The so-called Capmix technique for energy extraction is based on the cyclic expansion of electrical double layers to harvest dissipative energy arising from the salinity difference between freshwater and seawater. Its optimal performance requires a careful selection of the electrical potentials for the charging and discharging processes, which must be matched with the pore characteristics of the electrode materials. While a number of recent studies have examined the effects of the electrode pore size and geometry on the capacitive energy extraction processes, there is little knowledge on how the surface properties of the electrodes affect the thermodynamic efficiency. In this work, we investigate the Capmix processes using the classical density functional theory for a realistic model of electrolyte solutions. The theoretical predictions allow us to identify optimal operation parameters for capacitive energy extraction with porous electrodes of different surface hydrophobicity. In agreement with recent experiments, we find that the thermodynamic efficiency can be much improved by using most hydrophilic electrodes.