Prediction of moisture transfer within material using a classic diffusive model may lack accuracy, since numerical simulations underestimate the adsorption process when a sample is submitted to variations of moisture level. Model equations are always established with assumptions. Consequently, some phenomena are neglected. This paper therefore investigates the impact of improving traditional diffusive models by taking into account additional phenomena that could occur in moisture transport within hygroscopic fibrous materials such as wood-based products. Two phenomena in the porous material are investigated: (1) non-equilibrium behaviour between water vapour and bound water, and (2) transport by air convection. The equations of each model are established by starting from averaging conservation equations for the different species considered within material (water vapour, bound water and air). In addition, the validity of assumptions currently used in the models is verified. Then the three models are compared with experimental data to highlight their capacity to predict both the vapour pressure and the mass of adsorbed water. This comparison tends to show a slight improvement in predictions with the new models. To increase our understanding of these models, the influence of the main parameters characterising phenomena (sorption coefficient, intrinsic permeability, Peclet number and Fourier number) is studied using local sensitivity analysis. The shape of the sensitivity coefficients shows that the first kinetics period is only impacted a little by the non-equilibrium. In other periods, the influence of the diffusion phenomenon represented by the Fourier number is much greater than that of the two other phenomena: advection and sorption. Nevertheless, the sensitivity study shows that these two phenomena have some influence on vapour pressure.