Bottom-up theoretical frameworks for upscaling transient mass transport in porous media

Hamid, Md Abdul

Permalink

https://hdl.handle.net/2142/129855 Copy

Description

Title

Bottom-up theoretical frameworks for upscaling transient mass transport in porous media

Author(s)

Hamid, Md Abdul

Issue Date

2025-07-13

Director of Research (if dissertation) or Advisor (if thesis)

Smith, Kyle C

Doctoral Committee Chair(s)

Smith, Kyle C

Committee Member(s)

• Ewoldt, Randy H
• Pearlstein, Arne J
• Valocchi, Albert J

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Porous Media
• Transient Transport
• Upscaling
• Bottom-Up
• Hydrodynamic Dispersion

Abstract

Solute transport in porous media plays a fundamental role in a wide range of engineering, environmental, and biomedical systems. Understanding how dissolved species move through these complex structures, where advection, diffusion, and interfacial reactions all contribute, is essential for optimizing the performance of electrochemical reactors, groundwater remediation technologies, and biological tissue scaffolds. However, the multiscale nature of these transport phenomena presents significant modeling challenges. Conventional upscaling approaches often rely on empirical correlations and time-invariant effective parameters, which overlook critical pore-scale dynamics, particularly under transient conditions. This thesis addresses these shortcomings by developing bottom-up theoretical frameworks that systematically link pore-scale transport physics with macroscopic behavior under time-varying conditions. The first framework begins with a pseudo-steady approximation suitable for saturated porous media experiencing slow transient relative to pore-scale diffusion. This formulation is developed using a representative unit cell under the assumption of negligible macroscopic diffusion (i.e., dispersion). Its validity is assessed using nondimensional parameters (Péclet, Sherwood, and Fourier numbers) through dynamic analysis of redox flow battery cycles. The reactive liquid/solid interfaces are modeled using a spatially uniform, time-dependent Dirichlet boundary condition, justified under the assumption of a large Damköhler number (Da≫1). Additional validity criteria are established for three classes of electrochemical reactions, accounting for variations in kinetics and stoichiometry. Building on this foundation, a second framework adopts a spectral bottom-up approach to study porous systems where transient effects are significant, but macroscopic concentration gradients remain negligible. The mass conservation equations are transformed into the frequency domain using Fourier transformation, resulting in two frequency-dependent, volume-averaged transport coefficients interpreted as transfer functions (TFs). The first, the spectral Sherwood number, quantifies interfacial reactive flux. The second TF captures deviations from ideal advection due to microscale variations in local velocity and concentration fields. These transfer functions are integrated into a bottom-up transient model (B-UTM) of a redox flow cell to simulate dynamic polarization behavior. The B-UTM exhibits improved agreement with experimental data and outperforms conventional models that rely on a constant Sherwood number. Additionally, it enables simulation of near- and over-limiting current operation, which traditional models cannot capture. A regime map generated from the model illustrates that short-duration over-limiting operation is feasible, suggesting a strategy to enhance charge capacity in redox flow battery systems under transient loading. To overcome the limitation of assuming negligible macroscopic gradients, a third theoretical framework, the omni-temporal theory, is introduced. This framework extends the frequency-domain model by incorporating macroscopic diffusion (i.e., dispersion) through rigorous volume averaging. A key element of the theory is an ansatz that assumes a linear relationship between local concentration deviations and the macroscopic concentration gradient. This leads to two closure problems, the solutions of which enable systematic upscaling. Three frequency-dependent, Darcy-scale transport coefficients are derived and interpreted as transfer functions: an effective reaction rate TF, an advection suppression TF, and an effective diffusion tensor. The first two extend previous transfer functions to systems with non-negligible macroscopic gradients. The diffusion tensor captures the combined effects of molecular diffusion, dispersion, and tortuosity. Notably, the framework reveals that tortuosity is not solely a geometric property but emerges dynamically from microscale transport interactions that depend on frequency. The omni-temporal theory is validated by numerically solving the frequency-dependent advection–dispersion–reaction equation and benchmarking its predictions against microscopically resolved direct numerical simulations (DNS). The model demonstrates excellent agreement with DNS and outperforms traditional models that use time-invariant diffusion coefficient. It accurately captures transient dispersion in both pre-asymptotic and asymptotic regimes, offering a unified multiscale framework for modeling time-dependent transport in porous media. The modeling approaches developed in this thesis evolved from pseudo-steady to spectral and finally to omni-temporal formulations, each providing increased accuracy and broader applicability across a range of transient regimes. These frameworks enable reliable simulation of time-varying transport processes and are applicable to systems including electrochemical devices, CO₂ sequestration, enhanced oil recovery, drug delivery, and contaminant migration in aquifers. Furthermore, the theoretical frameworks developed in this study can be extended to heat transfer problems by leveraging the mathematical analogies between heat and mass transport.

Graduation Semester

2025-08

Type of Resource

Thesis

Handle URL

https://hdl.handle.net/2142/129855

Copyright and License Information

Copyright 2025 Md Abdul Hamid

Owning Collections