Development of lattice Boltzmann CO2 dissolution model
In this study, a novel lattice Boltzmann model (LBM) of CO2 dissolution at porous scale is proposed and developed to predict the CO2 dispersion and dissolution in geo-formations. The developed LBM dissolution model consists of an interfacial momentum interaction model, a mass transfer model and a convection (advection) model. Shen-Chen’s pseudopotential model using Equation of State (EOS) of real fluids is tested for momentum interaction model. It is found that a sharp interface can be maintained by optimizing the interaction strengths of two fluids with minimum numerical diffusion in the interfacial momentum interaction model. This makes it possible to model physical diffusion and interfacial tension individually. A new diffusion force, describing the particle diffusion driving by chemical potential at given solubility, is proposed for mass transfer model by applying the interparticle interaction pseudopotential concept. The dissolution is governed by coupling mechanism of diffusion and convection. The interface between the solute of CO2 and solvent water is monitored by the solubility, which changes and indicates the moving of interface as CO2 dissolving. The solution is considered as the mixture of dissolved CO2 and water. Instead of using an additional Lattice that is requested by the existed LBM, the further dispersion of dissolved solutes is attached to the Lattice of water, by which the cost of computing memory size and time is significantly reduced. The developed LBM dissolution model is calibrated by the data from Lab experiment of dissolution of CO2 droplet in water at a state of CO2 geological storage about 1000m depth. The calibration is made by comparison of simulation results with the data, in terms of the shrinking rate of CO2 droplet and the concentration distribution of dissolved CO2 in the solution layer. As the whole, the numerical predictions are well agreement with those of lab experiment. The developed model is then applied to investigate the mechanism of dispersion and dissolution of CO2 droplet in channels at pore scale, in terms of the effects of the Eo number, channel width and channel tilt angle. It is found under the state at 1000m depth that it is difficult for a dissolving CO2 droplet, unlike that of an immiscible droplet, to reach to a ’terminal velocity’. Because of the shrinking, dissolving CO2 droplets accelerate from a quiescent state to a maximum velocity and then decelerate in the channels. The ratio of droplet diameter (Do) to channel width (Lx), M=Do/Lx, and the inclination are the parameters that significantly affect the dynamics of dissolving CO2 droplets. The smaller the channel width or the tilt angle of the pores of the geoformation, the slower of stored CO2 can penetrate vertically and dissolve out. While, as the channel width increases to provide enough space, M<1, the shrinking rate is independent of the channel width and wobbling of droplets is observed at the region with the Re number of 300-600 and the Eo number of 20-43. The interactions of droplets in the channels (M=1 and M=0.3) are investigated by simulating of a pair of droplets dispersion and dissolution, with an initial distance of 4.5 times of droplet diameter. Comparison is made to that of single droplet in terms of the rising velocity and shrinking rate. It is found that the shrinking rate of the upper droplet is larger than that of the following droplet when the following droplet moves into the solution field of the upper droplet. The following droplet rises, when M=1 and M=0.3, faster than that of the upper droplet and also than that of the single droplet under the same conditions. The coalescence of two droplets is observed in the channel at M=0.3, which is due to the action of tail vortex of the upper droplet on the following droplet. The following droplet accelerates at a different wobbling frequency with that of the upper droplet. As the implication in model development, in term of numerical stability, the so called ’non-linear implicit trapezoidal lattice Boltzmann scheme’, proposed by Nourgaliev et al. , is re-examined in order to simulate the large density ratio of two-fluid flows. It is found from the re-derivation that the scheme is a linear scheme in nature. Therefore, the re-derived scheme is more efficient and the CPU time can be reduced. The test cases of the simulation of a steady state droplet using SC EOS show that re-derived scheme improves the numerical stability by reducing the spurious velocity about 21.7% and extending the density ratio 53.4% as relaxation time of the improved scheme is 0.25, in comparison to those from the traditional explicit scheme. Meanwhile, in the multicomponent simulation, with the same density distribution at steady state, the improved scheme reduces both the magnitude and spreading region of the spurious velocity. The spurious velocity of the improved method reduces approximate 4 times than that of the explicit scheme.