In this literature survey, different aspects of dynamics of two-phase flow in porous media are discussed. This review is based on the results of developed dynamic pore-network models and their applications. Thus, those concepts of dynamics of two-phase systems are addressed that have been already discussed in previous studies. Since it is not always possible to study different aspects of laboratory experiments, dynamic pore-network models were developed to gain new insights into the process. This characteristic is the major advantage of pore-network models, which give a better understanding of the physics of a process at pore scale as well as at the scale of representative elementary volume. Dynamic pore-network models are reviewed under different classifications; structure, computational algorithm, and local rules and applications.

Current macroscopic theories of two-phase flow in porous media are based on the extended Darcy's law and an algebraic relationship between capillary pressure and saturation. Both of these equations have been challenged in recent years, primarily based on theoretical works using a thermodynamic approach, which have led to new governing equations for two-phase flow in porous media. In these equations, new terms appear related to the fluid–fluid interfacial area and non-equilibrium capillarity effects. Although there has been a growing number of experimental works aimed at investigating the new equations, a full study of their significance has been difficult as some quantities are hard to measure and experiments are costly and time-consuming. In this regard, pore-scale computational tools can play a valuable role. In this paper, we develop a new dynamic pore-network simulator for two-phase flow in porous media, called DYPOSIT. Using this tool, we investigate macroscopic relationships among average capillary pressure, average phase pressures, saturation and specific interfacial area. We provide evidence that at macroscale, average capillary pressure–saturation–interfacial area points fall on a single surface regardless of flow conditions and fluid properties. We demonstrate that the traditional capillary pressure–saturation relationship is not valid under dynamic conditions, as predicted by the theory. Instead, one has to employ the non-equilibrium capillary theory, according to which the fluids pressure difference is a function of the time rate of saturation change. We study the behaviour of non-equilibrium capillarity coefficient, specific interfacial area, and its production rate versus saturation and viscosity ratio.A major feature of our pore-network model is a new computational algorithm, which considers capillary diffusion. Pressure field is calculated for each fluid separately, and saturation is computed in a semi-implicit way. This provides more numerical stability, compared with previous models, especially for unfavourable viscosity ratios and small capillary number values.

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.

Summary: Low-salinity waterflooding (LSF) is one of the least-understood enhanced-oil-recovery (EOR)/improved-oil-recovery (IOR) methods, and proper understanding of the mechanism(s) leading to oil recovery in this process is needed. However, the intrinsic complexity of the process makes fundamental understanding of the underlying mechanism(s) and the interpretation of laboratory experiments difficult. Therefore, we use a model system for sandstone rock of reduced complexity that consists of clay minerals (Na-montmorillonite) deposited on a glass substrate and covered with crude-oil droplets and in which different effects can be separated to increase our fundamental understanding. We focus particularly on the kinetics of oil detachment when exposed to low-salinity (LS) brine. The system is equilibrated first under high-salinity (HS) brine and then exposed to brines of varying (lower) salinity while the shape of the oil droplets is continuously monitored at high resolution, allowing for a detailed analysis of the contact angle and the contact area as a function of time. It is observed that the contact angle and contact area of oil with the substrate reach a stable equilibrium at HS brine and show a clear response to the LS brine toward less-oil-wetting conditions and ultimately detachment from the clay substrate. This behavior is characterized by the motion of the three-phase (oil/water/solid) contact line that is initially pinned by clay particles at HS conditions, and pinning decreases upon exposure to LS brine. This leads to a decrease in contact area and contact angle that indicates wettability alteration toward a more-water-wet state. When the contact angle reaches a critical value at approximately 40 to 50°, oil starts to detach from the clay. During detachment, most of the oil is released, but in some cases a small amount of oil residue is left behind on the clay substrate. Our results for different salinity levels indicate that the kinetics of this wettability change correlates with a simple buoyancy- over adhesion-force balance and has a time constant of hours to days (i.e., it takes longer than commonly assumed). The unexpectedly long time constant, longer than expected by diffusion alone, is compatible with an electrokinetic ion-transport model (Nernst-Planck equation) in the thin water film between oil and clay. Alternatively, one could explain the observations only by more-specific [non- Derjaguin–Landau–Verwey–Overbeek (DLVO) type] interactions between oil and clay such as cation-bridging, direct chemical bonds, or acid/base effects that tend to pin the contact line. The findings provide new insights into the (sub) pore-scale mechanism of LSF, and one can use them as the basis for upscaling to, for example, pore-network scale and higher scales (e.g., core scale) to assess the impact of the slow kinetics on the time scale of an LSF response on macroscopic scales.