Traditionally, wettability has been considered key in predicting the nature of two-phase flow
through porous media. In this thesis, the local geometry is shown to also have a significant
impact, and the interaction between geometry and wettability is studied using a variety of
modelling approaches.
First, quasi 2D approximations of interfacial curvature, present in current pore-network
models, are extended to three dimensions. The new expressions for threshold capillary
pressure are calibrated using high-resolution direct numerical simulations. The effects of
pore-space expansion and sagittal interface curvature on displacement are quantified and
shown to be a key step in improving network model accuracy. The extended network model
predictions for relative permeability and capillary pressure agree well with experiments for a
water-wet Bentheimer sandstone, demonstrating that the inclusion of 3D interfacial curvature
leads to more accurate predictions.
Next, the extended network model predictions are compared to lattice-Boltzmann simulations
for two synthetic geometries with varying wettabilities. Macroscopic capillary pressures
between the two models, and with experiments, agree at intermediate saturations but differ
at the end-points. Direct methods at readily accessible resolutions fail to capture layer flow,
leading to abnormally large initial wetting and residual non-wetting saturations. Pore-by-pore
analysis indicates that the absence of layer flow limits displacement to invasion-percolation
in mixed-wet systems. Network models, which can easily capture layer effects, provide
predictions closer to experimental observations. However, discrepancies persist for mixed-wet
systems due to a limited understanding of mixed-wet displacement.
Finally, the stability and displacement of interfaces in mixed-wet media is addressed. Theo-
retical and numerical considerations reveal that interface stability depends on both the local
geometry and wettability. An explanation is provided for the observed low capillary pressure
displacement in mixed-wet systems, along with an empirical expression predicting threshold
displacement pressure in a 3D geometry with realistic pore-space expansion.