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.

中文翻译：

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孔隙尺度对多孔介质自然对流宏观特性的影响

多孔介质中的自然对流是深部咸水层中 CO 2 长期储存的基本过程。通常，多孔介质中传质的细节是从体积平均的 Darcy-Oberbeck-Boussinesq (DOB) 方程的数值解中推断出来的，即使这些方程没有考虑多孔介质的微观特性。根据 DOB 方程，多孔介质中的自然对流由瑞利数唯一确定。然而，与实验相比，DOB 模拟产生了舍伍德数与瑞利数 ($Ra$) 的线性标度，以获得高值 $Ra$ ($Ra\gg 1300$)。在这里，我们执行直接数值模拟 (DNS)，完全解析孔隙内的流场。我们表明边界层厚度由孔径而不是瑞利数决定，如前所述。大羽和原羽尺寸随着孔径的增大而增加。我们的 DNS 结果显示了高孔隙率下舍伍德数的非线性缩放，对于相同的瑞利数，DNS 预测的舍伍德数在低孔隙率下更高。可以得出结论，舍伍德数的缩放取决于孔隙度和孔隙尺度参数，这与实验研究一致。