In this manuscript a mathematical model describing the secondary drying stage of a freeze-drying process is presented. The model consists in governing equations for the transport of an air-vapour mixture in a porous medium. The production of water vapour due to the desorption of bound water is accounted for by means of a source term in the equation for the water vapour concentration. We show how, in the limit of small Peclet numbers, the model can be solved analytically. In addition, we provide with an explicit expression for the total time for the secondary drying stage of the freeze-drying process amenable for real time control applications.