Onset of Mobilization and the Fraction of Trapped Foam in Porous Media

Usually, foam in a porous medium flows through a small and spatially varying fraction of available pores, while the bulk of it remains trapped. The trapped foam is under a pressure gradient corresponding to the pressure gradient imposed by the flowing foam and continuous wetting liquid. The imposed pressure gradient and coalescence of the stationary foam lamellae periodically open flow channels in the trapped foam region. Foam lamellae in each of these channels flow briefly, but channels are eventually plugged by smaller bubbles entering into the trapped region. The result is a cycling of flow channels that open and close throughout the trapped foam, leading to intermittent pulsing of foam flow in that region.The dynamic behavior of foam trapped in porous media is modeled here with a pore network simulator. We predict the magnitude of the pressure drop leading to the onset of flow of foam lamellae in the region containing trapped foam. This mobilization pressure drop depends only on the number of lamellae in the flow path and on the geometry of the pores that make up this path.The principles learned in this study allow us to predict the fraction of foam that is trapped in a porous medium under given flow conditions. We present here the first analytic expression for the trapped foam fraction as a function of the pressure gradient, and of the mean and standard deviation of the pore size distribution. This expression provides a missing piece for the continuum foam flow models based on the moments of the volume-averaged population balance of foam bubbles.     

A lattice model of foam flow in porous media: A percolation approach

Because fluid flow in porous media is opaque to most observational techniques simulations of the processes occurring in porous media have become important. Typical reservoir simulations treat the flow as taking place in some averaged (Darcy-scale) medium but simulations can also be carried out at the level of the network of pores and throats of the porous medium. We report the results of a pore-scale investigation of mechanisms for the alteration of mobility by foam lamella blockage in a network of these spaces and channels of porous media. Saturation and relative permeability curves are obtained using well-known power-law expressions of percolation theory and a rescaling of the percolation parameter readily permits a number of lamella-blocking mechanisms to be treated. An explanation of the shift in breakthrough gas saturation and the deformation of the shape of permeabilityvs saturation curves upon introduction of foam is provided for a variety of blocking mechanisms. The qualitatively different features seen in experimental studies of modification of gas mobility by foam can be rationalized using only two parameters which characterize the throat-size at which blockage commences and the degree of blockage.     

Three-Phase Fractional Flow Analysis for Foam-Assisted Non-aqueous Phase Liquid (NAPL) Remediation

Among numerous foam applications in a wide range of disciplines, foam flow in porous media has been spotlighted for improved/enhanced oil recovery processes and shallow subsurface in situ NAPL (non-aqueous phase liquid) remediation, where foams can reduce the mobility of gas phase by increasing effective gas viscosity and improve sweep efficiency by mitigating subsurface heterogeneity. This study investigates how foams interact with and displace oleic contaminants in remediation treatments by using MoC (Method of Characteristics)-based three-phase fractional flow theory. Six different scenarios are considered such as different levels of foam strength (i.e., gas mobility reduction factors), different initial conditions (i.e., initially oil/water or oil/water/gas present), foam stability affected by water saturation $({S}_{\mathrm{w}})$ and oil saturation $({S}_{\mathrm{o}})$ , and uniform versus non-uniform initial saturations. The process is analyzed by using ternary diagrams, fractional flow curves, effluent histories, saturation profiles, time–distance diagrams, and pressure and recovery histories. The results show that the three-phase fractional flow analysis presented in this study is robust enough to analyze foam–oil displacements in various conditions, as validated by an in-house numerical simulator built in this study. The use of numerical simulation seems crucial when the foam process becomes very complicated and faces multiple possible solutions.     

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.     

The Effect of Pore Structure on the Electrical Conductivity of Ti

Open-pore Ti foam samples with porosity in the range of 10–70% and average pore size of 150–400 μm was fabricated by powder metallurgy method using polymethyl methacrylate (PMMA) as space holder initially. The resulting foam is anisotropic: the pores are spheroidal, being shorter along the pressing direction than in the pressing plane. The pore anisotropy decreases as the size of the polymethyl methacrylate (PMMA) particles used increases and hence with pore size, which leads to a higher conductivity in the plane of the pressing. As the porosity increases, the conductivity of porous Ti decreases dramatically. The porosity e{\varepsilon} dependence of the electrical conductivity σ could be well described by Maxwell approximation, while the differential effective medium approximation is only suitable to porous Ti with finite size of 400 μm in the porosity range of 40–70%, i.e., high porosity metal with randomly oriented spheroids.     

Numerical Analysis of Foam Motion in Porous Media Using a New Stochastic Bubble Population Model

We present a numerical analysis of the stochastic population balance (SPB) theory for foam motion in porous media. The theory condenses into a set of non-linear partial differential equations in the saturation, pressure, and bubble density. We solve the equations using the IMPES method and perform sensitivity and parametric analysis. Finally, we compare the saturation profiles obtained numerically with those obtained from CT scan foam experiments. The agreement between the theory and experiments confirms that the stochastic population balance model describes adequately foam dynamics in porous media.     

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      

Smoothed Particle Hydrodynamics Model of Non-Aqueous Phase Liquid Flow and Dissolution

A smoothed particle hydrodynamics model was developed to simulate the flow of mixtures of aqueous and non-aqueous phase liquids in porous media and the dissolution of the non-aqueous phase in the aqueous phase. The model was used to study the effects of pore-scale heterogeneity and anisotropy on the steady state dense non-aqueous phase liquid (DNAPL) saturation when gravity driven DNAPL displaces water from initially water saturated porous media. Pore-scale anisotropy was created by using co-oriented non-overlapping elliptically shaped grains to represent the porous media. After a steady state DNAPL saturation was reached, water was injected until a new steady state DNAPL saturation was reached. The amount of trapped DNAPL was found to be greater when DNAPL is displaced in the direction of the major axes of the soil grains than when it is displaced in the direction of the minor axes of the soil grains. The amount of trapped DNAPL was also found to increase with decreasing initial saturation of the continuous DNAPL phase. For the conditions used in our simulations, the saturation of the trapped DNAPL with a smaller initial DNAPL saturation was more than 3 times larger than the amount of trapped DNAPL with a larger initial saturation. These simulations were carried out assuming that the DNAPL did not dissolve in water. Simulations including the effect of dissolution of DNAPL in the aqueous phase were also performed, and effective (macroscopic) mass transfer coefficients were determined. The U.S. Government’s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

Pore Network Analysis of Resistivity Index for Water-Wet Porous Media

Pore network analysis is used to investigate the effects of microscopic parameters of the pore structure such as pore geometry, pore-size distribution, pore space topology and fractal roughness porosity on resistivity index curves of strongly water-wet porous media. The pore structure is represented by a three-dimensional network of lamellar capillary tubes with fractal roughness features along their pore-walls. Oil-water drainage (conventional porous plate method) is simulated with a bond percolation-and-fractal roughness model without trapping of wetting fluid. The resistivity index, saturation exponent and capillary pressure are expressed as approximate functions of the pore network parameters by adopting some simplifying assumptions and using effective medium approximation, universal scaling laws of percolation theory and fractal geometry. Some new phenomenological models of resistivity index curves of porous media are derived. Finally, the eventual changes of resistivity index caused by the permanent entrapment of wetting fluid in the pore network are also studied.Resistivity index and saturation exponent are decreasing functions of the degree of correlation between pore volume and pore size as well as the width of the pore size distribution, whereas they are independent on the mean pore size. At low water saturations, the saturation exponent decreases or increases for pore systems of low or high fractal roughness porosity respectively, and obtains finite values only when the wetting fluid is not trapped in the pore network. The dependence of saturation exponent on water saturation weakens for strong correlation between pore volume and pore size, high network connectivity, medium pore-wall roughness porosity and medium width of the pore size distribution. The resistivity index can be described succesfully by generalized 3-parameter power functions of water saturation where the parameter values are related closely with the geometrical, topological and fractal properties of the pore structure.     

Liquid distribution and electrical conductivity in foam

Experiments were conducted with aqueous foam generated by bubbling nitrogen through anionic, cationic and nonionic surfactant solutions. The ratio of the electrical conductivity of the foam to that of the liquid was found to increase monotonically with the volumetric liquid fraction in the foam. The choice of surfactant as well as the degree of inhomogeneity in bubble size were found to be without effect on the relationship. However, for a fixed liquid fraction, it was found that decreasing the mean bubble size can decrease the conductivity ratio somewhat, as well as accelerate the approach toward Lemlich's limit for low density foam. This effect was attributed to increased suction within the Plateau borders.     

Dynamics and radiation of a single bubble under conditions of abnormal compressibility of a bubbly liquid

An equation is proposed for the pulsation of a single cavity in an abnormally compressible bubbly liquid which is in pressure equilibrium and whose state is described by the Lyakhov equation. In the equilibrium case, this equation is significantly simplified. Numerical analysis is performed of the bubble dynamics and acoustic losses (the profile and amplitude of the radiation wave generated on the bubble wall from the side of the liquid). It is shown that as the volumetric gas concentration k₀ in the equilibrium bubbly medium increases, the degree of compression of the cavity by stationary shock wave decreases and its pulsations decrease considerably and disappear already at k₀ = 3%. In the compression process, the cavity asymptotically reaches an equilibrium state that does not depend on the value of k₀ and is determined only by the shock-wave amplitude. The radiation wave takes the shape of a soliton whose amplitude is much smaller and whose width is considerably greater than the corresponding parameters in a single-phase liquid. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 51–57, May–June, 2007.     

In-Situ Capillary Trapping of CO<Subscript>2</Subscript> by Co-Injection

Co-injection of water with CO₂ is an effective scheme to control initial gas saturation in porous media. A fractional flow rate of water of approximately 5–10% is sufficient to reduce initial gas saturations. After water injection following the co-injection, most of the gas injected in the porous media is trapped by capillarity with a low fractional volume of migrating gas. In this study, we first derive an analytical model to predict the gas saturation levels for co-injection with water. The initial gas saturation is controlled by the fractional flow ratio in the co-injection process. Next, we experimentally investigate the effect of initial gas saturation on residual gas saturation at capillary trapping by co-injecting gas and water followed by pure water injection, using a water and nitrogen system at room temperature. Depending on relative permeability, initial gas saturation is reduced by co-injection of water. If the initial saturation in the Berea sandstone core is controlled at 20–40%, most of the gas is trapped by capillarity, and less than 20% of the gas with respect to the injected gas volume is migrated by water injection. In the packed bed of Toyoura standard sand, the initial gas saturation is approximately 20% for a wide range of gas with a fractional flow rate from 0.50 to 0.95. The residual gas saturation for these conditions is approximately 15%. Less than approximately 25% of the gas migrates by water injection. The amount of water required for co-injection systems is estimated on the basis of the analytical model and experimental results.     

Investigation of the flow stability of liquids with incipient gas bubbles in porous media

The stability of the steady-state flow regimes of a liquid with dissolved gas in a porous medium is investigated in the region of the saturation pressure. It is shown that under certain conditions periodic and stochastic self-oscillations caused by the accumulation in the porous medium and subsequent entrainment of the very small gas bubbles formed as a result of pressure reduction may arise. Experimental data that confirmed the theoretical results are presented. Ufa. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 66–73, March–April, 1994.     

On the stability of Taylor bubbles inside a confined highly porous medium

This work focuses on the local hydrodynamics of a multiphase gas–liquid flow forced into an innovative medium of high porosity (96%): an open cell solid foam. The gas (nitrogen) and liquid (ethanol) phases are injected at constant flow-rates in a millichannel to form a well-controlled Taylor flow which enters the porous medium. Based on a fluorescence technique, the apparent liquid holdup in the porous medium is quantified, and its evolution in time and along the porous medium extracted from spatiotemporal diagrams. The analysis of the main frequency, when varying the gas–liquid flow-rate ratio, leads to the identification of two hydrodynamic regimes. A model based on a scaling analysis is proposed to quantify the dimensionless numbers describing the transition between both regimes. It points out that the bubble length fixed by the Taylor flow is the control parameter. The model prediction of the critical bubble length at which the transition occurs is in good agreement with the experimental observations.     

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.     

Foam Mobility in Heterogeneous Porous Media

It is shown experimentally that in situ generation of foam is an effective method for achieving gas mobility control and diverting injected fluid to low permeability strata within heterogeneous porous media. The experimental system is composed of a 0.395 porosity, 5.35 µm² synthetic sandstone and a 0.244 porosity, 0.686 µm² natural sandstone. The cores are arranged in parallel and communicate through common injection and production conditions. Nitrogen is the gas phase and alpha-olefin sulfonate (AOS 1416) in brine is the foamer. Three types of experiments were conducted. First, gas alone was injected into the system after presaturation with the foamer solution. Second, gas and foamer solution were coinjected at an overall gas fraction of 90% into cores presaturated with surfactant. Each core accepted a portion of the injected gas and liquid according to the mobility within the core. Lastly, gas and foamer solution were coinjected into the individual, isolated porous media in order to establish baseline behavior. The results are striking. It is possible to achieve total diversion of gas injection to the low permeability medium in some cases. The results also confirm previous predictions that foamed gas can be more mobile in lower permeability porous media.     

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.     

The Blocking Ability and Flowing Characteristics of Steady Foams in Porous Media

Foam flow experiments were carried out to study the influence factors such as surfactant concentration, foam quality, injection rate of liquid and gas, permeability of porous media, temperature, and oil saturation on blocking ability and flowing characteristics of steady foams in porous media. Foam blocking mechanisms and flowing characteristics were summarized according to the experimental results and foam migration behavior. The results showed that the pressure distribution of flowing foams was linearly descending in porous media at steady state. The results further showed that the foam size and quality in pores along the sand pack were almost uniform, that is, foam generation and destruction gradually reached dynamic equilibrium at steady state. In porous media, the blocking ability of steady foams increased with the concentration of the foaming agent and the increase in the permeability of porous media, but the blocking ability decreased with the increase in the temperature, the shearing rate, and the oil saturation of the porous media. Foam resistance factor reached maximal value at the foam quality of 85% in porous media.     

Age dependence of the drag force in an aqueous foam

The drag force on a sphere moving through an aqueous foam is measured as the foam ages. After an initial period, the steady-state drag decreases with age T as T ^{−0.54±0.14}. As the mean bubble size R in the foam coarsens as T ^0.5, this implies that the drag force scales as The transient buildup of the force when the sphere starts to move is described by a single exponential approach to the steady-state drag while its relaxation when the motion stops is described by the sum of three exponential relaxations. This is as for fresh foam, but the coefficients and time constants vary systematically with age. For the most part, these quantities also show a power law scaling with T. The age dependence of the quantities determined in this study is discussed in terms of the mean bubble size.     

Micro Bubbles in Solution–Gas Drive in Heavy Oil: Their Existence and Importance

This work investigates the existence and importance of the micro bubbles in heavy oil subjected to solution?Cgas drive. The term ??micro bubble?? will be used to refer to the free-gas phase that flows with the oil, no faster and no slower. Two types of experiments are reported here; slow and fast experiments. These experiments were previously reported by Sheikha and Pooladi-Darvish (SPE Res Eval Eng 12(3):390?C398, 2009) and were used to investigate the effects of pressure gradient and depletion rate of oil recovery. In this work, we investigate the nature of two-phase flow, and find that in the slow runs, the flow was characterized by single-phase flow of oil until a gas saturation of 2±1% was reached. Above this gas saturation, bulk flow of gas was observed at mobilities much higher than that of micro bubbles. Recovery factor of the slow tests was below 4%. In the fast runs, flow of bubbles is observed shortly after they are formed in porous media. The gas mobility and fractional flow remain low until a gas saturation of 7±1% is reached. Flow of gas between approximately 2 and 7% gas saturation is consistent with that of micro bubbles. Gas fractional flow increases sharply at gas saturations above approximately 7%. The results indicate that the attainment of high recovery values (12?C14%) observed in the fast experiments is partially as a result of low mobility of micro-gas bubbles. The pressure decline rate of each flow experiment was varied independent of its respective withdrawal rate. This did not alter the difference in recovery and mobility behaviour of the fast and slow experiments; the fast experiments exhibited a significant period of low mobility gas flow consistent with flow of micro bubbles. Regardless of the pressure decline rate, the slow experiments did not exhibit this period of low mobility gas flow.