The apparent viscosity of foam flowing through smooth capillaries was measured experimentally, and a mathematical model was developed. Foam texture (a measure of bubble volume) is a key parameter in determining the following properties of foam flowing through a capillary:whether the foam exists as bulk foam or as a chain of bubbles where each pair of bubbles is separated by an individual lamella,the number of lamellae per unit length of the capillary, andthe radius of curvature of the gas-liquid interface. The apparent viscosity is the sum of three contributions:that from slugs of liquid between bubbles,the resistance to deformation of the interface of a bubble passing through a capillary, andthe surface tension gradient that results when surface active material is swept from the front of a bubble and accumulates at the back of it. The sensitivity of both measured and calculated apparent viscosity is presented as a function of bubble size, capillary radius, ratio of bubble radius to capillary radius, velocity, quality, and surface tension gradient. Introduction An early conceptual model for the relative permeability of two-phase flow was the bundle of capillary tubes model. In this model, the wetting phase flowed in the smaller capillaries and the nonwetting phase flowed in the larger capillaries. The relationship between the flow rate and pressure drop in a capillary was described by the pressure drop in a capillary was described by the Hagen-Poiseuille law. The flow of a discontinuous nonwetting phase, such as a foam, cannot be described by the Hagen-Poiseuille law. The purpose of this investigation was to determine the relationship between flow rate and pressure drop for the flow of foam through a capillary. This relationship is described by an apparent viscosity that is required to modify the Hagen-Poiseuille law for the flow of foam. Our previous observations of flow of foam lamellae in transparent porous models showed that lamellae move from pore to pore by translation. Breaking and re-forming of lamellae were rare; so was bubble coalescence. These observations suggest that the apparent viscosity of foam or lamellae in uniform, smooth capillaries is related to and, indeed, is one component of the mobility of foam in porous media. A reasonable conceptual model of a natural porous medium is a bundle of interconnected capillaries of different sizes and containing constrictions. All capillary sections, or pores, near to one another have the same capillary pressure. Thus, phase saturations may differ from pore to pore, but the radii of curvature of the gas/ liquid interfaces are equal. When flow in such an array of capillaries is modeled, resistance to flow in parallel channels of both the same and different sizes is conceived to be in parallel. Flow in smooth, uniform pore sections is in series with flow through constrictions. The component of resistance owing to smooth, uniform pore sections is approximated by resistance to flow in smooth, uniform capillaries. Measurements and theory presented here show that the most important variable affecting foam viscosity in uniform, smooth capillaries is foam texture (bubble size). Foam of finer texture has more lamellae per unit length and, as a result, greater resistance to flow. This is true both for flow of bulk foam and series of lamellae. The principal factors affecting apparent viscosity of foam in uniform capillaries are dynamic changes at gas/liquid interfaces. These are illustrated in Fig. 1.Slugs of liquid between gas bubbles resist flow.Viscous and capillary forces result in interfaces that are deformed against the restoring force of surface tension. The extent of this deformation and the resulting bubble shape partially determine apparent viscosity as a function of flow rate.Another factor determining apparent viscosity as a function of velocity is expansion of the interface at the leading end of a bubble, accompanied by compression at the trailing end. This sweeping action causes surface active material to be depleted at the front and to accumulate at the back of the bubble. The result is a surface tension gradient that resists flow. Scaling of Foam Texture and Capillary Radius Since foam texture is a measure of the average volume or equivalent radius of its bubbles, one would expect that an important scale factor is the ratio of this equivalent radius to the equivalent radius of a porous medium or the radius of a capillary. This ratio can be expressed either as the wetted perimeter per unit area of the solid or as the number of lamellae per unit length of capillary. These quantities are denoted as nL and are referred to as the number of equivalent lamellae per unit length. This concept is illustrated in Fig. 2. SPEJ P. 176

Summary. The stability of foam lamellae is limited by capillary pressure. Consequently, as the fractional flow of gas in a foam is raised at a fixed gas velocity, the capillary pressure in a porous medium at first increases and then approaches a characteristic value, here called the "limiting capillary pressure." If the gas fractional flow is increased after the limiting capillary pressure has been attained, coalescence coarsens foam texture, the liquid saturation remains constant, and the relative gas mobility becomes proportional to the ratio of gas-to-liquid fractional flow. The limiting capillary pressure varies with the surfactant formulation, gas velocity, and permeability of the medium. Introduction The mobility of a gas flowing through a porous medium is lower when it is dispersed within a liquid as a foam. Consequently, foams can improve volumetric sweep in oil-recovery processes that use gases. To apply foams optimally, the factors that influence their transport must be understood. Previous research has shown that the mobility of a foam depends heavily on its texture, which is the distribution of bubble sizes within the dispersion. The texture of foam, in turn, is governed by mechanisms that generate and destroy bubbles inside porous media: capillary snap-off and division create bubbles, while mass transfer between bubbles resulting from condensation/evaporation or diffusion and coalescence (lamella rupture) diminish bubble density. Falls et al. recently developed a model to describe the rate of foam generation by capillary snap-off and demonstrated how it could be used to simulate foam generation and flow in a simple, one-dimensional displacement. We report here the initial steps toward achieving the same level of understanding for coalescence. On the basis of how soap films and bulk foams behave, we hypothesize in particular thatthe rate of coalescence of foam bubbles lamellae in porous media depends on capillary pressure andlamellae in porous media cannot withstand capillary pressures above a porous media cannot withstand capillary pressures above a limiting value. The way this limiting capillary pressure should influence the transport of foams through porous media is subsequently detailed. Finally, experiments in which capillary pressure and foam mobility are measured concurrently are reported; these confirm that capillary pressure does indeed play a major role in determining coalescence and phase mobilities of foams in porous media. Capillary Pressure's Role In Foam Stability Outside Porous Media The behavior of soap films is described qualitatively by Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, the classic theory of colloid stability. When gas/liquid interfaces are present, ionic surfactant molecules from an aqueous solution adsorb preferentially at the interfaces, thereby creating charged surfaces. The overlap of the electric fields from these charged layers imparts stability to a foam lamella. Long-ranged, attractive van der Waals forces tend to destabilize the system.DLVO theory considers how double-layer repulsion balances against the van der Waals forces. Films that are stable to small perturbations result only when the repulsive forces are stronger that perturbations result only when the repulsive forces are stronger that the attractive ones. Imposing capillary pressure (capillary pressure is the difference between gas- and liquid-phase pressures) on a lamella forces the charged surfaces closer to one another. The double-layer repulsion must balance the van der Waals forces plus the capillary pressure. As the capillary pressure is raised, the work required to break the film decreases. At a sufficiently high capillary pressure, this work may become so small that mechanical disturbances or even thermal fluctuations may rupture the film.DLVO theory thus predicts that capillary pressure should play a role in determining the stability of foams outside porous media. This conclusion is backed by experimental studies of how capillary pressure affects that lifetimes of soap films and bulk foams. These suggest that there is a characteristic capillary pressure above which the lifetimes of lamellae become exceedingly pressure above which the lifetimes of lamellae become exceedingly short. The value of the "critical" capillary pressure varies with the surfactant formulationi.e., the type and concentration of surfactant and electrolyte. Critical capillary pressures found by Khristov et al. for single films and bulk foams made from 0.001 M sodium dodecyl sulfate solutions are recorded in Table 1. The critical capillary pressure increases as the concentration of sodium chloride is raised. pressure increases as the concentration of sodium chloride is raised. At first glance, this would appear to go against what is expected from DLVO theory: at higher electrolyte levels, the length over which the electric field from the charged surfactant layers decay should shorten and the repulsive forces should weaken. This effect may be offset, however, because salt raises the surface concentration of surfactant at the gas/liquid interfaces. (NaCl's ability to raise the critical capillary pressure of foam films may explain why salt must be added to enable some steam-foam-forming surfactants to reduce steam Mobility.)Khristov et al. also noticed that bulk foams break at lower capillary pressures than do single films created from the same solution. They attributed this tothe films in the bulk foams having larger radii than the single to and"collective effects," where disturbances from the rupture of one film cause its neighbors to break. Concepts and Consequences of a Limiting Capillary Pressure for Foam In Porous Media The stability of foams in porous media may likewise depend on capillary pressure. In porous media, however, all lamellae do not simultaneously coalesce at some "critical" capillary pressure. Instead, because lamellae are convected or are generated in situ, the capillary pressure increases up to a limiting capillary pressure as the gas fractional flow is raised. With further increase in gas fractional flow, the capillary pressure remains at its limiting value while the foam texture becomes coarser. The limiting capillary pressure for foams in porous media should vary with more than just surfactant formulation: gas velocity and the permeability of the medium can also be expected to be important variables. SPERE P. 919

The mobility of a foam depends heavily on its texture, which is the distribution of bubble sizes in the dispersion. To incorporate this variable in a mechanistic simulator, the usual conservation equations are coupled with balances on the densities of flowing and stationary bubbles in the foam. This approach to modeling foam flow is illustrated with a simulation of a displacement in which foam is generated in situ by capillary snap-off.

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Oil recovery by waterflooding in fractured formations is often dependent on spontaneous imbibition. However, spontaneous imbibition is often insignificant in oil-wet, carbonate rocks. Sodium carbonate and anionic surfactant solutions are evaluated for enhancing oil recovery by spontaneous imbibition from oil-wet carbonate rocks. Crude-oil samples must be free of surface-active contaminants to be representative of the reservoir. Calcite, which is normally positively charged, can be made negative with sodium carbonate. The ease of wettability alteration is a function of the aging time and temperature and the surfactant formulation. Formation Wettability Spontaneous imbibition in carbonate formations often does not occur or is slow compared to sandstone formations. 12-17 Treiber

Summary In this paper, recent advances in surfactant enhanced oil recovery (EOR) are reviewed. The addition of alkali to surfactant flooding in the 1980s reduced the amount of surfactant required, and the process became known as alkaline/surfactant/polymer flooding (ASP). It was recently found that the adsorption of anionic surfactants on calcite and dolomite can also be significantly reduced with sodium carbonate as the alkali, thus making the process applicable for carbonate formations. The same chemicals are also capable of altering the wettability of carbonate formations from strongly oil-wet to preferentially water-wet. This wettability alteration in combination with ultralow interfacial tension (IFT) makes it possible to displace oil from preferentially oil-wet carbonate matrix to fractures by oil/water gravity drainage. The alkaline/surfactant process consists of injecting alkali and synthetic surfactant. The alkali generates soap in situ by reaction between the alkali and naphthenic acids in the crude oil. It was recently recognized that the local ratio of soap/surfactant determines the local optimal salinity for minimum IFT. Recognition of this dependence makes it possible to design a strategy to maximize oil recovery with the least amount of surfactant and to inject polymer with the surfactant without phase separation. An additional benefit of the presence of the soap component is that it generates an oil-rich colloidal dispersion that produces ultralow IFT over a much wider range of salinity than in its absence. It was once thought that a cosolvent such as alcohol was necessary to make a microemulsion without gel-like phases or a polymer-rich phase separating from the surfactant solution. An example of an alternative to the use of alcohol is to blend two dissimilar surfactants: a branched alkoxylated sulfate and a double-tailed, internal olefin sulfonate. The single-phase region with NaCl or CaCl2 is greater for the blend than for either surfactant alone. It is also possible to incorporate polymer into such aqueous surfactant solutions without phase separation under some conditions. The injected surfactant solution has underoptimum phase behavior with the crude oil. It becomes optimum only as it mixes with the in-situ-generated soap, which is generally more hydrophobic than the injected surfactant. However, some crude oils do not have a sufficiently high acid number for this approach to work. Foam can be used for mobility control by alternating slugs of gas with slugs of surfactant solution. Besides effective oil displacement in a homogeneous sandpack, it demonstrated greatly improved sweep in a layered sandpack.

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Gas hydrates dominated by methane naturally occur in deep marine sediment along continental margins. These compounds form in pore space between the seafloor and a sub-bottom depth where appropriate stability conditions prevail. However, the amount and distribution of gas hydrate within this zone, and free gas below, can vary significantly at different locations. To understand this variability, we develop a one-dimensional numerical model that simulates the accumulation of gas hydrates in marine sediments due to upward and downward fluxes of methane over time. The model contains rigorous thermodynamic and component mass balance equations that are solved using expressions for fluid flow in compacting sediments. The effect of salinity on gas hydrate distribution is also included.The simulations delineate basic modes of gas hydrate distribution in marine sediment, including systems with no gas hydrate, gas hydrate without underlying free gas, and gas hydrate with underlying free gas below the gas hydrate stability zone, for various methane sources. The results are scaled using combinations of dimensionless variables, particularly the Peclet number and Damkohler number, such that the dependence of average hydrate saturation on numerous parameters can be summarized using two contour maps, one for a biogenic source and one for upward flux from a deeper source. Simulations also predict that for systems at steady state, large differences in parameters like seafloor depth, seafloor temperature and geothermal gradient cause only small differences in average hydrate saturation when examined with scaled variables, although important caveats exist. Our model presents a unified picture of hydrate accumulations that can be used to understand well-characterized gas hydrate systems or to predict steady-state average hydrate saturation and distribution at locations for which seismic or core data are not available.