A Model for Foam Generation in Homogeneous Media
- S.I. Kam (U. of Texas at Austin) | W.R. Rossen (U. of Texas at Austin)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2003
- Document Type
- Journal Paper
- 417 - 425
- 2003. Society of Petroleum Engineers
- 5.2.1 Phase Behavior and PVT Measurements, 5.6.5 Tracers, 5.7.2 Recovery Factors, 1.6.9 Coring, Fishing, 2.5.2 Fracturing Materials (Fluids, Proppant), 5.4.2 Gas Injection Methods, 5.1.1 Exploration, Development, Structural Geology, 4.3.4 Scale, 4.1.5 Processing Equipment, 3.2.4 Acidising, 5.3.1 Flow in Porous Media, 3 Production and Well Operations, 4.1.2 Separation and Treating
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Recent laboratory research in a wide range of porous media shows that creating foam in steady flow in homogeneous media requires exceeding a minimum pressure gradient ?pmin. Data fit trends predicted by a model in which foam generation depends on attaining sufficient ?p to mobilize liquid lenses present before foam generation. Data show three regimes: a coarse-foam regime at low ?p, strong foam at high ?p, and, in between, an unstable transient regime alternating between weaker and stronger foam.
Here, for the first time, a population-balance foam model incorporates a bubble-creation function that depends on pressure gradient. The new model reproduces the three foam regimes seen in the laboratory, the abrupt occurrence of foam generation at a threshold velocity or pressure gradient, hysteresis in experimental results, the interplay between foam stability and foam generation, the effect of injected-liquid fractional flow on foam generation, and foam behavior in the high-quality and low-quality steady-state strong-foam regimes. Once strong foam is created, the details of the lamella-creation function have little further effect on its rheology, which is controlled by other mechanisms. The fractional-flow curves predicted for foam are complex. This model is a necessary step toward quantitative prediction of foam performance in the field.
Gas injection is one of the most popular methods to enhance oil recovery from petroleum reservoirs worldwide.1 But the low viscosity and low density of the gas phase causes instability and inefficiency in the displacement front because of gravity override, gas channeling, and viscous fingering.2
Foams are capable of reducing gas mobility within porous media and therefore greatly improving sweep efficiency.3,4 Moreover, foam can reduce gas mobility more in higher-permeability strata and thereby help mitigate the effects of reservoir heterogeneity. Foam is used as well in matrix acid well stimulation5,6 and on a pilot basis for environmental remediation.7,8
Application of foam in porous media requires foam generation. "Foam generation" means creation of an effective foam of low gas mobility in the porous medium from a condition of high gas mobility. Most experimental studies of foam generation have been conducted at fixed, increasing flow rates and fixed foam quality (injected gas volume fraction) and find an abrupt, drastic increase in pressure gradient at the onset of foam generation. In at least some cases, foam generation requires high flow rates or high pressure gradients.9-12 In some applications where pressure gradient is limited, or foam is to be created far from the injection well, foam generation may be problematic.
Foam generation reflects the creation of large numbers of liquid films, or lamellae, that separate gas bubbles. Lamellae can be created in situ by different mechanisms, such as leave-behind, snap-off, lamella mobilization and division, and gas evolution.4,9 Leave-behind applies only to drainage processes and is thought, if left to itself, to result in a coarse, ineffective foam.13 Gas evolution is only applicable to thermal processes or upon substantial pressure depletion. Therefore, research on foam generation has focused on snap-off and lamella division. Snap-off happens when capillary pressure at a pore throat falls below a threshold value; a large number of lamellae can be created as long as fluctuations in capillary pressure continue and lamellae continue to be mobilized.4 Most discussion of snap-off focuses on its occurrence when gas invades a liquid-occupied pore.9,14 This mechanism is problematic as an explanation for steady-state lamella creation.15,16
Rossen and Gauglitz propose a model for foam generation triggered by lamella mobilization and subsequent division10: specifically, the conditions for the onset of foam generation. In the model, in steady gas-liquid flow, the higher the value of water fractional flow fw, the lower are both the minimum pressure gradient for foam generation and the corresponding minimum gas velocity for foam generation. With one adjustable parameter, the theory fits data for the onset of foam generation in Berea cores as a function of fw from fw=30% to fw=1%. The model does not describe foam generation beyond the initiation of the process.
Other models for the onset of foam generation include that of Radke and Ransohoff,9 which is based on snap-off, and that of Tanzil et al.,11 based on lamella mobilization but not employing percolation theory.
Gauglitz et al.12 examine data for foam generation in a wide variety of media using three different types of experiments: first, fixed foam quality and fixed ?p across the core (Type 1); second, fixed foam quality and fixed flow rates (similar to previous studies in the literature, Type 2); and finally, fixed ?p and fixed water flow rate (Type 3). In Type 1 and 3 experiments, instead of a sudden jump in ?p, researchers report a decrease in flow rate as foam generation begins. Fig. 1 shows a typical result for a Type 1 experiment and Fig. 2 a Type 3 experiment. At low ?p, there is a "coarse foam" regime with little reduction in gas mobility. At high ?p, there is a "strong foam" regime with a large reduction in gas mobility. Between these two regimes there is a third, unstable or transient regime. In this regime, flow rate fluctuates over time and it becomes difficult to maintain constant ?p across the core. When ?p is plotted vs. flow rates of gas and liquid, one finds a surface reminiscent of catastrophe theory17: a branch of the surface at low ?p, a folding over in the transient regime, and a folding back for the strong-foam regime. An example is shown below.
The data of Gauglitz et al.12 fit the trend predicted by Rossen and Gauglitz10 over two-and-a-half orders of magnitude in permeability in sandpacks and beadpacks. In consolidated core, the trend with permeability is less clear, because the geometrical parameters needed by the percolation theory are not as well defined.
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