The momentum transfer across fluid interfaces in multi-phase flow leads to a non-negligible viscous coupling effect. In this study, we use the lattice Boltzmann method (LBM) as a direct simulator to solve the three-phase flow at pore scale. The viscous coupling effects are investigated for various fluid configurations in simple pore geometries with different conditions in terms of saturation, wettability and viscosity ratio. It is found that the viscous coupling effect can be significant for certain configurations. A parametric modification factor for conventional three-phase conductance model is then proposed to estimate the viscous coupling effect. The modification factor as a function of viscosity ratios can be easily incorporated into existing pore network model (PNM) to eliminate errors from viscous coupling effect. Moreover, an elegant approach using machine learning technique is proposed to predict the multi-phase permeability by a trained Artificial Neural Network (ANN) from the direct simulation database. Such data-driven approach can be extended to develop a more sophisticated PNM for a better prediction of transport properties taking account of the viscous coupling effects.