Trapped Gas Fraction During Steady-State Foam Flow

Trapped or stationary gas contributes significantly to the extent of gas mobility reduction for aqueous foams. Simultaneous measurements of effluent bubble sizes and trapped gas saturation in sandstone are reported for the first time. Roughly 80% of the gas saturation in an aqueous foam is stationary at steady state in this permeable porous medium. The experiments show that as gas velocity increases, the trapped gas fraction decreases. Similarly, as injected gas–liquid ratio increases, the trapped gas fraction decreases. Hence, the absolute velocities of gas and aqueous surfactant solution are fundamental to foamed-gas mobility reduction for they help determine in situ foam texture. Effluent foam bubbles range in size from 60 to 120 μm in diameter. The smaller the effluent bubble, the smaller is the fraction of mobile gas. Scaling laws from network percolation theory are used to engender a mechanistic understanding of the various parameters identified as important in the experimental program. The closed form approimation predicts that the trapped gas fraction is a weak function of pressure gradient, foam-bubble size, and the permeability of the porous medium. Moreover, the theory reproduces well the newly obtained experimental data.     

Coupling of Foam Drainage and Viscous Fingering in Porous Media Revealed by X-ray Computed Tomography

We investigate the development foam in granular porous media and the subsequent flow of the surfactant solution, where the fluid fraction variations are visualized and quantified using X-ray computed tomography. It is found that foam flows in a front like manner leading to a residual liquid fraction of 0.18±0.01, far from the inlet surface of the porous sample. A desaturation backward wave is also observed during foam development. We provided direct evidence that the flow of surfactant solution in porous media containing foam gives rise to superposition of a drainage wave and a characteristic viscous fingering pattern. In the wave the liquid fraction ranges from the above residual value to nearly 0.25±0.01. The liquid fraction associated with the viscous fingering decays as a function of distance but the inlet value increases up to 0.06±0.01. Certain ideas about the physics of foam flow in porous media are revised in the light of our findings.     

Effect of bubble size on void fraction fluctuations in dispersed bubble flows

It is known that bubble size affects seriously the average void fraction in bubbly flows where buoyant velocities vary considerably with bubble size. On the contrary, there is no systematic literature report about bubble size effects on the intensity and frequency of void fraction fluctuations around the average void fraction. This work aims to provide such information. An electrical impedance technique is employed along with non-intrusive ring electrodes to register void fraction fluctuations down to 10⁻⁵. Bubble size fluctuations are estimated from high resolution optical images. Experiments are conducted in co-current upward dispersed bubble flow inside a 21 mm tube with average bubble size between ∼50 and ∼700 μm. Water and blood simulant are used as test liquids with velocity from ∼3 to ∼30 cm s⁻¹. The above resemble conditions of Decompression Sickness (DCS) in the bloodstream of human vena cava. It is found that the intensity and frequency of void fraction fluctuations vary appreciably with bubble size at constant gas and liquid flow rates. Moreover, these variations are not random but scale with bubble size. As a first step to quantify this effect, an empirical expression is derived that relates average bubble size to the ratio standard deviation/average value of void fraction.     

Surfactant Concentration and End Effects on Foam Flow in Porous Media

Foaming injected gas is a useful and promising technique for achieving mobility control in porous media. Typically, such foams are aqueous. In the presence of foam, gas and liquid flow behavior is determined by bubble size or foam texture. The thin-liquid films that separate foam into bubbles must be relatively stable for a foam to be finely textured and thereby be effective as a displacing or blocking agent. Film stability is a strong function of surfactant concentration and type. This work studies foam flow behavior at a variety of surfactant concentrations using experiments and a numerical model. Thus, the foam behavior examined spans from strong to weak.Specifically, a suite of foam displacements over a range of surfactant concentrations in a roughly 7m², one-dimensional sandpack are monitored using X-ray computed tomography (CT). Sequential pressure taps are employed to measure flow resistance. Nitrogen is the gas and an alpha olefin sulfonate (AOS 1416) in brine is the foamer. Surfactant concentrations studied vary from 0.005 to 1wt%. Because foam mobility depends strongly upon its texture, a bubble population balance model is both useful and necessary to describe the experimental results thoroughly and self consistently. Excellent agreement is found between experiment and theory.     

Development of co-current air–water flow in a vertical pipe

Measurements of the cross-sectional distribution of the gas fraction and bubble size distributions were conducted in a vertical pipe with an inner diameter of 51.2 mm and a length of about 3 m for air/water bubbly and slug flow regimes. The use of a wire-mesh sensor obtained a high resolution of the gas fraction data in space as well as in time. From this data, time averaged values for the two-dimensional gas fraction profiles were decomposed into a large number of bubble size classes. This allowed the extraction of the radial gas fraction profiles for a given range of bubble sizes as well as data for local bubble size distributions. The structure of the flow can be characterized by such data. The measurements were performed for up to 10 different inlet lengths and for about 100 combinations of gas and liquid volume flow rates. The data is very useful for the development and validation of meso-scale models to account for the forces acting on a bubble in a shear liquid flow and models for bubble coalescence and break-up. Such models are necessary for the validation of CFD codes for the simulation of bubbly flows.     

Controlled foam generation using cyclic diphasic flows through a constriction

Numerous industrial and academic applications of liquid foams require a fine control over their bubble size distribution and their liquid content. A particular challenge remains the generation of foams with very small bubbles and low liquid content. A simple technique which fulfils these different criteria, the “double-syringe technique”, has been exploited for decades in hospital applications. In this technique, the foaming liquid and gas are pushed repeatedly back and forth through the constriction that connects two syringes. After having motorised the technique we investigate here the influence of the different processing conditions on the obtained foam properties in a quantitative manner. We show that this technique is unique in producing foams with the same characteristic bubble size distributions over a wide range of processing conditions (tubing, fluid velocities,...), making it an ideal tool for controlled foam generation. In contrast to other techniques, the liquid fraction in the double-syringe technique can be varied without impacting the bubble size distribution. Using high-speed imaging we show that bubbles are dispersed in the aqueous phase at two different places in the device via a hitherto unreported fragmentation mechanism. We put in evidence that the obtained bubble size distributions are largely independent of most processing parameters with the exception of the geometry of the constriction and the foam formulation. We put forward a first analysis of the non-dimensional numbers of the flow and compare our results with bubbles size distributions obtained from fragmentation processes. Future work on simplified model systems is required to explain the observed mechanisms.     

A Pore Scale Study of Non-Newtonian Effect on Foam Propagation in Porous Media

CO₂ injection is one of the most promising techniques to enhance oil recovery. However, an unfavorable mobility ratio, reservoir heterogeneity and gravity segregation can reduce the macroscopic sweep efficiency. In situ foaming of injected CO₂ is the method that has the most potential for improving sweep efficiency based on controlling CO₂ mobility. This study investigates the foaming behavior of N,N,N′-trimethyl-N′-tallow-1,3-diaminopropane (DTTM) surfactant with CO₂ in a transparent porous microflow model with natural rock pore structures. It focuses on the effect of the salinity induced non-Newtonian behavior of DTTM solution on foam propagation. The performance of foams stabilized by 0.5 wt% DTTM solution over the viscosity range from 0.71 (at 5 wt% NaCl) to 41 cp (at 20 wt% NaCl) was compared with conventional polymer-enhanced foams whose liquid phase contained a commonly used foaming surfactant, C15–18 Internal Olefin Sulfonate (C15–18 IOS) and a hydrolyzed polyacrylamide. Such comparisons have also provided insight into the respective impacts of liquid phase viscosification by worm-like surfactant micelles and polymer on foam texture associated with its rheological characteristics. It was found that at low aqueous phase viscosity (injection liquid viscosity of 0.71 cp) the maximum achievable viscosity of DDTM foam was around 1000 cp, which was 80 times IOS stabilized foam. The interfacial tension of DTTM was higher than that of IOS, resulting coarser foam texture and higher individual lamella resistance. An increase in DTTM solution viscosity by a factor of 33 decreased foam generation and viscosity for gas injection. This was not observed for the simultaneous injection of gas and DTTM solution. Overall, the effect of liquid phase viscosity on transient foam behavior during gas injection is similar for both DTTM and IOS regardless of the difference in the nature of viscosifying agents (WLM vs 3330 s polymer). An increase in gas injection pressure without liquid injection delayed foam propagation and reduced the magnitude of foam viscosity. The results from this study indicated that DTTM surfactant is an important alternative to commercially available polymers that have been used to enhance foam performance in porous media. This particular surfactant type also overcomes several disadvantages of polymers such as limited temperature and salinity tolerance, shear degradation, and filtering in low permeability formations.

     

Void fraction,bubble velocity and bubble size in two-phase flow

Experiments were performed in atmosphereic vertical air-water flows, for void fractions between 0.25 and 0.75 (cross-sectional averages) and superficial liquid velocities of 1.3, 1.7 and 2.1 m/s. Local values of void fraction and bubble velocity as well as the bubble diameter were measured by means of a resistivity probe technique. Reliable values were obtained for the local void fraction over the entire range $\text{0 ≤ α ≤ 1}$. The void fraction profiles appeared to have a local maximum at the pipe center, local maxima close to the wall were obviously absent. The resistivity probes are shown to measure the velocity of the interface between the conducting and nonconducting phases, which equals the gas velocity only for low void fractions. The measured data for void fraction and bubble velocity were correlated by means of power law distribution functions, with exponents given by a function of the cross-sectionally averaged void fraction. The Sauter mean diameters for the bubble size spectra found, agree reasonably well with diameters predicted by a theoretical model based on the energy dissipation in the flow.     

An experimental study of the heat transfer in PS foam insulation

Heat transfer mechanisms in 14 samples of vacuum insulation panels (VIPs) are examined to reveal the influence of porous foam structure on VIP performance. The samples were produced by in-house equipment that was able to vary the foam structure by modulating the process temperature and pressure. Two parameters are proposed to describe the foam structure, namely, the broken cell ratio and the average cell size. Under a specific solid volume fraction, the average cell size shows a linear dependence on the broken cell ratio. Furthermore, the radiation and conduction heat transport data correlate well with these parameters. Radiation heat transfer increases as the broken cell ratio (cell size) increases, but solid conduction decreases as the broken cell ratio (cell size) increases. Consequently, an optimum broken cell ratio (cell size) exists such that the total heat transport is minimum under a specific solid volume fraction. However, the majority of VIP heat transfer is solid conduction. Solid conduction accounts for more than 80% of the total heat transport and is largely affected by the solid volume fraction. A rule of thumb for improving VIP performance is to reduce the solid volume fraction as much as possible to eliminate solid conduction, and maintain the cell size at an optimum value that is dependent on the solid volume fraction.     

Effect of surfactants on liquid loading in vertical wells

Most gas wells produce some amount of liquid. The liquid is either condensate or water. At high rates, the gas is able to entrain liquid to the surface; however, as gas well depletes, the liquid drops back in a gas well (called liquid loading) creating a back pressure on the reservoir formation. Addition of surfactants to the well to remove liquid is one of the common methods used in gas wells. Liquid loading in vertical gas wells with and without surfactant application was investigated in this study. Anionic, two types of amphoteric (amphoteric I and amphoteric II), sulphonate and cationic surfactants were tested in 2-inch and 4-inch 40-feet vertical pipes. Pressure gradient and liquid holdup are measured. Visual observation with a high speed camera was used to gain insight into the direction of foam flow in intermittent flow and foam film flow under annular flow conditions.Liquid loading is initiated when the liquid film attached to the wall in annular flow starts flowing downwards. Introduction of foam causes the gas velocity at which film reversal occurs to decrease; this shift increases with increasing surfactant concentration and it is more pronounced in 2-inch pipe than in 4-inch pipe. That is, the benefit of surfactants is much more pronounced in 2-inch pipe than in 4-inch pipe. The reason for postponement of liquid loading is reduction in the liquid holdup at low gas velocities which reduces the liquid holdup in foam flow compared to air-water flow. However, at higher gas velocities, the pressure drop in 2-inch compared to 4-inch pipe increases rapidly as the surfactant concentration increases. The selection of optimum concentration of the surfactant is a balance between the reductions in the gas velocity at which liquid loading occurs compared to increase in the frictional loss as the concentration increases. We provide guidelines about the selection of the surfactant concentration.Visual observations using high speed camera show differences in the behavior under foam flow conditions. Unlike air-water flow, the liquid film attached to the wall is replaced by thick foam capturing the gas bubbles. The type of roll waves which carry the liquid in 2-inch pipe is different than what was observed in 4-inch pipe. Compared to 4-inch pipe, the roll waves in 2-inch pipe are much thicker. This partly explains the differences in 2-inch versus 4-inch pipe behavior.     

Experimental investigation of three-phase flow in a vertical pipe: Local characteristics of the gas phase for gas-lift conditions

Laboratory experiments have been performed on the flow of oil, water and air through a vertical pipe in order to study the gas-lift technique for oil–water flows. Special attention was paid to the phase inversion phenomenon, by which the continuous phase switches to the dispersed phase and vice versa. By using different types of gas injectors the influence of the bubble size of the injected air on the efficiency of the gas-lift technique (in particular at the point of phase inversion) was studied. Also the gas and liquid mixture velocities were varied. The air bubbles were detected by means of optical fibre probes. Local measurements of the time-averaged gas volume fraction, bubble size and bubble velocity were carried out, as well as pressure measurements.     

Lattice gas simulations of two-dimensional liquid foams

Liquid foam is a dense random packing of gas bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to investigations of the physical properties of foams, and the situation becomes even more complicated if the flow of the liquid through the foam is considered too. Here we propose a fresh approach to tackling these issues by introducing a discrete two-dimensional hybrid lattice gas model of liquid foams. While lattice gas models have been used to model two-phase liquids in the past, their application to the study of liquid foams is novel and proves promising. We represent bubble surfaces by a finite number of nodes, and model the surrounding liquid as a lattice gas (with a finite number of liquid particles). The gas in the bubbles is treated as an ideal gas at constant temperature. The model is tested by choosing an arbitrarily shaped bubble that evolves into a circular shape in agreement with Laplaces law. The model is then employed to simulate periodic ordered and disordered dry and wet foams. Since our model is specifically designed to handle wet foams up to a critical liquid fraction of 0.16 (void fraction of random packing of disks), we are able to compute the variation in coordination number (average number of neighbours of a bubble) over the whole range of liquid fractions, and we find it to be a linear function of the shear modulus.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, 11–13 September 2003.     

Fiber-optic probe measurements of void fraction and bubble size distributions beneath breaking waves

Experiments were performed to determine the accuracy of single-tip fiber-optic probes for making simultaneous measurements of the void fraction and bubble size distributions under breaking waves. Tests in a vertical bubble column showed that the normalized RMS error in the void fraction measurements was ∼10%. The relationship between bubble rise time and bubble velocity was investigated in a unidirectional flow cell. Similar to previous studies the rise time and bubble velocity were found to be related by a power law equation. The probes can provide mean bubble velocities accurate to ±10% when a minimum of ∼15 individual bubble velocities are averaged. The fiber-optic probes were deployed beneath a plunging breaking wave in a laboratory wave channel. The slope and shape of the bubble cord length size distribution measured with the probes was found to agree closely with the size distribution measured from digital video recordings. The probes were then positioned in the splash-up zone of a plunging breaker and the resulting cord length distribution had a shape and slope that was in agreement with previous measurements. These results demonstrate that single-tip fiber optic probes can provide accurate simultaneous measurements of the void fraction and bubble sizes inside the dense bubble clouds entrained by breaking waves.     

Oil emulsion separation with fluidic oscillator generated microbubbles

Surfactants stabilise oil droplets in water, forming a dispersed oil–water emulsion. Treatment of oily effluents is a serious challenge owing to the high stability and colloidal nature of the oil droplets. In many applications, microbubbles are employed for separation purposes due to their buoyancy and increased surface area to volume ratio. This property has been exploited in the water treatment industry for separation in a process known as dissolved air flotation (DAF). Though practically efficient, the process is energy intensive operating at >5 bars and consequently consuming ∼90% of the total energy required in water purification plants. In this study microbubbles were produced by fluidic oscillation via a no-moving part diverter valve to cut down the energy consumption considerably. Microbubbles are applied for the separation of emulsified oil in a process known as microflotation. The mean bubble size generated by fluidic oscillation from the 50 μm pore diffuser was ∼100 μm, otherwise coarse bubbles were produced under steady flow. The effect of surfactant concentration on oil droplet size was investigated. It was found that oil droplet size varied inversely proportional to surfactant concentration. In addition, it was found that the oil removal efficiency also depends on the surfactant concentration. The maximum oil removal efficiency by Microflotation was found to be 91% under lowest surfactant concentration tested (0.3 wt%) whilst at highest surfactant concentration used (10 wt%); lowest recovery efficiency (19.4%) was recorded.     

Analysis of the characteristic lengths in the bubble and slug flow regimes generated in a capillary T-junction

We present an analysis of the geometry of the continuous and disperse phases in the bubble and slug flow regimes in air–water mixtures generated in a capillary T-junction of 1  mm internal diameter. Bubble size dispersion is very low in the considered flow patterns. The concept of unit cell is used to identify two characteristic lengths of the two-phase flow, namely, the unit cell length and the bubble length. The relationship between these lengths and the gas and liquid superficial velocities, gas mean velocity, bubble generation frequency and volume average void fraction is analysed. We conclude that in the considered configuration the unit cell and bubble lengths can be predicted either by the ratio of the gas–liquid superficial velocities or the volume average void fraction.     

Oscillatory Marangoni convection around the air bubble in a vertical surfactant stratificationConvection de Marangoni oscillante autour d'une bulle d'air dans une stratification verticale surfactante

The solutocapillary Marangoni convection around a gas bubble in the inhomogeneous binary mixture of miscible fluids with a vertical surfactant concentration gradient was studied experimentally. A new phenomenon, the oscillatory instability of the surfactant mass transfer, near the bubble boundary, was detected and investigated. The interpretation of this effect as an interaction between the surfactant adsorption at the bubble free surface and solutocapillary and buoyancy convective mechanisms is proposed. The experimental data on oscillation period in relation to bubble dimensions, time, liquid layer thickness, physico-chemical fluid parameters and concentration gradients are presented and discussed. To cite this article: K. Kostarev et al., C. R. Mecanique 332 (2004).     

Dynamics of a Taylor bubble in steady and pulsatile co-current flow of Newtonian and shear-thinning liquids in a vertical tube

A computational analysis is carried out to ascertain the effects of steady and pulsatile co-current flow, on the dynamics of an air bubble rising in a vertical tube containing water or a solution of Carboxymethylcellulose (CMC) in water. The mass fraction (m_f) of CMC in the solution is varied in the range 0.1% ⩽ m_f ⩽ 1% to accommodate zero-shear dynamic viscosities in the range 0.009–2.99 Pa-s. It was found that the transient and time-averaged velocities of Taylor bubbles are independent of the bubble size under both steady as well as pulsatile co-current flows. The lengths of the Taylor bubbles under the Newtonian conditions are found to be consistently greater than the corresponding shear-thinning non-Newtonian conditions for any given zero-shear dynamic viscosity of the liquid. In contrast to observations in stagnant liquid columns, an increase in the dynamic viscosity of the liquid (under Newtonian conditions) results in a concomitant increase in the bubble velocity, for any given co-current liquid velocity. In shear-thinning liquids, the change in the bubble velocity with an increase in m_f is found to be relatively greater at higher co-current liquid velocities. During pulsatile shear-thinning flows, distinct ripples are observed to occur on the bubble surface at higher values of m_f, the locations of which remain stationary with reference to the tube for any given pulsatile flow frequency, while the bubble propagated upwards. In such a pulsatile shear-thinning flow, a localised increase in dynamic viscosity is accompanied near each ripple, which results in a localised re-circulation region inside the bubble, unlike a single re-circulation region that occurs in Newtonian liquids, or shear-thinning liquids with low values of m_f. It is also seen that as compared to frequency, the amplitude of pulsatile flow has a greater influence on the oscillating characteristics of the rising Taylor bubble. The amplitude of oscillation in the bubble velocity increases with an increase in the CMC mass fraction, for any given value of pulsatile flow amplitude.     

Effects of surfactant on liquid film thickness in the Bretherton problem

The effects of insoluble and soluble surfactant on the motion of a long bubble propagating through a capillary tube are investigated computationally using a finite-difference/front-tracking method. Emphasis is placed on the effects of surfactant on the liquid film thickness between the bubble and the tube wall. The numerical method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible Navier–Stokes equations. A non-linear equation of state is used to relate surface tension coefficient to surfactant concentration at the interface. Computations are first performed for soluble cases and then repeated for the corresponding clean and insoluble cases for a wide range of governing non-dimensional parameters in order to investigate the effects of surfactant and surfactant solubility. The computed film thickness for the clean case is found to be in a good agreement with Taylor’s law indicating the accuracy of the numerical method. We found that both the insoluble and soluble surfactant generally have a thickening effect on the film thickness, which is especially pronounced at low capillary numbers. This thickening effect strengthens with increasing sensitivity of surface tension to interfacial surfactant coverage mainly due to the enhanced Marangoni stresses along the liquid film. It is also observed that film thickening shows a non-monotonic behavior for variations in Peclet number. The validity of insoluble surfactant assumption is assessed for various non-dimensional numbers and it is demonstrated that insoluble assumption is valid only when capillary number is very low, i.e., Ca ≪ 1 and when surface tension is highly sensitive to interfacial surfactant coverage, i.e., the elasticity number is large.     

多孔介质中稳定泡沫的流动计算及实验研究

将多孔介质简化为一簇变截面毛管束,根据多孔介质的颗粒直径、颗粒排列方式、孔喉尺度比及束缚水饱和度,计算出变截面毛细管的喉道半径和孔隙半径. 在考虑多孔介质喉道和孔隙中单个气泡的受力和变形基础上,利用动量守恒定理,推导出单个孔隙单元内液相的压力分布和孔隙单元两端的压差计算公式,最终得到多孔介质的压力分布计算公式. 利用长U型填砂管对稳定泡沫的流动特性进行了实验研究. 研究结果表明:稳定泡沫流动时多孔介质中的压力分布呈线性下降,影响泡沫在多孔介质中流动特性的因素包括:多孔介质的孔喉结构、泡沫流体的流量和干度、气液界面张力、气泡尺寸,其中孔喉结构和泡沫干度是影响泡沫封堵能力的主要因素.关键词: 稳定泡沫;多孔介质;变截面毛管;流动;表观粘度;压力分布;实验研究      

DISCRETE MODELLING OF TWO-DIMENSIONAL LIQUID FOAMS

Liquid foam is a dense random packing of gas or liquid bubbles in a small amount of immiscible liquid containing surfactants. The liquid within the Plateau borders, although small in volume, causes considerable difficulties to the investigation of the spatial structure and physical properties of foams, and the situation becomes even more complicated as the fluid flows. To solve these problems, a discrete model of two-dimensional liquid foams on the bubble scale is proposed in this work. The bubble surface is represented with finite number of nodes, and the liquid within Plateau borders is discretized into lattice particles. The gas in bubbles is treated as ideal gas at constant temperatures. This model is tested by choosing an arbitrary shape bubble as the initial condition. This then automatically evolves into a circular shape, which indicates that the surface energy minimum routine is obeyed without calling external controlling conditions. Without inserting liquid particle among the bubble channels, periodic ordered and disordered dry foams are both simulated, and the fine foam structures are developed. Wet foams are also simulated by inserting fluid among bubble channels. The calculated coordination number, as a function of liquid fractions, agrees well with the standard values.