Model for Displacement of Herschel-Bulkley Non-Newtonian Fluid by Newtonian Fluid in Porous Media and Its Application in Fracturing Fluid Cleanup

Abstract

Abstract Recent laboratory and field studies performed by oil and gas service companies indicate that fracturing polymer may exhibit yield stress after water leak-off. Its rheology may be described by Herschel-Bulkley model. It is reported in the literature that yield stress might be responsible for low fracturing fluid cleanup efficiency. In this paper, we derive an extended analytical Buckley-Leverett type model for the displacement of non-Newtonian Herschel-Bukley fluid (e.g. fracturing fluid) by Newtonian fluid (e.g. hydrocarbon/water). Using this model, we study the effect of yield stress and other rheological parameters on fracturing fluid displacement efficiency. Parametric analysis indicates that high values of yield stress τ0, consistency index K’ and flow behavior index n’ lead to low displacement efficiency. It is found that, for a given set of relative permeabilities, if a pressure gradient is not enough to overcome a critical pressure gradient, non-Newtonian fracturing fluid will not flow and only Newtonian fluid will be produced. It is demonstrated that low displacement efficiency can be overcomed by increasing displacing rate.