The aim of this work is to provide closure laws for a macroscopic model of the heat and momentum transfer of real rock packings. We use X-ray nanotomography to obtain the geometry of two real rock packings (basalt and gravel). To address preferential flow paths on non-periodic REV, we have developed a method to properly extract closure laws on non-periodic REV from thermally fully developed pore-scale flow simulations. Several pore-scale simulations are performed over a range of Reynolds numbers (5–243) with a Prandtl number of 0.7. Then there are proposals for closure laws for real rocks, which are of completely arbitrary shape. These laws are based on a Nusselt number correlation and a dimensionless drag force correlation extracted from the pore scale simulations. The Nusselt number correlation is an extension for arbitrary shapes, i.e. real rocks, of the one proposed by Sun et al. (2015). The dimensionless drag force correlation is an original expression in excellent agreement with the experimental datas of Allen et al. (2013). The results support the hypothesis that the mean Sauter diameter is a key parameter that captures the similar behaviour of real rock packings, either for heat or momentum transfer. As this parameter cannot be replaced by other characteristic lengths in the closure laws, it needs to be properly evaluated, for example using nanotomography. For optimising the design of real rock-packed beds, the proposed closure laws allow accurate upscaling of heat transfer and pressure losses.