions. To date there is no theory that is good in predicting both large-scale non-Fickian spreading and solute mixing. Neither give existing theories practical advice on performing large-scale conservative-transport experiments to quantify solute mixing. The proposed project builds on the fact that purely kinematic deformation of water parcels carrying solutes in heterogeneous formations is fully reversible, whereas diffusive mixing is irreversible. The interaction between deformation and small-scale diffusive mixing in solute transport in such formations cause partial reversibility of solute spreading: Upon flow reversal the spatial extent of a solute plume shrinks, but does not revert to the original initial state. The project will analyze second-central moments of solute plumes (of which half the rate of change define dispersion coefficients) in heterogeneous porous media with uniform-in-the-mean flow subject to flow reversal. The applicant presumes that the irreversible fraction of dispersion, after equal times of forward and backward motion, can be taken as a metric of solute mixing. In non-radial push-pull experiments the target quantity is the spread of the breakthrough curve of the returning solute in the injection/extraction cross-section. The analysis is done by particle-tracking random-walk simulations in 3-D virtual domains, by first-order stochastic-perturbative methods for the theoretical analysis of spatial moments, by the development of a new correlated Continuous-Time Random-Walk approach with memory of preceding steps and random exchange with the mean for the analysis of temporal moments, and by experiments in a ca. 2m × 1m quasi 2-D flow domain using refractive-index matching fluids to optimize detection by light-transmission imaging. The experiments will include detecting the breakthrough curve of the returning solute. It is hypothesized that linear stochastic theory predicts ensemble and effective moments well for cases with mild heterogeneity. Increasing the inverse Péclet number, the degree of heterogeneity, and its anisotropy should increase the irreversible fraction of dispersion. Second-central moments are expected to shrink upon flow reversal and increase again before the plume center reaches its original position. The shrinking time and the reversible contribution to ensemble dispersion should scale with the local Péclet number. This project develops new theoretical and experimental approaches to distinguish spreading and mixing in heterogenous porous media, which controls the behavior of reactive compounds.

• DFG Programme: Research Grants
• International Connection: Spain
• Cooperation Partner: Professor Dr. Marco Dentz