Upscaling Mixing-Controlled Reactions in Unsaturated Porous Media.

We study mixing-controlled chemical reactions in unsaturated porous media from a pore-scale perspective. The spatial heterogeneity induced by the presence of two immiscible phases, here water and air, in the pore space generates complex flow patterns that dominate reactive mixing across scales. To assess the impact of different macroscopic saturation states (the fraction of pore volume occupied by water) on mixing-controlled chemical reactions, we consider a fast irreversible reaction between two initially segregated dissolved species that mix as one solution displaces the other in the heterogeneous flow field of the water phase. We use the pore-scale geometry and water distributions from the laboratory experiments reported by Jiménez-Martínez et al. (Geophys. Res. Lett. 42: 5316-5324, 2015). We analyze reactive mixing in three complementary ways. Firstly, we post-process experimentally observed spatially distributed concentration data; secondly, we perform numerical simulations of flow and reactive transport in the heterogeneous water phase, and thirdly, we use an upscaled mixing model. The first approach relies on an exact algebraic map between conservative and reactive species for an instantaneous irreversible bimolecular reaction that allows to estimate reactive mixing based on experimental conservative transport data. The second approach is based on reactive random walk particle tracking simulations in the numerically determined flow field in the water phase. The third approach uses a dispersive lamella approach that accounts for the impact of flow heterogeneity on mixing in terms of effective dispersion coefficients, which are estimated from both experimental data and numerical random walk particle tracking simulations. We observe a significant increase in reactive mixing for decreasing saturation, which is caused by the stronger heterogeneity of the water phase and thus of the flow field. This is consistently observed in the experimental data and the direct numerical simulations. The dispersive lamella model, parameterized by the effective interface width, provides robust estimates of the evolution of the product mass obtained from the experimental and numerical data.

Upscaling of transport through discrete fracture networks via random walk: A comparison of models.

Many models have been created for upscaled transport modeling in discrete fracture networks (DFNs). Random walk examples of these are the Markov directed random walk (MDRW), Monte Carlo solution of the Boltzmann transport equation (BTE), and the spatial Markov model (SMM). Each model handles the correlation between the random walk steps using different techniques and has successfully reproduced the results of full-resolution transport simulations in DFNs. However, their predictive capabilities under different modeling scenarios have not been compared. We construct a set of random 2D DFNs for three different fracture transmissivity distributions to comparatively evaluate model performance. We focus specifically on random walk models to determine what aspects of the space and time step distributions (e.g., correlation and coupling) must be accounted for to get the most accurate predictions. For DFNs with low heterogeneity in fracture transmissivity, accounting for correlation generally leads to less accurate predictions of transport behavior, but as the fracture transmissivity distribution widens, preferential pathways form and correlation between modeling steps becomes important, particularly for early breakthrough predictions.

A Method to Represent a Well in a Three-Dimensional Discrete Fracture Network Model.

In discrete fracture network (DFN) modeling, fractures are randomly generated and placed in the model domain. The rock matrix is considered impermeable. Small fractures and isolated fractures are often ignored to reduce computational expense. As a result, the rock matrix between fractures could be large and intersections may not be found between a well introduced in the model and the hydraulically connected fracture networks (fracture backbones). To overcome this issue, this study developed a method to conceptualize a well in a three-dimensional (3D) DFN using two orthogonal rectangular fractures oriented along the well's axis. Six parameters were introduced to parameterize the well screen and skin zone, and to control the connectivity between the well and the fracture backbones. The two orthogonal fractures were discretized using a high-resolution mesh to improve the quality of flow and transport simulations around and along the well. The method was successfully implemented within dfnWorks 2.0 (Hyman et al. 2015) to incorporate a well in a 3D DFN and to track particles leaving an injection well and migrating to a pumping well. Verification of the method against MODFLOW/MODPATH found a perfect match in simulated hydraulic head and particle tracking. Using three examples, the study showed that the method ensured the connectivity between wells and fracture backbones, and honored the physical processes of flow and transport along and around wells in DFNs. Recommendations are given for estimating the values of the six introduced well parameters in a real-world case study.

Contributions of biofilm-induced flow heterogeneities to solute retention and anomalous transport features in porous media.

Microbial biofilms are ubiquitous within porous media and the dynamics of their growth influence surface and subsurface flow patterns which impacts the physical properties of porous media and large-scale transport of solutes. A two-dimensional pore-scale numerical model was used to evaluate the impact of biofilm-induced flow heterogeneities on conservative transport. Our study integrates experimental biofilm images of Paenibacillus 300A strain in a microfluidic device packed with cylindrical grains in a hexagonal distribution, with mathematical modeling. Biofilm is represented as a synthetic porous structure with locally varying physical properties that honors the impact of biofilm on the porous medium. We find that biofilm plays a major role in shaping the observed conservative transport dynamics by enhancing anomalous characteristics. More specifically, when biofilm is present, the pore structure in our geometry becomes more spatially correlated. We observe intermittent behavior in the Lagrangian velocities that switches between fast transport periods and long trapping events. Our results suggest that intermittency enhances solute spreading in breakthrough curves which exhibit extreme anomalous slope at intermediate times and very marked late solute arrival due to solute retention. The efficiency of solute retention by the biofilm is controlled by a transport regime which can extend the tailing in the concentration breakthrough curves. These results indicate that solute retention by the biofilm exerts a strong control on conservative solute transport at pore-scale, a role that to date has not received enough attention.

Impact of confined geometries on hopping and trapping of motile bacteria in porous media.

We use a random walk particle-tracking (RWPT) approach to elucidate the impact of porous media confinement and cell-cell interactions on bacterial transport. The model employs stochastic alternating motility states consisting of hopping movement and trapping reorientation. The stochastic motility patterns are defined based on direct visualization of individual trajectory data. We validate our model against experimental data, at single-cell resolution, of bacterial E. coli motion in three-dimensional confined porous media. Results show that the model is able to efficiently simulate the spreading dynamics of motile bacteria as it captures the impact of cell-cell interaction and pore confinement, which marks the transition to a late-time subdiffusive regime. Furthermore, the model is able to qualitatively reproduce the observed directional persistence. Our RWPT model constitutes a meshless simple method which is easy to implement and does not invoke ad hoc assumptions but represents the basis for a multiscale approach to the study of bacterial dispersal in porous systems.

On Modeling Ensemble Transport of Metal Reducing Motile Bacteria.

Many metal reducing bacteria are motile with their run-and-tumble behavior exhibiting series of flights and waiting-time spanning multiple orders of magnitude. While several models of bacterial processes do not consider their ensemble motion, some models treat motility using an advection diffusion equation (ADE). In this study, Geobacter and Pelosinus, two metal reducing species, are used in micromodel experiments for study of their motility characteristics. Trajectories of individual cells on the order of several seconds to few minutes in duration are analyzed to provide information on (1) the length of runs, and (2) time needed to complete a run (waiting or residence time). A Continuous Time Random Walk (CTRW) model to predict ensemble breakthrough plots is developed based on the motility statistics. The results of the CTRW model and an ADE model are compared with the real breakthrough plots obtained directly from the trajectories. The ADE model is shown to be insufficient, whereas a coupled CTRW model is found to be good at predicting breakthroughs at short distances and at early times, but not at late time and long distances. The inadequacies of the simple CTRW model can possibly be improved by accounting for correlation in run length and waiting time.

Mean first-passage time for superdiffusion in a slit pore with sticky boundaries.

This Brief Report examines Levy motion in a slit pore with sticky boundaries, i.e., boundaries that absorb particles for a random amount of time. A set of equations is developed that can explicitly be solved for mean travel distance to a plane for a particle released from the origin and can iteratively be used to compute mean first-passage time (MFPT). Results from the theory compare favorably with Monte Carlo simulations.