Averaging model for cuttings transport in horizontal wellbores

This paper presents a theoretical analysis of the problem of cuttings transport for a two-region system composed of a fluid bed (ω-region) and a stationary bed of drill cuttings, which is considered as a porous medium (η-region) in the two-phase system. The ω-region is made up of a solid phase (σ-phase) dispersed in a continuos fluid phase (β-phase), while the η-region consists of a stationary solid phase (σ-phase) and a fluid phase (β-phase). The volume averaging method was applied in this study. Volume-averaged transport equations were derived for both the fluid bed and the porous medium regions. These equations are based on the non-local form of the volume-averaged momentum transport equation that is valid within the bounded region. Outside this region, the non-local form reduces to the classic volume-averaged transport equation. From these equations, a one-equation model was obtained, and the constraints that the one-equation model must satisfy were applied. For estimating the averaged pressure drop and the averaged velocity, the one-equation model was solved numerically by using the finite-difference technique in the implicit scheme. Numerical results are in agreement with experimental data and theoretical results reported in the literature.