Convective drying at the pore scale is modelled using a two-component two-phase pseudopotential lattice Boltzmann model (LBM). Two lattice Boltzmann equations are solved, one for liquid water and its vapour and one for dry air. Water vapour is assumed to be well mixed with air forming wet air, while air can also be dissolved in liquid water at low concentration. The approach is shown to be able to model the binary diffusion of vapour and air in the gas phase following Fick’s law. Numerical stability is guaranteed using the lattice Boltzmann cascaded collision operator, which also provides flexibility to vary the mass fraction of water vapour from 2% up to 90% of the gas mixture. Contact angles can be chosen in a wide range extending a single-component approach to two-component systems. The model is validated based on microfluid drying experiments showing good agreement. Convective drying of a dual-porosity medium is simulated blowing drier air over the surface of the medium. We observe two drying regimes, a first drying period at a higher drying rate followed by a second drying period at reduced drying rate. The transition from the first to the second period is observed when capillary pumping from large pores to fine pores at the surface fades out. Explorations varying inflow air velocity (Re number), vapor concentration and contact angle allow defining a universal law relating the average evaporation rate during the first period to the environmental parameters and fluid-solid wetting properties. The influence of different dual porosity arrangements on drying rate is analyzed. Finally, a pore-network toy model is developed that allows designing the drying characteristics of porous media based on the choice of their pore volume distribution.