Phase-Field-based Lattice Boltzmann Methods And Numerical Simulation For Pore-Scale Multiphase Flow

Carbon capture,storage and utilization(CCUS)technology is an important choice for China's low-carbon economic development.In particular,carbon dioxide enhanced oil recovery technology can not only achieve large-scale carbon storage,but also meet the practical needs of improving the recovery rate of unconventional oil and gas reservoirs.In the process of carbon dioxide enhanced oil recovery,a key scientific problem is to understand the flow mechanism of multiphase and multicomponent fluids in the pore scale.As it is difficult for laboratory micro-scale experiments to obtain fluid flow information from the micro pores in porous media,pore-scale numerical simulation has become an important tool for investigating the mechanism of multiphase flow in porous media.Among pore-scale numerical simulation methods,the lattice Boltzmann(LB)method has received extensive attention and been widely applied due to its great ability in handling complex geometric of the solid matrix and computational efficiency with natural.However,the existing LB models for two-phase flows still have some shortcomings and deficiencies in terms of phase interface tracking and numerical stability,which need to be solved.Based on theoretical analysis,the present dissertation first develops several LB models based on the phase-field theory,which are then employed to study the two-phase fluid flows at the pore scale to explore the mechanism of improving oil recovery.The main works of the dissertation are summarized as follows:1.A multi-scale expansion analysis of the lattice Boltzmann model for the Cahn-Hilliard(CH)equation is performed to determine the differences between the target CH equation and the recovered governing equation.The higher-order error terms are identified and then the main truncation error is successfully eliminated by introducing a new correction term in the LB model.In addition,considering the facts that a drop can shrink spontaneously or even disappear in phase field model and the importance of wettability for the pore scale simulation,we investigate the influence of wettability on the spontaneous behavior of a drop theoretically and a theoretical relationship between the critical radius of droplet vanishing and the contact angle is built.The theoretical results show that the smaller the contact angle is,the larger the interface thickness is,the larger the computational domain,the larger the critical radius of droplet is.2.In view of the critical influence of surface tension on the interface behavior of two phases and many available surface tension force formulations in phase field LB models,which can be roughly divided into four categories: stress tensor form,potential energy form,pressure form and continuum surface force(CSF)form,the performances of each surface tension force formulation are addressed and compared by a series of benchmark problems.The results show that the potential form is a good choice for steady-state and small surface deformation problems while the stress form is preferred for dynamical problems.3.In view of the facts that the order parameter tends to exceed its physical range and the density ratio is relatively small in simulations,a two-phase LB model with multiple-relaxation-time collision operator is developed based on the CH equation.The proposed model is able to maintain the order parameter in a reasonable range.As a result,the present model can successfully simulate the two-phase flow with density ratio up to 1000 and has a better characteristics of volume conservation.Based on the proposed model,the hydrodynamic behavior of a single droplet through a long channel is investigated.Under the condition of hydrophilic,there are four kinds of droplet break-up behaviors that can be observed on the upper surface,the inner surface and the lower surface of the channel,which leads to the retention of small droplets.The small droplets after the droplet burst in the channel are not affected by the gravitational force and only related to the surface tension and wettability;under the condition of hydrophobic,the droplet cannot break up and always pass through the channel in the considered simulations.4.In view of the partial miscible displacement phenomenon in the carbon dioxide flooding process,a general diffuse interface model for modeling such process is well established.In this model,the evolutions of both component concentration and phase volume fraction are respectively governed by the conserved and non-conserved phase field equations in addition to flow equations.Then a LB model that can recover the correct macroscopic governing equations is developed.The processes of carbon dioxide dissolution in unsaturated solution and precipitation in supersaturated solution are repeated successfully.Finally,the developed model is used to simulate the partial miscible displacement process in both a uniform pore structure and a fracture pore structure obtained from the real core structure,and the effect of carbon dioxide dissolving crude oil and reducing its viscosity on enhancing oil recovery is studied.The results show that the increase of saturation concentration of carbon dioxide in oil phase can effectively improve oil recovery for high permeability and uniform pore structure while has little effect on oil recovery for the low permeability and fracture pore structure.In summary,the present dissertation has improved and developed the current phase field LB models in terms of capturing phase interface accuracy and improving numerical stability.Furthermore,the developed LB models are employed to study the dynamic process of drop passing through the pore throat structure and the displacement process of partially miscible carbon dioxide in porous media.The mechanism of flow at pore-scale is revealed which is helpful for developing new techniques for improving the recovery of unconventional oil and gas reservoirs and the carbon dioxide storage.