Simulation of DNAPLs migration in saturated porous media by means of Lattice Boltzmann Models

The aim of the research is to implement a numerical model inspired by the Lattice Boltzmann (LB) theory able to simulate the complex scenario of contamination of DNAPLs (Dense Non Aqueous Phase Liquids) in saturated porous media. Groundwater contamination is nowadays recognized as a serious environmental problem. Among different polluting substances, the contamination by NAPLs continues to persist as a significant problem in industrialized nations. More specifically, an accidental release at the ground surface of DNAPLs, which include a variety of organic compounds denser than water, can lead to long-term contamination of both the unsaturated and saturated zones. Once released, the DNAPLs tend to migrate mainly vertically in the subsurface under gravity and capillary forces. Since they are slightly soluble in both water and air, they can exist in the subsurface as a separate and immiscible fluid phases and migrate to significant depths below the water table giving rise to aqueous phase plumes depending on the slow dissolution kinetics with persistence of the source for a long period. Furthermore, during DNAPLS migration in both unsaturated and saturated media, DNAPLs can be trapped by capillary forces in the porous medium (i.e. residual DNAPLS saturation). Predicting the source localization, often unknown, and the fate of these organic chemicals in the subsurface is challenging. Because of the difficulty in defining the separate phases migration in porous media and the further complication of the soil heterogeneity, a significant effort has been carried out for the investigation of DNAPLs motion and transport by means of experimental tests and image analysis and fate and transport modeling mainly of the dissolved phases. Nevertheless, further effort is requested to model the separate phase motion in porous media. On the basis of this context, numerical methods can be a support for understanding and investigating the fluids behavior in complex systems such as porous media. Different approaches to modeling flows through porous media can be considered. The classical macro-scale multiphase models however do not explicitly account for many important physical phenomena in which the phases are involved. As an alternative, a mesoscopic model known as Lattice Boltzmann (LB) has been successfully applied to saturated porous media and it has been widely used for its ability to deal with complex geometries as well as its capacity to simulate fluid flow and transport at the pore-scale. The LBM originates from the kinetic theory of gases and represents the microscopic phenomena by means of a statistical (macroscopic) description. The LBM has been shown to recover the conservation laws of mass, momentum and energy and the CFD community agrees that it has reached an high degree of maturity to solve the Navier- Stokes equations for incompressible fluids in single and multiphase environments. Compared to traditional CFD, the LBMs lead to an easier implementation of multi-phase and multi-component flows and they are applied in many fields such as geologic storage of CO2, Petroleum Engineering or reactive and melting/dissolution phenomena. Even more dealing with multiphase fluids, LBMs provides several advantages compared to the traditional CFD, such as the ability to model the interface dynamics between the different phases and to simply handle the forcing terms involved in the non- wetting phase migration in a porous media e.g. capillary forces, viscous forces and buoyancy forces. In the thesis, a multiphase multicomponent LB model is therefore presented to simulate DNAPLs migration in saturated porous media. Once described the main DNAPLs physical-chemical properties and the multiphase multicomponent LB theory, the implemented model is validated by means of different analytical solutions. Firstly, the interfacial tension phenomenon is analyzed by means of the bubble coalescence and the spinodal decomposition simulations: a sharp interface of few lattice nodes thickness is present between the two fluid phases in function of the tension parameter. The model has proved to recover the Young-Laplace Law, which correlates the pressure difference (at equilibrium) between the regions inside and outside a bubble of fluid 1 surrounded by the fluid 2, to 1/R, where R is the radius of the bubble. Then, the wettability effects are analyzed and validated by determining the contact angle measure and comparing it with the analytical solution in Huang et al. (2007). Finally, the multiphase Poiseuille flow is simulated and compared to the results obtained from Dou et al. (2012) .Different simulations varying the forces applied to the two fluids are then carried out to investigate the impacts of the drag forces, the viscosity effects and the velocity profiles in the channel. Regarding the simulations of the DNAPLs migration in saturated porous media, the results obtained aimed to investigate the influence of the gravity, viscous and capillary forces on DNAPLs motion. Specifically, the role of these forces is characterized by means of different dimensionless numbers, which vary during the conducted simulation tests; the simulations results confirm that, once the DNAPL is released, an increase in contaminant amount and a more radial migration of DNAPL occurs in proximity of the release point when the capillary number “Ca” (ratio between the viscosity and the capillary forces) increases. Contrarily, when the Bond number “Bo” (ratio between the buoyancy and the capillary forces) exceeds the “Ca” number, the gravity assumes a “destabilizing” role leading to the formation of gravity driven fingers. The influence of the hydraulic gradient on DNAPLs migration is also investigated. When a hydraulic gradient is applied, the separate phase shift towards the water flow direction occurs and the pooled DNAPL accumulated above the fine lenses is less. However, the DNAPL phase is also able to move backwards the flow direction when the hydraulic gradient does not let it to exceed the capillary pressure between the pores situated downgradient, explaining the not totally removal of pools over the fine lens even with higher hydraulic gradients. Finally, “trapped DNAPLs” are present: the gravity-driven fingers extend between the pores until they are too long and break. The disconnected mass can be immobilize as blobs and ganglia for the capillary forces. It can be concluded that the development of a model that reproduces the motion of immiscible fluids starting from the microscale- mesoscopic scale is of particular interest and importance. On one hand, it can be useful to investigate the DNAPLs scenario of contamination as well as the reactions and physical microscale processes that significantly influence their macroscale behavior; on the other hand, it is worth to underline its potential use as a tool to support any projects of environmental remediation, in which the identification of the source of contamination and the prediction migration dynamics of contaminants in porous media are essential in selecting the best remediation technology to apply. Although further research and investigation are needed to simulate the DNAPLs migration paths in real contaminated sites, the LB method can provide good results in such a field. The model can therefore be applied to investigate the migration behavior of these separate phases in saturated porous media. However, further effort has to be spent in order to provide a tool able to simulate greater contaminated domains: the potential use of upscaling techniques, without losing the intrinsic microscopic information provided by the LB model, can be suggested.