In this work, a numerical model for isothermal liquid-vapor phase change (evaporation) of the two-component air-water system is proposed based on the pseudopotential lattice Boltzmann method. Through the Chapman-Enskog multiscale analysis, we show that the model can correctly recover the macroscopic governing equations of the multicomponent multiphase system with a built-in binary diffusion mechanism. The model is verified based on the two-component Stefan problem where the measured binary diffusivity is consistent with theoretical analysis. The model is then applied to convective drying of a dual-porosity porous medium at the pore scale. The simulation captures a classical transition in the drying process of porous media, from the constant rate period (CRP, first phase) showing significant capillary pumping from large to small pores, to the falling rate period (FRP, second phase) with the liquid front receding in small pores. It is found that, in the CRP, the evaporation rate increases with the inflow Reynolds number (Re), while in the FRP, the evaporation curves almost collapse at different Res. The underlying mechanism is elucidated by introducing an effective Péclet number (Pe). It is shown that convection is dominant in the CRP and diffusion in the FRP, as evidenced by Pe > 1 and Pe < 1, respectively. We also find a log-law dependence of the average evaporation rate on the inflow Re in the CRP regime. The present work provides new insights into the drying physics of porous media and its direct modeling at the pore scale.