Fractional-Flow Theory for Non-Newtonian Surfactant-Alternating-Gas Foam Processes

Abstract

Foam can improve sweep efficiency in gas-injection-enhanced oil recovery. Surfactantalternating-gas (SAG) is a favored method of foam injection. Laboratory data indicate that foam can be non-Newtonian at low water fractional flow f w , and therefore during gas injection in a SAG process. We investigate the implications of this finding for mobility control and injectivity, by extending fractional-flow theory to gas injection in a non-Newtonian SAG process in radial flow. We make most of the standard assumptions of fractional-flow theory (incompressible phases, one-dimensional displacement through a homogeneous reservoir, instantaneous attainment of local equilibrium), excluding Newtonian mobilities. For this initial study, we ignore the effect of changing or non-uniform oil saturation on foam. Non-Newtonian behavior at low f w implies that the limiting water saturation for foam stability varies as superficial velocity decreases with radial distance from the well. We discretize the domain radially and perform Buckley-Leverett analysis on each narrow increment in radius. Solution characteristics move outward with fixed f w. We base the foam model parameters and non-Newtonian behavior on laboratory data in the absence of oil. We compare results to mobility and injectivity determined by conventional simulation, where grid resolution is usually limited. For shear-thinning foam, mobility control improves as the foam front propagates from the well, but injectivity declines somewhat with time. This change in mobility ratio is not that at steady state at fixed water fractional flow in the laboratory, however, because the shock front in a non-Newtonian SAG process does not propagate at fixed fractional flow (though individual characteristics do). Moreover, the shock front is not governed by the conventional condition of tangency to the fractionalflow curve, though it continually approaches this condition. Injectivity benefits from the increased mobility of shear-thinning foam near the well. The foam front, which maintains a constant dimensionless velocity for Newtonian foam, decelerates somewhat with time for shear-thinning foam. For shear-thickening foam, mobility control deteriorates as the foam front advances, though injectivity improves somewhat with time. Overall, however, injectivity suffers from reduced foam mobility at high superficial velocity near the well. The foam front accelerates somewhat with time. Conventional simulators cannot adequately represent these effects, or estimate injectivity accurately, in the absence of extraordinarily fine grid resolution near the injection well.

Factors Influencing the Rheology of Methane Foam for Gas Mobility Control in High-Temperature, Proppant-Fractured Reservoirs

“…The shear-thinning rheology in the range of viable field flow rates is a favorable outcome given that in the near-wellbore conditions, gas injectivity, as desired, would be relatively higher and would, therefore, reduce the amount of time and energy required to inject the target gas slug. On the other hand, as the foam penetrates deeper into the fracture network, the shear rate decreases, resulting in higher foam viscosity and improved conformance control deeper in the formation [24,83]. The shear-thinning rheology in the range of viable field flow rates is a favorable outcome given that in the near-wellbore conditions, gas injectivity, as desired, would be relatively higher and would, therefore, reduce the amount of time and energy required to inject the target gas slug.…”

“…The shear-thinning rheology in the range of viable field flow rates is a favorable outcome given that in the near-wellbore conditions, gas injectivity, as desired, would be relatively higher and would, therefore, reduce the amount of time and energy required to inject the target gas slug. On the other hand, as the foam penetrates deeper into the fracture network, the shear rate decreases, resulting in higher foam viscosity and improved conformance control deeper in the formation [24,83].…”

Breakdown of similarity solutions: a perturbation approach for front propagation during foam-improved oil recovery

“…Hence, the front itself consists of the zone of finely textured foam, separating (as mentioned above) coarsely textured, collapsed foam upstream from liquids (surfactant solution and oil) downstream. Foam in porous media is of course a rheologically complex fluid (which among other things) can exhibit shear thinning behaviour [19,22,25,[28][29][30]. For the purposes to be considered here though, what matters is that at the front, we have a finely textured foam, which has very low mobility.…”