The Use of Fractional-Flow Theory for Foam Displacement in Presence of Oil
- Daniel J. Mayberry (Oil Search Ltd.) | Seung I. Kam (Louisiana State University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- August 2008
- Document Type
- Journal Paper
- 707 - 718
- 2008. Society of Petroleum Engineers
- 1.6 Drilling Operations, 2.5.2 Fracturing Materials (Fluids, Proppant), 1.14 Casing and Cementing, 1.10 Drilling Equipment, 4.3.4 Scale, 5.2 Reservoir Fluid Dynamics, 1.6.9 Coring, Fishing, 5.2.1 Phase Behavior and PVT Measurements, 5.7.2 Recovery Factors, 5.3.2 Multiphase Flow, 5.4.2 Gas Injection Methods, 4.1.2 Separation and Treating
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Foam has been extensively used in improved and enhanced oil recovery processes in the petroleum industry over decades. Foam is capable of reducing gas mobility dramatically in porous media, and thus helps keep displacement fronts stable by controlling the mobility ratio between injected gas and reservoir fluids. In this study, models were constructed to investigate the mechanisms of foam displacement in porous media using three-phase fractional-flow theory and ternary diagrams. The strength of foam in the presence of oil was accounted for by using a mobility reduction factor (MRF) for the gas phase that can be routinely measured in laboratory coreflood experiments. The use of MRF is a typical way of describing foam rheology in local steady-state modeling.
Results were analyzed in terms of saturation paths in the ternary diagrams, saturation velocities, sweep efficiency and effluent history. Two different initial conditions were selected to demonstrate the importance of initial saturation on the displacement: one with oil phase dominant ((Sw , So) = (0.2, 0.8)) and the other with water phase dominant ((Sw , So) = (0.8, 0.2)). At low MRF (i.e., no foam or weak foam), the efficiency of foam displacement was primarily governed by fast-moving spreading waves that rapidly broke through the porous medium resulting in poor sweep efficiency. An increase in MRF (i.e., stronger foam) altered the nature of the displacement front by making it more piston-like through the development of "shock" fronts and improved sweep efficiency significantly. Once shock fronts dominated the displacement, the importance of initial saturation on the mechanisms of displacement became less pronounced. Calculations also demonstrated that a decrease in oil viscosity made the oil phase more mobile and the formation of shock fronts more prolific, significantly enhancing sweep efficiency.
The results in this study imply that if basic fluid properties, injection and initial saturation conditions, and MRF are known, one can reliably predict the mechanisms of foam displacement in porous media even in the presence of oil. The solutions obtained from the three-phase fractional-flow analysis were in good agreement with simulation results in a wide range of MRF values and initial core conditions.
Foams are used in a variety of applications in the petroleum industry from drilling, fracturing, and completion through to near-wellbore treatment and enhanced oil recovery (EOR) (Schramm 1994; Prud'Homme and Khan 1996). Foams are expected to circulate rock cuttings out of the hole in drilling operations, transport solids deep into the reservoir in fracture stimulations, and place solids in cementing operations (Kam et al. 2002; Hutchins and Miller 2005; Kuru et al. 2005). Foams are used in improved oil recovery processes such as near-wellbore applications to divert the treatment fluid into the layers in need of acid and in EOR to reduce the mobility of the injected gas phase and hence improve reservoir sweep (Smith 1988; Kovscek and Radke 1994; Rossen 1996; Martinsen and Vassenden 1999; Wassmuth et al. 2001; Tanzil et al. 2002; Terdre 2003; Kam et al. 2007a). Shallow subsurface application to remediate nonaqueous-phase liquid is another example of foam in porous media that allows injected remediation chemicals to sweep groundwater layers with different permeabilities. The use of foams to surmount permeability variations is being developed as a promising technology for aiding in-situ remediation schemes including soil flushing, chemical oxidation, and bio-remediation (Peters 1996; Hirasaki et al. 2000; Mamun et al. 2002).
Foam in porous media is defined as the "dispersion of the gas phase in the liquid phase such that the liquid phase is connected and at least some part of the gas phase is made discontinuous by the thin liquid films of water" (Rossen 1996; Gauglitz et al. 2002). Surface-active agents, called surfactants, are required to make thin liquid films stable. The thin liquid films, called lamellae, are what endow a significant reduction in gas mobility (Ransohoff and Radke 1988; Falls et al. 1989; Schramm 1994; Prud'Homme and Khan 1996).
Two types of foams in porous media have been observed in foam displacement experiments. Even though there are no strict guidelines, it is believed that coarsely textured "weak" foam reduces gas mobility by a factor of up to tens or hundreds, and finely textured "strong" foam typically reduces gas mobility by a factor of tens, or hundreds, of thousands (Ransohoff and Radke 1988; Gauglitz et al. 2002; Tanzil et al. 2002; Chen et al. 2004). The degree of gas mobility reduction in the presence of foam is determined by the number of lamellae in porous media, or foam texture, which is an outcome of complicated mechanisms of bubble creation and destruction (Falls et al. 1988; Kovscek et al. 1995; Bertin et al. 1998; Kam et al. 2007b).
In general, there are two different ways to conduct modeling and simulation of foams. The first is the use of mechanistic foam simulations in which computational algorithms keep track of foam texture using bubble population balance in the gas phase as well as material balance for individual phases (Kovscek et al. 1995; Kovscek et al. 1997; Bertin et al. 1998; Myers and Radke 2002; Dholkawala et al. 2007; Kam et al. 2007b; Kam 2008). Dynamic foam rheology is normally updated at each time step, for instance by incorporating mathematical descriptions of bubble creation and destruction, foam yield stress, effective gas viscosity, and trapped gas saturation.
The other way to conduct modeling and simulation of foams is the use of local steady-state modeling that takes advantage of an MRF measured in fixed-rate foam coreflood experiments in the absence of oil (Rossen et al. 1995; Cheng et al. 2002). This method assumes immediate attainment of local steady state in which gas transport can be described as:
ug = [ kkrg (Sw ) / ug MRF ]?P ....[EQ. 1]
where k is absolute permeability, Sw is water saturation, ?P is pressure gradient, and ug , krg and ug are the superficial velocity, relative permeability, and viscosity of gas phase, respectively. Although this local steady-state modeling cannot capture dynamic transient foam behavior, the concept of MRF greatly simplifies foam modeling in porous media.
The presence of oil has a certain degree of impact on foam rheology, which can be apprehensible by the measurement of film stability (Bernard and Jacobs 1965; Jensen and Friedmann 1987; Kristiansen and Holt 1992; Bergeron et al. 1993; Schramm 1994; Prud'Homme and Khan 1996). Among many of the parameters available in literature, the use of entering and spreading coefficients has been regarded as a reliable technique to identify foam stability in the presence of oil: the entering coefficient determines whether an oil droplet can enter the interface between gas and water, and the spreading coefficient measures whether the oil droplet is likely to spontaneously spread between gas and water phases. If both entering and spreading are favored by the formula derived by thermodynamics, foam stability can be undermined by the oil (Bernard and Jacobs 1965; Lau and O'Brien 1988; Bergeron et al. 1993; Myers and Radke 2002). If either entering or spreading is unfavorable (i.e., either not entering or entering but not spreading), the oil is expected to cause little or no effect on foam stability. Previous studies show that most hydrocarbon oils have a detrimental effect on foams but many chlorinated or fluorinated oils do not. More details on thin film stability in the presence of oil can be found elsewhere (Rong 2002).
The influence of oil on foam displacement is more complicated because of the dynamic process associated with movement of foam films in a complex pore network. Earlier studies (Minssieux 1974; Mannhardt et al. 2000) found the amount of gas content during foam injection (i.e., foam quality) plays an important role in the stable propagation of foam front and the ultimate oil recovery. An experimental study using a micromodel (Manlowe and Radke 1990) shows that using entering and spreading coefficients may not be sufficient enough to describe foam behavior; the sweep efficiency can still be high if a pseudoemulsion is formed. An effort can be found to measure the MRF during foam flow in the presence of oil in a wide range of commercial surfactants (Mannhardt et al. 2000).
The main objective of this study is to characterize the nature of foam displacement in the presence of oil (i.e., three-component three-phase flow of oil, gas, and surfactant solution) at different initial core conditions, inlet injection conditions, MRF values, and oil viscosities by using fractional-flow theory. The cases tested in this study are simultaneous injection of gas and water at fixed rates into a porous medium initially saturated with oil and water.
Note that the terms water, oil, and gas in this study represent an aqueous phase with surfactants, oleic phase, and gaseous phase, respectively. This three-pseudocomponent and three-phase system makes our analysis more convenient with no need to take complicated phase behavior into account. The MRF can be regarded as a parameter that delineates complex foam mechanisms, mobility of gas in the presence of foam, and the interactions between foam and oil. For example, MRF = 1 represents the case when no foams can be created or injected foams break down immediately due to the detrimental effect of the oil.
This study does not intend to solve complex foam flow and/or propagation mechanisms accounting for mechanistic descriptions of bubble creation and destruction in the presence of oil. Rather, the focus is made on the development of a technique that can handle the complicated nature in a relatively simple and comprehensible way in order to acquire the insight into fundamentals. This model does not keep track of mechanistic foam properties explicitly such as foam texture, gas trapping, gas viscosity, and relative permeability functions.
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