In enhanced oil recovery (EOR) by fluids injection, capturing and understanding the interfacial interactions at the pore scale and detailing the mobilization of trapped oil have significant scientific and economic implications [1]. In this study, we used microfluidic porous devices to observe and analyse fluids dynamics and displacement mechanisms. We investigated in particular the effects of the viscosity ratio M (viscosity of aqueous phase relative to oil phase) and Capillary Number (Ca) on oil mobilization trends, non-wetting fluid trapping, and oil ganglia characteristics and becoming. Building upon these experimental results, we developed a diffuse interface (phase-field) approach to model the bi-phasic flow behaviour of two viscous immiscible fluids (aqueous solution and oil) in confined domains. The model is founded on a set of partial differential equations (PDEs) consisting of the mass conservation equation of the oil – that includes a convective and a diffusive term – and the mass and momentum conservation equations of the oil-aqueous solution considered as a mixture. All together these equations constitute a Cahn-Hilliard-Navier-Stokes (CH-NS) system of equations. The phase-field approach (CH equations) describes phase separation and evolution, accounting for interfacial energy and phase morphology changes, while the NS equations provide continuum mechanics forces accounting for the effect of capillary forces related to the presence of fluid-fluid interfaces [2]. The weak form of the PDEs is implemented and solved in the open source finite element platform Fenics. Fluids properties (such as viscosity, interfacial tension, etc.) and wetting parameters are beforehand experimentally measured. Different viscosity ratios, M, and Capillary Numbers, Ca, are considered to study how the physics at play is impacted. The numerical results are qualitatively and quantitatively compared with the experimental ones to demonstrate the reliability of the proposed mathematical model.