We present a model for upscaling the time-dependent effective retardationfactor in hierarchical porous media with multimodal reactive mineral facies.The model extends the approach by Deng et al. (2013) in which they expanded aLagrangian-based stochastic theory presented by Rajaram (1997) in order todescribe the scaling effect of retardation factor. They used a first-orderlinear approximation in deriving their model to make the derivation tractable.Importantly, the linear approximation is known to be valid only to variances of0.2. In this article we show that the model can be derived with a higher-orderapproximation, which allows for representing variances from 0.2 to 1.0. Wepresent the derivation, and use the resulting model to recalculate thetime-dependent effective retardation for the scenario examined by Deng et al.(2013).
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