Characterization of karst systems, especially the assessment of structure and geometry of conduits along with forecast of state-variables, are essential for groundwater quality/quantity management and implementation/rehabilitation of large-scale engineering projects in karst regions. These objectives can be fully met by utilizing process-based discrete-continuum models, such as MODFLOW-2005 CFPv2, as employed here. However, such tools should be used with the caveat of the potential non-uniqueness of results. This research focuses on the joint-inversion of discharge, water temperature, and solute concentration signatures of Freiheit Spring in Minnesota, USA, in response to a spatiotemporally small-scale hydraulic and transport experiment. Adopting the multi-model concept to address conceptual uncertainty, seven distinctive model variants were considered. Spring hydro-chemo-thermo-graphs for all variants were simultaneously simulated, employing joint-inversion by PEST. Subsequently, calibrated models were compared in terms of calibration performance, parameter uncertainties and reasonableness, as well as forecast capability. Overall, results reveal the reliability of the discrete-continuum flow and transport modeling, even at a spatiotemporally small-scale, on the order of meters and seconds. All conceptualized variants suggest almost identical conduit tracer passage sizes which are close to the flood-pulse method estimates. In addition, the significance of immobile conduit-associated-drainable storages in karst hydrodynamic modeling, which is uniquely provided in our model code, was highlighted. Moreover, it was demonstrated that the spring thermograph and hydrograph carry more information about the aquifer characteristics than the chemograph. However, this last result can be site-specific and depends on the scale of the experiment and the conceptualized variants of the respective hydrological state.

Employing kinetic interface sensitive (KIS) tracers, we investigate three different types of glass-bead materials and two natural porous media systems to quantitatively characterize the influence of the porous-medium grain-, pore-size, and texture on the “mobile” interfacial area between an organic liquid and water. By interpreting the breakthrough curves (BTCs) of the reaction product of the KIS tracer hydrolysis we obtain a relationship for the specific interfacial area (IFA) and wetting saturation. The immiscible displacement process coupled with the reactive tracer transport across the fluid-fluid interface is simulated with a Darcy-scale numerical model. The results show that the current reactive transport model is not always capable to reproduce the breakthrough curves of tracer experiments and that a new theoretical framework is required. Total solid surface area of the grains, i.e., grain surface roughness, is shown to have an important influence on the capillary-associated IFA by comparing results obtained from experiments with spherical glass beads having very small or even no surface roughness and those obtained from experiments with the natural sand. Furthermore, a linear relationship between the mobile capillary associated IFA and the inverse mean grain diameter can be established. The results are compared with the data collected from literature measured with high-resolution microtomography and partitioning tracer methods. The capillary associated IFA values are consistently smaller because KIS tracers measure the mobile part of the interface. Through this study, the applicability range of the KIS tracers is considerably expanded and the confidence in the robustness of the method is improved.

Previous laboratory experiments with KIS tracers have shown promising results with respect to the quantification of fluid-fluid interfacial area (IFA) for dynamic, two-phase flow conditions. However, pore-scale effects relevant for two-phase flow (e.g. the formation of hydrodynamically stagnant/ immobile zones) are not yet fully understood, and quantitative information in how far these effects influence the transport of the tracer reaction products is not yet available. Therefore, a pore-scale numerical model that includes two-phase, reactive flow and transport of the KIS tracer at the fluid-fluid interface is developed. We propose a new method to quantitatively analyze how the concentration of the KIS-tracer reaction product in the effluent is affected by the presence of immobile zones. The model employs the phase field method (PFM) and a new continuous mass transfer formulation, consistent with the PFM. We verify the model with the analytical solution of a reaction-diffusion process for two-phase flow conditions in a conceptual capillary tube. The applicability of the model is demonstrated in NAPL/water drainage scenarios in a conceptual porous domain, comparing the results in terms of the spatial distribution of the phases and the quantified macro-scale parameters (saturation, capillary pressure, IFA and solute concentration). Furthermore, we distinguish the mobile and immobile zones based on the local Péclet number, and the corresponding solute mass in these two zones is quantified. Finally, we show that the outflow concentration can be employed to selectively determine the mobile part of the IFA.