DFG Project „Process-based characterisation of flow and transport in unsaturated fractured rocks“
In the context of the project a parallel Smoothed Particle Hydrodynamics (SPH) model was to be developed to characterize the unsaturated flow in fractured rocks and to develop a better process understanding for the residence time distribution. Gravitatively driven flows in unsaturated fractures usually exhibit a highly non-linear behavior and often cannot be detected by classical volume-effective methods such as the Richards equation and Van Genuchten parameterizations. In addition to the development of efficient numerical methods for process studies, laboratory experiments were carried out within the project. These were used to validate the developed model, but were also used for further studies that could not be simulated due to computational limitations. Laboratory experiments and numerical simulations were used to investigate the effect of fluid- and solids-specific parameters on flow behavior. These include (1) fluid properties, i.e. surface tension, viscosity, and equations of state, (2) wetting behavior and contact angle dynamics, (3) gap geometry such as roughness and opening width, (4) fracture network geometry, and (5) flow boundary conditions. In order to carry out the above studies, various code developments had to be carried out. A geometry generator was developed to create rough, natural surfaces and fracture networks. This enables the efficient generation of smooth or rough fracture systems or individual fractures taking into account all SPH-relevant geometry criteria. Primary developments concern the SPH Code: A new stable boundary condition was developed for simulating flows with free surfaces on continuously rough surfaces, including the effects of surface tension. Further developments include injection and runoff boundary conditions, interaction forces to generate surface tension, and the implementation of a no-slip boundary condition. The code was validated with the help of laboratory experiments. To this end, the behaviour of small-scale droplet flows along a synthetic surface, which is interrupted by a horizontal gap, was investigated. In addition, the behaviour of different flow modes (drops, trickles) and the flow rate-dependent transitions between the flow regimes were investigated. These are perfectly in line with the numerical experiments. In further numerical and experimental studies the influence of flow edge conditions on the residence time distribution and the breakthrough curves was clearly shown. Systems with the same fluid input rate but different number of injection points were compared, so that either drop flow or runnel flow prevails. This resulted in contra-intuitive behavior: Systems with predominant drop flow (i.e. lower flow rate per inlet channel) exhibit an increased „bypass“ behaviour, i.e. fluid initially flows preferably over the horizontal gap opening. For runnel flows, the horizontal gap acts as a much more effective buffer, and is usually almost completely filled up until corresponding capillary pressures are built up and then the discharge is increased in the vertical direction. An analytical solution was developed for the system, which attributes these processes to classical piston flow and then a change to a washburn regime. The effect of roughness on the flow and wetting behavior (macroscopic contact angle) was initially investigated on standardized roughness geometries using SPH simulations. Especially on microscopically hydrophilic surfaces, rough geometry elements cause deviations in the fluid-solid interaction surfaces (Cassie, Wenzel, Cassie-Wenzel regime) and can thus lead to an increase in macroscopic contact angles up to hydrophobic behavior. The effect of the orientation of roughness relative to the direction of flow was also investigated. It was shown that classic capillary and bond number scaling models remain valid even for rough surfaces. For systems in which the preferred direction of roughness coincides with the direction of flow, a drastic increase in capillary numbers could be shown, which is due to lotus-effect-like processes. In the case of a vertical orientation of the roughness to the flow, flow velocities are significantly reduced.