Solvent-based processes have shown great potential for enhancing the heavy oil/bitumen recovery as an alternative to thermal recovery methods. Molecular diffusion coefficient is a key parameter for designing these recovery processes which controls the rate of mass transfer between the solvent and oil phase. The objective of this study is to present an experimental technique and a corresponding mathematical model to determine the diffusivity of a gaseous solvent in heavy oil. Magnetic Resonance Imaging (MRI) is employed to obtain the concentration profiles and a moving mesh technique is used to model the diffusion and swelling process. The volume change due to gas dissolution is included in the model and is tracked by a moving interface and the Vignes equation is used to represent the concentration-dependency of diffusivity. The concentration profiles, swelling rate, concentration-dependent diffusion coefficient, infinite dilution diffusivities, gas solubility at different pressures, and the mixture density are all obtained from the proposed experimental and numerical methodology. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.