Gas injection and water-alternating-gas (WAG) displacements are becoming increasingly important as EOR processes in a wide range of reservoirs. Although the conservation equations can be written down, the resulting multiphase macroscopic flow equations contain quantities which are not well understood, viz. the three-phase relative permeabilities and capillary pressures (denoted 3PRPs and 3PCPs in this paper). There are a number of published empirical correlations for three-phase relative permeability (3PRP) based on the corresponding two-phase relative permeability functions e.g. Stone Models I and II1,2, the Baker saturation-weighting model3, etc. These models are purely empirical and have only been partially validated for data in strongly water wet rocks and most reservoirs are not strongly water wet. In addition, these models embody very little understanding of the pore scale physics of three-phase flow. Recently, a number of advances have been made on the understanding of the pore scale physics of three-phase flow in water wet porous media4 and also in systems of non-uniform wettability5–8, where the water-wet case is a particular limiting case. How this pore scale physics works through to the effective macroscopic flow parameters is still a matter of active research.
In the current work, the results of 1D macroscopic simulations are presented using theoretical three-phase relative permeabilities and capillary pressures (3PRPs and 3PCPs) based on very simple pore-scale models. These 3PRP models have been used to perform a range of 1D gas injection, three-phase macroscopic WAG simulations where gas and water have been alternately injected into a system initially at a constant oil and water saturation. The objective of these simulations is to study the structure of the saturation profiles and the phase paths experienced locally in the system. These calculations demonstrate the macroscopic consequences of the local properties (capillary dominated 3PRPs and 3PCPs) on the global flows.
In viscous dominated WAG simulations (Pc = 0), shock and rarefactions appear depending on the nature of the fractional flow functions. We identify cases where this leads to phase banking and quasi two-phase flow and where it leads to fully developed three-phase flow through most of the system. The pore scale physics provides the input (3PRPs) for these viscous dominated calculations and carries no information about the emergent shock/rarefaction behaviour. This means that some interpretation must be made when analyzing "phase displacement paths" in laboratory experiments. The effect of introducing three-phase capillary pressure into the flow calculations (Pc ? 0) is to break up the shock structure if it exists by smearing out the fronts in a diffusive manner which tends to "pull together" the different viscous dominated phase paths making them closer to the microscopic (capillary dominated) phase path. Since the "phase paths" are different under capillary and/or viscous domination, care should be taken in interpreting these in the context of deriving the correct three-phase flow functions i.e. the 3PRP and 3PCP.
In our view, the essential "prediction" of a 3 phase displacement process is the phase path of the displacement. For example, suppose a local region of the porous medium is at initial water and oil saturations, Swi and Soi (where Swi + Soi = 1) and that both phases are mobile. If gas is then injected it may displace either water only or oil only or both water and oil. This displacement is described by a trajectory on the ternary phase diagram (examples below). If the process is carried out under conditions of local capillary equilibrium (as it must be if the "local" scale is sufficiently small, possibly at the pore scale), then this trajectory should be predictable from the basic pore-scale physics of the 3 phase displacement process.