  The thesis investigates the flow of non-Newtonian fluids in porous media
using pore-scale network modeling. Non-Newtonian fluids show very complex time
and strain dependent behavior and may have initial yield stress. Their common
feature is that they do not obey the simple Newtonian relation of
proportionality between stress and rate of deformation. They are generally
classified into three main categories: time-independent, time-dependent and
viscoelastic. Two three-dimensional networks representing a sand pack and Berea
sandstone were used. An iterative numerical technique is used to solve the
pressure field and obtain the flow rate and apparent viscosity. The
time-independent category is investigated using two fluid models: Ellis and
Herschel-Bulkley. The analysis confirmed the reliability of the non-Newtonian
network model used in this study. Good results are obtained, especially for the
Ellis model, when comparing the network model results to experimental data sets
found in the literature. The yield-stress phenomenon is also investigated and
several numerical algorithms were developed and implemented to predict
threshold yield pressure of the network. An extensive literature survey and
investigation were carried out to understand the phenomenon of viscoelasticity
with special attention to the flow in porous media. The extensional flow and
viscosity and converging-diverging geometry were thoroughly examined as the
basis of the peculiar viscoelastic behavior in porous media. The modified
Bautista-Manero model was identified as a promising candidate for modeling the
flow of viscoelastic materials which also show thixotropic attributes. An
algorithm that employs this model was implemented in the non-Newtonian code and
the initial results were analyzed. The time-dependent category was examined and
several problems in modeling and simulating the flow of these fluids were
identified.
