Date of Award

August 2021

Degree Type


Degree Name

Master of Science



First Advisor

Krishna M. Pillai

Committee Members

Marcia Silva, Nidal Abu-Zahra, Roshan D'Souza, Qian Liao, Xiaoli Ma


adsorption, contaminant removal, micro-macro coupling, permeability estimation, upscaling, volume averaging


Contaminant transport in porous media is a well-researched problem across many scientific and engineering disciplines, including soil sciences, groundwater hydrology, chemical engineering, and environmental engineering. In this thesis, we attempt to tackle this multiscale transport problem using the upscaling approach, which leads to the development of macroscale models while considering a porous medium as an averaged continuum system.

First, we describe a volume averaging-based method for estimating flow permeability in porous media. This numerical method overcomes several challenges faced during the application of traditional permeability estimation techniques, and is able to accurately provide the complete permeability tensor of a porous sample in a single simulation. Several anisotropic unit cells are created in two- and three-dimensions based on three different parameters: (1) unit-cell size, (2) particle shape, and (3) aspect ratio of the particles inside the unit cells. The results from the volume averaging-based method show good agreement on comparison with the conventional Stokes-Darcy flow technique for the two- and three-dimensional models. We also find that the proposed method provides much faster results than the Stokes-Darcy flow technique for 3D unit-cell geometries.

Next, the cartridges used in commercial water filters are mostly created by packing particles or beads that can be assumed to be of mono-modal size distribution and thus create single-scale porous media. In this thesis, we employ the volume averaging method to upscale the phenomenon of solute transport (which include both diffusion and advection) accompanied with adsorption in such homogeneous porous media. Our novel contribution in this research is the development of a micro-macro coupling between the microscopic and macroscopic length scales, which forms the basis of our macroscale models to reflect the macroscopic behaviour of the system. Two versions of the macroscale models are proposed: (a) complete Volume Averaged Model (VAMc) and (b) simplified Volume Averaged Model (VAMs), which involve two effective transfer coefficients, namely, the total dispersion tensor and the adsorption-induced vector.

Further, in order to investigate one of the critical design parameters of a porous water filter, the 'hydraulic detention time' of the polluted water in the filter, we carry out an extensive numerical investigation of the proposed macroscale models. For this, first we nondimensionalize the pore-scale and macroscale models, which leads to surfacing of two important dimensionless numbers, namely, the Damkohler number and the Peclet number. Next, we develop a 2-D geometry of porous media made up of a chain of 100 identical unit cells for testing the above-mentioned models. The numerical simulations corresponding to the dimensionless pore-scale model, which are referred to as the Direct Numerical Simulation (DNS), and the dimensionless macroscale models, which are referred to as the Volume Averaged Model (VAM), are conducted on the chain-of-unit-cells geometry. The intrinsic average concentration predictions from the macroscale models display excellent results on comparison with the pore-scale (or DNS) outcomes. We also assess the importance of large fluid-solid interfacial area inherent in porous adsorbents by varying the porosity and number of particles inside the artificially-prepared porous-media models. The total dispersion tensor coefficient is validated and found to be in excellent agreement with the literature. Our findings reveal that an increase in the interfacial area of the models leads to higher effective transfer coefficient values.

Last, we perform adsorption experiments in an effort to evaluate the effectiveness of the proposed macroscale models. For this, three trials of column-flow experiment are conducted using an adsorbent made up of functionalized zeolite material to remove phosphorus from synthetically prepared influent. Micro-CT scans of zeolite material are used to develop a unit-cell representative of the pore space inside the actual adsorbent medium. The numerical simulations on the unit-cell provide realistic effective transfer coefficient values; however, a large difference between the concentration predictions from theory and experimental results is noted. The lack of adherence to the time-scale constraints is assessed to be the primary reason behind this discrepancy. We offer different recommendations in order to improve the experiments and accurately gauge the effectiveness of the macroscale models.

Overall, these models have the potential to improve the state-of-the-art technologies for modeling contaminant transport in porous water filters by providing useful recommendations based on numerical simulations, and may be used as a tool for the optimization of the design of porous water filters.