Two-Region Average Model for Cuttings Transport in Horizontal Wellbores I: Transport Equations

Abstract

The aim of this article is to derive a mathematical model without length-scale restrictions for cuttings transport in horizontal wellbores using the non-local forms of the volume averaging method, which is a technique used to derive transport equations for multiphase systems and one of the main approaches in two-phase flow modeling. The theoretical derivation of the cuttings transport problem is for a two-region system composed of a fluid bed (ω region) and a stationary bed (η region) of drill cuttings that it is considered as a porous medium. The volume-averaged mathematical model obtained in this work consists of the mass and momentum equations for the ω and η regions. The model was the starting point to obtain one-equation models for both regions. The one-equation models together with adequate jump conditions can be used to predict the hydrodynamics of the ω and η regions. The mathematical derivations of the momentum and mass flux transfer jump conditions are presented in Part II of this article.