| Fingering refers to interface instability phenomenon. Generally, it is caused by the viscosity ratio between fluids; hence sometimes it is called viscous fingering. Viscous fingering phenomenon is an important feature of multiphase flow. In many engineering applications, such as chemical engineering, oil recovery field and remediation of underground water contamination, it plays a crucial role. For example, in the oil recovery field, the early occurrence of viscous fingering phenomenon will decrease sweep efficiency and result in the breakthrough of displacing fluid, therefore, the oil recovery is reduced. Viscous fingering phenomenon in immiscible displacement is a complex fluid dynamic problem related to the capture of phase interface, multi-component multi-phase flow theory and fluid flow in complex geometry. The various impact factors include the structure of porous media, surface wettability and fluid properties. So far, the intrinsic mechanism is not yet clear, so the study of viscous fingering phenomenon is quite important for both theory and application. In this paper, in order to solve the problem encountered in the simulation of fluids with various density ratio and viscosity ratio by the original Shan-Chen (SC) model, a new scheme of LBM model for multi-component is proposed. In addtion, viscous fingering phenomenon in immiscible displacement in a channel and porous media will be investigated by the lattice Boltzmann method, respectively. The effects of various factors on fingering pattern and displacement efficiency will be studied. The main contents are as follows:(1) Based on the original SC model, a new model for modelling immiscible fluids with various density ratio and viscosity ratio is proposed. In the new model, the incorporation scheme of the force is improved to remove the discretization error. The lattice speeds and lattice speeds of sound for fluid components are different, hence, the streaming distances of fluid components during a time step are different, and they are related to the density ratio. The particle distribution functions at the lattice points are determined by bilinear extrapolation scheme. Besides, the strategy for solid boundary condition is specified. The new model has been validated by modelling the displacement of decane by water at various volume fluxes in a circular tube with various diameters. Compared with the experimental data, the relative errors of average displacing velocity and displacement time are within 3.2%. The new model has a good conservativeness. By choosing suitable boundary condition and properly handling the flow domain, this model can be used to simulate low velocity displacement in which the displacing velocity is smaller than the pseudo-velocity. (2) The effect of various impact factors on fingering phenomenon in a channel are analysed detailly, such as capillary number (Ca), viscosity ratio (M), Bond number (Bo) as well as surface wettability (represented by contact angleθ). Specific focuses are put on the situations whether the effect of gravity is considered or not. The interface patterns are compared under different circumstances. The displacement efficiencies in various conditions are examined by the breakthrough time and areal sweep efficiency. Simulations show that the interface is symmetric to the channel center without consideration of gravity and it is asymmetric when the gravity is taken into account. There is an offset between the interface front and channel center, and the intersections between the interface and channel upper/lower boundaries are different. In the same condition, for M>1, the displacement efficiency decreases when the effect of gravity is incorporated. With the increasing of Ca, Bo and M, the fingering phenomenon becomes more and more obvious. When the contact angle of displacing fluidθ, is larger than 90°, the fingering phenomenon is enhanced, and when the contact angle of displacing fluidθ1 is smaller than 90°, the fingering phenomenon is suspended. The more significant the viscous fingering is, the lower the displacement efficiency is. In conclusion, from the economic benefit, in order to achieve higher displacement efficiency, as for the immiscible displacement in a channel, it is better to maintain small capillary number, small viscosity ratio, small Bond number and small contact angle of displacing fluid.(3) Compared to the situation in a channel, the existence of solid materials makes fingering phenomenon in porous media more complicated. The interface is symmetric when the gravity is ignored, and it is asymmetric when the gravity is considered. The interface front has a tendency of moving along the direction of gravity. In some circumstances, there are isolated droplets of displaced fluid adhering to the solid materials or being trapped in the displacing fluid. The staggered arrangement of solid materials suspends the occurrence of fingering. There is no significant fingering as Ca increases. In the limited viscosity ratio range (M=1～5), due to the constant injecting velocity of displacing fluid and staggered arrangement of solid materials, final interface pattern is similar in the case of M≥3. As Bo increases, the moving downwards tendency of the interface becomes more obvious. The finger front is narrow and long. In the end of displacement, the finger is the most strongest for Bo=0.218～0.229. Accordingly, the isolated droplets of displaced fluid adhering to the solid materials are bigger. No matter the gravity is taken into account or not, the effect of surface wettability on viscous fingering is the same as that in the case of displacement in a channel (enhancing or suspending). The difference is that, when the gravity is considered, there are isolated droplets of displaced fluid adhering to the solid materials which cannot be displaced. For various conditions, the more significant the viscous fingering is, the lower the displacement efficiency is. In the same situation, the existence of gravity decreases displacement efficiency.
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