Numerical investigations of the role of hysteresis in heterogeneous two-phase flow systems

Various groundwater applications often involve the flow of two immiscible fluids in heterogeneous porous media. In problems that involve the assessment of travel times of hazardous substances in the unsaturated zone or monitoring and predicting the fate of groundwater contaminations, efficient tools and approaches need to be developed to achieve accurate predictions of two-phase flow behavior in heterogeneous porous media. However, this is not an easy task, as heterogeneities -observed on different spatial scales- have a strong influence on the distribution of the fluid phases and therefore form a significant source of uncertainty. Moreover, the prediction of two-phase flow in heterogeneous porous media becomes complicated through alternating drainage and imbibition conditions taking place in the complex heterogeneous pore structure that lead to hysteresis effects in the capillary pressure-saturation relationship. Numerical simulations are widely used to predict hysteretic two-phase flow in heterogeneous porous media in lab or field applications. This approach, however, demands good knowledge on the hydraulic properties of the materials that form the heterogeneous structures involved in the application. Traditionally, the hydraulic properties and the hysteretic behavior of porous media are empirically determined on the local scale with lab experiments conducted on material samples. On the other hand, alternative methods suggest the direct determination of hydraulic properties, including hysteretic capillary pressure-saturation relationships, from a pore-scale consideration. This is done using available information on the pore structure of a material. Nevertheless, it remains unclear how accurate predictions can be in problems of hysteretic two-phase flow in porous media, even when advanced state-of-the-art methods are used on different scales for the determination of the hydraulic properties. The first part of this thesis deals with the implementation of two hysteresis concepts in a numerical model for the simulation of two-phase flow in heterogeneous porous media. Special attention is given on the combination of the hysteresis concepts with a capillary interface condition for the treatment of material interfaces and the approximation of saturation discontinuities due to heterogeneities. This provides an efficient and consistent approach for the prediction of hysteretic two-phase flow in heterogeneous porous media. In the second part, predictions made with the numerical implementations of the hysteresis concepts are compared to measurements from a 1-D monitored transient experiment, that involves successive alternating drainage and imbibition conditions. Conclusions related to the importance of hysteresis and the possibilities of the applied hysteresis concepts are drawn. Furthermore, the comparative study presents remarks on the beneficial combination of different approaches -from the modeling and the experimental viewpoint- that lead to reliable predictions on hysteretic two-phase flow. The last part of this work focuses on predictions of hysteretic two-phase flow made with hydraulic properties determined on different spatial scales. In this case, numerical simulations of drainage and imbibition are compared to experimental measurements in a 3-D heterogeneous structure. The hydraulic properties that are used as input for the numerical simulations are determined with two approaches: -On the local scale with multistep outflow/inflow experiments. -On the pore scale with advanced image analysis and lattice Boltzmann flow simulations in mapped sand geometries. The comparative study in this case reveals the possibilities for predictions of hysteretic two-phase flow made with hydraulic properties determined on different scales (local and pore scale), indicates sensitivities in such hydraulic properties, reveals the significant influence of material interfaces in heterogeneous structures and finally detects the apparent temporal- and spatial-scale dependency of non-wetting phase trapping effects during imbibition processes. Conclusions related to the observed hysteresis are drawn, considering the assumptions and the conceptual differences involved in the different approaches. Finally the comparison between simulations and experiment triggers a discussion on the potentials of our modeling approaches in the case of heterogeneous structures, shows how one needs to approach applications of hysteretic two-phase flow in heterogeneous porous media and what aspects must be taken into account when dealing with different scales.