Development of a Mechanistic Foam Simulator: The Population Balance and Generation by Snap-Off

Abstract

Falls, A.H. SPE, Shell Development Co. Hirasaki, G.J. SPE, Shell Development Co. Patzek, T.W. Patzek, T.W. SPE, Shell Development Co. Gauglitz, D.A.* Shell Development Co. Miller, D.D.** SPE, Shell Development Co. Ratulowski, T.+ Shell Development Co. Summary. The mobility of a foam depends heavily on its texture, which is the distribution of bubble sizes in the dispersion. To incorporate this variable in a mechanistic simulator, the usual conservation equations are coupled with balances on the densities of flowing and stationary bubbles in the foam. This approach to modeling foam flow is illustrated with a simulation of a displacement in which foam is generated in situ by capillary snap-off. Introduction Many EOR schemes use gases; steamdrives and CO2 floods are well-known examples. Although such processes can be highly efficient when stabilized by gravity or unique permeability distributions, they ordinarily exhibit poor volumetric sweep efficiencies. Gases have mobilities that are much higher than those of liquids and thus tend to override or to channel through oil in a formation. This decreases the amount of oil that the gas contacts as well as the time for gas to break through to producing wells. A gas displacement process can be improved if the mobility of the gas can be decreased. As laboratory and field studies have demonstrated, one way to do this is to disperse the gas as a foam in a continuous liquid phase. In fact, foams are so effective in controlling gas mobility that they not only hold promise for steam and CO2 processes but may one day control injection profiles and serve as drive fluids for surfactant and caustic slugs. Despite the potential of foams in oil recovery, however, a model that can describe and predict their flow through porous media has yet to be developed. To this end, we have examined aqueous foams as they moved through simple porous media without oil present, From this work, we have identified some of the factors governing the rheology, generation, and destruction of foams in pore space. This paper describes these mechanisms and demonstrates how mathematical models for them can be incorporated into a simulator. This mechanistic simulator could ultimately be used to calibrate simpler, phenomenological simulations or to interpret and design field-scale displacements. Basic Concepts Definition of Foam in Porous Media. The structure of foam inside a porous medium can differ from that of the "bulk" or "polyhedral" foams commonly encountered as dishwashing suds and shaving creams. To avoid confusion, we have defined foam inside a porous medium as a dispersion of gas in a liquid such that the liquid phase is continuous (i.e., connected) and at least some part of the gas is made discontinuous by thin liquid films called lamellae. This definition encompasses both bulk foams, in which the average bubble size is much smaller than the dimensions of the pore space, and so-called individual-lamellae foams, in which the bubble size exceeds the pore size. The lamellae may be short-lived, as in the foams called "unstable." In these, the flow of gas is impeded by foam films that "break and then reform." Lamellae may also be longer-lived and translate from pore to pore. Types of Foams in Porous Media. Within this definition, there are two classes of foams. The first is a "continuous-gas" foam (Fig. 1), in which there exists at least one gas channel that is continuous (i.e., uninterrupted by lamellae) over a macroscopic portion of the sample. Foam lamellae are present but are portion of the sample. Foam lamellae are present but are stationary and simply prevent gas from flowing through part of the pore network. Thus, gas can flow through the pore network without pore network. Thus, gas can flow through the pore network without having to displace lamellae. The second is called a "discontinuous-gas" foam (Fig. 2), in which all the gas phase is made discontinuous by lamellae and there are no gas channels that are continuous over large distances. For gas to flow, lamellae must be transported through the pore system. How Foam Influences Phase Mobilities Effects on Liquid Mobility. In a water-wet porous medium, the liquid-phase relative mobility does not depend on whether the gas exists as a foam. Most of the liquid resides either in smaller pores, which do not contain gas, or next to the solid in pores pores, which do not contain gas, or next to the solid in pores that are occupied by both phases. As long as the amount of liquid carried in lamellae is small compared with the total flux of liquid, the mobility of the liquid can be taken as the usual function of its saturation. How Foam Reduces Gas Mobility. The ways that foam reduces gas mobility can be understood from the simple diagram of Fig. 1. If a portion of the gas phase is continuous (Fig. 1), foam diminishes the cross-sectional area through which gas is able to flow. We consider this to be strictly a relative permeability effect, the foam creating a large effective trapped-gas saturation. On the other hand, when all the gas phase is discontinuous (Fig. 2), not only can its relative permeability be smaller, but it appears to have a larger viscosity. For gas to flow, lamellae must be forced through the pore network. Relative Permeability Effects. The variables that affect the relative permeability of gas in a foam have not yet been conclusively identified. As mentioned above, we believe gas relative permeability to be proportional to the area through which gas flows. The area through which gas flows should, in turn, depend on the pressure gradient and the density of stationary bubbles (texture). The gas relative permeability can increase only if the pressure gradient is large enough to mobilize stationary lamellae. SPERE P. 884