# questions about two phase LBM

hi everyone:
I want to write a two-phase LBM code. I intend to use two phase LBM code to calculate relative permability and do some drainage simulation. But there are some details I do not understand. As I know there are three two phase LB method. 1 Rothman Keller color model 2 shan chen model 3 free energy method.
Firstly, I wonder to know how to initialize two distribution function fr and fb.As for a single phase LBM, just set rho equal to 1,and each direction of distribution function value is 1/9 for D2Q9 case. While, I do not know how to deal with two phase LBM. I think one pore node can contain both fr and fb because it will make the code easier. For example, a matrix value of 2D flow field is (0 means pore 1 means gain), porosity is 60%,we can set fr fb both  for D2Q9 case. But actually one pore contain either fulid1 or fulid2, so is that means one pore node just contain one distribution function, so confused. Secondly, the ratio of fluid1 to fluid2 is 1, which means the saturation of both fluid1 and fluid2 is 0.5. How to set that, is that also use the distribution function. Thank you for helping.