Numerical Simulation Of Two-phase Flow Of CO₂ And Brine Based On Stochastic Partial Differential Equations

Over the past two centuries,the amount of CO₂released into the atmosphere by people using fossil fuels has been increasing,leading to the greenhouse and a variety of natural disasters.As a result,CO₂emissions from the use of fossil fuels have become a major source of climate change.Carbon capture and sequestration?CCS?is one of effective ways to reduce carbon dioxide emissions,especially in the deep brine aquifers.When a part of CO₂is dissolved in brine,the mass transfer occurs because of the different concentrations of CO₂and brine.The mass transfer and the heterogeneous porous structure will result in different flow rates of CO₂,which will lead to advection and diffusion of CO₂.The diffusion and advection of CO₂in heterogeneous porous media are analyzed based on the study of CO₂geological storage in deep brine aquifers.Firstly,the stochastic spatial function based on the CO₂-brine two phase flow mass conservation equation is set up to describe the advection and diffusion of CO₂travel in heterogeneous porous media at steady state flow condition in this paper,.It has been considered the formation parameters of CO₂travel such as permeability,porosity in heterogeneous porous media,and introduced the change of time scale and space scale.The partial differential equation of CO₂under the condition of diffusion and advection in random velocity field is established.Then,the random travel process of CO₂in heterogeneous porous media is quantified by joint probability distributions and joint statistical moments?mean and variance?,and then the diffusion and advection model of CO₂molecules in random velocity field is established under the condition of non-linear and immiscibility in heterogeneous porous media.The micro mechanism of diffusion and advection in heterogeneous porous media is revealed by numerical simulation.Through the ralationship among saturation,capillary pressure and relative permeability,the influence of diffusion and advection is quantitatively analyzed by storage.Finally,the general conclusion of steady state flow of CO₂diffusion and advection in heterogeneous porous media was verified by simulating Sleipner CO₂-brine storage in Norway.The results show that it is more significant to analyze the random flow of CO₂in heterogeneous porous media.