Slumping Flows in Narrow Eccentric Annuli: Design of Chemical Packers and Cementing of Subsurface Gas Pipelines
In well construction, there are an increasing number of scenarios in which plugs are being set in annular geometries, whether as cement plugs or simply in the form of chemical packers. The generic reason for setting of such plugs is to hydraulically isolate different regions of a wellbore (or hole). An interesting practical problem in such situations is to predict the rheological properties that are necessary to prevent the annular plug fluid from flowing under the action of buoyancy, or indeed to predict how far the plug material may flow for given rheological properties. The answers to these questions provide valuable information for operational design. Mathematically, these flows are modeled using a Hele-Shaw style approximation of the narrow annulus. Since fluids used in the wellbore are non-Newtonian, typically shear-thinning and with a yield stress, the relationship between the local modified pressure gradient and the gap-averaged velocity field is nonlinear. If the yield stress of the fluids is sufficiently large, relative to the applied pressure over the gap, there is no flow. In the porous media context, there is direct analogy with problems of nonlinear seepage and in particular with non-Darcy flows with limiting pressure gradient. The study of such flows was both pioneered and developed by V.M. Entov, to whose memory this paper is dedicated.
KeywordsVisco-plastic fluid Nonlinear seepage Cementing Yield stress Variational method
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