Multiphase Flow Simulation using Lattice Boltzmann Model incorporating a Crossover Equation of State

Abstract

Multiphase flows are involved in many practical applications such as CO2 injection in porous media initially saturated with brine water, spray combustions, oil and gas, nuclear power plants and other industrial and agricultural processes. Conventional Computational Fluid Dynamics (CFD) techniques, which assumes the fluid as a continuum, faces challenges in tracking the interface in multiphase flows. This is majorly due to the fact that the generic phase interface forms and is maintained because of inter-molecular forces that originate at meso- or micro-scales. An effective representation scale of such forces at continuum can be achieved only by models that come at a high computational cost. In this work, we use a multiphase Lattice Boltzmann Model (LBM) which offers a meso-scale solving framework with the purpose to study multiphase systems and the corresponding fluid behavior at the given conditions in pore-scale domains. More specifically, we apply the multiphase Shan-Chen’s pseudopotential Lattice Boltzmann Model due to its proven ability to capture the sharp interface in intricate microscopic domains and to its efficient parallelization. In pseudopotential LBM, the phase separation is maintained thanks to the introduction of a body force depending on the gradient of a scalar function, called effective mass. By choosing the specific forms of the effective mass, different equations of state (EoS) can be incorporated into the model, including the most popular cubic ones such as the Van der Waals, the Peng-Robinson or the Carnahan-Staring. Such cubic EoS are known for their high accuracy when applied to fluids at subcritical conditions. However, these EoS fail in representing the non-analytical behavior of a generic fluid in the vicinity of the critical point evidenced by long-scale density fluctuations. This limitation can be amended by using a crossover formulation of the considered EoS. The crossover EoS uses non-analytic scaling laws asymptotically close to the critical point, while away from the critical point it becomes the original classical EoS; besides in the limit of zero density it reproduces ideal gas behavior. Accurate prediction of fluid properties at super/near-critical conditions is important for different applications including the flow in porous media where surface tension plays a major role.In this thesis, a crossover formulation of a generic EoS is incorporated into the pseudopotential LBM. That significantly extends the capability of pseudopotential LBM to model fluid properties closer and above the critical point. This work also shows simulation results for multicomponent flows in complex geometries. This is motivated by the goal to build a model which can accurately predict the supercritical CO2 flow in brine-saturated porous media, as found in deep saline aquifers. Specifically, two-component flow in a T-mixer passing cylindrical obstacles and immiscible multicomponent flow in a channel to study fingering effects are presented.