Foam injection is a promising means of reducing the relative mobility of gas, and hence improving the sweep efficiency of gas, in CO₂ and H₂ storage, soil-contaminant removal in aquifer remediation, enhanced oil recovery, and matrix-acid well stimulation. Theory (Rossen and Gauglitz, 1990; Ashoori et al., 2012) and experiments (Gauglitz et al., 2002; Yu et al., 2019, 2020) indicate that both foam generation and propagation in steady flow in porous media require the attainment of a sufficiently large superficial velocity or pressure gradient ∇P. Here we examine several foam-simulation models for their ability to represent a minimum velocity, or trigger, for foam generation. We define criteria for representation of such a trigger. For simplicity, we assume a homogeneous porous medium and absence of an oleic phase. We examine the Population-Balance (PB) models of Kam and Rossen (2003) and one of its variants (Kam, 2008), and the PB model of Chen et al. (2010); and the implicit-texture (IT) models in CMG-STARS (Computer Modeling Group, 2017) and of Lotfollahi et al. (2017). Our result show that the PB models of Kam and Rossen and its variant, and the IT models of CMG-STARS and of Lotfollahi et al. do represent a minimum velocity for foam generation. They achieve this by modeling an abrupt decrease in gas mobility with increasing pressure gradient over some range of ∇P. The model of Chen et al. (2010) is based on the model of Kovscek and Radke (1996), which was not intended to represent a trigger for foam generation (Kovscek and Radke, 1993). We cannot say categorically whether it could predict a trigger for any set of model parameter values. Instead, we derive criteria that must be satisfied by the choice of parameters to represent a trigger for foam generation. In simulations of radial foam propagation the STARS foam model predicts that foam propagation fails at the radius at which local ∇P cannot maintain strong foam, not at a greater velocity and ∇P as seen in experiments (Yu et al., 2020). In addition, we identify a fundamental challenge in representing foam generation at the large ∇P at the wellbore in a numerical simulation: conventional simulators do not represent ∇P at the wellbore. Foam generation at the very high superficial velocity at the well radius is not represented in the absence of truly exceptional grid refinement.

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Creating a gas-liquid foam means dispersing gas as individual bubbles in an aqueous solution, in which each gas bubble is separated by liquid films or lamella. The most common form of liquid foam (as opposed to solid foams, like polymer sponges) seen in day-to-day life is bulk foam. This refers to a foam that rests in a large container (or flows in a free open space) that has a volume considerably larger than the bubble size. Foam in a porous medium, however, resides and flows in a network of narrow pore spaces. The behaviour of foam is therefore complicated by many complex capillary phenomena...@en

Since the 1980s experimental and field studies have found anomalously slow propagation of foam that cannot be explained by surfactant adsorption. Friedmann et al. (1994) conducted foam-propagation experiments in a coneshaped sandpack and concluded that foam, once formed in the narrow inlet, was unable to propagate at all at lower superficial velocities towards the wider outlet. They hence concluded that long-distance foam propagation in radial flow from an injection well is in doubt. Ashoori et al. (2012) provide a theoretical explanation for slower or non-propagation of foam at decreasing superficial velocity. Their explanation connects foam propagation to the minimum velocity or pressure gradient required for foam generation in homogeneous porous media (Gauglitz et al., 2002). The conditions for propagation of foam are less demanding than those for creation of new foam. However, there still can be a minimum superficial velocity necessary for propagation of foam, except that it could be significantly smaller than the minimum velocity for foam generation from an initial state of no-foam. At even lower superficial velocity, theory (Kam and Rossen, 2003) predicts a collapse of foam. In this study, we extend the experimental approach of Friedmann et al. in the context of the theory of Ashoori et al. We use a cylindrical core with stepwise increasing diameters such that the superficial velocity in the outlet section is 1/16 of that in the inlet. N2 foam is created and stabilized by an alpha olefin sulfonate surfactant. Previously (Yu et al., 2019), we mapped the conditions for foam generation in a Bentheimer sandstone core as a function of total superficial velocity, surfactant concentration and injected gas fraction (foam quality). In this study, we extend the map to include the conditions for propagation of foam, after its creation in the narrow inlet section at greater superficial velocity. Thereafter, by reducing superficial velocity, we map the conditions for foam collapse. Our results suggest that the minimum superficial velocities for foam generation, propagation and maintenance increase with increasing foam quality and decreasing surfactant concentration, in agreement with theory. The minimum velocity for propagation of foam is much less than that for foam generation, and that for foam maintenance is less than that for propagation. The implications of our lab results for field application of foam are discussed.@en

The propagation of foam in an oil reservoir depends on the creation and stability of the foam in the reservoir, specifically the creation and stability of foam films, or lamellae. As the foam propagates far from the injection well, superficial velocity and pressure gradient decrease with distance from the well. Experimental (Friedmann et al. Steam-foam mechanistic field trial in the midway-sunset field. SPERE. 1994, 9 (4), 297-304) and theoretical (Ashoori, et al. Roles of Transient and Local Equilibrium Foam Behaviour in Porous Media: Traveling Wave. Colloids Surf. A 2011, 337 (1-3), 228-242). studies relate concerns about foam propagation at low superficial velocity to the minimum velocity or pressure gradient for foam generation near the well (Gauglitz et al. Foam Generation in Homogeneous Porous Media. Chem. Eng. Sci. 2002, 57, 4037-4052; Rossen et al. Percolation Theory of Creation and Mobilization of Foams in Porous Media. AI Chem Eng. J. 1990, 36, (8)). The objective of this work is to measure the impact of surfactant concentration and gas fractional flow on foam generation. Theory (Kam et al. Model for Foam Generation in Homogeneous Media. SPE J. 2003, 8 (4): 417-42, SPE-87334-PA; Rossen 1990) relates foam generation to gas fractional flow and, indirectly, to the stability of foam films, or lamellae, which in turn depends on surfactant concentration (Apaydin et al. Surfactant Concentration and End Effects on Foam Flow in Porous Media. (Apaydin et al.Transp Porous Media. 2001, 43, 511-536). However, the link between foam generation and surfactant concentration has not been established experimentally. In our experiments, nitrogen foam is generated in a core of Bentheimer sandstone. The foam-generation experiments consist of measuring the minimum velocity for foam generation as a function of gas fractional flow at three surfactant concentrations well above the critical micelle concentration. Experimental results show that the minimum velocity for foam generation decreases with increasing liquid fraction, as shown by previous foam generation studies (Friedmann et al., 1994; Rossen and Gauglitz, 1990). Additionally, our results show that this velocity decreases with increasing surfactant concentration, far above the CMC. We also propose a workflow for screening out the experimental artifacts that can distort the trigger velocity.@en

The propagation of foam in an oil reservoir depends on the creation and stability of the foam in the reservoir, specifically the creation and stability of foam films, or lamellae. As the foam propagates far from in injection well, superficial velocity and pressure gradient decrease with distance from the well. Experimental (Friedmann et al., 1994) and theoretical (Ashoori et al., 2011) studies relate concerns about foam propagation at low superficial velocity to the minimum velocity for foam generation near the well (Rossen and Gauglitz, 1990; Gauglitz et al., 2002). The objective of this work is to measure the impact of surfactant concentration and gas fractional flow on foam generation. Theory (Rossen and Gauglitz, 1990; Kam and Rossen, 2003) relates foam generation to gas fractional flow and, indirectly, to the stability of foam films, or lamellae, which in turn depends on surfactant concentration (Apaydin and Kovcsek, 2001). However, the link between foam generation and surfactant concentration has not been established experimentally. In our experiments, nitrogen foam is generated in a core of Bentheimer sandstone. The foamgeneration experiments consist of measuring the critical velocity for foam generation as a function of gas fractional flow at three surfactant concentrations well above the critical micelle concentration. Experimental results show that critical velocity decreases with increasing liquid fraction, as shown by previous foam generation studies (Rossen and Gauglitz, 1990; Friedmann et al., 1991). Additionally, our results show that the critical velocity decreases with increasing surfactant concentration, far above the CMC. We also propose a workflow for screening out the experimental artifacts that can distort the trigger velocity.

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The model of Stone (1982) and Jenkins (1984) predicts the extent of gravity override at steady state during gas-liquid co-injection in an enhanced oil recovery (EOR) process. The model is accurate for WAG injection if the slug sizes are sufficiently small. The model is exact for homogeneous reservoirs if the standard assumptions of fractional-flow theory apply (Rossen and Van Duijn, 2004). Stone and Jenkins relate the distance to complete gravity segregation to total mobility in the mixed zone and the thickness of the override zone beyond this point to mobilities in the override and underride zones. Namani et al. (2012) and Jamshidnezhad (2009) have proposed extensions to Stone and Jenkins' model for dipping reservoirs. The accuracy of these correlations were tested in this study for a wide range of conditions and angle of reservoir dip using 2D computer simulations. Both correlations are approximately correct, but deviate from observed behaviour at large dip angle. Specifically, gravity override occurs at shorter distances than predicted by Namani et al. for up-dip injection, but longer distances for down-dip injection at moderate dip angles. Jamshidnezhad's correlation works reasonably well for down-dip injection except at large dip angles, for which segregation occurs at much shorter distances than predicted. Much of the sweep of gas occurs not at steady-state, however, but during the transient period before steady state is attained. During the period of three-phase flow, mobilities are lower; as suggested by Stone's approach, this temporarily extends the mixed zone beyond that at steady state. In up-dip injection, the override zone is extended much deeper into the reservoir during the period when gas first enters than at steady state. The oil swept during this period can greatly exceed that represented in the mixed zone in any of these models: even though the mixed zone is reduced, overall sweep can be greatly increased by this effect. This extension of the override zone during transient flow follows the logic of Jenkins' derivation of the thickness of the override zone based on mobilities. Unfortunately, there is no single exact equation for gravity segregation in dipping reservoirs as for horizontal reservoirs, even at steady state. Therefore behaviour varies somewhat from case to case. @en