A note on upscaling retardation factor in hierarchical porous media with multimodal reactive mineral facies

TL;DR

This paper develops a higher-order approximation model to accurately upscale the time-dependent effective retardation factor in hierarchical porous media with multimodal reactive mineral facies, extending previous linear models.

Contribution

It introduces a higher-order approximation for the retardation factor model, enabling accurate scaling for larger variances beyond 0.2.

Findings

The higher-order model accurately recovers previous results for small variances.

The model extends applicability to variances up to 1.0.

Recalculation confirms the model's improved accuracy.

Abstract

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