Foam mechanisms are many and complex, but in some cases the mechanisms that dominate foam properties can be represented in simple models. For instance, fractional-flow methods can reproduce the predictions of much-more-complex foam simulators while highlighting the mechanisms controlling behavior. Fractional-flow methods indicate that the effectiveness of foam processes that alternate injection of liquid and gas ("SAG" processes) depends on foam strength at extremely high foam quality, conditions difficult to control in the laboratory. Ironically, surfactant formulations made with lower surfactant concentration, that form weaker foams in steady-state flow, can foam stronger, longer-lived foams in dynamic SAG processes than foams made with higher surfactant concentration, because water drains more slowly from the "weaker" foams in the SAG process. A numerical simulator that incorporates the relation between capillary pressure and foam stability extends simplified foam modeling to cases where fractional-flow methods do not apply. Applications of this simulator to one-dimensional (ID) foam displacements match predictions of analytical models based on laboratory data. Applications to 2D flow show that the ability of foam to correct gravity override is controlled both by the dimensions of the reservoir and the allowable rise in injection-well pressure. In flow through layers in capillary contact, the interplay between capillary cross-flow and foam collapse depends on both the dimensions of the layers and the relative magnitudes of the capillary and viscous pressure differences.

Foam can improve sweep efficiency in gas-injection improved-oil-recovery processes. The success of continuous-injection foam processes in overcoming gravity override in homogeneous, anisotropic (kx kz) radial or rectangular reservoirs depends on a single dimensionless number first proposed by Stone and Jenkins for gas flooding without foam. Their model fits foam simulation results remarkably well over a wide range in reservoir properties and geometry, flow rates, foam quality and foam strength, density difference between phases, initial reservoir pressure, and model for the mechanisms of foam collapse. This approach leads to optimal design strategies for such processes. It may be impossible, however, for a continuous-injection foam process to suppress gravity override in some cases, due to limitations on injection-well pressure. The possibility of gravity override within the foam bank should be considered in evaluating foam propagation in field trials of foam processes Introduction Gases, such as steam, carbon dioxide, natural gas, and nitrogen, are used as driving fluids in improved-oil-recovery (IOR) processes. However, these gases have high mobilities compared with oil and, thus, tend to finger through oil as well as to channel selectively through zones of high permeability. Also, because they are less dense than oil, these gases tend to migrate to the top of the reservoir, overriding oil-rich zones. Gas channeling and gravity override lead to poor sweep efficiency. Foam can significantly reduce gas mobility and overcome these problems under certain conditions, and therefore, improve sweep efficiency. This paper examines the ability of foam to overcome gravity override in homogeneous reservoirs. By inspectional analysis, Shook et al. obtain five scaling numbers rigorously sufficient to characterize a two-phase immiscible displacement process, given certain assumptions. These assumptions include incompressible, completely immiscible phases; a homogeneous, rectangular, horizontal, possibly anisotropic (kx kz) reservoir; absence of dispersion; and relative permeabilities that fit Corey expressions. (Six groups are required to characterize a process in a tilted reservoir.) For a foam process, the number of groups required would be much larger, due to the complexities of representing foam behavior. However, though a complete characterization is not guaranteed with fewer groups, it is possible that only a portion of these groups effectively govern behavior under many conditions. Shook et al. for instance, found that only three groups are needed to characterize waterfloods under a wide range of conditions, and Craig correlated waterflood sweep efficiency in terms of a gravity number and a reservoir aspect ratio. Suitable definitions for these two parameters for foam processes would be [1] [2] where Ng is gravity number, the ratio of the vertical driving force for segregation to horizontal pressure gradient; RL is reservoir aspect ratio; Pf is the lateral pressure gradient within the foam bank in the absence of gravity segregation; is the difference in densities between gas and liquid; g is gravitational acceleration; L and H are reservoir length and height, respectively; and kx and kz are absolute horizontal and vertical permeabilities. Note that Eq. 2 uses the first power of the ratio of horizontal to vertical permeability rather than the square root of this ratio as proposed by Shook et al. and Rossen et al.; the reason is discussed below. Others have noted the importance of the relative magnitude of viscous and gravity forces in foam processes and other processes. A similar analysis may apply to capillary crossflow with foam.

A foam is a dispersion of a large volume of gas in a continuous liquid phase, stabilized by surfactant. Foams can improve sweep efficiency and oil recovery in gas-injection enhanced oil recovery projects (Hirasaki, 1989a,b; Smith, 1988;Rossen, 1994). An important issue for these foam processes is the ease of foam generation in porous media. Previously, Rossen and Gauglitz (1990) derived a percolation model for foam generation in steady gas-liquid flow in porous media. More recent advances in percolation theory require modification of this model, as described in this note.Briefly, Rossen and Gauglitz assumed that the liquid films or lamellae present in foam block a randomly selected fraction(1 -f) of the pore throats in the medium. Creating the large number of lamellae that define a foam from the relatively few present initially requires displacing these lamellae from their pore throats so they can multiply by the processes of lamella division and repeated snapoff (Ransohoff and Radke, 1988;Rossen, 1994). Displacing lamellae from pore throats to initiate the generation process requires imposing a pressure difference across the throat of order one or a few kPa (a few tenths of a psi). "Generating" foam, therefore, depends on lamella mobilization, which depends on the magnitude of the pressure drop AP across individual pore throats blocked by lamellae.Rossen and Gauglitz's model predicts that the minimum pressure gradient for foam generation V Pmln decreases nearly linearly asfapproaches f c , the percolation threshold for the pore network, from either direction. Discontinuous Gas FoamThere are two cases, depending on the value off. Iff, the fraction of throats not initially blocked by lamellae, is less than the percolation thresholdf,. for the pore network (Stauffer, 1992), then no gas can flow unless some of these lamellae are displaced. (We use f andf,. here, rather than the customary percolation symbols p and p,. (Stauffer, 1992), to avoid confusion with pressure and capillary pressure.) Since for f

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Surfactant-alternating-gas (SAG) foam processes can in principle combine high gas injectivity with low mobility at the front of the foam bank. Such a process can give the appearance of extremely shear-thinning behavior, in that the pressure gradient is remarkably low near the well. However, this appearance is due to the effects of declining water saturation near the well, not to the effects of high near-well flow rates on foam mobility. Preliminary simulation results suggest that as long as mobility is low in a region away from the well, high gas mobility near the well need not lead to gravity override. Indeed, since increased injectivity allows higher injection rates and thereby increased flow rates and pressure gradients away from the well, increased mobility near the well may help to reduce the risk of gravity override. Introduction Surfactant-alternating-gas (SAG) injection has several advantages for foam enhanced-oil-recovery (EOR) projects. SAG injection minimizes contact between water and gas in surface facilities and piping, which can be important when the gas, for instance CO2, forms an acid upon contact with water. Alternating injection of small slugs of gas and fluid can promote foam generation in the near-well region. A major additional advantage of SAG injection is increased gas injectivity: as water is displaced from the near-well region during gas injection, foam weakens there, gas mobility rises and injectivity increases. The increase reflects the enormous importance of the near-well region to injectivity in radial flow. This advantage is especially important in relatively low-permeability formations without much excess injectivity If injectivity is low during gas injection, gas injection rate must be reduced or fracturing may result. The advantage of increased injectivity is deceptive, of course, if foam has disappeared from the entire formation rather than merely weakened in the near-well region. There are several reasons for concern that this may occur: First, it is claimed that foam generation requires high flow velocities attainable only in the near-well region, though others disagree. Thus, the reasoning goes, if the near-well region dries out during gas injection and foam generation ceases there, no foam can be created anywhere during this period, and the foam process stalls or collapses. The minimum flow rate for foam generation depends on gas-liquid surface tension, which is much lower for CO2 foams than for N2 foams used in many laboratory studies of foam generation. Therefore this effect may not be important for CO2 foams. Moreover, exceeding the minimum flow rate for "generation" is not necessary if only a relatively weak, "leave-behind" foam is required. The second reason for concern is that high-mobility gas near the well may simply finger through or override lower- mobility foam away from the well during gas injection. Recent simulation results suggest that the ability of foam to overcome gravity override depends in part on a dimensionless gravity number Ng that depends on local pressure gradient P: [1] where is the difference in densities between gas and aqueous phase (referred here throughout as "water"), and g is gravitational acceleration. Local pressure gradient is related to local flow rates and foam strength through Darcy's law: [2] where uw and ug are local volumetric fluxes, i.e., superficial or "Darcy" velocities, of water and gas; k is permeability; is local total relative mobility; w is water viscosity; and krw is water relative permeability, a function of water saturation Sw. Large values of Ng promote gravity override, which can occur even in the presence of foam at low flow rate and P. The recent simulations concerned continuous foam injection into a two-dimensional (2D), rectangular, homogeneous reservoir, in which P is uniform and constant within the foam bank. The exact criteria for gravity override in SAG displacements in radial flow, in which P is neither uniform nor constant, are not yet clear. P. 521