Abstarct: In this thesis, simulation of single and multi-components, multi-phase flows with lattice Boltzmann method (chan & chen model) are discussed. In the first part, we focus on devel-oping of chan & chen model to simulate flows with high density ratios. To achieve this goal non-ideal equation of state such as Redlich-Kwong, Carnahan-Starling and Peng-Robinson are used. The results of the use of different equations of state, in terms of spurious currents are illustarated and the coexistence curves obtained from the simulations are compared with the theoretical curves predicted by the Maxwell equal-area construction. All the equations of state have better results than chan& chen equation of state in decreasing spurious cur-rents and receiving high density ratio. To validate the written code and show the capabili-ties of the developed method in simulation of multi-phase fluids with high density ratios, several two phase physics such as coalescence of two droplets and free fall of a drop on the surface with different wettability property are simulated; results were according to the pre-vious ones that were done by other researchers. Furthermore, penetration pattern and rate of droplet in laxyered porous media with hydrophilic and hydrophobic surfaces is studied with R-K equation of state. The influences of porosity and hydrophillicity property of surface were investigared. In second part, simulation of multi component multi phase flows with a different ap-proach has been done; the concentration is on a specific issue, drop penetration into the po-rous medium. Porous medium has uniqe characteristics; it is generated by locating square obstacles randomly that the porosity is controllable in each laxyer. In this study, the regime of drop penetration in laxyered poros medium is investigated by using phase diagram and viscous fingering and capillary fingering regimes are observed and studied. The effect of porosity and hydrophilic/hydrophobic surface on penetration rate and penetration pattern is studied. The results show in hydrophobic situation rate of penetration for porosity more than 0.75 is higher, so that penetration rate in hydrophobic situation is considered as ideal situation. In that case fluid just pass the cavities like fingers and go ahead in vertical direc-tion so the pattern of penetration is finger type, as in hydrophilic one the fluid go ahead colony and because of penetration in cross direction, the rate of penetration is lower. The pattern of penetration is piston-type regime. Then, some solution is given to close the pene-tration rate to ideal one; So, moreover change the porosity laxyer, a new parameter has been defined as hydrophobicity coefficient which could be adjusted in different laxyer. The effect of laxyers with different hydrophobicity coefficient on penetration rate and pattern is con-sidered. The comparison between results show there are the layout of porosity laxyer and hy-drophobicity coefficient that make the penetration rate close to ideal condition. By splitting the laxyers in some parts and adjusting this coefficient the direction of fluid was determined and the fluid is guided in specified path, which has a lot important in oil exploitation, fuel cell industry, enviromental issues like penetration of rain water in soil and to prevent sedi-mention in chimneys and tubes and i.e.