Insights into the Relationships Among Capillary Pressure, Saturation, Interfacial Area and Relative Permeability Using Pore-Network Modeling

Abstract

To gain insight in relationships among capillary pressure, interfacial area, saturation, and relative permeability in two-phase flow in porous media, we have developed two types of pore-network models. The first one, called tube model, has only one element type, namely pore throats. The second one is a sphere-and-tube model with both pore bodies and pore throats. We have shown that the two models produce distinctly different curves for capillary pressure and relative permeability. In particular, we find that the tube model cannot reproduce hysteresis. We have investigated some basic issues such as effect of network size, network dimension, and different trapping assumptions in the two networks. We have also obtained curves of fluid-fluid interfacial area versus saturation. We show that the trend of relationship between interfacial area and saturation is largely influenced by trapping assumptions. Through simulating primary and scanning drainage and imbibition cycles, we have generated two surfaces fitted to capillary pressure, saturation, and interfacial area (P c -S w -a nw ) points as well as to relative permeability, saturation, and interfacial area (k r -S w -a nw ) points. The two fitted three-dimensional surfaces show very good correlation with the data points. We have fitted two different surfaces to P c -S w -a nw points for drainage and imbibition separately. The two surfaces do not completely coincide. But, their mean absolute difference decreases with increasing overlap in the statistical distributions of pore bodies and pore throats. We have shown that interfacial area can be considered as an essential variable for diminishing or eliminating the hysteresis observed in capillary pressure-saturation (P c -S w ) and the relative permeability-saturation (k r -S w ) curves.

Uniqueness of Specific Interfacial Area–Capillary Pressure–Saturation Relationship Under Non-Equilibrium Conditions in Two-Phase Porous Media Flow

“…This analysis corroborates previous experimental and computational studies (e.g., Reeves and Celia 1996;Held and Celia 2001;Cheng et al 2004;Chen et al 2007;Joekar-Niasar et al 2008, 2010bPorter et al 2009). It is presented here in order to establish equilibrium P c -S w -a nw surface needed for comparison to the corresponding non-equilibrium surface.…”

“…In another study that compares experimental and pore-network model results for glass beads experiments, a similar conclusion was reached (Joekar-Niasar et al 2010b). These results indicated that inclusion of a nw leads to the removal or significant reduction of hysteresis in P c -S w relationship (see e.g., Reeves and Celia 1996;Held and Celia 2001;Cheng et al 2004;Chen et al 2007;Joekar-Niasar et al 2008;Porter et al 2009). All these studies have a common characteristics: the analyses were conducted under equilibrium conditions in which the capillary interfaces do not move in mostly granular media.…”

A New Method for Generating Pore-Network Models of Porous Media

“…The radii of sites were given by an uncorrelated truncated lognormal probability distribution and the radii of bonds were determined by size of the sites which are located at the two ends of each bond. This scheme was adopted from Acharya et al (2004) and used by Joekar-Niasar et al (2007). The resulting porosity is shown in Table 2.…”

Multiphase lattice Boltzmann simulations for porous media applications

“…Pore-network models [8][9][10][11][12][13][14][15][16] are a viable tool for understanding multiphase flows at the pore scale, and they are computationally efficient. These models, however, are based upon simplified representations of the complex pore geometry [17], which restricts their predictive capability and accuracy.…”