Reactive transport in saturated/unsaturated porous media is numerically upscaled to the space-time scale of a hypothetical measurement through coarse-grained space-time (CGST) averages. The reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged microscopic quantities. The latter are further used to verify the CGST-GRW numerical approach. The upscaling approach is applied to biodegradation processes in saturated aquifers and variably saturated soils and the CGST averages are compared to classical volume averages. One finds that if the process is characterized by slow variations in time, as in homogeneous reaction systems, the differences between the two averages are negligible. Instead, the differences are significant and can be extremely large in simulations of time-dependent biodegradation processes in both soils and saturated aquifers.

翻译：饱和/非饱和多孔介质中的反应输运过程，通过粗粒化时空（CGST）平均被数值升尺度至假想测量的时空尺度。反应输运在细粒度达西尺度上建模，采用参与反应的实际分子数，这些分子经历由全局随机游走（GRW）模拟描述的平流与扩散运动。CGST平均验证类似于局部平衡方程的恒等式，使我们能够根据平均微观量推导出流速和本征扩散系数的表达式。后者进一步用于验证CGST-GRW数值方法。该升尺度方法被应用于饱和含水层和变饱和土壤中的生物降解过程，并将CGST平均与传统体积平均进行比较。研究发现：若过程以时间缓慢变化为特征（如均质反应系统），两种平均之间的差异可忽略不计；而在土壤和饱和含水层中模拟时间依赖型生物降解过程时，差异显著且可能极大。