Understanding transport and retention mechanisms in porous media is essential in environmental and industrial processes such as subsurface contamination, water filtration and polymer flooding in oil reservoirs. In this article, new averaged equations for colloid transport and retention in porous media are obtained based on the master equation. In addition, new boundary conditions are discussed and an accurate and robust numerical scheme to evaluate the model empirical parameters is proposed. The numerical scheme, which allows incorporating generalized isotherms and retention kinetics, is validated by comparing the obtained solutions with analytical expressions available in the literature. In addition, good agreement between proposed model and the studied experimental data was observed and allowed concluding that the influence of longitudinal hydrodynamic dispersion on retained concentrations can be neglected for large times (\(T > 1\ pvi\)). Finally, it was shown that transport and retention coefficients (including dispersion coefficient) can be simultaneously obtained by numerically solving the inverse problem for any effluent concentration data, suggesting that tracer injection experiments are not necessary in order to quantify the hydrodynamic dispersion coefficient.

了解多孔介质中的运输和滞留机理对于环境和工业过程至关重要，例如地下污染，水过滤和油藏中的聚合物驱。在本文中，基于主方程获得了胶体在多孔介质中的迁移和保留的新平均方程。此外，讨论了新的边界条件，并提出了一种精确，鲁棒的数值方案来评估模型的经验参数。通过将获得的溶液与文献中可用的分析表达式进行比较，可以验证允许合并等温线和保留动力学的数值方案。此外，在建议的模型和研究的实验数据之间观察到良好的一致性，并且可以得出结论，可以长期忽略纵向水动力分散对保留浓度的影响（\（T> 1 \ pvi \））。最后，结果表明，通过数值求解任何废水浓度数据的反问题，可以同时获得迁移系数和保留系数（包括弥散系数），这表明为了量化流体动力弥散系数而不必进行示踪剂注入实验。