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42909-AC9
Spatial and Temporal Fluctuations in Foam Generation in Porous Media
Foam is used to increase oil recovery in gas-injection enhanced-oil-recovery processes, improve the performance of acid well-stimulation treatments, and increase recovery of toxic wastes in aquifer remediation processes. In many cases the pressure gradient applied to the foam is likely to be limited. Under conditions of injection at limited pressure gradient, foam exhibits three steady states at some pressure gradients, with the middle state (the one likely to correspond to the applied pressure gradient) instable and fluctuating with respect to flow rate through the foam. This behavior is reminiscent of spinodal decomposition in thermodynamics or, more broadly, catastrophe theory in dynamic systems. The question of how the foam fluctuates in time and space is important to foam applications and also of fundamental scientific interest.
Foam stability is affected by other factors as well, including gravity segregation within an oil reservoir or aquifer, causing the foam to dry out and break.
Our progress during this year was strongly affected by a move in institutions. Work on modeling foam generation as a discontinuous jump between steady states was revised for publication in journal. In this work we show that the complex dynamics of foam generation can be represented in a local-steady-state simulator with discontinuous jumps between steady states, as long as the system does make those jumps. An important finding in this work is that the capillary-pressures of the different states is crucial to the steady state that exists after the jump. If, for instance, the existence of foam changes capillary pressure as a function of water saturation, as several studies suggests it does, it can introduce an additional steady state into a displacement and greatly alter the nature of foam diversion. Earlier work with a population-balance model for foam generation, described in last year's report, was also revised for journal publication.
We continued to pursue an interest in gravity segregation in foam processes, which can destabilize foam for lack of water even in the presence of surfactant. A basic problem with continuous injection of foam is that most of the injection pressure is dissipated in the near-well region, whereas most gravity segregation occurs at greater distances from the well. This means that for cases where injection-pressure is limited it may be impossible to prevent gravity segregation beyond a certain distance from the well. Shear-thinning (pseudoplastic) fluids can address this problem because pressure dissipation near the well is reduced. Many foams are shear-thinning, which suggests this should be an advantage. During this year we completed simulations of gravity segregation with shear-thinning foam, and found that such foams can sweep up to twice the reservoir volume of a process involving Newtonian fluids Later in the year we completed an analytical model for this process, that suggests that benefits of up to a fourfold increase in volume may be possible in the limit of maximum shear-thinning (zero power-law coefficient).
The mobility of foam in porous media depends on the extent to which foam traps gas in place, reducing the fraction of gas that flows. The extent of gas trapping is measured indirectly by injecting a gas tracer along with the foam. If the tracer merely flowed with the moving gas fraction the measurement would be unambiguous, but it also diffuses into the trapped gas. Therefore one models the convection/diffusion process, fitted to the effluent tracer-concentration profile, and infers the flowing gas fraction from the model fit. We show that this model fit is non-unique: different 3D distributions of flowing and trapped gas give nearly the same inferred flowing-gas fractions.
During this year we initiated a PhD project to pursue our original goals of modeling the instability of foam states. We hope to report on this project in the coming year's report.
