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Natural convection in porous media is a fundamental process for the long-term storage of CO 2 in deep saline aquifers. Typically, details of mass transfer in porous media are inferred from the numerical solution of the volume-averaged Darcy–Oberbeck–Boussinesq (DOB) equations, even though these equations do not account for the microscopic properties of a porous medium. According to the DOB equations, natural convection in a porous medium is uniquely determined by the Rayleigh number. However, in contrast with experiments, DOB simulations yield a linear scaling of the Sherwood number with the Rayleigh number ( $Ra$ ) for high values of $Ra$ ( $Ra\gg 1300$ ). Here, we perform direct numerical simulations (DNS), fully resolving the flow field within the pores. We show that the boundary layer thickness is determined by the pore size instead of the Rayleigh number, as previously assumed. The mega- and proto-plume sizes increase with the pore size. Our DNS results exhibit a nonlinear scaling of the Sherwood number at high porosity, and for the same Rayleigh number, higher Sherwood numbers are predicted by DNS at lower porosities. It can be concluded that the scaling of the Sherwood number depends on the porosity and the pore-scale parameters, which is consistent with experimental studies. 

One of the most controversial topics in the field of convection in porous media is the issue of macroscopic turbulence. It remains unclear whether it can occur in porous media. It is difficult to carry out velocity measurements within porous media, as they are typically optically opaque. At the same time, it is now possible to conduct a definitive direct numerical simulation (DNS) study of this phenomenon. We examine the processes that take place in porous media at large Reynolds numbers, attempting to accurately describe them and analyze whether they can be labeled as true turbulence. In contrast to existing work on turbulence in porous media, which relies on certain turbulence models, DNS allows one to understand the phenomenon in all its complexity by directly resolving all the scales of motion. Our results suggest that the size of the pores determines the maximum size of the turbulent eddies. If the size of turbulent eddies cannot exceed the size of the pores, then turbulent phenomena in porous media differ from turbulence in clear fluids. Indeed, this size limitation must have an impact on the energy cascade, for in clear fluids the turbulent kinetic energy is predominantly contained within large eddies. 

Our recently published papers reporting results of Direct Numerical Simulation (DNS) of forced convection flows in porous media suggest that in a porous medium the size of turbulent structures is restricted by the pore scale. Since the turbulent kinetic energy is predominantly contained within large eddies, this suggests that turbulent flow in a porous medium may carry less energy that its counterpart in a clear fluid domain. We use this insight to develop a practical model of turbulent flow in composite porous/fluid domains. In such domains, most of the flow is expected to occur in the clear fluid region; therefore, in most cases the flow in the porous region either remains laminar or starts its transition to turbulence even if the flow in the clear fluid region is fully turbulent. This conclusion is confirmed by comparing appropriate Reynolds numbers with their critical values. Therefore, for most cases, using the Forchheimer term in the momentum equation and the thermal dispersion term in the energy equation may result in a sufficiently good model for the porous region. However, what may really affect turbulent convection in composite domains is the roughness of the porous/fluid interface. If particles or fibers that constitute the porous medium (and the pores) are relatively large, the impact of the roughness on convection heat transfer in composite porous/fluid domains may be much more significant than the impact of possible turbulence in the porous region. We use the above considerations to develop a practical model of turbulent flow in a composite porous/fluid domain, concentrating on the effect of interface roughness on turbulence.