Cuttings Transport Modeling—Part 2: Dimensional Analysis and Scaling

Abstract

SummaryAs a follow-up to part one of this series (Busch et al. 2018a), we present a holistic dimensional analysis (DA) for the problem of cuttings transport in an annular wellbore element. We account for the non-Newtonian or, more precisely, shear-thinning and yield behavior of the drilling fluid by using non-Newtonian scaling concepts for generalized Newtonian fluids (GNFs) available in the literature.We first perform a nondimensional analysis for the Herschel-Bulkley (HB) material function (also known as the yield power-law [YPL] model) and establish a respective space of nondimensional numbers (Π-space) as well as a generic corresponding nondimensional cuttings-transport-process relationship. In a second step and to ease the derivations, we focus on the power-law (PL) material function and introduce a convenient reference shear rate that allows the evaluation of the reference viscosity in the established nondimensional quantities. Finally, on the basis of the established Π-space for the PL fluid, we generalize the specific PL case to the currently recommended HB material function by means of a local PL approximation, following the concept of Metzner and Reed (1955). Furthermore, we provide the results for both pipe and annuli because the former is often used in solid-transport studies.Compared to the Newtonian case, the obtained Π-spaces are increased by one or two nondimensional numbers accounting for the shear-thinning behavior or yield and shear-thinning behavior, respectively. It follows that when scaling cuttings transport processes, it is not entirely accurate to, for example, represent a Bingham fluid with a PL fluid because these exhibit different rheological behaviors. In addition, we show that the established process relationship must be nonmonomial, in contrast to the monomial forms used in various cuttings transport studies. Furthermore, we demonstrate that typical nondimensional numbers such as Reynolds, Shields, Archimedes, and Froude numbers arise from the analyses and we discuss some relevant differences.The presented Π-spaces might be used for scaling of process parameters as well as for quantitative comparison of results of one cuttings transport study with those of another. In addition, they could be used to scale wellbore parameters to a laboratory setup or vice versa. Finally, the established process relationship provides a framework for cuttings transport correlations by fitting comprehensive experimental data sets and could potentially be used to improve real-time models.