Viscosities of foams

Mitchell, B. J., Viscosity of Foam, Doctoral Thesis, University of Oklahoma, January 1970. 

In an early work [52], A. M. Kraynik proposed another formula for determining lcr. According to [52], densities and viscosities of foamed and unfoamed melt have to be known in order to calculate lcr. Determination of these parameters is by no means easy, which is why Eq. (17) appears better than the one proposed by A. M. Kraynik. 

A - effective viscosity of foam in bubble-flow regime, mPa s... 

Any additives that can act to reduce the viscosity of foam films, and thereby increase the liquid drainage rate, will tend to reduce foam stability as a result. This includes any chemicals that can reduce surface viscosity and/or surface elasticity. Some alcohols can be use to produce these effects. 

The experimental data in Table 5.3 demonstrate this relation. At equal initial conditions (no, a, etc.) the drainage rate is inversely proportional to the viscosity of foaming solution. 

The data presented about the influence of various factors on drainage rate refer mainly to low expansion ratio foams (n < 20-25). With the increase in viscosity of foaming solution and foam expansion ratio, deviations from Eq. (5.46) are observed for certain values of the considered parameters. This is expressed as the minimum in the r/AVi vs. t kinetic curves... 

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. 

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. 

Figure 3. Combined effects of bubble radius, r, and capillary radius R, on apparent viscosity of foam circles are experimental data, and curves are theoretically calculated. (Reproduced with permission from reference 29. Copyright 1992 Society of Petroleum Engineers.)...

Another possibility is that an effective viscosity of foam, such as the one measured and calculated by Hirasaki and Lawson (7) for capillary tubes, can be used in equation 3. Although such a choice would require the assumption of some arbitrary value for relative permeability, it could be used to give useful predictions for flow resistance in the reservoir. There is disagreement as to which of the choices steers the best course to follow. It is perhaps wisest to use an empirical approach, to measure only what is possible to measure at this time, and to wait patiently and receptively for future revelations. 

The relative mobility is usually given in reciprocal centipoises [or in (Pa-s)-1]> which suggests another quantity of interest the effective viscosity of the foam. We could also define the effective viscosity of foam, /xefp as simply the reciprocal of the relative mobility. 

Foam does not exhibit wall-building characteristics, and the effects of formation fluid viscosity are negligible compared to the viscosity of foam under shear conditions (25, 26). For those reasons, foam is viscosity controlled. Thus... 

The understanding that foams are pseudohomogeneous was a fundamental development that Blauer et al. (7) used to develop an expression for the effective viscosity of foams. 

Because of the nature of foams, the rheological character of foam fluids is difficult to quantify. The viscosity of foams is primarily dependent upon foam quality and external-phase fluid viscosity. Stimulation fluids are subjected to pressure variations from surface to downhole conditions therefore, foam quality and viscosity will change accordingly. In order to overcome the changing conditions experienced during stimulations, the foam fluids are designed to reach a specified quality at downhole conditions. 

The values of / were calculated from the experimental data and correlated as a function of a modified Reynolds number, fie = (r F where p/ = viscosity of foam. In making the correlation it was assumed (1) that the average foam density was one-third the density of the normal liquid, (2) that the viscosity of the foam, p/, was one-third the true viscosity of the liquid, and (3) that Lo was equal to two times the hydrostatic head in the outlet calming section. Thus,... 

Fr = total vapor flow rate for plate Fir velocity based on total perforation area 7 = surface tension, dynes per cm. p/ density of foam, lbs. per cu. ft. pv vapor density PL = liquid density p viscosity p/ viscosity of foam... 

Falls, A., J. Musters and J. Ratulowski, The apparent viscosity of foams in homogeneous bead packs, SPERE 4, 155-164 (1989). 

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