A Two-Region Hydraulic Averaging Model for Cuttings Transport During Horizontal Well Drilling
Authors: Salazar-Mendoza R. , Garcia-Gutierrez A. 
Published: March 2010

Abstract
The two-region hydraulic averaging model was used to analyze the problem of cuttings transport during horizontal well drilling. This model considers a two-phase two region system composed of a moving bed (ω-region) and a stationary bed of drill cuttings modelled as a porous medium (η-region). The ω-region is made up of a solid phase (σ-phase) dispersed in a continuous 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 to obtain the volume-averaged transport equations for both the moving 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 interface region. The three main flow patterns of the horizontal cuttings transport process analyzed were: Case 1 - fully suspended flow, Case 2 - flow with a stationary bed and Case 3 - flow with a moving bed. The one-dimensional models for all cases were solved numerically using the finite difference technique with an implicit scheme. The numerical results were compared with experimental data and theoretical results reported in the literature and a good agreement was found.

Introduction
Due to the presence of two phases (solid and liquid) where the solid particles tend to settle at the bottom of the pipe(1), the hydraulic transport of solid particles in horizontal pipes is a very complex physical phenomenon. Such a phenomenon is relevant in several areas, such as the chemical, geothermal, mining and oil industries.
In the oil industry, horizontal drilling is used to exploit reservoirs exhibiting thin pay zones to solve the problems related to water and gas conning, to obtain greater drainage area and to maximize the productive potential in naturally fractured reservoirs. However, a major deterrent in horizontal drilling is the reduction in performance of the transport of solid rock fragments called cuttings transport(2).
A detailed review of published experimental data reveals that the cuttings transport characteristics change with an increase in wellbore angle. Tomren et al.(3) and Ford et al.(4) carried out experimental work on cuttings transport in inclined wellbores and observed the existence of different layers that might occur during mud and cuttings flow in a wellbore: a stationary bed, a sliding bed and a heterogeneous suspension or clear mud. Leising and Walton(5), Sifferman and Becker(6) and Peden et al.(7) reported that under a certain range of well deviation, the cuttings bed in annuli is unstable. Doron and Barnea(8) carried out experimental work on solid-liquid flow in pipes and observed the existence of three mainflow patterns: fully suspended flow, flow with a stationary bed and flow with a moving bed.
On the other hand, numerous mathematical and empirical models for the prediction of cuttings transport in horizontal and directional wells have been developed by several researchers(9–18). However, many of the previous models (two- and three-layer approaches) have been constructed on an intuitive basis rather than on a rigorous analysis of the governing point equations and boundary conditions. Intuitive analysis often leads to hidden assumptions and unsupported simplifications.