The article reports a numerical study of entropy generation due to the double-diffusive natural convection in a 3D heterogeneous porous cubic saturated with power-law fluids and submitted to horizontal thermal and concentration gradients. The governing equations based on a generalized non-Darcy model are solved by using the compact high order finite volume method. This approach is devised to detect the effects of the heterogeneity level, the buoyancy ratio and the porous thermal Rayleigh number on the fluid flow and its associated irreversibility characteristics. The results show that the mean Nusselt and Sherwood number reduce, while the total entropy generation increases, as the level of heterogeneity increases by the exponential distribution of the permeability; the mean Nusselt, Sherwood number and total entropy generation increases as the porous thermal Rayleigh number increases or the buoyancy ratio increases (decreases) for the thermal dominated flow (solutal dominated flow) by the heat and mass transfer performance. Apart from that, our numerical tests of the approach on the shear-thinning, the Newtonian and shear-thickening fluids show that the impacts of different power-law indexes on the entropy generation due to fluid friction, heat and mass transfer are mainly manifested in rheological properties, which elucidate that the shear-thinning fluids is more effective than shear-thickening fluids. The studies may help us establish a physically reasonable methodology to systemically assess fluid flow and energy consumption in heterogeneous porous media in the real world. (C) 2016 Elsevier Ltd. All rights reserved.