Judging the Generalized Newtonian Fluid assumption for cuttings transport modelling by applying time scale comparisons

Cellulose (PAC) solutions are often employed as drilling fluid model systems in experimental laboratory studies to investigate cuttings transport. For this purpose, PAC solutions are typically assumed to behave purely viscous, i.e. they do not show time-dependent/thixotropic and/or viscoelastic properties and are thus modelled with a Generalized Newtonian Fluid (GNF) constitutive equation. However, PAC solutions feature both viscoelastic and thixotropic properties on different time scales1. In this study, cuttings transport process time scales are compared with rheological time scales for PAC solutions1. Using the concepts of Deborah and Weissenberg numbers as well as Pipkin spaces for two spatial scales, an arbitrary annular (wellbore) section and the particle scale, we show that PAC solutions may not necessarily satisfy a GNF formulation under all circumstances. In particular, for Lagrangian unsteady flows, e.g. due to flow start-up, particle acceleration and/or spatially developing flows, the GNF framework is not entirely valid and leads to some error. We suggest several actions to minimize the magnitude of the error.