Abteilung Wasserressourcen und Trinkwasser

Transported chemical reactions in unsaturated porous media are relevant to environmental and industrial applications. Continuum scale models are based on equivalent parameters derived from analogy with saturated conditions and cannot appropriately account for incomplete mixing. It is also unclear how the third dimension controls mixing and reactions. We obtain three-dimensional (3D) images by magnetic resonance imaging using an immiscible nonwetting liquid as a second phase and a fast irreversible bimolecular reaction. We study the impact of phase saturation on the dynamics of mixing and the reaction front. We quantify the temporally resolved effective reaction rate and describe it using the lamellar theory of mixing, which explains faster than Fickian (t^0.5) rate of product formation by accounting for the deformation of the mixing interface between the two reacting fluids. For a given Péclet, although stretching and folding of the reactive front enhance as saturation decreases, enhancing the product formation, the product formation is larger as saturation increases. After breakthrough, the extinction of the reaction takes longer as saturation decreases because of the larger nonmixed volume behind the front. These results are the basis for a general model to better predict reactive transport in unsaturated porous media not achievable by the current continuum paradigm.

We study pore-scale dynamics of reactive transport in heterogeneous, dual-porosity media, wherein a reactant in the invading fluid interacts chemically with the surface of the permeable grains, leading to the irreversible reaction A_aq + B_s → C_aq. A microfluidic porous medium was synthesized, consisting of a single layer of hydrogel pillars (grains), chemically modified to contain immobilized enzymes on the grain surfaces. Fluorescence microscopy was used to monitor the spatiotemporal evolution of the reaction product C_aq at different flow rates (Péclet values) and to characterize the impact on its transport. The experimental setup enables delineation of three key features of the temporal evolution of the reaction product within the domain: (i) the characteristic time until the rate of C_aq production reaches steady state, (ii) the magnitude of the reaction rate at steady state, and (iii) the rate at which C_aq is flushed from the system. These features, individually, are found to be sensitive to the value of the Péclet number, because of the relative impact of diffusion (vs advection) on the production and spatiotemporal evolution of C_aq within the system. As the Péclet number increases, the production of C_aq is reduced and the transport becomes more localized within the vicinity of the grains. The dual-porosity feature causes the residence time of the transported species to increase, by forming stagnant zones and diffusive-dominant regions within the flow field, thus enhancing the reaction potential of the system. Using complementary numerical simulations, we explore these effects for a wider range of Péclet and Damköhler numbers and propose nonlinear scaling laws for the key features of the temporal evolution of C_aq.

Uncertainty estimation plays an important part in practical hydrogeology. With most of the subsurface unobservable, attempts at system characterization will invariably be incomplete. Uncertainty estimation, then, must quantify the influence of unknown parameters, forcings, and structural deficiencies. In this endeavor, numerical modeling frameworks can resolve a high degree of subsurface complexity and its associated uncertainty. Where boundary uncertainty is concerned, however, numerical frameworks can be restrictive. The interdependence of grid discretization and its enclosing boundaries render exploration of uncertainties in their extent or nature challenging. The analytic element method (AEM) may be an interesting complement, as it is computationally efficient, economic with its parameter count, and does not require enclosure through finite boundaries. These properties make AEM well suited for uncertainty estimation, particularly in data-scarce settings or exploratory studies. In this study, we explore the use of AEM for flow field uncertainty estimation, with a particular focus on boundary uncertainty. To induce diverse, uncertain regional flow more easily, we propose a new element based on a Möbius transformation. We include this element in a simple Python-based AEM toolbox and benchmark it against MODFLOW. Coupling AEM with a Markov Chain Monte Carlo routine using adaptive proposals, we explore its use in a synthetic case study. We find that AEM permits efficient uncertainty estimation for groundwater flow fields, which may form a basis for stochastic Lagrangian transport modeling or can support advanced model design by informing the placement of numerical model boundaries.