The success of surfactant-alternating-gas (SAG) foam processes depends on foam behavior at very low liquid fractional flow fw - i.e., on whether and how foam breaks as it dries out during gas injection. It is difficult to conduct steady-state corefloods at extremely low fw, however. Therefore simulation studies of foam SAG processes rely on extrapolating steady-state data taken at much higher values of fw. Unfortunately, grossly different results are predicted depending on how these data are extrapolated. This Berea coreflood study of SAG foam processes uses a unique coreflood apparatus in which both water saturation Sw and capillary pressure Pc are measured throughout the flood. Steady-state data were obtained to as low a value of fw as feasible, followed by continuous gas injection. Because Sw and pressure drop were measured during this period, the fractional-flow function could be extrapolated below the range in fw of the steady-state data. During steady-state foam injection, for fw >0.01, foam weakened and Swfell as fw decreased. Foam was stable to a remarkably high value of capillary pressure. Between fw = 0.008 and 0.002, foam weakened sharply, and, remarkably, reimbibition occurred: Sw rose and Pc fell as fw decreased. This suggests that the fractional-flow curve for foam is not single-valued. Stated differently, there are at least two steady states, a "strong foam" and "weak foam" state, over a range of water saturations, and the behavior observed depends oninjection history. This sudden foam collapse and reversion to the "weak foam"behavior under dry conditions mirrors the sudden jump to "strong foam" state reported in studies of foam generation. For lower fw and during gas injection, Sw again declined as fw declined. Implications of these results for field design of foam SAG processes are discussed. In particular, we illustrate how to extrapolate from a properly designed coreflood to field scale 1D displacement using fractional-flow methods. Introduction As applied to gas injection improved-oil-recovery (IOR) processes, foam has the potential to relieve several common problems through better areal sweep, better vertical sweep (less gravity override), less viscous fingering, diversion of gas from higher-permeability (or previously-swept) layers, and/or reducing handling costs associated with large gas throughput (Schramm, 1994;Rossen, 1995). The foam may be administered by continuous coinjection of gas and surfactant solution, or by injecting a slug of surfactant solution followed by injection of a gas slug. The latter strategy is known as a surfactant-alternating-gas (SAG) process. SAG injection has certain advantages over continuous foam injection in foam IOR processes. SAG injection minimizes contact between gas and water in the injection facilities, which can help reduce corrosion. The alternating imbibition/drainage cycles in SAG injection can help to create foam in the reservoir (Rossen and Gauglitz, 1990; Chou, 1991). Finally, SAG injection can achieve the paradoxical benefits of high injectivity and low mobility at the displacement front (Rossen et al., 1995). High injectivity results as foam near the well dries out, weakens and collapses, while stronger, wetter foam further from the well maintains mobility control. Recent simulation results (Shi, 1996)show that SAG processes can overcome gravity override with less rise in injection-well pressure than is possible with continuous foam injection. The benefits of SAG foam injection are made clear by fractional-flow analysis. In fractional-flow methods (Buckley and Leverett, 1941; Helfferichand Klein, 1970; Lake, 1989; Rossen et al. 1994; Zhou and Rossen, 1995), one constructs wave diagrams for the displacement process from fractional- flow curves and initial and injection conditions. Saturation waves move with dimensionless velocities equal to the slope of the fractional-flow curve at the given saturations. P. 567^

Factors key to the success of foam diversion processes for matrix acidization were measured in Berea cores. Foam mobility was low in high-permeability (847-md) Berea and higher in low-permeability (92 md) Berea, suggesting effective foam diversion. Injection of surfactant solution, emulating foam-compatible acid injected following foam, trapped some of the foam in place. but imputed diversion of acid was not as complete as diversion of foam itself. After a period of injection of liquid, more gas was displaced, starting from the core inlet, and mobility rose further. Using these coreflood results, fractional-flow methods predict effective acid diversion between layers differing in permeability in field application. A sensitivity study indicates that the size of the preflush and the propagation rates of foam within rock are secondary factors in the success of foam diversion in the field. Foam strength and especially gas trapping following foam injection are the keys to successful application. In a process in which gas trapping following foam injection is ineffective, or is less effective in high-permeability layers, a continuous-injection foamed-acid process would outperform a process of alternating slugs of foam and acid. Further data, especially in field cores, are needed to confirm these conclusions. Introduction Foams are widely used to divert acid to desired intervals in matrix acidization treatments. The goal of such a diversion process is to reduce the injectivity of acid into layers where less is needed and thereby divert it into layers more in need of stimulation. Foams do not directly alter the mobility of an aqueous phase such as acid in rock; relative permeability krw is the same function of water saturation Sw in the presence of foam as in its absence. The individual liquid films, or lamellae, that aerate gas bubbles in a foam do restrict the flow of gas, however. By driving down gas mobility, foam indirectly forces down Sw and thereby krw(Sw), accomplishing the process goal of lower acid injectivity into the given layer. Moreover, foams are stronger, reducing liquid mobility more, in higher-permeability layers, diverting acid into lower-permeability intervals that otherwise would not receive much acid. Whether foams are stronger in more-heavily-damaged rock than less-damaged rock is less clear. Many foams collapse in the presence of oil, which could also help divert acid into productive, oil-bearing intervals. We do not address the effects of oil or of formation damage on foam further here, however. The key to foam effectiveness in acid diversion is the ability of acid following foam to maintain low water saturation and low krw(Sw) during acid injection following foam. To accomplish this the acid slug must contain surfactant and be formulated for compatibility with foam. There are no published data on this property for acid slugs, but there are data for surfactant slugs without acid. Persoff et al. found that surfactant injected without acid or gas following foam maintained for some time the same low Sw and krw(Sw) created by the foam, evidently by trapping all the gas in the foam in place. This effect is highly desirable in foam diversion. Bernard et al. found less complete trapping of gas by surfactant solution injected after foam. Zerhboub et al. found that diversion of a surfactant slug following foam can be increased by adding a brief shut-in period following foam injection. Exactly how the shut-in period works is not yet clear. There are various injection strategies for a foam diversion process: injecting foam with or without a surfactant preflush; foaming the acid itself or alternating acid injection with foam; designing an acid formulation either to destroy or maintain foam; incorporating a shut-in period between foam and acid injection. There are few data in the literature to guide choices among these alternatives, although there is a wide body of literature on foams for diverting gas flow in enhanced oil recovery (EOR). Building on this literature, Zhou and Rossen developed a model for the foam diversion process based on fractional-flow methods. They conclude that the best foam process is one in which an optimally-sized preflush precedes foam injection and the acid slug is compatible with the foam. The preflush satisfies surfactant adsorption in the near- well region and greatly accelerates foam propagation there. Since preflush injection precedes any diversion or damage removal, most reflush by far enters the high-permeability or least-damaged layers. Therefore the preflush accelerates foam propagation most in the layer that is to be blocked, because that layer receives the most preflush. It is important to design the acid slug for compatibility with foam in order that the acid slug not immediately destroy the diversion brought about by foam. Zhou and Rossen conclude that both foamed acid and schemes of alternate injection of acid and foam can be effective in diversion. P. 347^

The method of characteristics, or fractional-flow theory, is extremely useful in understanding complex Enhanced Oil Recovery (EOR) processes and in calibrating simulators. One limitation has been its restriction to Newtonian rheology except in rectilinear flow. Its inability to deal with non-Newtonian rheology in polymer and foam EOR has been a serious limitation. We extend fractional flow methods for two-phase flow to non-Newtonian fluids in one-dimensional cylindrical flow, where rheology changes with distance from injection well. The fractional flow curve is then a function of position and we analyze the characteristic equations for two applications-polymer and foam floods. For polymer flooding, we present a semi-analytical solution for the changing fractional flow curve where characteristics and shocks collide. The semi-analytical solution is shown to give good agreement with the finite-difference simulation thus helping us understand the development and resolution of shocks. We discuss two separate cases of foam injection with or without preflush. We observe that the fractional flow solutions are more accurate than finite-difference simulations on a comparable grid and hence the method can be used to calibrate simulators. For SAG (alternating-slug) foam injection, characteristics and shocks collide, making the fractional-flow solution complex. Nonetheless, one can solve exactly for changing mobility near the well, to greater accuracy than with conventional simulation. The fractional-flow method extended to non-Newtonian flow can be useful both for its insights for scale-up of laboratory experiments and to calibrate computer simulators involving non-Newtonian EOR. It can also be an input to streamline simulations.

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

The In-situ Conversion Process, called ICP, is a thermal recovery process that was developed to produce oil and gas from kerogen-bearing oil shale. In-situ conductive heating of the oil-shale reservoir converts its kerogen (hydrogen-rich solids) into oil and gas (fluids) plus coke (hydrogen-deficient solids).While coke is left behind on the rock, hot vapor and heavy oil flow through the thermally altered oil shale to producer wells, and predicting ICP recovery performance depends on having an accurate characterization of the flow and storage behavior of the oil shale. However the rock fabric changes radically during ICP -the rock's porosity and permeability change with time in a complex way. While changing pore geometry (and pore-wall composition) also results in changing relative-permeability (k r ) and capillary-pressure (P c ) curves, this work focuses on the evolution of oil and gas saturations (which dictate how k r 's and P c 's influence ICP performance), as well as the change in porosity and its resulting alteration of oil-shale permeability.Numerous pyrolysis experiments were performed in the laboratory, where crushed oil shale was heated and effluents were monitored. Furthermore, through a series of otherwise identical experiments that were stopped at different degrees of conversion, changes in the oil-shale solids were determined by analyzing the spent rock. Through these experiments, a reservoir simulation model was developed that, for a variety of oil shales and time scales, captures the chemical-reaction kinetics for the solids and fluids, and the phase behavior of the fluids. Sensitivity studies with this model identified the changing oil-shale fluid-transport properties as a key driver for ICP performance.In this work, the ICP simulation model is used to illustrate ICP reservoir physics for different oil shales. Simulations reveal how changing in-situ fluid compositions (due to chemical reactions, temperature increase, etc.) not only result in changing fluid properties, but also complex behavior with time for oil and gas saturations, and this saturation history governs in part the flow of oil and vapor to producers and thus ICP performance. The early time following kerogen conversion is a period of higher oil saturation and thus higher oil mobility, illustrating how ICP production can include the flow of both vapor and heavy oil to producer wells.Another key to ICP success is the permeability history that results from the evolving porosity. As kerogen converts to fluids, porosity first increases (owing to reactive grain loss), then decreases (from the deposition of coke). While porosity behavior was determined from grain volumes measured in crushed-rock experiments, some complementary tests on pyrolyzed intact rock reveal increasing oil-shale permeability during ICP, which enables production from rock whose original permeability is quite low. Also simulations show that 90% of the pattern pyrolyzes after there are already permeable pathways developed connecting the pyrolyzing regions to the produce...