Injectivity in Non-Newtonian two-phase flow

A recent study [Rossen et al., 2011] developed a fractional-flow model (an extension of the Buckley-Leverett theory for a waterflood) for non-Newtonian two-phase flow (surfactant solution and gas) around a well. In this fractional-flow model two effects are represented: the decrease in water saturation Sw during gas injection in a SAG process and the non-Newtonian mobility with respect to radial position in the near-wellbore region, respectively. An important implication of this model is the relationship between these effects and injectivity. In this paper we create a model which determines injectivity as a function of time from data for water saturation and radial position, for shear thinning foam, modeled as a power-law fluid, in the near-wellbore region. We take the results generated by Rossen et al. and recast them in a form from which injectivity can be calculated. We compare the results, with both changing water saturation and non-Newtonian rheology, to two simpler cases: the effect of non-Newtonian rheology alone (effective viscosity changes with radial distance but Sw is assumed uniform) and the effect of water saturation alone (Sw varies with radial position but non-Newtonian effects are ignored) on injectivity. From these results we analyse whether or not it is essential to model both effects as in Rossen et al. We observe that the effects of non-Newtonian rheology on injectivity are far greater than those due to changing water saturation Sw in the near-wellbore region and that it is therefore not necessary to model both effects; one only needs to account for shear thinning. One limitation of this fractional flow model is that it disregards foam collapse. We found that this collapse of foam near the well has a much larger effect on injectivity than shear-thinning behavior. In order to determine how much the non-Newtonian rheology and nonuniform water saturation really affect injectivity, the foam model needs to be extended to include foam collapse. Furthermore, the factor (rw/re) in dimensionless position xD should not be disregarded in the MOC calculations, as it was in Rossen et al. [2011]. Doing so affects mobilities very close to the well and therefore affects injectivity. The model described in this paper focuses on non-Newtonian “strong” (shear thinning) foam flow; however, the approach could also be extended to polymer injection.Geoscience & EngineeringCivil Engineering and Geoscience