Doctor of Philosophy (PhD)


Craft & Hawkins Department of Petroleum Engineering

Document Type



Nanomaterials have recently gained much interest in the field of petroleum engineering and environmental engineering. Understanding the particle transport mechanisms in geological porous media is important to design fit-for-purpose nanomaterials and certain operating parameters for practical usage of those materials. It has been known that natural rock has multi-scale porosity (macroporosity and microporosity) in nature. The microporosity can have a strong impact on the flow and mass transport, but the microscale physics and macroscopic consequences remain poorly understood.

The first part of this dissertation introduces a new higher-order, locally mass conserving FEM method. Stokes equation and Darcy equation are solved for macroporosity and microporosity, respectively. Thereafter, a generic Eulerian-Lagrangian approach is developed to simulate solute (massless particles) transport within a FEM velocity field defined in an underlying mesh. The developed numerical models are implemented into a CPU code for fluid flow and a GPU code for particle tracking. Utilizing the developed numerical models, several direct numerical simulations are conducted to elucidate solute transport and mass transfer characteristics in synthetic multi-scale porous media under various pore structures and Peclet numbers. Finally, further comparative simulations between the micro-continuum approach and DNS are performed to quantify the applicability and limitations of the micro-continuum approach for simulating solute transport in multi-scale porous media.

Results demonstrate that the conservative, accurate, and efficient Eulerian–Lagrangian approach developed in this work, offers a compelling alternative to existing numerical methods to simulate solute/particle transport problems in multi-scale porous media. Also, the pore-scale mechanistic study of solute transport in multi-scale porous media sheds new light on various aspects of particle-related digital rock physics. It demonstrates that increased Peclet number results in a lower mass transfer rate of releasing and longer tailing. Finally, we demonstrate that the multi-scale Brinkman equation with effective parameters that matching the velocity field with DNS fails to predict the transport solution in the microporous regions. The optimal effective viscosity has different value for different flow conditions (confined or exposed region) and using purpose (flow or transport solution).



Committee Chair

Thompson, Karsten

Available for download on Thursday, October 31, 2024