Recent studies of foam-diversion processes for matrix acidization identify gas trapping during post-foam liquid injection as the key to foam effectiveness. Laboratory studies identify two degradation processes during this period: a rapid increase in mobility throughout the core, followed by a slower further rise in mobility starting at the core inlet. New coreflood results indicate that pressure gradient VP during the first process is insensitive to a shut-in period after foam injection but depends weakly on liquid flow rate. A small fall in gas saturation accounts for the first rise in mobility. which appears to depend on mobilization of foam bubbles (i.e., on P) rather than foam collapse (i.e., on capillary pressure). The second rise in mobility appears to be due to gas dissolution in injected liquid. Therefore this transition, which is harmful to field performance, can be avoided by including a small amount of gas with the injected acid.

Process modeling illustrates that some designs that appear successful in laboratory linear corefloods can perform poorly in the field due to the geometry of radial flow. The fractional-flow approach, together with coreflood pressure data for multiple sections along the core, provides a uniquely simple and insightful framework for interpretation of laboratory results and extrapolation to the field.

The simple diversion model of Hill and Rossen 1 can successfully model foam processes in which the secondary degradation of foam during liquid injection is avoided by including gas with the acid.


Foam is used in enhanced oil recovery to reduce gas injectivity and improve sweep efficiency and in well stimulation to divert matrix acid treatments into low-permeability or more-damaged layers. During production operations foams can reduce coning of a gas cap.

In matrix acidization foam diverts acid from higher-permeability (or less-damaged) layers to lower-permeability (or more-damaged) layers. The injection sequence can be either (1) surfactant preflush followed by alternating slugs of foam and foam-compatible acid, (2) surfactant preflush followed by alternating slugs of foam and foam-incompatible acid, or (3) continuous injection of foamed acid. Zerhboub et al. report that in laboratory studies of slug processes a brief shut-in time after the foam injection helps diversion of acid.

To divert acid, foam must reduce the relative permeability of the liquid phase. Foams do not directly alter water viscosity or the relation between water relative permeability krw and water saturation


where krwf is water relative permeability in the presence of foam, krwo is water relative permeability in the absence of foam; henceforth we refer simply to water relative permeability krw, which applies in both situations. However, foams o reduce gas mobility greatly, and as a result Sw and krw are forced down. The reduction of gas mobility stems from two mechanisms:

  1. trapping of up to 80-99% of the gas phase even as foam flows at high pressure gradient P.

  2. increased effective viscosity of the gas that does flow.

The two effects are intimately related, because both depend on the capillary forces on gas bubbles, on bubble size and on pressure gradient. As a result, any distinction between gas relative permeability and as viscosity in a flowing foam is ambiguous. Some report gas mobility with foam to be shear-thinning, and others find it to be nearly Newtonian.

Gas trapping during fluid-injection following foam is essential to successful acid diversion. means that effective diversion depends on mechanism (1) above, but the gas saturation and the amount of gas trapped depends on the complex processes of creation, destruction and trapping of bubbles during the preceding foam displacement. These bubble-generation and -destruction mechanisms are not completely understood, but capillary pressure Pc is an important factor in the interplay that determines bubble size. The effect of capillary pressure explains foam's ability to divert flow between the layers differing in permeability, for instance, as the effect of higher Pc in the low-permeability layer weakening the foam there.

Modeling Foam Diversion

Equation (1) suggests that foam modeling is simple] if one knows water saturation in the presence of foam; one can then compute pressure gradient as a function of flow rates using Darcy's law and (1) without concern for the complexity of gas-phase mobility. One can model some foam displacements remarkably well, for instance, by assuming that Pc and Sw are held fixed within the foam. This model is called the "fixed-limiting capillary pressure" (fixed-Pc*) model. More generally, if one measures Sw or P experimentally, one can determine the other using Eq. (1) if the function krw(Sw) is known.

P. 781

This content is only available via PDF.
You can access this article if you purchase or spend a download.