Foam Dynamics Research Articles

Dynamic X-ray micotomography of microfibrous cellulose liquid foams using deep learning

Using X-ray microcomputed tomography (micro-CT) as a 3D microstructural analysis tool elucidates the time evolution of foam Plateau borders and nodes, providing unprecedented vision of foam dynamics. Deep learning facilitates the capability by allowing for quantifiable images to be collected at the time scale of five minutes. The stability mechanism of microfibrous cellulose is assessed demonstrating that trapping of fibers in the foam structure results in a critical concentration that marks an arrested foam. The mechanism of arrest is explained by 3D structural information extracted from micro-CT and confocal laser scanning microscopy images demonstrating the entanglement of cellulose fibers. A detailed analysis of the micro-CT data is provided to substantiate the quantitative nature of the digital images and assess advanced deep learning approaches. It is demonstrated that deep learning allows for the dynamic imaging of liquid foams whereas traditional data processing approaches cannot capture accurate geometrical information of foam structure.

Effects of water salinity on the foam dynamics for EOR application

Factors limiting foam injection for EOR application are exceptionally low rock permeability and exceedingly high salinity of the formation water. In this regard, foam formation using internal olefin sulfonate is investigated over a wide salinity range (1, 5, 8, 10, and 12% NaCl) through 10 mD limestone. The relationships between pressure drop (dP), apparent viscosity, liquid flow rate, total flow rate, salinity, foam texture, and length of foam drops at the outlet used as an indicator of viscosity are studied. Foaming is observed up to 12% NaCl, compared to a maximum of 8% NaCl in similar core-flooding experiments with 50 mD limestone and 255 mD sandstone. Thus, the salinity limit of foam formation has increased significantly due to the low permeability, which can be explained by the fact that the narrow porous system acts like a membrane with smaller holes. Compared to the increasing dP reported for highly permeable rocks, dP linearly decreases in almost the entire range of gas fraction (fg) at 1–10% NaCl. As fg increases, dP at higher total flow rate is higher at all salinities, but the magnitude of dP controls the dependence of apparent viscosity on total flow rate. Low dP is measured at 1% and 10% NaCl, and high dP is measured at 5, 8, and 12% NaCl. In the case of low dP, the apparent viscosity is higher at higher total flow rate with increasing gas fraction, but similar at two total flow rates with increasing liquid flow rate. In the case of high dP, the apparent viscosity is higher at lower total flow rate, both with an increase in the gas fraction and with an increase in the liquid flow rate. A linear correlation is found between dP or apparent viscosity and liquid flow rate, which defines it as a governing factor of foam flow and can be considered when modeling foam flow.

Discrete gravity dynamics from effective spin foams

The first computation of a spin foam dynamics that provides a test of the quantum equations of motions of gravity is presented. Specifically, a triangulation that includes an inner edge is treated. The computation leverages the recently introduced effective spin foam models, which are particularly numerically efficient. Previous work has raised the concern of a flatness problem in spin foam dynamics, identifying the potential for the dynamics to lead to flat geometries in the small ℏ semiclassical limit. The numerical results presented here expose a rich semiclassical regime, but one that must be understood as an interplay between the various parameters of the spin foam model. In particular, the scale of the triangulation, fixed by the areas of its boundary triangles, the discreteness of the area spectrum, input from loop quantum gravity, and the curvature scales around the bulk triangles, all enter the characterization of the semiclassical regime identified here. In addition to these results on the dynamics, we show that the subtle nature of the semiclassical regime is a generic feature of the path integral quantization of systems with second class constraints.

Gompertz Law in Clean Foam Coalescence

Clean foams tend to age with time through sequential coalescence events. This study evaluates aging dynamics in clean foams by measuring bubble populations from coalescence simulation experiments and adopting biological population dynamics analysis. The population dynamics of bubbles in clean foams during coalescence show that the mortality rates of individual bubbles change exponentially with time, regardless of initial simulation conditions, consistent with the Gompertz mortality law commonly observed in biological aging. This result would be beneficial in understanding the aging dynamics of clean foams.

Strain-rate dependency and impact dynamics of closed-cell aluminium foams

Strain rate sensitivity and deformation mechanisms of closed-cell aluminium foams under low-velocity impact loadings are investigated in this study. Instrumented drop-weight impact experiments and Finite Element (FE) modelling were conducted to explore the deformation rate dependency of aluminium foams (manufactured by CYMATTM corporation). An X-ray micro-Computed Tomography (XCT) reconstructed foam geometry was used in the FE modelling approach to explore actual deformation mechanisms and strain rate sensitivity of foams. The deformation and pore collapse mechanisms were explored through investigating the stress and plastic strain contours. Our results show that the FE modelling with rate-dependent material properties agreed with the dynamic experimental results. The foam showed significant rate sensitivity within the examined range of strain rates. Our modelling and experimental results collectively indicate that the rate sensitivity of the base material is the primarily responsible for enhancing strength during impacts. Furthermore, the FE modelling with rate-independent material properties and unique foam topology confirms the negligible inertia effect at low velocity impacts.

Screening High-Temperature Foams with Microfluidics for Thermal Recovery Processes

Thermal recovery processes, and in particular, Steam-assisted gravity drainage (SAGD), are the most common and practical in situ technology for bitumen extraction. While SAGD is effective, steam injection results in poor steam chamber growth and distribution with poor conformance specifically in areas with poor formation geology and bedding properties. These factors result in economic and environmental costs. Co-injecting foaming surfactants with noncondensable gases along with steam is an alternative solution to control the steam chamber behavior and its advancement throughout the formation. Selecting appropriate foaming surfactants is essential for successful implementation of a foam-steam processes. Conventional laboratory methods provide some indication of foaming surfactant performance but fail to reflect reservoir conditions and time scales. Microfluidics is well suited to assess the relevant pore-scale performance of foaming surfactants, at relevant conditions, with tight control over experimental parameters. Here, we develop a microfluidic approach to generate nitrogen-foam and assess stability and mobility control performance at relevant temperature (>150 °C) with results compared to those of traditional bulk foam analysis. The microconfinement associated with porous media creates more stable foam at reservoir-relevant temperatures and pressures. Direct visualization of the foaming dynamics, subsequent stability, and mobility testing in porous media provide a rapid assessment of foam performance as well as a diagnostic of surfactant product failures such as precipitation and phase decomposition, findings that directly informed pilot operations here. This screening also enables down-selection of the most promising agents for subsequent testing with candidate reservoir oil, in conventional cores or micromodels.

Numerical investigations of foam-assisted CO2 storage in saline aquifers

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.

Effects of Asphalt Foaming on Damage Characteristics of Foamed Warm Mix Asphalt

In the asphalt foaming process, the foaming water content (FWC) controls the formation and characteristics of water bubbles. These water bubbles are expected to be expelled from the foamed warm mix asphalt (WMA) during mixing and compaction. However, foaming water may not be completely expelled, rather some of the microbubbles may be trapped in the foamed WMA even after compaction. These microbubbles, or undissipated water, can diffuse over time and cause damage to the foamed WMA. To this end, this study has determined the effects of foaming on the fatigue, moisture damage, and permanent deformation characteristics of foamed WMA. Foamed asphalt and mixtures were designed with varying FWCs and they were tested using linear amplitude sweep, multiple stress creep recovery, four-point flexural beam, and Hamburg wheel tracking tests. Primarily, asphalt foaming dynamics were assessed with a laser-based non-contact method. A simplified viscoelastic continuum damage concept and a three-phase permanent deformation model were used for damage evaluation. The study reveals that foaming softens the binder, which results in slightly higher rutting and moisture susceptibility, though an equivalent or slightly improved fatigue characteristic compared with the regular hot mix asphalt.

Scaling Laws in the Dynamics of Collapse of Single Bubbles and 2D Foams.

Avalanches of rupturing bubbles play an important role in the dynamics of collapse of macroscopic liquid foams. We hypothesized that the occurrence of cascades of rupturing bubbles in foams depends, at least in part, on the power released during the rupture of a bubble. In this paper, we present results on the dynamics of single bubble bursting obtained by analyzing the pressure wave (sound) emitted by the bubble when collapsing. We found that the released energy varies linearly with bubble size, the frequency of the emitted sound follows a power law with exponent 3/2 (compatible with the Helmholtz resonator model) and the duration of a rupturing event seems to be independent of bubble size. To correlate the dynamics of individual bubbles with the dynamics of foams, we studied the occurrence of avalanches on bubble rafts and found that the phenomenon appears to be a self-organized criticality (SOC) process. The distribution functions for the size of the avalanches are a power law with exponents between 2 and 3, depending on the surfactant concentration. The distribution of times between ruptures also follows a power law with exponents close to 1, independently of the surfactant concentration.

Numerical analysis of spin foam dynamics and the flatness problem

In this paper, we apply a recently proposed numerical algorithm for finding stationary phase points in spin foam amplitudes. We study a spin foam amplitude with three vertices and a bulk face in 4d BF theory. We fix the boundary coherent states to three possible triangulations, one with zero deficit angle on the bulk face and two with non-zero deficit angle. We compute the amplitude numerically and we find a stationary phase point already at low spins in all the three cases. We comment on how this result contrasts with the claims of flatness problem in spin foam theories. We point out where these arguments may be misleading and we propose further computations to definitively answer the question.

Utilization of microcomputed tomography and pore network modeling to characterize foam dynamics

Drainage and diffusive coarsening are strongly interrelated mechanisms, which need to be studied in conjunction to acquire a thorough understanding of foam dynamics and stability. We show that microcomputed tomography (μ-CT) and pore network modeling (PNM) are valuable tools to characterize foam dynamics. Unlike existing technologies, the presented approach allows for the temporal and spatial measurement of Plateau border thickness and the volume of nodes, which are useful to study foam drainage. The coordination number of the nodes show a deviation from Plateau’s law as the foam becomes wetter. Additionally, the PNM results demonstrate a power-law relationship between permeability (κ) and liquid fraction (Φl) with an exponent of 2.6, which aligns with a channel-dominated flow regime. Overall, the proposed methodology provides a novel means to examine relevant parameters that influence foam stability and would be a valuable tool to study existing models related to foam dynamics.

Foam Dynamics in Limestone Carbonate Cores.

There is an increasing interest in foam applications in heterogeneous carbonate reservoirs to improve gas sweep and mitigate a high gas–oil ratio (GOR) in production wells. However, foam has been studied in sandstones more than in carbonates, and there are few experimental investigations considering matrix transport properties of foam in carbonates. Thus, this study takes a fundamental approach to improve our understanding of foam generation and transport process in the absence and presence of remaining oil in carbonates by co-injection of Alpha Olefin Sulfonate (AOS) solution and nitrogen (N2) in outcrop Indiana Limestone at high pressure and temperature after satisfying adsorption. In the oil-free core, development of the foam generation transient period and its transition into steady-state foam was rapid for all gas fractions, where the strongest foam was obtained at 90% gas fraction. Foam properties were successfully reproduced at different gas fractions. At remaining oil saturation, foam generation and propagation were significantly delayed and were observed at a high AOS surfactant concentration (5 wt %). Persistent foams were obtained both with and without remaining oil present, which withstood pressure gradients of N2 up to 0.5 bar/m for extended times. Therefore, if correctly designed, foam gas shut-off can be a low-cost low-risk technique to reduce problems with high GOR, gas-handling, and gas reinjections.

Relationship between interfacial and foaming properties of a Porphyra dioica seaweed protein concentrate

Porphyra dioica macroalgae can be regarded as a food-grade protein source that can be used for the stability of dispersed food systems. This work is focused on the foaming properties of a seaweed protein concentrate (SWE) from Porphyra dioica . The characterisation of air-water (A/W) interfacial layers formed after the SWE adsorption was carried out by means of interfacial tension, interfacial viscoelastic measurements and step deformation tests. These results were related to those obtained for SWE stabilized foams. Interfacial shear measurements indicate that not extensive protein-protein interactions at the A/W interface were developed (G' s = 1.0 ± 0.1·10 −2 mPa m), whereas the dilatational response (E' s = 23.5 ± 0.5 mN/m) match with the formation of a rigid interface as a result of a densely packed structure. Even if the foaming properties obtained for SWE (overall foam capacity, OFC, = 0.74 ± 0.01 mL/s) are similar to those reported for other commercial protein systems, its lower stability (t 1/2 = 204 ± 4 s) would indicate the need of adding stabilizers for an adequate shelf life of the final food product. The suitability of combining dilatational and interfacial shear rheology to predict the dynamics of dispersed systems was proven to be relevant to acquire insights of complex interfaces. • Porphyra dioica algae could be a food-grade protein source for dispersed systems. • Dilatational response indicated the formation of a rigid interface. • The weak interfacial shear response suggested the formation of a densely packed structure. • Dilatational and interfacial shear rheology was combined to predict the dynamics of foams. • Foaming properties were similar to those reported for commercial protein systems.

Effect of silica nanoparticles on the impregnation process, foaming dynamics and cell microstructure of styrene-methyl methacrylate copolymer/n-pentane foams

In the present study, two-step foaming procedure with a designed in-situ foaming observation apparatus was used to study the foaming dynamics of styrene-methyl methacrylate (St-MMA) copolymer/nanosilica composites. For this purpose, the St-MMA copolymer was synthesized using suspension copolymerization and its nanocomposites were prepared using solution method. The foaming dynamics was studied through temperature-induced (two-step batch foaming) method. Furthermore, the effects of content, size and surface chemistry of silica nanoparticles on the impregnation process, the foaming dynamics and the final morphology of prepared foams were investigated. The impregnation data showed that the presence of silica nanoparticles in matrix prolonged the impregnation and decreased diffusion coefficient. This effect would be clearer where nanoparticle contents are high and the temperature is quite above Tg. The foaming dynamics results illustrated that the nucleation and foaming rate were enhanced with the nanoparticle addition and its size reduction. At the St-MMA copolymer foaming system, the silica nanoparticles with hydrophilic surface chemistry are more efficient in comparison to hydrophobic nanoparticles where all foaming dynamics and the final microstructure parameters were improved.

Local description of foam flow, deformation and pressure drop in narrow constricted channels

We study in extensive detail the flow of dry and wet gas-liquid foams through a narrow two-dimensional channel comprising a complex constriction. The effects of constriction profile and size of aperture, foam flowrate, liquid holdup and liquid viscosity are experimentally investigated and a sophisticated image analysis procedure is developed to extract local fields of foam flow and deformation. Foam dynamics are scrutinised and interpreted in terms of local velocity distribution, elastic strain (texture tensor), plastic deformation (T1 events) and pressure drop. Important foam transformations occur in the vicinity of the constriction. For the first time, the relationship between pressure drop, flowrate and size of constriction aperture is investigated.

The effect of rock microheterogeneity on steam foam rheology

The injection of steam into a heavy oil reservoir as an enhanced oil recovery method is a mature technology. However, due to steam's high mobility, this process can suffer from gravity override, viscous fingering, and loss to thief zones. Steam foam has been used successfully in the 1970's and 1980's to improve the sweep efficiency of steam injection processes, however more work needs to be done to better understand and optimize the process for successful commercial field implementation. Recent development of better surfactants for high temperature foams above 200 °C enabled application in more reservoirs, but the physics of steam foam in varying reservoir properties has been neglected. The purpose of this work is to study the change in the rheological behavior of steam foam in rocks with varying degrees of microheterogeneity. Core floods were conducted using 1-D sand packs to determine the apparent viscosity of steam foam in varying conditions of permeability, foam quality, and shear rate. Homogenous and heterogeneous sand packs with low and high permeability were used to study the effect of rock microheterogeneity on steam foam behavior. Furthermore, the quality and velocity of the foam were varied to better understand how to optimize a steam foam process in reservoirs with varying rock quality. Based on the results, it is concluded that permeability and foam quality govern the trend of apparent viscosity growth and decay for a given sand permeability. It is determined that there is an offset of optimum foam quality between high and low permeability sands. Steam foam performs better at higher foam qualities in high permeability systems. The heterogeneity of a sand does not affect this. It was also determined that at high velocities, the shear thinning effect on steam foam is offset by new foam generation in heterogeneous sands. This phenomenon keeps the apparent viscosity of the foam stable, both in low and high permeability environments. While the permeability of the sand more significantly influences foam viscosity, it was concluded that the microheterogeneity of a sand pack also affects foam dynamics. The complexity of the pore network in a heterogeneous environment aids in the generation of foam. Overall, this work has added knowledge to the understanding of steam foam rheology in porous media. With advances in both foaming surfactant formulations and the understanding of steam foam physics, the field application of steam foam can be better optimized when taking into consideration the reservoir environment.

Characterizing the Role of Fluorocarbon and Hydrocarbon Surfactants in Firefighting-Foam Formulations for Fire-Suppression

Fluorosurfactants used in current firefighting foams must be replaced with environmentally-friendly surfactants; however, current fluorine-free surfactants have subpar fire performance. Understanding how a surfactant affects fire performance of a foam is essential for developing new fluorine-free replacement surfactants. Surfactants can affect foam’s ability to form a barrier between a fuel-pool surface and the fire, thereby suppressing the fuel feeding the fire and extinguishing it. Fire extinction performance, fuel transport through a foam layer, foam degradation by fuel, and foam spread rate were measured for solutions containing a mixture of fluorocarbon and hydrocarbon surfactants as well as the individual surfactants to understand the roles of different surfactants in a formulation. The measurements show that surfactants that reduce foam degradation and fuel transport rates through a foam covering a hot pool result in faster fire extinction. Small synergistic effects for the mixture of fluorocarbon surfactant (Cap) and a hydrocarbon surfactant (Gluc215) were found in foam degradation rate and fuel transport rate through a foam layer. The surfactant mixture had 30% longer foam lifetime and two times smaller fuel flux through a foam layer than the fluorosurfactant solution (Cap) and differed with the hydrocarbon surfactant solution (Gluc215) by more than a factor of ten. However, when a different hydrocarbon surfactant (TX100) was used in a mixture with the fluorocarbon surfactant, synergism was not observed. The small synergistic effects resulted in a small reduction in fire extinction times at high foam application rates (> 500 mL/min) at which foams can cover the pool surface quickly. At small foam application rates (< 500 mL/min), effects of foam spread rates become significant; the fluorocarbon surfactant (Cap) formed wetter foam that spread quicker and led to smaller fire extinction times than those for the surfactant mixture (Cap + Gluc215). Thus, the foam spread, foam degradation, and fuel transport rate measurements performed in the presence of a hot fuel but in the absence of a fire can explain the surfactant’s effects on fire extinction times for the six formulations. Traditionally, aqueous film formation was thought to be the key for fire suppression of AFFF rather than the foam dynamics described in this work. Additional properties such as static and dynamic surface tensions, foam bubble diameter distribution, bubble coarsening, liquid drainage from the foam, and expansion ratio were also measured in the absence of a fuel, but did not explain the trends in extinction performance among the surfactants.

Dynamics and stationary configurations of heterogeneous foams.

We consider the variational foam model, where the goal is to minimize the total surface area of a collection of bubbles subject to the constraint that the volume of each bubble is prescribed. We apply sharp interface methods to develop an efficient computational method for this problem. In addition to simulating time dynamics, we also report on stationary states of this flow for ≤ 21 bubbles in two dimensions and ≤ 17 bubbles in three dimensions. For small numbers of bubbles, we recover known analytical results, which we briefly discuss. In two dimensions, we also recover previous numerical results, computed using other methods. Particular attention is given to locally optimal foam configurations and heterogeneous foams, where the volumes of the bubbles are not equal. Configurational transitions are reported for the quasi-stationary flow where the volume of one of the bubbles is varied and, for each volume, the stationary state is computed. The results from these numerical experiments are described and accompanied by many figures and videos.

A multiphase level set approach to motion of disconnected fluid ganglia during capillary-dominated three-phase flow in porous media: Numerical validation and applications

We present a multiphase level set (MLS) approach to capillary-controlled, three-phase displacement in porous media, and use it to simulate displacements of disconnected fluid ganglia surrounded by two other fluid phases (i.e., double displacements), which are important pore-scale mechanisms for oil recovery and CO2 storage. After a comprehensive model validation on several new benchmark cases, including 3-D simulations of double displacements in a straight angular tube, we show two new applications of the MLS method. First, we simulate three-phase capillary pressure curves for gas invasion along constant oil saturation paths in sandstone. The results show significant oil redistribution by double displacements, which leads to fluctuations of gas/oil capillary pressure due to oil volume preservation, whereas oil/water capillary pressure increases mostly monotonically, yet the pressure level is lower than in the corresponding two-phase oil/water system. Further, gas/water capillary pressure is lower when mobile oil is present in the sample. The second application demonstrates the suitability of MLS method to describe foam dynamics both with and without oil present in the pore space. MLS method successfully describes well-known foam interfacial properties, and it also captures the rise of displacement capillary pressure when adding gas bubbles between continuous gas and water inside a pore channel.

A CT-scanner study of foam dynamics in porous media

We report an experimental study of N2-foam injection in a Bentheimer sandstone coupled with X-ray Computed Tomography (CT-scanner). The measurements of pressure drop and gas saturation at different flow rates and foam qualities allowed us to describe the foam dynamics under transient and steady-state flow conditions. The brine displacement by foam shows a transient piston-like displacement pattern taking place in two successive phases. Saturation profiles reveal permanent entrance effects related to the injection procedure, and transient downstream end effects related to the gradual foam build-up. Entrance effects are attenuated with a high foam quality and at low total flow rate. The rheological behavior of foam was studied in terms of apparent foam viscosity and foamed-gas mobility as a function of foam quality and gas interstitial velocity. In the low-quality regime, foam exhibits a shear-thinning behavior that can be modelled by a power function. Furthermore, for a fixed total velocity, the quasi-invariance of strong foam apparent viscosity values is shown to result from the slight increase of trapped gas saturation, within the commonly-admitted assumption of invariant foam texture in the low-quality regime. An increase in gas mobility was observed above a certain value of the foam quality. That transition between low-quality and high-quality regimes was related to a limiting capillary pressure of foam in the porous medium under consideration.