Foam flow in porous media

Laboratory studies of foam flow in porous media suggest that the relative foam mobility is approximately inversely proportional to the permeability. This means that foam has potential as a flow-diverting agent, in principle sweeping low-permeability regions as effectively as high-permeability regions [716]. 

The thin liquid films bounded by gas on one side and by oil on the other, denoted air/water/oil are referred to as pseudoemulsion films [301], They are important because the pseudoemulsion film can be metastable in a dynamic system even when the thermodynamic entering coefficient is greater than zero. Several groups [301,331,342] have interpreted foam destabilization by oils in terms of pseudoemulsion film stabilities [114]. This is done based on disjoining pressures in the films, which may be measured experimentally [330] or calculated from electrostatic and dispersion forces [331], The pseudoemulsion model has been applied to both bulk foams and to foams flowing in porous media. 

To control features of the flow itself (examples include drag reduction by addition of polymer or microbubbles, magnetic stabilization of fluidized beds, foam flow in porous media for mobility control, antimisting or cavitation suppression via polymer additives) and, finally,... 

EOR process requires a detail study not only of foam behaviour in porous media but also of the options to control it. Foam flow in porous media during EOR is a complex, multifaceted process. A number of papers are dedicated to that topic, including some reviews [e.g. 13,14,18] which describe the experimental set-up used in the study of foams in porous media. We will focus on those illustrating the efficiency of EOR from oil pools and the role of some important factors, involving the effect of foam properties, especially of the critical capillary pressure. 

Mast, in a pioneering 1972 paper, reported visual observations of foam flow in etched glass micromodels (37 ) His observations showed that some of the conflicting claims about the properties of foam flow in porous media were probably due simply to the dominance of different mechanisms under the various conditions employed by the separate researchers (37). Mast observed most of the various mechanisms of dispersion formation, flow, and breakdown that are now believed to control the sweep control properties of surfactant-based mobility control (37,39-41). 

A constricted tube model is used to analyze viscous and capillary effects associated with foam flow in porous media. The foam moves through the pore structure as single layer, continuous bubble trains. Capillary resistance stems from the drainage and imbibition surfaces as well as the internal lamellae structure. 

In the present paper, pore level descriptions of bubble and bubble train displacement in simple constricted geometries are used in developing mobility expressions for foam flow in porous media. Such expressions provide a basis for understanding many of the previous core flood observations and for evaluating the importance of foam texture and interfacial mobility. Inclusion of the effects of pore constrictions represents an extension of the earlier efforts of Hirasaki and Lawson (1). 

These observations, coupled with the effects of bubble texture (1,13-15) and various history dependent phenomena, clearly demonstrate the inadequacy of conventional fractional flow approaches to describe foam flow in porous media. Also, early approaches which treated the foam simply as a fluid of modified viscosity are also inadequate in explaining the above characteristics. To achieve a fuller understanding of such phenomena, a detailed description of the pore level events is required. In what follows, a simple pore level model is utilized to explain some of the above macroscopic features and to identify some of the key pore level mechanisms. 

The present paper has provided a basis on which foam flow in porous media can be analyzed and described. The gas mobility was found to be dictated by static capillary effects (mobilization pressure), dynamic capillary effects (dynamic effects altering bubble train... 

The scope of possible foam applications in the field warrants extensive theoretical and experimental research on foam flow in porous media. A lot of good work has been done to explain various aspects of the microscopic foam behavior, such as apparent foam viscosity, bubble generation by capillary snap-off, etc.. However, none of this work has provided a general framework for modeling of foam flow in porous media. This paper attempts to describe such a flow with a balance on the foam bubbles. 

Numerous studies (2-12) have shown that the behavior of foams flowing in porous media depends on a host of variables, e.g., capillary pressure, capillary number, foam quality, presence of oil, and composition of oil, but is dominated by foam texture (5,6)... 

To arrive at an approximate description of foam flow in porous media, it is recognized that each bubble and its environment are characterized by the following variables and parameters ... 

As mentioned before. Equations (5) and (6) are the differential transport equations of average bubbles and could be written from scratch without the convoluted derivations invoked here. Unfortunately, modeling of foam flow in porous media is a lot more complicated than Equations (3) and (6) lead us to believe. Having started from a general bubble population balance, we discovered that flow of foams in porous media is governed by Equations (2) and (3), and that Equations (5) and (6) are but the first terms in an infinite series that approximates solutions of (2) and (3). 

Mechanistic prediction of foam flow in porous media seems to be impossible without a transport equation governing foam texture, i.e., foam bubble size. 

Researchers have investigated the nature of the foam flow by examining the mechanisms of foam generation (l ). An extensive study (1 ), that is quite relevant to the mechanism of foam flow in porous media, has shown that the apparent viscosity of foam in a capillary tube decreases rapidly as the ratio of bubble radius-to-tube radius is increased. 

Hirasaki, G. J. Lawson, J. B. Mechanisms of Foam Flow in Porous Media Apparent Viscosity in Smooth Capillaries April 1985. 

In this chapter, we discuss much of the work accomplished since Fried, but without attempting a complete review. Useful synopses are available in the articles and reports of Hirasaki (2, 3), Marsden (4), Heller and Kuntamukkula (5), Baghidikian and Handy (6), and Rossen (7). Our goals are to present a unified perspective of foam flow in porous media to delineate important pore-level foam generation, coalescence, and transport mechanisms and to propose a readily applicable one-dimensional mechanistic model for transient foam displacement based upon gas-bubble size evolution [i.e., bubble or lamella population-balance (8, 9)]. Because foam microstructure or texture (i.e., the size of individual foam bubbles) has important effects on flow phenomena in porous media, it is mandatory that foam texture be accounted for in understanding foam transport. 

This discussion follows the goals listed previously. First, we describe how foam is configured within porous media, and how this configuration controls foam transport. Next, we review briefly pertinent foam generation and coalescence mechanisms. Finally, we incorporate pore-level microstructure and texture-controlling mechanisms into a population-balance to model foam flow in porous media consistent with current reservoir-simulation practice (10). Attention is focused on completely water-wet media that are oil free. Interaction of foam with oil is deferred to Chapter 4. 

Population-Balance Modeling of Foam Flow in Porous Media... 

Because the mobility of the foam phase is a strong function of texture (9, 18, 20, 26, 33, 48), mechanistic prediction of foam flow in porous media... 

Foam flow in porous media is a complex, multifaceted process. Macroscopic results are the ensemble average of many pore-scale events that lead to bubble evolution and pore-wall interaction during multiphase flow. Foam in porous media is best understood when the undergirding pore-level phenomena are elucidated and quantified. 

Liu, D. Brigham, W. E. Transient Foam Flow in Porous Media with Cat Scanner Topical Report U.S. Department of Energy Washington, DC, March 1992. 

This chapter will focus on the stability of foams flowing in porous media when in the presence of crude oil. Many laboratory investigations of foam-flooding have been carried out in the absence of oil, but comparatively few have been carried out in the presence of oil. For a field application, where the residual oil saturation may vary from as low as 0 to as high as 40% depending on the recovery method applied, any effect of the oil on foam stability becomes a crucial matter. The discussion in Chapter 2 showed how important the volume fraction of oil present can be to bulk foam stability. A recent field-scale simulation study of the effect of oil sensitivity on steam-foam flood performance concluded that the magnitude of the residual oil saturation was a very significant factor for the success of a full-scale steam-foam process (14). 

Foams flowing in porous media can be very sensitive to contact with any crude oil that may be encountered. Furthermore, the degree of sensitivity depends upon both the nature of the foam and the nature of the oil. Whereas many foams are quite sensitive to oil contact, it is also true that some foams are very resistant to oil contact. 

In order to evaluate the usefulness of C02 foam as a displacing fluid, more quantitative reference must be made to some of the topics that were introduced more qualitatively and more briefly in the introductory discussions of this chapter. The flow of foam in pipes has been discussed. For foam flowing in pipes, the pipe diameter is much larger than the cell size, and no shear flow occurs throughout most of the cross-section of the mass of foam in the pipe. The shearing strain is concentrated instead in a thin water-film around the inside perimeter of the pipe, and the foam plug rides on this film of water. This circumstance is quite different from that in which foam flows in porous media, in which immobile containing boundaries are close to every part of the flow. The flow of a hypothetical foam in porous media, which consisted of a mass of bubbles in every pore, would be almost impossible. This follows from some of the theoretical work about the motion of two-dimensional arrays of foam cells. 

Effective Foam Viscosity For foam flowing in porous media, the foam s effective viscosity is that calculated from Darcy s law. This value is an approximation because foams are compressible and are also usually non-Newtonian. 

Limiting Capillary Pressure For foam flow in porous media, the maximum capillary pressure that can be attained by simply increasing the fraction of gas flow. Foams flowing at steady state do so at or near this limiting capillary pressure. In the limiting capillary pressure regime, the steady-state saturations remain essentially constant. 

Hirasaki G., Lawson J. B., Mechanism of foam flow in porous media apparent Viscosity in smooth Capillaries, Soc. Petr. Engng., 1986, Vol. 25, p. 176-190. 

Sharma, M.K. and Shah, D.O., Surface Properties of Foaming Agents in Relation to Foam Flow in Porous Media., 184th Natl. Meet., ACS, Washington, D.C.,... 

Farajzadeh, R., Muruganalhan, R. M., Rossen, W. R., Krastev, R., 2011. Efiect of gas type on foam film permeability and its implications for foam flow in porous media. Adv. Colloid Interface Sci. 168 71-78. 

Average bubble size and distribution of sizes may vary significantly. Bubble size is affected by the foam quality and the variables that control quality. Fig. 5.101 43 ghows typical data on size distributions. Foams with a relatively large distribution of bubble sizes are more likely to be unstable. 42 Pore sizes in reservoir rocks are usually smaller than the foam-bubble sizes shown in Fig. 5.101. The foam flow in porous media might therefore be expected to be affected by foam quality and bubble size, and this is die case. 

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