A two-equation continuum model is developed to simulate the mass transfer in drying porous media. The main goal is to capture the so called non-equilibrium effect. To this end, we operate in a regime where the liquid phase is immobile so that non-equilibrium mass exchange between liquid and vapor phase dominates. The formulation of the model relies on an upscaling technique. This notably permits to formulate the non-local equilibrium phase change term on a firmer basis. The upscaling also indicates that there is no reason to consider an enhancement factor in the vapor diffusion model. The macroscopic model parameters are determined from pore network drying simulations. The same simulations are also used as a reference to compare with the predictions of the non-local equilibrium continuum model. The solution of the two-equation continuum model proves that this model simulates the non-local equilibrium effect with reasonable accuracy. Also, the simulations indicate that the non-local equilibrium effect is especially significant at the porous medium surface.