  Multi-component lattice Boltzmann models operating in a wide range of fluid
viscosity values are developed and examined. The algorithm is constructed with
the goal to enable engineering applications without sacrificing simplicity and
computational efficiency present in the original Shan-Chen model and D3Q19
lattice scheme. Boundary conditions for modeling friction and wettability
effects are developed for discrete representation of surfaces within a
volumetric approach, which results in accurate flow simulation in complex
geometry. Numerical validation of our models includes comparison to previous
studies and analytical solutions. The results are shown to be robust and
accurate up to an extremely small kinematic viscosity value of $0.0017$ lattice
units and the extremely high ratio of components' kinematic viscosities of
hundreds and up to a thousand. This improvement is significant compared to
previous studies with Shan-Chen model \cite{2013_Yang,2004_Kang,2010_Dong}, in
which reasonable accuracy was kept only at the viscosity ratio up to 10 in the
Poiseuille flow and the fingering simulation.
