Experiments in homogeneous and heterogeneous sand-packed columns showed that the foam mobility in the two cases could differ by two orders of magnitude. The difference is because of the generation of foam lamellae by snap-off for flow across an abrupt increase in permeability. This mechanism is shown to be dependent on the degree of permeability contrast and the gas fractional flow. It has important implications for the degree of gravity segregation of gas and liquid in field-scale recovery processes.
Foam has been used to improve the sweep efficiency of enhanced oil recovery1–4 and aquifer remediation processes5–8 because of its effect in reducing gas mobility. Gas, as a bulk fluid, has a very low viscosity compared with oil and water. However, when gas is in a dispersed phase, as in foam, its apparent viscosity is greatly increased (i.e., its mobility is greatly reduced). Yet foam still has a lower average density than resident liquids in a reservoir or aquifer. This density contrast tends to promote gravity segregation. Stone9 and Jenkins10 developed models to predict the extent of gravity segregation in water-alternating-gas (WAG) injection. A key parameter in this model is the permeability anisotropy or the kv/kh ratio, where kv and kh are vertical and horizontal permeabilities, respectively. This anisotropy is based on single-phase flow. We infer here from 1D experiments and calculations that the effective anisotropy for foam flow in stratified systems may be much greater than for single-phase flow. The implication is that gravity segregation for foam flow in stratified systems may be much less than predicted by the Stone-Jenkins model.
Anisotropy in foam mobility was seen in an aquifer remediation field test that we conducted in a heterogeneous alluvial formation beneath Hill Air Force Base, Utah.6,8 Foam was used to divert injected surfactant solution to zones of lower permeability and to the base of the aquifer where the contaminant was located. The field test showed that foam could be generated in situ and propagated even in a shallow, unconfined aquifer. Air was injected intermittently with aqueous surfactant solution at low injection pressure (2 to 8 psi above hydrostatic). The in-situ formation of foam was evident from the reduced injection rate observed while maintaining constant injection pressure and from foam production at the multilevel monitoring well located 15 ft (4.6 m) away from the injector (Fig. 1). Simulation results8 demonstrated that, in the absence of foam, gas would not have been able to propagate far enough to reach the monitoring well. Yet the photograph in Fig. 1 clearly shows foam being produced from the two upper monitoring intervals (B and C, see Fig. 2). While the lowest monitoring interval A is producing emulsified contaminant in the photograph, foam was intermittently produced there as well, even though it is below the injection interval. The observations indicated that foam was propagated horizontally, despite relatively high foam mobility.
In simulating the field test using a modified UTCHEM reservoir simulator,8 an anisotropy in foam mobility must be used in order to history-match field observations. With an effective foam viscosity of 1 cp, matching required use of a ratio of vertical to horizontal gas mobilities (?v/?h)g of 0.1 wherever foam is present. This anisotropy factor is used in addition to explicit modeling of permeability layering. The additional resistance of foam to vertical flow is attributed to both capillary entry effect and foam generation by snap-off at permeability discontinuities. Fig. 2 shows the simulated foam propagation profiles at three different times. As can be seen, the simulation results indicate that a considerable amount of gas was propagated horizontally from the injector to the extractor.
The effects of capillarity in impeding nonwetting-phase flow across layers in series are well known.11 These capillary effects are important for any type of multiphase flow in heterogeneous or stratified porous media, especially when flow rates are low, permeability varies over short distances (inches or centimeters), and permeability contrasts are large.12,13 Such conditions exist in many reservoirs and aquifers with episodic or periodic fluctuations in the depositional process. In such layered media, capillarity causes the entrapment of the nonwetting phase in high-permeability regions upstream of low-permeability layers.14,15 This capillary entrapment can significantly affect oil recovery even on the reservoir scale.16 Van Duijn et al.17 showed that when an oil/water displacement front arrives at a sudden permeability decrease, the front will stop, waiting for the oil saturation to build up before it enters the low-permeability region. The same entrapment effect creates resistance to gas flow perpendicular to stratification.
In the presence of surfactants, capillarity also contributes to foam generation by snap-off. Yortsos and Chang12 studied the variation of capillary pressure for nonwetting-phase flow across permeability variation in series. They showed that, for flow from a low-permeability to high-permeability region, capillary pressure decreases (wetting-phase saturation increases) in the low permeability region as it approaches the permeability increase. Similar findings have also been made by Chaouche et al.14 in bead-pack experiments and pore-network simulations. Furthermore, van Duijn et al.17 showed that, during drainage, capillary pressure might become discontinuous at a permeability jump, indicating that one of the flowing phases loses continuity upstream of the permeability jump. Van Lingen18 pointed out that the subsequent pressure drop across the sudden permeability increase induces snap-off. Snap-off at the sudden permeability increase may be important to foam flow in heterogeneous reservoirs.
Between the two mechanisms by which capillarity impedes foam flow perpendicular to stratification, foam generation by snapoff is potentially more important than capillary entrapment. In the presence of foam-stabilizing surfactant, foam generated by snapoff can reduce gas mobility by orders of magnitude. Therefore, this study focuses on snap-off at a sudden permeability increase.