Reservoir Simulation of Foam Displacement Processes

Steam injection has had a profound impact on the production of heavy crude oil. Steam, however, is inviscid compared to a viscous oil and is not the ideal displacement agent. Field studies and laboratory tests have shown that foaming the steam phase through the aid of a suitable surfactant in aqueous solution can achieve mobility control of injected gases and mitigate the effects of gravity override. Thus, production is improved. Unfortunately, simulation models and simulation tools that accurately gauge the effects of foam on gas mobility in porous media are not readily available. Recent advances in modeling gas mobility in the presence of foam are reviewed. These include the socalled bubble population balance method, scaling arguments to obtain representative foam texture and hence gas mobility, and semi-empirical alteration of gas mobility. The bubble population balance is then illustrated by means of a few sample calculations. Introduction Field application of foam is becoming a proven technology, surfactant costs withstanding, to control the mobility of gaseous phases in porous media. Typical applications span from steam1-4 and CO2 foam5 to alleviate gravity override and channeling, production well treatments to reduce gas-oil ratio (GOR)6,7, to gelled-foams8 for long-lasting plugging of high permeability channels. Foam processes have also been studied and field tested for use as groundwater aquifer clean up methods9-11. To date, there have been about 25 major steam-foam projects implemented12. The attributes of fields subjected to foam are varied. Fields range from thick, steeply dipping sands where the objective is to improve vertical sweep, to flat, moderately thick reservoirs where gravity override is a concern, to improving injection profiles in layered reservoirs so that steam is injected into unheated zones. Foams are also useful to improve the distribution of heat during steam soaks. With this considerable body of field knowledge in regard to steam foam, it would seem that we should be able to chose and evaluate candidate fields effectively. However, the highly nonlinear flow properties of foam in porous media and the widely varying chemistry of surfactants with respect to temperature and sensitivity to oil make generalizations difficult. Thus, more efficient application of foam EOR processes, especially steamfoam, would result from a comprehensive model of the process. In particular, a mechanistic model would expedite scale-up of the process from the laboratory to the field and the extrapolation of results from one field to another. Foams in Porous Media It is widely accepted that foam bubble size controls the mobility of foam in porous media13. Finely textured foams (small bubble size) are much less mobile than coarsely textured foams (large bubble size). It is also well known that foam flow behavior is strictly nonNewtonian13,14. In order to understand the phenomena that a foam simulator must be capable of reproducing, the configuration of foam within rock pore space and the pore-level events that alter the size and shape of bubbles are discussed briefly. Figure 1 depicts schematically a picture of the porelevel distribution of foam that has emerged from micromodel observations, pore-level modeling, and core floods14-17. In this highly schematic picture, sand grains are cross-hatched. For illustrative purposes only, the largest channels lie at the middle of the figure whereas the smallest lie at the bottom. Wetting surfactant solution is denoted as the dotted phase. Foam bubbles are either unshaded or darkly shaded, depending upon whether they are stationary or flowing. Due to strong capillary forces, wetting liquid occupies the smallest pore spaces and clings to the surface of sand grains as wetting films. The aqueous, wetting phase maintains continuity throughout the pore structure shown in Fig. 1 so that the aqueous-phase relative permeability function is unchanged in the presence of foam18-23. Minimal volumes of liquid transport as lamellae. Unshaded flowing foam transports as trains of bubbles through the largest and least resistive flow channels. Because the smallest pore channels are occupied solely by wetting liquid and the largest pore channels carry flowing foam, significant bubble trapping occurs in the intermediate-sized pores. Bubble volumes are roughly the same as individual pore volumes, or larger, and lamellae span across pore cross sections completely. This configuration is denoted a confined foam, as opposed to a bulk foam17. This terminology acknowledges the role of the porous medium in constricting foam configuration and shaping bubbles. Foam reduces gas mobility by decreasing gas relative permeability and increasing gas effective viscosity. Stationary or trapped foam blocks a large number of channels that otherwise carry gas. Gas tracer studies measure the fraction of gas trapped within a foam at steady state in sandstones to lie between 85 and 99% 15,24. Bubble trains within the fraction that does flow encounter drag because of the presence of pore walls and constrictions25, and because the gas/liquid interfacial area of a flowing foam bubble is constantly rearranged by viscous and capillary forces13. Bubble and trains of bubbles are in a constant state of rearrangement. Bubbles and lamella transport some distance, are destroyed, and then regenerated. Further, trains halt when the local pressure gradient is insufficient to keep them mobilized, and other trains then begin to flow. Foam texture arises from a balance between varied and complicated foam generation and destruction mechanisms. Regardless of whether foam bubbles are generated in situ or externally, they are molded and shaped by the porous medium14,16. Foam generation is largely a mechanical process, and it is sensibly independent of the type of surfactant. Bubbles are created by snap-off and division at germination sites that are a function of pore geometry of fluid occupancy. Surfactant stabilizes the gas/liquid interface of foam bubbles and prevents coalescence. Hence, foamer concentration and formulation affect the rate of foam coalescence. The interaction of foam bubbles and oil is also important to gas mobility. Some foams are stable in the presence of oil while others are not. Sensitivity to the presence of oil increases foam coalescence. Thus, foam bubble size increases, and subsequently the foam mobility increases also. While there is no general agreement and a theory consistent with all observations of stability, foam stability in the presence of oil does appear to correlate with the oil entering coefficient26. That is, if oil can enter the gas-surfactant solution interface the oil can destabilize the foam. More thorough reviews of foam generation, coalescence, and transport on the pore level are given by Chambers and Radke16 and Kovscek and Radke17. Simulator Attributes It is unlikely that any simulation approach/simulator can reproduce all observations of foam phenomena. It is also not necessary that a process simulation model be mechanistic in order to be successful. However, there are certain attributes that appear to be important for successful foam modeling on the reservoir scale: · Gas mobility must be reduced in the presence of foam. In a simulation approach, this may be accomplished by reducing the gas relative permeability, increasing the gas viscosity, or a combination of both. · Computed foam mobilities should incorporate some notion of non-Newtonian foam flow behavior because flow rates vary between the well-bore region and deep in the reservoir. Moderate to finely textured foams are decidedly shear thinning. · Foam properties vary with surfactant concentration and must be modeled. Likewise foam stability in the presence of oil varies with surfactant type and must be modeled. · Surfactant transport, partitioning, and adsorption must be accommodated accurately. · The method should be predictive rather than merely history matching. In summary, foam properties vary with space and time, and must be modeled accordingly. Likewise, surfactant/brine transport must be modeled in some fashion. Foam Flow Simulation Methods A variety of methods have been proposed to incorporate foam into reservoir simulators. They range from empirical and semi-empirical alteration of gas mobility to population balance methods. We discuss the methods and the simulators that result. Empirical Methods. Perhaps the simplest means of including the effects of foam in a simulator is through the use of a constant mobility reduction factor, MRF. That is, the gas relative permeability is divided by a constant value