Long-distance propagation of foam is one key to deep gas mobility control for enhanced oil recovery and CO2 sequestration. It depends on two processes—convection of bubbles and foam generation at the displacement front. Prior studies with N2 foam show the existence of a critical threshold for foam generation in terms of a minimum pressure gradient r pmingen or minimum total interstitial velocity vmint,gen, beyond which strong-foam generation is triggered. The same mechanism controls foam propagation. There are few data for r pmingen or vmint,gen for CO2 foam.

We extend previous studies to quantify r pmingen and vmint,gen for CO2 foam generation and, for the first time, relate r pmingen and vmint,gen to factors including injected quality (gas volume fraction in the fluids injected) fg, surfactant concentration Cs, and permeability K. In each experiment, steady pressure gradient ∇p is measured at fixed injection rate and quality, with total interstitial velocity vt increasing and then decreasing in a series of steps. The trigger for strong-foam generation features an abrupt jump in ∇p upon an increase in vt.

In most cases, the data for ∇p as a function of vt identify three regimes, which are coarse foam with low ∇p, an abrupt jump in ∇p, and strong foam with high ∇p. The abrupt jump in ∇p upon foam generation confirms the existence of r pmingen and vmint,gen for CO2 foam. We further show how r pmingen and vmint,gen scale with fg, Cs, and K. Conditions that stabilize lamellae reduce the values of the thresholds: Both r pmingen and vmint,gen increase with fg and decrease with increasing Cs or K. Specifically, r pmingen scales with fg as (fg)2 and vmint,gen scales as (fg)4, and both r pmingen and vmint,gen scale with Cs as (Cs)−0.4. The effect of K on the thresholds for foam generation is greater than the effects of fg and Cs. Our data in artificial consolidated cores show that r pmingen scales with K as K−2 for CO2 foam, in comparison with K−1 for N2 foam in unconsolidated sand/bead packs. More data are needed to verify these correlations.

It is encouraging that r pmingen in the cores with K = 270 md or greater is less than 0.17 bar/m (~0.75 psi/ft), two to three orders of magnitude less than for N2 foam. Such low r pmingen can be easily attainable throughout a formation. This suggests that limited ∇p deep in formations is much less of a restriction for long-distance propagation of CO2 foam than for N2 foam. Foam propagation could still be challenging in low-K reservoirs (r pmingen ~10 bar/m for K = 27 md). Nevertheless, formation heterogeneity and alternating slug injection of gas and liquid help foam generation and can reduce the values of r pmingen.@en

In stratified porous media, non-uniform velocity between layers combined with thermal conduction across layers causes spreading of the thermal front: thermal Taylor dispersion. Conventional upscaling not accounting for this heterogeneity within simulation grid blocks underestimates thermal dispersion, leading to overestimation of thermal breakthrough time. We derive a model for effective longitudinal thermal diffusivity in the direction of flow, αeff, to represent the effective thermal dispersion in two-layer media. αeff, accounting for thermal Taylor dispersion, is much greater than the thermal diffusivity of the rock itself. We define a dimensionless number, NTC, a ratio of times for longitudinal convection to transverse conduction, as an indicator of transverse thermal equilibration of the system during cold- or hot-water injection. For NTC > 5, thermal dispersion in the two-layer system closely approximates a single layer with αeff. This suggests a two-layer medium satisfying NTC > 5 can be combined into a single layer with an effective longitudinal thermal diffusivity αeff. In application to a geothermal reservoir, one can apply the model to perform upscaling in stages, i.e. combining two layers satisfying the NTC criterion in each stage. The αeff model accounting for the fine-scale heterogeneity within simulation grid blocks would enhance the prediction accuracy of thermal breakthrough time and thus thermal lifetime.@en

Foam is a promising means to assist in the permanent, safe subsurface sequestration of CO₂, whether in aquifers or as part of an enhanced-oil-recovery (EOR) process. Here we review the advantages demonstrated for foam that would assist CO₂ sequestration, in particular sweep efficiency and residual trapping, and the challenges yet to be overcome. We also review the research and field-trial literature on CO₂ foam sweep efficiency, capillary gas trapping in foam, issues involved in surfactant selection for CO₂ foam applications, foam field trials, and the state of the art from laboratory and modelling research on CO₂ foam properties, in order to present the prospects and challenges for foam-assisted CO₂ sequestration. Challenges to foam-assisted CO₂ sequestration include the following: 1) verifying the advantages indicated by laboratory research at the field scale 2) optimizing surfactant performance, while further reducing cost and adsorption if possible 3) long-term chemical stability of surfactant, and dilution of surfactant in the foam bank by flow of water. Residual gas must reside in place for decades, even if surfactant degrades or is diluted. 4) optimizing injectivity and sweep efficiency in the field-design strategy.

@en

Foam is utilized in enhanced oil recovery and CO₂ sequestration. Surfactant-alternating-gas (SAG) is a preferred approach for placing foam into reservoirs, due to it enhances gas injection and minimizes corrosion in facilities. Our previous studies with similar permeability cores show that during SAG injection, several banks occupy the area near the well where fluid exhibits distinct behaviour. However, underground reservoirs are heterogeneous, often layered. It is crucial to understand the effect of permeability on fluid behaviour and injectivity in a SAG process. In this work, coreflood experiments are conducted in cores with permeabilities ranging from 16 to 2300 mD. We observe the same sequence of banks in cores with different permeabilities. However, the speed at which banks propagate and their overall mobility can vary depending on permeability. At higher permeabilities, the gas-dissolution bank and the forced-imbibition bank progress more rapidly during liquid injection. The total mobilities of both banks decrease with permeability. By utilizing a bank-propagation model, we scale up our experimental findings and compare them to results obtained using the Peaceman equation. Our findings reveal that the liquid injectivity in a SAG foam process is misestimated by conventional simulators based on the Peaceman equation. The lower the formation permeability, the greater the error.

@en

Aqueous foam is a dispersion of gas in liquid, where the liquid acts as the continuous phase and the gas is separated by thin liquid films stabilized by a surfactant. Foam injection is a widely used technique in various applications, including CO2 sequestration, enhanced oil recovery, soil remediation, etc. Surfactant-alternating-gas (SAG) is a preferred approach for foam injection, and injectivity plays a vital role in determining the efficiency of the SAG process. Different gases can be applied depending on the process requirements and availability. However, the underlying mechanisms by which gas composition impacts injectivity are not yet fully understood. In this work, the effect of gas composition on fluid behavior and injectivity in a SAG process was investigated using three gases: N2, CO2, and Kr. Our observations revealed that gas solubility in liquid was key for the formation and evolution of liquid fingers, and therefore was very important for liquid injectivity. A lower gas solubility in liquid led to a slower increase in surfactant solution injectivity. In addition, the development of surfactant solution injectivity took significantly longer when the surfactant solution was partially pre-saturated compared to when it was unsaturated. Additionally, the propagation of the collapsed-foam bank during gas injection was accelerated when the gas had a greater solubility in water.@en

Microfluidic devices offer unique opportunities to directly observe multiphase flow in porous media. However, as a representation of flow in geological pore networks, conventional microfluidics face several challenges. One is whether steady simultaneous two-phase flow through a two-dimensional network is possible without fluctuating occupancy of the pore constrictions. Flow without fluctuations can occur only if the flow paths of the two phases can cross on the 2D network; this requires that wetting phase can form a bridge across the gap between grains at a pore constriction while non-wetting phase flows through the constriction. We consider the conditions under which this is possible as a function of the local capillary pressure and the geometry of the constriction. Using the Surface Evolver software, we determine conditions for stable interfaces in constricted geometries, the range of capillary pressures at which bridging can occur, and those where the wetting phase would re-invade the constriction to block the flow of the non-wetting phase (“snap-off”). If a constriction is long and either straight or uniformly curved, snap-off occurs at the same capillary pressure as bridging. For constrictions of concave shape, which we represent as constrictions between cylindrical grains, however, we find a range of capillary pressures at which bridging is stable; the range is greater the narrower the diameter of the cylinders (i.e. the more strongly concave the throat) relative to the width of the constriction. For smaller-diameter pillars, the phenomenon of “Roof” snap-off as non-wetting phase invades a downstream pore body, is predicted not to occur.

@en

The main objective of this study is to understand the vertical sweep efficiency with miscible CO2-water-coinjection as a secondary recovery method, from multiple perspectives: phase behavior, total relative mobility, fluid densities/viscosities, the driving forces and consequent phase distributions etc. We also seek to provide insights into modeling approaches for representing the injection process by comparing compositional simulation results to those of the fractional-flow method and the model of Stone and Jenkins ( Stone, 1982 ; Jenkins, 1984 ).

We combine compositional simulation and analytical models to interpret the dynamics that affect vertical sweep efficiency in miscible CO2-water-coinjection. Stone’s model for gravity segregation at steady state predicts three phase-distribution zones: mixed zone, override zone and underride zone. In addition to these three zones, we identify from simulations an extended mixed zone and extended override zone in miscible CO2-water-coinjection, contributing to additional oil recovery and CO2 trapping. The extended zones are a result of dispersion that reflects physical and numerical dispersion in the gas-oil displacement front. To the extent that it reflects numerical dispersion, the extended zones can be considered as a numerical artifact.@en

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.

@en

Foam is a promising means to assist in the permanent, safe subsurface sequestration of CO2, whether inaquifers or as part of an enhanced-oil-recovery (EOR) process. Here we review the advantages demonstratedfor foam that would assist CO2 sequestration, in particular sweep efficiency and residual trapping, and thechallenges yet to be overcome. CO2 is trapped in porous geological layers by an impermeable overburden layer and residual trapping,dissolution into resident brine, and conversion to minerals in the pore space. Over-filling of geologicaltraps and gravity segregation of injected CO2 can lead to excessive stress and cracking of the overburden.Maximizing storage while minimizing overburden stress in the near term depends on residual trapping inthe swept zone. Therefore, we review the research and field-trial literature on CO2 foam sweep efficiencyand capillary gas trapping in foam. We also review issues involved in surfactant selection for CO2 foamapplications. Foam increases both sweep efficiency and residual gas saturation in the region swept. Both propertiesreduce gravity segregation of CO2. Among gases injected in EOR, CO2 has advantages of easier foamgeneration, better injectivity, and better prospects for long-distance foam propagation at low pressuregradient. In CO2 injection into aquifers, there is not the issue of destabilization of foam by contact with oil,as in EOR. In all reservoirs, surfactant-alternating-gas foam injection maximizes sweep efficiency whilereducing injection pressure compared to direct foam injection. In heterogeneous formations, foam helpsequalize injection over various layers. In addition, spontaneous foam generation at layer boundaries reducesgravity segregation of CO2. Challenges to foam-assisted CO2 sequestration include the following: 1) verifying the advantagesindicated by laboratory research at the field scale 2) optimizing surfactant performance, while furtherreducing cost and adsorption if possible 3) long-term chemical stability of surfactant, and dilution ofsurfactant in the foam bank by flow of water. Residual gas must reside in place for decades, even if surfactantdegrades or is diluted. 4) verifying whether foam can block upward flow of CO2 through overburden, eitherthrough pore pathways or microfractures. 5) optimizing injectivity and sweep efficiency in the field-designstrategy. We review foam field trials for EOR and the state of the art from laboratory and modeling research onCO2 foam properties to present the prospects and challenges for foam-assisted CO2 sequestration.

@en

Foam is applied in enhanced oil recovery to improve the sweep of injected gas and increase oil recovery, by greatly reducing the mobility of gas. In the laboratory, X-ray computed tomography is commonly used to evaluate the performance of foam in core plugs. However, foam properties, such as bubble size and capillary pressure, are much more difficult to measure. In recent years, microfluidic models have gained much attention because they easily facilitate the imaging study of in-situ foam. However, it is still challenging to estimate capillary pressure, in a model with a uniform depth of etching. In this paper, we report a novel technique to estimate water saturation and capillary pressure of foam in two 1-meter-long model fractures. Both model fractures are made of glass plates. They have different roughness and hydraulic apertures. Unlike microfluidics with uniform depth of etching, our model fractures each has a variation of aperture. We characterize the roughness and represent the aperture distribution of the fracture as a network of pore bodies and pore throats. In this study, foam is pre-generated and then injected into the fractures. The inlet and outlet valves are closed for 24 hr after foam reaches steady-state. We use a high-speed camera to visualize foam in the fractures. We use ImageJ software to analyze foam texture and quantify bubble density, average bubble size and polydispersivity. In addition, we estimate water saturation and capillary pressure by analyzing images in terms of fracture geometry. We found that water in foam resides in locations of narrow aperture, Plateau borders, lamellae between bubbles, and water films on glass walls. Water-filled zones of narrow aperture and Plateau borders account for almost all the water. During the re-distribution of water and gas in static foam, in-flow and out-flow of water must take paths along the network of Plateau borders and water-occupied zones, as they are the only continuous paths for water flow. In both model fractures, the decrease in water saturation coincides with an increase in capillary pressure, as expected. This novel technique of estimation of water saturation and capillary pressure of foam provides insights for studies of foam in naturally fractured reservoirs with complex geometry, where measuring such foam properties is challenging. This analysis is possible because aperture varies along our model fractures, unlike most microfluidic devices. Our technique would also have an application to foam aquifer remediation and CO ₂ sequestration.

@en

Foam is remarkably effective in the mobility control of gas injection for enhanced oil recovery (EOR) processes and CO₂ sequestration. Our goal is to better understand immiscible three-phase foam displacement with oil in porous media. In particular, we investigate (i) the displacement as a function of initial (I) and injection (J) conditions and (ii) the effect of improved foam tolerance to oil on the displacement and propagation of foam and oil banks. We apply three-phase fractional-flow theory combined with the wave-curve method (WCM) to find the analytical solutions for foam-oil displacements. An n-dimensional Riemann problem solver is used to solve analytically for the composition path for any combination of J and I on the ternary phase diagram and for velocities of the saturations along the path. We then translate the saturations and associated velocities along a displacement path to saturation distributions as a function of time and space. Physical insights are derived from the analytical solutions on two key aspects: the dependence of the displacement on combinations of J and I and the effects of improved oil-tolerance of the surfactant formulation on composition paths, foam-bank propagation and oil displacement. The foam-oil displacement paths are determined for four scenarios, with representative combinations of J and I that each sustains or kills foam. Only an injection condition J that provides stable foam in the presence of oil yields a desirable displacement path, featuring low-mobility fluids upstream displacing high-mobility fluids downstream. Enhancing foam tolerance to oil, e.g. by improving surfactant formulations, accelerates foam-bank propagation and oil production, and also increases oil recovery. Also, we find a contradiction between analytical and numerical solutions. In analytical solutions, oil saturation (S_o) in the oil bank is never greater than the upper-limiting oil saturation for stable foam (fmoil in our model). Nevertheless, in numerical simulations, S_o may exceed the oil saturation that kills foam in the oil bank ahead of the foam region, reflecting a numerical artifact. This contradiction between the two may arise from the calculation of pressure and pressure gradient using neighboring grid blocks in a numerical simulation. The analytical solutions we present can be a valuable reference for laboratory investigation and field design of foam for gas mobility control in the presence of oil. More significantly, the analytical solutions, which are free of numerical artifacts, can be used as a benchmark to calibrate numerical simulators for simulating foam EOR and CO2 storage processes.

@en

By trapping gas, foam can improve the sweep efficiency in enhanced oil recovery. In this study, to understand gas trapping in fractures, we have conducted experiments in a model fracture with a hydraulic aperture of 80 μm. One wall of the fracture is rough, and the other wall is smooth. The fracture is made of two glass plates and the direct visualization of foam flow inside the fracture is facilitated using a high-speed camera. ImageJ has been used to perform image analysis and quantify the properties of the foam. We find that pre-generated foam has been further refined inside the model. Foam flow reaches local equilibrium, where the rate of bubble generation equals that of bubble destruction, within the model. Foam texture becomes finer and less gas is trapped as the interstitial velocity and pressure gradient increase. Shear-thinning rheology of foam has also been observed. The behavior of gas trapping in our model fracture is different from that in other geological porous media. The fraction of trapped gas is much lower (less than 7%). At the extreme, when velocity increases to 6.8 mm/s (pressure gradient to 1.8 bar/m), all the foam bubbles are flowing and there is no gas trapped inside the fracture.@en

Foam injection is one efficient way to mitigate gravity segregation during CO2 injection into porous media. The effect of gravity segregation on foam propagation in heterogeneous porous media is not yet fully resolved. To assess CO2 foam transport for enhanced oil recovery (EOR) and for CO2 storage processes in heterogeneous reservoirs, an accurate prediction of foam behavior is essential. In this study, we investigate the effect of heterogeneity on gravity segregation in the presence of foam. For nonlinear analysis, we use an extension of an Operator-Based Linearization (OBL) approach proposed recently. The OBL approach helps to reduce the nonlinearity of complex physical problems by transforming the discretized nonlinear conservation equations into a quasi-linear form based on state-dependent physical operators. The state-dependent operators are approximated by discrete representation on a uniform mesh in parameter space. In our study, foam in porous media is described using an implicit-Texture (IT) foam model with two flow regimes. We first validate the numerical accuracy of the foam simulation with OBL by comparing segregation length using the IT foam model with Newtonian rheology to analytical solutions. Next, the foam-model parameters are fit to foam-quality scan data for four sandstone formations ranging in permeability by an order of magnitude using a least-squares optimization approach. We then construct several hypothetical models containing two communicating layers with different permeability and thickness ratios to examine foam s effect on gravity segregation. The numerical results of the segregation length in homogeneous domains show good agreement with analytical solutions, except in a transition zone beneath the override zone which is not included in the analytical model. Through fractional-flow theory, we find that the transition zone is not a numerical artefact, but caused by low gas relative-mobility during the transient displacement process. Permeability affects both the mobility reduction of wet foam in the low-quality regime and the limiting capillary pressure at which foam collapses. Thus the segregation length varies with permeability and foam strength. In two-layer models, the thickness of the top layer plays an important role in the ultimate segregation length. A thin top layer does not affect segregation in the bottom layer, while a thicker top layer dominates the segregation length, with less influence of the bottom layer.

@en

Foam coarsening by diffusion (Ostwald ripening) has been well studied in bulk foams. However, it is less well understood in porous media. In particular, the mechanisms that may slow or stop coarsening have not been fully investigated. In this paper, we report an experimental study of foam coarsening in two 1-m-long and 15-cm-wide model fractures. The model fractures, Model 1 and Model 2, are made of glass plates and have different roughness. Model 1 has a regular roughness with hydraulic aperture of 46 μm. Model 2 has an irregular roughness with hydraulic aperture of 78 μm. The two model fractures are transparent, which allows direct investigation of foam in the fractures. We characterize the fracture geometries by studying the aperture distribution in the two model fractures. Both model fractures are then represented by a 2D network of pore bodies and pore throats. To study coarsening, we inject pre-generated foam at different foam qualities (ratio of gas volumetric rate to total rate) into the model fractures. After foam reaches steady-state, we shut the inlet and outlet valves of the fractures for 24 h. Foam coarsens by gas diffusion during this period. We use a high-speed camera to record images of the static foam during coarsening at two fixed locations in the fracture: 19 and 73 cm from the inlet, separately. We then use ImageJ software to process the images to study foam texture and quantify coarsening process. By correlating the aperture histogram of model fractures and water-occupied area fraction, we estimate the local aperture at water-gas interfaces at each specific coarsening time. Using the local aperture, we further estimate the height of lamellae available for gas diffusion at the end of the coarsening experiments. Based on this information, we discuss whether coarsening stops at the end of the coarsening experiments because bubbles are in equilibrium in pressure, or slows nearly to a stop because bubbles lose contact through lamellae. Coarsening studies in bulk and microfluidics assume coarsening slows and stops when lamella curvature is zero. We show in our model fractures that the lack of lamellae in wet foams can also play a part. In addition, we adopt a novel technique to calculate water saturation and capillary pressure of foam in our model fractures. We then explain how these foam properties affect its coarsening behavior.@en

CO₂-foam injection is a promising technology for reducing gas mobility and increasing trapping within the swept region in deep brine aquifers. In this work, a consistent thermodynamic model based on a combination of the Peng-Robinson equation of state (PR EOS) for gas components with an activity model for the aqueous phase is implemented to accurately describe the complex phase-behavior of the CO₂-brine system. The phase-behavior module is combined with the representation of foam by an implicit-texture (IT) model with two flow regimes. This combination can accurately capture the complicated dynamics of miscible CO₂ foam at various stages of the sequestration process. The Operator-Based Linearization (OBL) approach is applied to improve the efficiency of the highly nonlinear CO₂-foam problem by transforming the discretized nonlinear conservation equations into a quasi-linear form based on state-dependent operators. We first validate our simulation results for enhanced CO₂ dissolution in a small domain with and without the presence of a capillary transition zone (CTZ). Then a 3D unstructured reservoir is used to examine CO₂-foam behavior and its effects on CO₂ storage. Simulation studies show good agreement with analytical solutions in both cases with and without CTZ. Besides, the presence of a CTZ enhances the CO₂ dissolution rate in brine. Foam simulations show that foams can reduce gas mobility effectively by trapping gas bubbles and inhibit CO₂ from migrating upward in the presence of gravity, which in turn improves the sweep efficiency and opens the unswept region for CO₂ storage. In the long run (post-injection), with the increasing effects of dissolution, the mechanism of residual trapping, due to the presence of foam, may not be significant. This work suggests a possible strategy to develop an efficient CO₂ storage technology.

@en

Foam injection is a promising enhanced-oil-recovery (EOR) technology that significantly improves the sweep efficiency of gas injection. Simulation of foam/oil displacement in reservoirs is an expensive process for conventional simulation because of the strongly nonlinear physics, such as multiphase flow and transport with oil/foam interactions. In this work, an operator-based linearization (OBL) approach, combined with the representation of foam by an implicit-texture (IT) model with two flow regimes, is extended for the simulation of the foam EOR process. The OBL approach improves the efficiency of the highly nonlinear foam-simulation problem by transforming the discretized nonlinear conservation equations into a quasilinear form using state-dependent operators. The state-dependent operators are approximated by discrete representation on a uniform mesh in parameter space. The numerical-simulation results are validated by using three-phase fractional-flow theory for foam/oil flow. Starting with an initial guess depending on the fitting of steady-state experimental data with oil, the OBL foam model is regressed to experimental observations using a gradient-optimization technique. A series of numerical validation studies is performed to investigate the accuracy of the proposed approach. The numerical model shows good agreement with analytical solutions at different conditions and with different foam parameters. With finer grids, the resolution of the simulation is better, but at the cost of more expensive computations. The foam-quality scan is accurately fitted to steady-state experimental data, except in the low-quality regime. In this regime, the used IT foam model cannot capture the upward-tilting pressure gradient (or apparent viscosity) contours. 1D and 3D simulation results clearly demonstrate two stages of foam propagation from inlet to outlet, as seen in the computed-tomography (CT) coreflood experiments: weak foam displaces most of the oil, followed by a propagation of stronger foam at lower oil saturation. OBL is a direct method to reduce nonlinearity in complex physical problems, which can significantly improve computational performance. Taking its accuracy and efficiency into account, the data-driven OBL-based approach could serve as a platform for efficient numerical upscaling to field-scale applications.

@en

In enhanced oil recovery, foam can effectively mitigate conformance problems and maintain a stable displacement front, by trapping gas and reducing its relative permeability in situ. In this study, to understand gas trapping in fractures and how it affects foam behavior, we report foam experiments in a 1-m-long glass model fracture with a hydraulic aperture of 80 μm. One wall of the fracture is rough, and the other is smooth. Between the two is a 2D porous medium representing the aperture in a fracture. The fracture model allows direct visualization of foam inside the fracture using a high-speed camera. This study is part of a continuing program to determine how foam behaves as a function of the geometry of the fracture pore space (AlQuaimi and Rossen in Energy & Fuels 33: 68-80, 2018a). We find that local equilibrium of foam (where the rate of bubble generation equals that of bubble destruction) has been achieved within the 1-m model fracture. Foam texture becomes finer, and less gas is trapped as interstitial velocity, and pressure gradient increase. Shear-thinning rheology of foam has also been observed. The fraction of trapped gas is significantly lower in our model (less than 7%) than in 3D geological pore networks. At the extreme, when velocity increases to 7 mm/s, there is no gas trapped inside the fracture. Our experimental results of trapped-gas fraction correlate well with the correlation of AlQuaimi and Rossen (SPE J 23: 788-802, 2018b) for fracture-like porous media. This suggests that the correlation can also be applied to gas trapping in fractures with other geometries.@en

In this study, to investigate how gravity affects foam in open vertical fractures, we report foam experiments in three 1-m-long, 15-cm-wide glass-model fractures. Each fracture has a smooth wall and a roughened wall. Between the two walls is a slit-like channel representing a single geological fracture. Three model fractures (Models A, B, and C) share the same roughness and have different hydraulic apertures of 78, 98, and 128 µm, respectively. We conduct foam experiments by horizontal injection in the three model fractures placed horizontally and sideways (i.e., with the model fractures turned on their long side), and in Model A placed vertically with injection upward or downward. Direct imaging of the foam inside the model fracture is facilitated using a high-speed camera. We find that foam reaches local equilibrium (LE; where the rate of bubble generation equals that of bubble destruction) in horizontal-flow experiments in all three model fractures and in vertical-flow experiments in Model A. In fractures with a larger hydraulic aperture, foam is coarser because of less in-situ foam generation. In the vertical-flow experiments in Model A, we find that the properties of the foam are different in upward and downward flow. Compared with downward flooding, upward flooding creates a finer-texture foam, as sections near the inlet of this experiment are in a wetter state, which benefits in-situ foam generation. Moreover, less gas is trapped during upward flooding, as gravitational potential helps overcome the capillarity and moves bubbles upward. In the sideways-flow experiments, gravity segregation takes place. As a result, drier foam propagates along the top of the fractures and wetter foam along the bottom. The segregation is more significant in fractures with a larger hydraulic aperture. At foam quality 0.8, gas saturation is 27.7\ and 19.3\0.8\ respectively. Despite the gravity segregation in all three model fractures, water and gas are not completely segregated. All three model fractures thus represent a capillary transition zone, with greater segregation with increasing aperture. Our results suggest that the propagation of foam in vertical natural fractures meters tall and tens of meters long, with an aperture of hundreds of microns or greater, is problematic. Gravity segregation in foam would weaken its capacity in the field to maintain uniform flow and divert gas in a tall fracture over large distances.@en

Surfactant-alternating-gas (SAG) is a preferred method of foam injection, which is a promising means of enhanced oil recovery. Liquid injectivity in a SAG process is commonly problematic. Our previous studies suggest that the liquid injectivity can be better than expected due to the existence of a collapsed-foam region formed during the gas-injection period ahead of the liquid-injection period. A single superficial velocity was used in those studies to examine the flow behavior during gas- and liquid-injection periods, separately. However, in radial flow from an injection well, superficial velocity decreases with distance from the injection well. Understanding the effect of superficial velocity on gas and liquid injectivities is important, but remains unexplored. In this study, we first examine gas injection at different superficial velocities following foam injection. We then study the effect of liquid superficial velocity on the liquid injectivity following a similar volume of gas injection. Our results show that during a prolonged period of gas injection following foam, the propagation velocity and the total mobility of the collapsed-foam bank are not significantly affected by the gas superficial velocity. During liquid injection after a period of gas injection, the dimensionless propagation velocities and the total mobilities of the forced-imbibition bank and the gas-dissolution bank follow a power-law dependence on the liquid superficial velocity. Liquid fingering through the weakened-foam region shows strongly shear-thinning behavior. It is also observed from X-ray computer-tomography experiments that the liquid fingers are wider if the liquid superficial velocity is greater. The impact of the shear-thinning behavior on the estimation of liquid injectivity in a field application is the subject of a companion paper.

@en

Gas-injection EOR processes have poor sweep efficiency due to conformance problems including channelling, gravity override and fingering. In naturally fractured reservoirs, sweep efficiency is further jeopardized, because gas breaks through fractures first, leaving most oil behind in the matrix. Strong foam can be created in fractures[1][2], thus diverting the flow of gas into matrix and hence increasing the oil recovery[3]. In the field, natural fractures are usually vertically oriented, because the least principle stress is in horizontal direction in most formations. Foam performance in fractured reservoirs is not only affected by fracture roughness, aperture, etc., but also by gravity. In this study, we investigate how gravity affect foam in fractures. To this end, we have conducted several sets of foam-scan experiments (i.e., a set of constant-total-velocity experiments each with a different gas fractional flow) on three glass model fractures (model A, model B and model C) with hydraulic aperture of 78, 99 and 128 µm respectively. The models have the same dimensions of 1 m x 0.15 m (L x W) and the same fracture roughness pattern. The transparency of glass models allows a direct investigation of foam texture inside the fracture using a high-speed camera. All experiments have been carried out at 20°C and 1 atm. Nitrogen is the gas phase, and surfactant solution is 1 wt % AOS C14-16. Experiments were carried out on all three models by placing the model either horizontally or on its side. Stable foam was created and reached local equilibrium in all horizontal-flow experiments, i.e., the rate of foam lamella creation was equal to the rate of destruction. The roughened fracture surface provided sufficient generation sites to re-create foam bubbles in sections further from the entry, hence maintaining a stable foam. In the sideways flow experiment, the effect of gravity on foam stability was not significant when fracture aperture was small (model A). As hydraulic aperture increased (model B and model C), the effect of gravity was more pronounced. Drier foam propagated along the top part of the fractures and wetter foam along the bottom. Gas saturation was 23% greater at the top than the bottom for model B, and 34% for model C. Foam was still stable during the sideways flow experiments in model B. However, foam breakage alternated with re-generation near the top in model C. We conclude that the application of foam in vertical natural fractures (meters tall and tens of meter long) with a aperture of hundreds of microns is problematic. The gravity segregation of phases for this foam would disable its capacity to divert gas flow from a tall fracture like our model into the matrix. As a result, there will be a gas-rich regime at the top of the fracture and a liquid-rich regime at the bottom. The regimes segregate more as the aperture increases. @en