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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 Summary: Foam 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. Key Points: Foam flow in media with oil corresponds to multiple steady states: which steady state occurs is key to success of gas mobility controlThe wave curve method, combined with the constraint of positive wave velocities, is capable of identifying the unique displacing stateThe choice of the displacing state depends on initial state; this dependence is captured by a boundary curve in ternary saturation space [ABSTRACT FROM AUTHOR]

A new capillary number (Nca) definition is proposed for 2‐D etched micromodels. We derive the new definition from a force balance on a nonwetting ganglion trapped by capillarity. It incorporates the impact of pore microstructure on mobilization. The geometrical factors introduced can be estimated directly from image analysis of the pore network etched in the micromodel, without conducting flow experiments. The improved fit of the new Nca to published data supports its validity. The new definition yields a consistent trend in the capillary‐desaturation curve. The conventional Nca definitions proposed for porous rock give a large scatter in the capillary‐desaturation curve for data in micromodels. This is due to the different type of flow in micromodels, as 2‐D networks, relative to 3‐D geological porous media. In particular, permeability is dominated by channel depth in micromodels with shallow depth of etching, and generally, there is no simultaneous multiphase flow under capillary‐dominated conditions. Applying the conventional definitions to results in micromodels may lead to misleading conclusions for fluid transport in geological formations. Plain Language Summary: Mobilization or trapping of fluids in porous media, fundamentally, is a result of a force competition. Numerous studies investigate mobilization efficiency using the capillary number (Nca), which represents a ratio of driving force for mobilization, that is, pressure or hydrostatic effects of gravity, to capillary resistance. The conventional Nca definitions were initially proposed for 3‐D porous media, yet many experimental studies use these definitions for 2‐D networks. Experimental observations and theoretical analysis show that flow in a 2‐D pore network, for example, a microfluidic device, is very different from that in 3‐D porous rock. We here propose a new definition of Nca to describe the efficiency of one phase displaced by another in a microfluidic device. The new definition is derived from a force balance on a trapped ganglion. The validity of the new definition is experimentally tested using data from micromodels in the literature. The new Nca definition, as an indicator for mobilization, may be applied to microfluidic studies of a variety of processes across the fields of groundwater, energy, and climate: removal of Nonaqueous Phase Liquid contaminants from aquifers and soils; enhanced recovery of oil in reservoirs; or trapping efficiency of CO2 in Carbon Capture, Utilization, and Storage. Key Points: A new capillary number (Nca) definition, derived from a force balance on a ganglion trapped by capillarity, is proposed for micromodelsThe improved fit of the new Nca to published data supports its validity by yielding a consistent trend in the capillary‐desaturation curveApplying conventional Nca definitions to micromodel results may lead to incorrect conclusions for fluid transport in geological formations [ABSTRACT FROM AUTHOR]

Simulation models for foam enhanced oil recovery are of two types: those that treat foam texture or bubble size explicitly (population-balance models) and those that treat the effects of foam texture implicitly through a gas mobility-reduction factor. The implicit-texture models all implicitly assume local equilibrium (LE) between the processes of foam creation and destruction. In published studies most population-balance models predict rapid attainment of local-equilibrium as well, and some have been recast in LE versions. In this paper we compare population-balance and implicit-texture (IT) models in two ways. First, we show the equivalence of the two approaches by deriving explicitly the foam texture and foam-coalescence-rate function implicit in the IT models, and then show its similarity to that in population-balance models. Second, we compare the models based on their ability to represent a set of N 2 and CO 2 steady-state foam experiments and discuss the corresponding parameters of the different methods. Each of the IT models examined was equivalent to the LE formulation of a population-balance model with a lamella-destruction function that increases abruptly in the vicinity of the limiting capillary pressure P c * , as in current population-balance models. The relation between steady-state foam texture and water saturation or capillary pressure implicit in the IT models is essentially the same as that in the population-balance models. The IT and population-balance models match the experimental data presented equally well. The IT models examined allow for flexibility in making the abruptness of the coalescence rate near P c * an adjustable parameter. Some allow for coarse foam to survive at high capillary pressure, and allow for a range of power-law non-Newtonian behavior in the low-quality regime. Thus the IT models that incorporate an abrupt change in foam properties near a given water saturation can be recast as LE versions of corresponding population-balance models with a lamella-destruction function similar to those in current PB models. The trends in dimensionless foam texture implicit in the IT models is similar to that in the PB models. In other words, both types of model, at least in the LE approximation, equally honor the physics of foam behavior in porous media. [ABSTRACT FROM AUTHOR]

We present the results of an experimental investigation of the effect of gas type and composition on foam transport in porous media. Steady-state foam strengths with respect to three cases of distinct gases and two cases containing binary mixtures of these gases were compared. The effects of gas solubility, the stability of lamellae, and the gas diffusion rate across the lamellae were examined. Our experimental results showed that the steady-state foam strength is inversely correlated with the gas permeability across a liquid lamella, a parameter that characterizes the rate of mass transport. The results are also in good agreement with existing observations that the foam strength for a mixture of gases is correlated with the less soluble component. Three hypotheses with different predictions of the underlying mechanism that explain the role of gas type and composition in foam strength are discussed in detail.

Understanding the role of pore-level mechanisms is essential to the mechanistic modeling and simulation of foam processes in porous media. Three different pore-level events can lead to foam formation: snapoff, leave behind, and lamella division. The initial state of the porous medium (fully saturated with liquid or already partially drained), as surfactant is introduced, also affects the different foam-generation mechanisms. Bubbles created by any of these mechanisms cause the formation of new bubbles by snapoff and leave behind as gas drains liquid-saturated pores. Lamellae are stranded unless the pressure gradient is sufficient to mobilize those that have been created. To appreciate the roles of these mechanisms, their interaction at the pore-network level was studied. We report an extensive pore-network study that incorporates the above pore-level mechanisms, as foam is created by drainage or by the continuous injection of gas and liquid in porous media. Pore networks with up to 10 000 pores are considered. The study explores the roles of the pore-level events, and by implication, the appropriate form of the foam-generation function for mechanistic foam simulation. Results are compared with previous studies. In particular, the network simulations reconcile an apparent contradiction in the foam-generation model of Rossen and Gauglitz [AIChE J. 36, 1176 (1990)], and identify how foam is created near the inlet of the porous medium when lamella division controls foam generation. In the process, we also identify a new mechanism of snap-off and foam generation near the inlet of the medium.