Then we have the mass balance equation for water species, we have liquid and vapour, so we have again the terms as before, change of degree of saturation, solid deformation, temperature, compressibility, then we have the diffusive flux and the terms which come in from something that is almost a mass balance equation.
Here appears for instance the thermal expansion coefficient, which is an average value of the contribution of vapour and water.
Finally we have the energy balance equation for the whole system.