Matthias Willmann

Coupling of mass transfer and reactive transport for nonlinear reactions in heterogeneous media

Fast chemical reactions are driven by mixing‐induced chemical disequilibrium. Mixing is poorly represented by the advection‐dispersion equation. Instead, effective dynamics models, such as multirate mass transfer (MRMT), have been successful in reproducing observed field‐scale transport, notably, breakthrough curves (BTCs) of conservative solutes. The objective of this work is to test whether such effective models, derived from conservative transport observations, can be used to describe effective multicomponent reactive transport in heterogeneous media. We use a localized formulation of the MRMT model that allows us to solve general reactive transport problems. We test this formulation on a simple three‐species mineral precipitation problem at equilibrium. We first simulate the spatial and temporal distribution of mineral precipitation rates in synthetic hydraulically heterogeneous aquifers. We then compare these reaction rates to those corresponding to an equivalent (i.e., same conservative BTC) homogenized medium with transport characterized by a nonlocal in time equation involving a memory function. We find an excellent agreement between the two models in terms of cumulative precipitated mass for a broad range of generally stationary heterogeneity structures. These results indicate that mass transfer models can be considered to represent quite accurately the large‐scale effective dynamics of mixing controlled reactive transport at least for the cases tested here, where individual transport paths sample the full range of heterogeneities represented by the BTC.

Delineation of connectivity structures in 2‐D heterogeneous hydraulic conductivity fields

Connectivity is a critical aquifer property controlling anomalous transport behavior at large scales. But connectivity cannot be easily defined in a continuous field based on information of the hydraulic conductivity alone. We conceptualize it as a connecting structure—a connected subset of a continuous hydraulic conductivity field that consists of paths of least hydraulic resistance. We develop a simple and robust numerical method to delineate the connectivity structure using information of the hydraulic conductivity field only. First, the topology of the connectivity structure is determined by finding the path(s) of least resistance between two opposite boundaries. And second, a series of connectivity structures are created by inflating and shrinking the individual channels. Finally, we apply this methodology to different heterogeneous fields. We show that our method captures the main flow channels as well as the pathways of early time solute arrivals. We find our method informative to study connectivity in 2-D heterogeneous hydraulic conductivity fields.

Conservative transport upscaling based on information of connectivity

Connected structures in highly heterogeneous hydraulic conductivity fields lead to channels and preferential pathways for the main fluid flux and fastest solute particles. Their spatial complement are zones of slow advection, where solutes are delayed, causing tailing of solute breakthrough curves. These delays depend on the inclusions size and the hydraulic conductivity contrast between inclusion and channel. The interplay between channels and small-scale low conductivity inclusions leads to anomalous transport at larger scales. We test whether a simple separation of transport processes between channels and inclusions could be used to parameterize an effective transport model accounting for anomalous transport. Effective transport is represented by a multi-rate mass transfer model (MRMT): fast channel transport is controlled by parameters of the mobile zone, while slow advective delays are controlled by parameters of the mobile-immobile exchange. We delineate the connected channels and analyze their connectivity followed by characterizing the low conductivity inclusions. We parameterize a MRMT model using connectivity and the statistics of the low permeable inclusions. Finally, we compare the parametrized MRMT with detailed numerical simulations in heterogeneous hydraulic conductivity fields with a clear separation between connected channel network and inclusions. In intermediately connected hydraulic conductivity fields only the cut-off time of the tails is represented while early and intermediate time behavior is not reproduced. We suggest that an effective model for the latter case should account for additional processes like variability in advective velocity. This article is protected by copyright. All rights reserved.

Stochastic dynamics of intermittent pore-scale particle motion in three-dimensional porous media: Experiments and theory

©2017. American Geophysical Union. All Rights Reserved. We study the evolution of velocity in time, which fundamentally controls the way dissolved substances are transported and spread in porous media. Experiments are conducted that use tracer particles to track the motion of substances in water, as it flows through transparent, 3-D synthetic sandstones. Particle velocities along streamlines are found to be intermittent and strongly correlated, while their probability density functions are lognormal and nonstationary. We demonstrate that these particle velocity characteristics can be explained and modeled as a continuous time random walk that is both Markovian and mean reverting toward the stationary state. Our model accurately captures the fine-scale velocity fluctuations observed in each tested sandstone, as well as their respective dispersion regime progression from initially ballistic, to superdiffusive, and finally Fickian . Model parameterization is based on the correlation length and mean and standard deviation of the velocity distribution, thus linking pore-scale attributes with macroscale transport behavior for both short and long time scales.