This paper is dealing with the mass and heat transport phenomena inside the paper sheet and shows how to deal with shrinkage during drying. The aim is identifying the intrinsic material properties being relevant for internal mass and heat transport. Two approaches will be followed. The first one is based on the description of microscopic mechanisms for mass and heat transport in a porous material, e.g. Darcy flow for liquid due to capillary forces and vapour diffusion due to a vapour pressure gradient, heat flow as a result of the mass flow and a temperature gradient. The contribution of each mechanism in the overall mass resp. heat fluxes is quantified by means of mechanistic transport parameters, such as vapour diffusivity, Darcy permeability, etc. In the second approach the heat and mass fluxes are related to both temperature and moisture gradients and the contribution of each driving force is weighed by a lump transport parameter. Finally, the coupling between the mechanistic and lump parameters is worked out.