Flowing foam relative permeability

Example 5,18—Calculation of Foam Relative Permeabilities and Mobilities. Raza measured flow resistance with foam flowing in a sand-packed tube with a diameter of 1.5 in. and a length of 12.0 in. In the experiments, a liquid foaming solution (brine containing surfactant) and nitrogen were simultaneously injected into the sandpack at fixed rates. Pressure drop across the sandpack was monitored, and the injection was continued until steady-state conditions were reached. Gas saturation at the end of the experiment was measured by weighing the tube. Temperature was 25°C. 

This ratio of dispersed phase (foam) and non-dispersed phase permeabilities indicates that the decrease in permeability of a foam relative to a non-dispersed phase is due largely to (1) the decrease in the fraction of pores occupied by flowing gas, (fc/f ), and (2) the low value of V q/Ui, In addition, we find the ratio of permeabilities increases with displacement rate when n < 1. 

Again, because the portion of foam that actually flows partitions into the largest and, hence, least resistive channels, the trapped fraction partitions into the intermediate-sized pores, and wetting liquid flows in the smallest most resistive channels (Figure 4), a Stone-type model (53) for relative permeability is appropriate. That is, the relative permeability of... 

Clearly, the relative permeability of the trapped foam is zero. However, knowledge of the fraction of foam trapped in the porous medium is needed to complete the flow model. In general, the fraction of foam... 

In principle, the framework of separating foam mobility into effective viscosity and relative permeability components also permits description of continuous foam. If only free gas flows, then nf is zero, and the bulk gas viscosity emerges naturally from equation 9. It is, however, no longer possible to couple the flowing and trapped textures. An independent theory for Xt is required. 

Nevertheless, it is important to point out that a lamella cannot be created directly at a pore-throat. Rather, a lens forms first with lamella creation occurring upon expansion into the adjacent pore-body, provided surfactant is available (see the discussion of foam-generation mechanisms). During two-phase flow without stabilizing surfactant present, lenses are still created by snap-off in Roof sites (54, 60) followed by expansion and rapid coalescence in the downstream pore-body, once the lens thins to a film. If stabilized lamellae are pictured to rupture before exiting the immediate downstream pore-body, they are not much longer lived than unstable lenses. Such processes are accounted for in measurements of continuum relative permeabilities. 

Some of these results can be brought together in Figure 11. Hanssen and Dalland (36) measured gas permeabilities for different foams (variable quality) in synthetic seawater flowing in relatively high-permeability (K =... 

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 effect of gas velocity at a constant liquid velocity on the relative permeability to gas (fcfg) is shown in Figure 5, for a sand pack of 2-darcy absolute permeability containing residual oil after steam-flooding (15 pore volume) at 180 °C (28). The fcrg is a measure of foam flow resistance the... 

In order to differentiate between foam effects, the effects of surfactant transport, and multiphase flow, a number of peripheral experiments were eonducted. Through additional corefloods the surfactant adsorption level was measured and the relative permeabilities between the different phases gas/oil/water were determined, as outlined in the Appendix. 

Due to the extensive research that has been conducted in the area of foam application in enhanced oil recovery, simulation of foam behaviour has become more feasible. Several methods of foam simulation have been developed population balance models [16, 17], fractional flow models [IS, 19], and models that alter the gas phase permeabilities [20, 21], Although the population balance models treat the foam generation mechanisms in a detailed fashion, they may be impractical to apply on large field scale simulations. Both the fractional flow model and the models that alter the gas phase permeabilities rely on history matching experimental data. The fractional flow model provides insight into onedimensional foam flow, but it may be more difficult to apply in three-dimensional situations. In the following section, the application of relative permeability alterations to model foam flow is investigated. 

In Figure 8, the experimental results from the (4 m/day frontal advance rate, oil free) short core flood are compared to the simulated pressure drops which were based on the limiting capillary pressure principle. In this particular case was chosen at 0.35 over a range of water fractional flows from 0.01 to 0.15 to closely match the experimental data. For Sw > a fractional flow curve was chosen which matched the experimental data closely by appropriately adjusting the gas phase relative permeability curve. The water relative permeability curve remains the same as defined in the Appendix under gas/water relative permeabilities. The composite foam fractional flow curve can be seen in Figure 9. Notice the vertical section in the curve for the foam flow case lies at = 0.35. 

The rheological description of foam flow in porous media has been treated in different ways. one approach has been to use the single-phase fluid viscosities to calculate relative permeabilities to each fluid on the basis of experimental measurements of flow rates and pressure drop in foam flow through a porous medium. 

Another approach to describing foam rheology has been to calculate an apparent foam viscosity from flow-rate and pressure-drop measurements made during flow through a porous medium, Darcy s law is used with the rock permeability, or water relative permeability if an oil phase is present, to calculate apparent foam viscosity. Results show that the apparent viscosity calculated in this manner is a strong function of foam quality, decreasing approximately linearly as foam quality increases. Ifiis approach essentially treats the foam as a single phase. 

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]. 

These tests show that CC -foam is not equally effective in all porous media, and that the relative reduction of mobility caused by foam is much greater in the higher permeability rock. It seems that in more permeable sections of a heterogeneous rock, C02-foam acts like a more viscous liquid than it does in the less permeable sections. Also, we presume that the reduction of relative mobility is caused by an increased population of lamellae in the porous medium. The exact mechanism of the foam flow cannot be discussed further at this point due to the limitation of the current experimental set-up. Although the quantitative exploration of this effect cannot be considered complete on the basis of these tests alone, they are sufficient to raise two important, practical points. One is the hope that by this mechanism, displacement in heterogeneous rocks can be rendered even more uniform than could be expected by the decrease in mobility ratio alone. The second point is that because the effect is very non-linear, the magnitude of the ratio of relative mobility in different rocks cannot be expected to remain the same at all conditions. Further experiments of this type are therefore especially important in order to define the numerical bounds of the effect. 

Thompson and Gdanski (34) also performed dual-core experiments to determine the best diversion method using foam, and the maximum permeability difference needed to achieve an equal flow rate through the core. Multiple diversion techniques were used, including foamed acid, multiple stages of foamed add, and various qualities of foamed brine. The tests showed that foamed brine reduced flow rates better than foamed add. Also, higher quality foamed brines were most effective. In order to effectively use foamed diversion fluids, the permeabilities of the zones of interest must be relatively similar. The limit on permeability differences is approximately a factor of 10. Otherwise, the more permeable zone will accept both the diversion and treatment fluids. 

---