Flow and transport in saturated and unsaturated fractured porous media: Development of particle-based modeling approaches

The main objective of this thesis is the development of particle-based flow and transport models to assist in the characterization of small-scale flow features and provide insight into the complex flow and transport dynamics on core- and fracture scales. Based on the evaluation of the simulation of flow in a fractured karst aquifer using a double continuum model and the Richards equation to describe unsaturated flow, the fundamental weaknesses of the approach are identified and new innovative methods are presented to capture the underlying preferential flow and transport features. The simulation of flow and transport in unsaturated fractured aquifers is extremely challenging due to the multitude of scales involved in the description of geometrical features, which often restrict the definition of a global representative elementary volume. Furthermore the hydraulic characteristics of a fractured aquifer can often only be obtained from integral approaches such as pumping and slug tests, spring discharge analyses and tracer tests in order to constrain the hydraulic parameter space. Double-continuum models provide a well-balanced approach in terms of the required field information and the resulting predictive modeling capacity. The first part of this thesis deals with the simulation of a fractured karst aquifer with a double-continuum model, where flow is governed by the Richards equation, van Genuchten parameters and inter-continua exchange is controlled by a linear exchange term. The steep recessions following a recharge event are the characteristic feature of karst springs and can be very well reproduced by the model. The secondary conduit continuum acts as the main connection to the spring and receives varying amounts of discharge from the fractured matrix system depending on the head difference. In order to avoid the simulation of rapid recharge through the unsaturated zone of the conduit continuum, the respective recharge boundary has been added to the bottom of the conduit continuum, essentially creating a bypass. A general drawback of the double-continuum approach has been the ambiguity of model results. The dualistic parameter space in combination with parameters that are difficult to determine, provokes the existence of several well calibrated systems, as demonstrated by extensive multidimensional sensitivity analyses. Especially in karst aquifers the vertical rapid recharge flow features, such as dissolution shafts and wide fractures or fault systems, contribute to the fastest components of the travel time spectrum and cannot be adequately represented by common volume effective modeling approaches, such as the Richards equation and van Genuchten relationships. Therefore the main part of the thesis is devoted to the development of two Smoothed Particle Hydrodynamics (SPH)codes to provide innovative numerical tools for the particle based simulation of small-scale free-surface flow and transport. SPH models rely on a Eulerian description of a flow field governed by the Navier-Stokes equation with particles moving according to classical Newton mechanics. The meshfree modeling approach allows a flexible treatment of the highly dynamic boundaries encountered on unsaturated fractures and porous media. A free-surface SPH model including the effect of surface tension has been employed to simulate droplet and film flow on smooth and rough fracture surfaces. A wide range of wetting conditions and Reynolds numbers is covered to obtain a set of characteristic dimensionless parameters. The model is shown to satisfy general scaling laws and dewetting dynamics governed by critical-state contact angle behavior. The generation of adsorbed films on initially dry surfaces is delineated and prewetted surfaces are shown to increase the velocities of droplets, thus highlighting the importance of co-existing flow modes. Several types of macroroughness are implemented to demonstrate the decline of droplet velocities compared to smooth surfaces. In order to bridge the gap between the macroscopic continuum description of the Navier-Stokes equation and the underlying atomistic effects described by statistical mechanics, a mesoscopic SPH model has been developed. This new discretization of the fully-coupled Landau-Lifshitz-Navier-Stokes and advection-diffusion equations allows to simulate advective flow and transport including the effects of fluctuating hydrodynamics which can dynamically adapt to the model scale. The combination of classical Fickian diffusion and thermodynamic fluctuations is described by an effective diffusion coefficient. Various numerical experiments show the accuracy of the model and wavenumber divergencies of interface concentration fields agree with recent laboratory experiments.