Three‐Phase Fractional‐Flow Theory of Foam‐Oil Displacement in Porous Media With Multiple Steady States

Abstract

Understanding the interplay of foam and nonaqueous phases in porous media is key to improving the design of foam for enhanced oil recovery and remediation of aquifers and soils. A widely used implicit-texture foam model predicts phenomena analogous to cusp catastrophe theory: The surface describing foam apparent viscosity as a function of fractional flows folds backwards on itself. Thus, there are multiple steady states fitting the same injection condition J defined by the injected fractional flows. Numerical simulations suggest the stable injection state among multiple possible states but do not explain the reason. We address the issue of multiple steady states from the perspective of wave propagation, using three-phase fractional-flow theory. The wave-curve method is applied to solve the two conservation equations for composition paths and wave speeds in 1-D foam-oil flow. There is a composition path from each possible injection state J to the initial state I satisfying the conservation equations. The stable displacement is the one with wave speeds (characteristic velocities) all positive along the path from J to I. In all cases presented, two of the paths feature negative wave velocity at J; such a solution does not correspond to the physical injection conditions. A stable displacement is achieved by either the upper, strong-foam state, or lower, collapsed-foam state but never the intermediate, unstable state. Which state makes the displacement depends on the initial state of a reservoir. The dependence of the choice of the displacing state on initial state is captured by a boundary curve. Plain Language SummaryFoam has unique microstructure and reduces gas mobility significantly. Foam injection into geological formations has broad engineering applications: removal of nonaqueous phase liquid contaminants in aquifers and soils, oil displacement in reservoirs, and carbon storage. Key to the success of foam is foam stability in the presence of oil or nonaqueous phase liquid. An experimentally validated foam model describes foam properties as a function of water, oil, and gas saturations. This model predicts that some injected fractional flows of phases correspond to multiple possible injection states with different saturations: strong-foam state with low mobility, intermediate state, and collapsed-foam state with high mobility. We show how to determine the unique displacing state, using three-phase fractional-flow theory and the wave-curve method. A physically acceptable displacing state is the one that gives only positive wave velocities. The choice of the displacing state depends on the initial state; the nature of the dependence is captured by a boundary curve. If the collapsed-foam state makes a displacement, that means ineffective gas-mobility control and, even in the absence of viscous instability, very slow oil displacement. Our findings and approach presented can help to predict the displacing state for a given initial state in geological formations.

Estimation of Local Equilibrium Model Parameters for Simulation of the Laboratory Foam-Enhanced Oil Recovery Process Using a Commercial Reservoir Simulator

“…The effect of crude oil on foam simulation has been extensively simulated using the fractional flow theory, 47 , 61 − 63 PB foam model, 64 and LE foam model. 33 , 46 In this section, the effect of oil on foam strength is evaluated by a simplified STARS foam model.…”

“…The effect of crude oil on foam simulation has been extensively simulated using the fractional flow theory, ,− PB foam model, and LE foam model. , In this section, the effect of oil on foam strength is evaluated by a simplified STARS foam model. Figure summarizes the effect of oil on steady-state foam PG by a so-called wet-foam model. , Only the foam mobility reduction factor (FM) is modified in the calculation, as described in eqs and .…”

Universality of Riemann solutions in porous media

“…Other cases where the universal solution behaviour is observed are reported in [1,24,36,44,48,55] as well as for the injection of CO 2 and CH 4 in NOTT-400 nanotubes, [25]. Moreover, preliminary results show that the universal solution behaviour persists for SAG injection (surfactant alternating gas) in the presence and absence of foam, see [35,46,53].…”

Probing the Effect of Wettability on Transport Behavior of Foam for Enhanced Oil Recovery in a Carbonate Reservoir

“…It is reported that the foam strength in porous media is largely influenced by the surfactant type and concentration, reservoir property (salinity, hardness, temperature, wettability, oil saturation, permeability, heterogeneity, etc. ), − operational methods (flow rate, injection scheme, foam quality, etc. ), ,− gas type, − local capillary pressure, and foam texture. − Note that the foam steady state may indicate a balance between the lamellae creation rate and lamellae coalescence rate.…”

“…It is universally accepted that oil has a detrimental effect on the foam stability, especially when the oil sample contains a large amount of light components. ,, The destabilization effect of oil on the foam stability has been extensively investigated, and several criteria have been proposed to predict the stability of foam in the presence of oil. Among them, the most reliable theory may be based on the stability of the pseudoemulsion film, i.e., the pseudoemulsion film disjoining pressure. , The other theories to account for the oil destabilization effect include lamellae number and the entering/spreading/bridging coefficients, which are calculated based on the surface/interfacial tension .…”