A Pore-Network Study of the Mechanisms of Foam Generation

Abstract

Abstract Understanding the role of pore-level mechanisms of foam generation in porous media is essential to the mechanistic modeling and simulation of foam IOR processes. Different foam models assume different foam-generation mechanisms, leading to substantially different algorithms for foam processes. The three pore-level events that lead to foam formation are snap-off, leave-behind and lamella division. As bubbles are created by any such mechanism, gas saturation increases, causing formation of new bubbles by snap-off and leave-behind as gas drains liquid-saturated pores. On the other hand, lamellae are stranded unless pressure gradient is sufficient to mobilize those that have been created. The initial state of the porous medium as surfactant is introduced (fully saturated with liquid, or already partially drained) also affects the different foam-generation mechanisms. To appreciate the roles of these mechanisms, their interaction at the pore-network level must be studied. We report here an extensive pore-network study that incorporates these pore-level mechanisms, as foam is created by drainage or the continuous injection of gas and liquid in porous media. Pore networks with up to 8,000 pores are considered, with rules for the formation and movement of foam lamellae by the three mechanisms enforced throughout. The study explores the roles of the mechanisms, and, by implication, the appropriate form of the foam-generation function for mechanistic foam simulation. Results are compared with previous studies. In particular, the network simulations reconcile an apparent contradiction in the foam-generation model of Rossen and Gauglitz, and identify how foam is created near the inlet of the porous medium when lamella division controls foam generation. In the process, we identify a new mechanism of snap-off and foam generation near the inlet of the medium. Introduction In the petroleum industry, foam is injected into porous media for two primary purposes: gas diversion to improve oil recovery,1–3 and acid diversion for matrix acid treatments.4,5 Foam is also used to direct the flow of remediation fluids in subsurface aquifer-remediation processes.6 A number of studies find that foam does not alter the relative permeability or viscosity of the liquid phase that makes up the foam.7–10 Foam does drastically reduce the mobility of gas, however. This reduction is inversely related to bubble size,11–14 i.e. it is directly related to the number of liquid films, or lamellae, that separate gas bubbles, per unit volume of gas in the pore space. Lamellae resist the movement of gas by resisting movement themselves: this resistance arises from the drive by each lamella to minimize its surface area, according to its interfacial tension. As described below, lamellae form in pore throats, Therefore, initiating movement of a lamella requires pushing it out of the pore throat, the position of minimum surface area, into the pore body, the position with larger surface area.12–17 The pressure drop required to mobilize a lamella, *Delta;Pmin, is inversely proportional to the minimum radius of curvature of the lamella as it is displaced, which is of the order of the radius of the pore throat R:Equation 1 where ? is the interfacial tension between liquid and gas. If lamellae block some throats, then the gas continues to flow as a Newtonian fluid, albeit with reduced relative permeability.18,19 If enough lamellae are present to block gas flow completely, then the gas behaves as though it had a yield stress, because it cannot flow unless the pressure gradient is sufficient to mobilize lamellae along some pathway through the pore network. Much of the gas may remain trapped even as some fraction of the gas flows.10,20 The pressure gradient required to keep lamellae moving along this path may be less than that required to initiate flow:13–17 Initiating flow requires mobilizing all the lamellae along the path from their initial positions in pore throats, where the resistance is greatest. Once lamellae are moving, their average resistance is less, because most of the time they are individually in positions of lower resistance. In addition to the effective yield stress, the drag on moving lamellae imparts a shear-thinning viscosity to the foam11,17, although this effect will be neglected here.