Flowing foam

Pour-in-PIace. The polyurethane forming mixture can be poured into a cavity which will then be filled by the flowing, foaming reaction... 

Micro-scale experiments involve the microscopic observation of flowing foams in etched-glass micromodels. Here the pore dimensions are typically on the order of hundreds of micrometers. Such experiments provide valuable and rapidly obtainable qualitative information about foam behaviour in constrained media under a variety of experimental conditions, including the presence of a residual oil saturation... 

Kristiansen, T.S. Holt, T. Properties of Flowing Foam in Porous Media Contaiing Oil in Proc., 12th International Workshop and Symposium, IEA Collaborative Project on EOR, Atomic Energy Agency Winfrith, UK, 1991. 

Fig. 10.19. Steady pressure gradient of flowing foam in glass bead packs as a function of sail concentration.

Mobility of the gas phase is reduced in two ways when a foam is used. First, liquid lamallae become trapped and block off a portion of the porous media. This results in a stationary foam fraction that can be nearly unity at low flow rates. Also lamellae present in the flowing foam fraction create an additional resistance to flow. The apparent viscosity of foam can be several orders of magnitude larger than the gas viscosity. 

Although the current permeability model properly reflects many of the important features of foam displacement, the authors acknowledge its limitations in several respects. First, the open pore, constricted tube, network model is an oversimplification of true 3-D porous structures. Even though communication was allowed between adjacent pore channels, the dissipation associated with transverse motions was not considered. Further, the actual local displacement events are highly transient with the bubble trains moving in channels considerably more complex than those used here. Also, the foam texture has been taken as fixed the important effects of gas and liquid rates, displacement history, pore structure, and foam stability on in situ foam texture were not considered. Finally, the use of the permeability model for quantitative predictions would require the apriori specification of fc, the fraction of Da channels containing flowing foam, which at present is not possible. Obviously, such limitations and factors must be addressed in future studies if a more complete description of foam flow and displacement is to be realized. 

To simplify further the description of foam flow, bubble velocity is removed from the set of internal variables. It is assumed that a fraction, Xr, of all bubbles is carried with velocity, v(x,t TT,o) as flowing foam (f). This assumption is justified because flowing bubbles remain in contact most of the time, and their average velocity, , can be related to Darcy s velocity of the gas phase, = u /([Pg.328]

As shown in Appendix A, Equation (1) can be averaged over the volume of the porous medium to yield the population balances of bubbles in flowing foam... 

Figure A-1. Two-dimensional characteristic function of flowing foam, x This function is defined to be one in regions of the porous medium occupied by flowing foam, and zero otherwise ...

Note that the gradient of X is nonzero only on the surfaces separating the flowing foam from other regions there it is equal to + 00, ... 

The following characteristic functions are defined here Flowing foam (f)... 

Indeed, as fluid flows, foam channels closed above grow in thickness at the bottom, thus creating an increasing counteraction to the gravitational force, which slows down the outflow until equilibrium is attained [214]. It should be noted that this effect is possible only in closed deformable channels with negative curvature, which are typical of foam. According to [324], the capillary rarefaction is a characteristic of the foam compressibility and determines its elastic resistance to the strain caused by the liquid redistribution. 

Anothaf option is the use of buffies. The use of ha flies2 in continuous flow foam columns improves removal efficiency and increases maximum hydraulic loading rates by reducing channeling in the fonm and other types of axial dispersion. 

Effective Viscosity. Considerable evidence indicates that in some gas-occupied channels, confined foam bubbles transport as bubble-trains. Effluent bubble sizes from 0.8-/ m2 Berea sandstone reflect expected sizes and their predicted shift with flow velocity (20). Likewise, pregenerated foam is reshaped to the same average exiting bubble size quite independent of the average inlet size (20). As with trapped foam, there is ample direct visual documentation of flowing foam bubble-trains in both micromodels (26) and in bead packs (9, 48). The flow resistance of transporting bubble-trains is best addressed in terms of an effective gas viscosity. 

Figure 4. Pore-level schematic of fluid distribution for a discontinuous-gas flowing foam. Flowing bubbles are unshaded, and trapped gas is darkly shaded. (Reproduced with permission from reference 38. Copyright 1990 Society of Petroleum Engineers.)...

In equation 4, the subscripts f and t refer to flowing and trapped foam, respectively, and ni is the foam texture or bubble number density. Thus, nf and t are, respectively, the number of foam bubbles per unit volume of flowing and stationary gas. The total gas saturation is given by Sg = 1 — Sw = S + St, and Qb is a source—sink term for foam bubbles in units of number per unit volume per unit time. The first term of the time derivative is the rate at which flowing foam texture becomes finer or coarser per unit rock volume, and the second is the net rate at which foam bubbles trap. The spatial term tracks the convection of foam bubbles. The usefulness of a foam bubble population-balance, in large part, revolves around the convection of gas and aqueous phases. 

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. 

Holt and Kristiansen (26, 27) obtained similar results for foams flowing in cores under North Sea reservoir conditions in that the presence of any of a number of residual oils (including a crude oil and a variety of pure hydrocarbon oils) reduced the effectiveness of flowing foams. Rater-man (28) measured the pressure drops obtainable for several foams flowing in sandstone cores under moderate pressure and in the presence of a residual pure alkane oil phase and found that the foams were destabilized by the oil. Schramm et al. (40) conducted foam-floods in sandstone cores and found a range of sensitivities to residual crude oil from oil-tolerant foams through to oil-sensitive foams. 

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