# Non-monotonic solutions for colloid-transport of size-distributed particles in porous media

## TL;DR

This paper introduces a novel 3x3 system of equations to explain non-monotonic retention profiles in colloid transport through porous media, validated by laboratory data and enabling better field-scale predictions.

## Contribution

It develops an exact upscaling method and a new analytical model for colloid transport with distributed particle properties, explaining NRP phenomena.

## Key findings

- Successfully matched laboratory NRP data with the upscaled model.
- Validated a 5-parameter model for binary colloids.
- Provided a simplified analytical solution for parameter tuning.

## Abstract

Non-monotonic retention profiles (NRP) have been observed in numerous studies of colloidal-nano flows in porous media. For the first time, we explain the phenomenon by distributed particle properties (size, shape, surface charge). We discuss colloidal-nano transport with fines attachment considering stochastically distributed filtration coefficient (particle attachment probability) and the influence of area occupation by particles on the rock surface. The distributed dynamic system allows for exact averaging (up-scaling) yielding a novel 3x3 system of equations for total concentrations. Besides the traditional equations of particle mass balance and capture-rate, the novel system contains a third independent equation for kinetics of site occupation during particle attachment. Ten laboratory tests exhibiting NRP have been successfully matched by the upscaled system for binary colloids. Ten laboratory tests with 7-parametric data arrays have been successfully matched by the 5-parameter model, which validates the model. The tuned parameters belong to their common intervals. The laboratory data tuning was significantly simplified by deriving the exact solution of upscaled equations. These results provide valuable insights for understanding the transport mechanisms and environmental impact in colloidal-nano flows exhibiting NRP. Besides, the upscaled system and the analytical model for 1D transport facilitate interpretation of the laboratory coreflood data and allows for the laboratory-based predictions for 3D colloidal-nano transport at the field scale.

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Source: https://tomesphere.com/paper/1905.08035