Effect of orbital motion of drill pipe on the transport of non-Newtonian fluid-cuttings mixture in horizontal drilling annulus

Accepted Manuscript Effect of orbital motion of drill pipe on the transport of non-Newtonian fluid-cuttings mixture in horizontal drilling annulus Boxue Pang, Shuyan Wang, Xiaoxue Jiang, Huilin Lu PII:

S0920-4105(18)30999-9

DOI:

https://doi.org/10.1016/j.petrol.2018.11.009

Reference:

PETROL 5481

To appear in:

Journal of Petroleum Science and Engineering

Received Date: 15 May 2018 Revised Date:

19 October 2018

Accepted Date: 4 November 2018

Please cite this article as: Pang, B., Wang, S., Jiang, X., Lu, H., Effect of orbital motion of drill pipe on the transport of non-Newtonian fluid-cuttings mixture in horizontal drilling annulus, Journal of Petroleum Science and Engineering (2018), doi: https://doi.org/10.1016/j.petrol.2018.11.009. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Effect of orbital motion of drill pipe on the transport of non-Newtonian

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fluid-cuttings mixture in horizontal drilling annulus

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Boxue Pang a, Shuyan Wang b,**, Xiaoxue Jiang a, Huilin Lu a,*

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School of Energy Science and Engineering Harbin Institute of Technology

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Harbin, 150001, P. R. China

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School of Petroleum Engineering Northeast Petroleum University

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Daqing, 163318, P. R. China

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* First Corresponding Author: [email protected] (Huilin Lu),

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** Second Corresponding Author: [email protected] (Shuyan Wang).

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Tel.: 010-045186412258.

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First author E-mail address: [email protected] (Boxue Pang).

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ACCEPTED MANUSCRIPT Abstract: The effect of orbital motion of drill pipe on the transport of non-Newtonian fluid and

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cuttings is simulated by means of the two-fluid model in combination with the kinetic theory of

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granular flow in the horizontal wellbore annulus. The drill pipe self-rotates around its own axis

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while pursuing a circular orbit around the axis of the wellbore annulus, in which the orbital radius is

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the eccentric distance of the drill pipe from the axis of the wellbore. The embedded sliding mesh

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method is adopted to achieve the effect of the orbital movement of the drill pipe wall on the

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liquid-solid mixture. The cuttings transport ratio (CTR) which is defined as the ratio of the

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concentration of injected cuttings to the concentration of cuttings retained in the annulus is chosen

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as the measurement to evaluate hole cleaning. Cuttings transport behaviors in the annuli with the

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four motion states of drill pipe are investigated respectively. Simulations indicate that if the drill

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pipe is not concentric, there must be the fluid force that causes the lateral movement of drill pipe

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when it rotates. The orbital motion of drill pipe improves cuttings transport ratio in the annulus due

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to the periodical stirring and entrainment effect on cutting particles. The tangential flow within the

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annulus is dominated by the orbital motion of drill pipe rather than the self-rotation. The secondary

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flow appears especially when the self-rotation and orbital motion of drill pipe are in the opposite

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direction. With the increase of the orbital radius, the cuttings transport ratio is improved and the

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pressure drop is reduced because of the agitation of the drill string against the flow field. Increasing

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the rotating speed of the drill pipe contributes to a better wellbore cleaning, while an excessive

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rotating speed causes a higher pressure drop. Although the orbital motion of the drill pipe improves

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the hole cleaning, it also greatly increases the resistance and resultant moment exerted by the

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liquid-solid mixture, especially at high rotation speeds and eccentricity ratios.

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Keywords: Cuttings transport; Orbital motion; Non-Newtonian fluid; Drill pipe rotation; 2

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ACCEPTED MANUSCRIPT Secondary flow; Pressure drop.

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1. Introduction High-efficiency drilling is essential for the exploitation of oil and gas fields. Inefficient

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cuttings transport will cause many problems in the process of drilling including high torque, high

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drag, premature bit wear, and even stuck pipe. Cuttings transport in drilling annulus is dominated by

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many variables including wellbore structure characteristics, flow rate and rheology of drilling mud

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and cuttings characteristics, etc. Drill pipe rotation induces tangential velocities of drilling fluids

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and cuttings and it is a factor that can not be ignored during hole cleaning. More and more

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researchers (Naganawa and Nomura, 2006; Wang et al., 2009; Guo et al., 2010; Han et al., 2010;

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Akhshik et al., 2016; Pang et al., 2018a, 2018b) have begun to pay attention to the effect of drill

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pipe rotation on hole cleaning. However, the vast majority of these researches were carried out in

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flow loops where the drill pipe was constrained to rotate around its own axis, which is not realistic

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in most cases of drilling process.

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At actual drilling operations, the motion of drill pipe changes at different positions along the

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well. In most cases the drill pipe is not constrained with centralizers and has both rotary and orbital

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motion (Sanchez et al., 1997). First, the flow-induced orbital motion for a rotating cylinder is one of

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the reasons. Flow-induced vibrations of the rotating rigid body are commonly encountered in fields

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of engineering. These oscillations are often not limited to one direction, which lead to an orbital

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motion of the body following an elliptical path (Baranyi, 2004). Stansby and Rainey (2001)

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conducted experiments with dynamic response of a rotating cylinder. It was observed that the

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dominant motion of the cylinder was an orbit combined with a steady offset, and gyroscopic effects

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occurred when the orbiting cylinder was inclined to the horizontal. Feng et al. (2007) performed

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ACCEPTED MANUSCRIPT numerical calculations to analyze the flow-induced force on the drill pipe when it was rotating

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eccentrically. Results showed that the orbital motion will occur, and in general, in the same

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direction as that for its self-rotation when the rotation was driven only by an external torque. On the

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other hand, the orbital motion is induced by the rotation of the crooked drill string. The drill string

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cannot be treated as a rigid rod due to the high ratio of its length to diameter, and it can be regarded

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as an absolutely flexible cable by geometrical similarity. Mechanical phenomena typical for elastic

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rods and the drill string stability loss can be observed (Sheppard et al., 1987; Aadnøy and Andersen,

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2001; Gulyaev et al., 2014). Due to the local geometrical imperfections of the axial trajectories of

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boreholes, the drill string is subjected to the contact and friction forces exerted by the borehole wall

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additionally (van der Heijden et al., 2002; Lim, 2003; Cunha, 2004; Gulyayev et al., 2011). The drill

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pipe is bent and deformed in the axial direction, and the rotation of the crooked pipe produces

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orbital revolution around the axis of the wellbore.

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As a consequence, the cuttings transport is more affected by the orbital motion of drill pipe

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rather than the self-rotation. It has also been observed in experiments (Avila et al., 2008; Ozbayoglu

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et al., 2008) that the orbital motion of drill pipe improved cuttings transport significantly. Even so,

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the orbital motion of drill pipe has often been ignored by researchers for two reasons: (1) The

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orbital motion improves hole cleaning and ignoring it was regarded as a conservative approach; (2)

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The dynamics of the inner pipe in the wellbore has not been fully understood. But the improvement

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on hole cleaning are too high to be ignored. The orbital motion of drill pipe is required for

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significant development in studies on cuttings transport (Ozbayoglu et al., 2008; Sorgun, 2010;

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Akhshik et al., 2015). In this work, the effect of orbital motion of drill pipe on the transport of

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drilling fluids-cuttings mixture in the horizontal well has been deeply investigated. While the drill

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pipe rotates around its own axis, it makes circular movement at a controllable angular velocity and

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ACCEPTED MANUSCRIPT rotation direction around the axis of wellbore. The fluid force on the rotating pipe and the tendency

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of flow-induced orbital motion are analyzed. Effects of rotational state, rotational speed and

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eccentricity ratio of the drill pipe on cuttings transport are predicted. The paper is intended to draw

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attentions of researchers on the orbital motion of drill pipe, and to explain how and why the orbital

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motion affects hole cleaning.

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2. Computational methodology

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An Eulerian–Eulerian model is prepared to investigate the flow of cutting particles and drilling

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mud through the horizontal annulus created by the casing wall and the orbiting pipe. The collisional

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interactions between cutting particles, and between the particles and the walls of the orbiting pipe

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and the wellbore are considered. The KTGF with a granular temperature is used to formulate

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collisional interactions (Gidaspow, 1994). Drilling fluids and cutting particles are coupled by

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interphase forces in the model. In formulating the CFD model, we assume that: (1) The drilling

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liquids are incompressible and their non-Newtonian rheological properties satisfy the power-law

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model; (2) The cuttings are all spherical particles and they have a uniform size; (3) Thermal effects

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are not included in the simulation of liquid-solid two-phase flow; (4) The orbit of the rotating pipe

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is always a circle centered on the axis of wellbore.

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2.1. Governing equations

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The governing equations for the flow of drilling fluids and cutting particles in the horizontal

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well are listed in Table.1. Non-Newtonian rheological properties for drilling fluids are established

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by power-law model (Eqs. (T1-4) - (T1-7)). As shear thinning fluid, the power law index of the

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drilling fluid used in the simulation is less than 1.0. The turbulent viscosity is computed from the

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shear-stress transport k-ω model (Wilcox, 1998) and the low Reynolds number correction is enabled

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(Menter, 1994). Closure equations for cuttings phase are listed in Eqs. (T1-10) - (T1-14), in which the particle

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pressure ps is the normal stress from collisions, and the stress tensor of cuttings τs is expressed in

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terms of shear viscosity µs and bulk viscosity ξs. The granular temperature is obtained from the

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equation of Ding and Gidaspow (1990).

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To couple the momentum transfer between drilling fluids and cutting particles, the drag force

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between the two phases is calculated by Huilin-Gidaspow model (Huilin et al., 2003), as shown in

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Eqs. (T1-15) - (T1-18). The virtual mass force is another interphase force between the two phases

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and it is given in Eq. (T1-19) (Drew and Lahey, 1993). Researches (Ding et al., 1995; Kendoush et

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al., 2007; Guskov, 2012; Wang et al., 2017) indicated that ignoring the virtual mass force in the

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liquid-solid flow causes the results to agree somewhat less with experiment, and considering the

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virtual mass force in the calculation of accelerated flows improves the results. In this work, the

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densities of drilling fluids and cuttings are on the same order of magnitude, and the orbital motion

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of the drill pipe periodically accelerates the tangential flow of cuttings at the lower wall. Therefore,

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the virtual mass force is included in the terms of interaction between two phases.

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2.2. Boundary conditions and geometric modeling

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The configuration of the computational domain is a horizontal annulus consisting of the

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orbiting pipe and the wellbore. As shown in Fig. 1, the orbital motion of drill pipe is specified as the

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circular movement at a constant revolution speed Ωd around the axis of wellbore. At the same time,

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the drill pipe rotates around its own axis at the rotation speed ωd. The orbital motion of drill pipe is

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in the same or opposite direction as that for its self-rotation. The orbital angle α is defined as the

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angle at which the drill pipe axis deviates counterclockwise from the negative y-axis. At the initial 6

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time of the calculation, the drill pipe locates at the lowest point of its revolution orbit and α = 0. The

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trajectory equations of the axis of the drill pipe can be expressed as:

π  O x′ = E cos  α −  , 2 

(1)

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π  O ′y = E sin  α − 2 

(2)

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α = Ωd t × 2π ,

 , 

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(3)

in which O′x and O′y are the x-component and the y-component of the coordinates of the drill pipe

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axis trajectory respectively, E is the eccentric distance of the drill pipe from the axis of the wellbore

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and t is the calculating time.

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Rheological parameters of drilling fluid are taken from experimental measurements (Kelessidis

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et al., 2006). The consistency factor and the flow behavior index are set to 0.9448 Pa·sn and 0.4097

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respectively. Other physical parameters including feed conditions for drilling fluids and cuttings,

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and wellbore structure parameters including annulus size and drill pipe rotation speed are taken

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from the literature (Sifferman et al., 1974) as summarized in Table 2. The orbital motion of the drill

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pipe around the borehole is hard to measure physically in practice, while studies (Avila et al., 2008)

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have shown that it mainly depends on the eccentricity and rotation speed of the drill pipe. In general,

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the higher the rotation speed, the higher the orbital revolution speed. Moreover, the orbital

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revolution speed is generally not higher than the motor speed. Therefore, the orbital revolution

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speed of 0-200 rpm can roughly cover most of the actual drilling conditions. Due to the high

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computational cost, today available computational power limits the study on cuttings transport by

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three-dimensional CFD method to a scale of the order of 100 m, although the size of the wellbore is

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of the order of 103 m (Aarsnes and Busch, 2018). The length of the numerical domain is chosen to

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be 6.0 m in the present work. The cuttings are continuously injected from the inlet into the annulus

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ACCEPTED MANUSCRIPT at a constant volume concentration of 4%. At the initial moment, the cuttings are uniformly

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distributed throughout the annulus with the same concentration as inlet. The exit of the drilling

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annulus is set to pressure boundary conditions for drilling fluids and cutting particles. At the walls,

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no-slip velocity boundary conditions are applied to the drilling liquids, and Johnson and Jackson

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(1987) boundary conditions are applied to the cutting particles. The coefficient of restitution for

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cutting particles is set to 0.9, and the coefficient of specularity between the cuttings and the walls is

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set to 0.1.

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The governing equations described above were solved by the CFD code ANSYS-Fluent 14.0

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(FLUENT, 2011) on each cell throughout the drilling annulus. The simulations were executed in the

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pressure-based implicit unsteady solver and the phase-coupled SIMPLE scheme was selected for

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pressure-velocity coupling. All calculations were performed using a constant time step of 1×10-5 s

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for satisfactory convergence and the time-average values of the desired variables were obtained

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after the cuttings flow in the annulus reaches a steady state.

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3. Meshing scheme and convergence analysis

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In order to achieve the effect of the orbital movement of the drill pipe wall on the liquid-solid

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mixture, the embedded sliding mesh method is used and the computational domain is divided into

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inner, middle and outer flow zones. The geometry of the annulus and the three flow zones are

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sketched in Fig. 2. The outer flow zone and the adjacent borehole wall are stationary, the mesh on

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middle flow zone rotates around the axis of the wellbore to provide orbital revolution of the drill

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pipe, and the mesh on inner flow zone self-rotates around the axis of the drill pipe while revolving

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with the middle zone. The drill string is a moving wall and makes synchronous movement with its

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adjacent inner zone at every moment. The connections between the outer and middle zones and

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ACCEPTED MANUSCRIPT between the middle and inner zones are achieved with two pairs of interfaces. The meshing scheme

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of the annulus with an orbiting pipe can also be seen in Fig. 2. First, the annulus cross-section is

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meshed into quadrilateral grid cells that are radially distributed. The tangential sizes of the meshes

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gradually increase from the inside to the outside. Then, the entire axial length of the annulus is

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swept in a cooper grid type with this cross section as the source surface to create hexahedral

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structured grids throughout the annulus.

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We meshed five sets of grids for the convergence study. As an important indicator to measure

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the transportation of cuttings in this work, the volume fraction of retained cuttings in the annulus is

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selected as the dependent variable of the convergence study. Fig. 3 shows the time history of the

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simulated volume fraction of the retained cuttings in annulus as a function of mesh resolutions. The

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cuttings are continuously injected into the wellbore at a constant concentration of 4%. Initially,

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cuttings continually deposit to the lower side of the annulus and the exit flux of cuttings is lower

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than that of inlet cuttings, so the volume fraction of the retained cuttings increases with time. After a

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period of computing time, the injection and output of cuttings reach a dynamic equilibrium. Due to

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the periodic agitation of the orbiting drill pipe, the volume fraction of the retained cuttings in the

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annulus fluctuates around an equilibrium value. The first three sets of cases are sensitivity analyses

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of tangential and radial mesh sizes. The time history of the cuttings volume fraction calculated by

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the grids #2 and the denser grids #1 is very close, while the result from the coarser grids #3 is

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greatly deviated from the former two. The cases #2, #4 and #5 are sensitivity analyses of axial mesh

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sizes. When the tangential and radial sizes of the grids remain the same as grids #2, increasing the

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axial size of the mesh element, we find that the calculation results produce little deviation until the

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axial size of the mesh element reaches 60 mm. The grids #4 are selected for numerical simulation in

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terms of calculation accuracy and computational cost in this work. The results of the cuttings

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transportation in the annulus are much less sensitive to the axial size than the tangential and radial

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sizes of the grids. For 3D simulation with high aspect ratio such as drilling annulus, it is a reliable

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and economical choice to appropriately increase the axial size of the grid element.

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4. Validation of the CFD model

Due to the lack of experimentation on cuttings transport taking the effect of orbital motion of

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drill pipe into account, simulations are performed and compared with the experimental results

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measured by Han et al. (2010) in the annulus with only drill pipe self-rotation. Detailed experiment

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parameters can be found in the literature (Han et al., 2010). Fig. 4 shows the time history of the

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simulated volume fraction of the retained cuttings in the annulus and the corresponding

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experimental values at different inlet velocities of liquids. Unlike the annulus with an orbiting drill

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pipe, after a period of computing time the volume fraction of the retained cuttings in the annulus

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with a self-rotating pipe fluctuates little. Without the periodic agitation of the orbiting drill pipe, the

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difference between the injection and output of cuttings is very small. The flow of cuttings stabilizes

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and the time-averaged value of cuttings concentration is obtained. The less the cuttings are left in

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the annulus, the more the cuttings are transported out, and the better the wellbore is cleaned. As

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shown, a higher velocity of drilling fluid leads to a lower volume fraction of the retained cuttings.

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Moreover, the higher the drilling fluid flow rate, the less computation time required for the cuttings

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flow regime to reach a steady state in the annulus. Comparing with experimental measurements, the

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ultimately time-averaged cuttings volume fraction obtained from simulations are reasonable, while

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the difference between them still exists. The error mainly lies on the non-Newtonian properties of

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carrier fluids defined in experiments which are only determined by liquid velocity and rotational

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speed of drill pipe because of the limitation of fluid rheological parameters provided by

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5. Results and discussion

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5.1. Flow pattern in the horizontal well with an orbiting drill pipe In order to show flow patterns of cuttings along the annulus in a complete orbital period, the

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distributions of cuttings concentration at four instantaneous moments are sketched in Fig. 5

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respectively. When the orbital angle of the drill pipe α is 0°, the drill pipe passes by the lowest point

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of its rotation orbit and the radial clearance between the drill pipe and the lower wall of wellbore is

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minimum. As the orbital angle is 180°, the drill pipe passes by the highest point of its rotation orbit

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and the radial clearance between the drill pipe and the lower wall of wellbore is maximum. When

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the orbital angle of the drill pipe is 90° and 270° respectively, the drill pipe passes by the rightmost

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and leftmost ends of the rotation orbit. The gap between the pipe and the lower wall of wellbore

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varies with the change of orbital angles and then affecting the local volume fractions of cuttings.

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Fig. 6 shows the profiles of granular temperature and volume fraction of cuttings along the

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axes starting from top point a, middle point b and bottom point c (marked in Fig. 5). Similar to the

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thermal temperature in the kinetic theory of gases, the granular temperature is a measure of the

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random oscillations of particles. The granular temperature θs is defined as θs = ‹Cs Cs›/3, where Cs

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is the fluctuation velocity of particles. In the present work, the granular temperature θs characterizes

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the intensity of the oscillations of the cuttings particles. The higher the granular temperature, the

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more intense the interaction between the cuttings particles. In the lower part (points b and c) of the

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annulus entrance, the concentration of cuttings gradually increases and the granular temperature

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increases sharply. The reason for this is that the uniformly distributed cutting particles are gradually

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deposited to the lower well wall, forming the cuttings bed, and the interactions between the particles

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ACCEPTED MANUSCRIPT and between the particles and the wall of drill pipe are enhanced, resulting in a higher granular

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temperature. At a distance of more than about 2.5 m from the inlet, the cuttings concentration

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reaches a steady state at each point, and the granular temperature also falls back to a relatively

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stable value. In the upper part (point a) of the annulus, the probability of collision between

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low-concentration cuttings is low and the granular temperature is low. In the lower part (point c) of

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the annulus, sedimentation and rolling of the cuttings significantly enhance the interaction between

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the particles. While in the middle part (point b) of the annulus, the orbital motion of the drill pipe

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exacerbates the pulsation of the particles, resulting in a higher granular temperature. It can be seen

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from Figs. 5~8 that the simulated results (including cuttings concentration, granular temperature,

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axial and tangential velocity) in the annulus reach a relatively stable state at a distance of more than

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2.5 m from the inlet, where the information of the two phases at the cross section can reflect the

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transportation of cuttings within the annulus. The 6-meter-long numerical domain can satisfy the

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formation of the fully developed sedimentary state of cuttings and meet the requirements of

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statistical results in the present work.

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Affected by the orbital motion of drill pipe, the distribution of cuttings concentration changes

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with time. The profiles of instantaneous cuttings concentration at the axial distance of 3 m in the

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annulus with an orbiting pipe at four orbital angles are shown in Fig. 7. Roughly, the deposition of

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cuttings is formed at the lower wall of the well, and the low volume fraction of cuttings exists at the

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upper region. Furthermore, affected by the orbital motion of drill pipe, the core zone distribution of

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cuttings concentration reveals swaying phenomena (Tomren et al., 1986). Interestingly, a high

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concentration region of cuttings near the right side of drill pipe is observed during the

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counterclockwise orbital motion of the drill pipe, especially when the orbital angle α is from 0° to

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90°. This indicates that the orbital motion of drill pipe produces an entrainment effect on the cutting

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ACCEPTED MANUSCRIPT particles. Fig. 8 (a) shows cuttings axial velocity along the annulus with an orbiting pipe as the orbital

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angle α is 0°. The wide gap in the upper part of the annulus is the velocity core zone where most of

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the cuttings are transported. Due to the resistance caused by cuttings accumulation, the velocities of

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cuttings are very small near the lower wall of the annulus. The profiles of cuttings axial velocity at

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four instantaneous moments of a drill pipe orbital period are illustrated in Fig. 9. Obviously, the

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distribution of cuttings velocity is closely related to the orbital angle. The maximum axial velocity

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of cuttings is always in the wide gap of the annulus and it rotates following the orbital motion of the

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drill pipe, and lagging behind that.

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Fig. 8 (b) shows cuttings tangential velocity in the annulus as the orbital angle α is 0°. The

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tangential velocity is the highest at the wall of drill pipe and it is the lowest at the inner wall of the

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casing. The secondary flow appears with the orbital motion of drill pipe. The profiles of tangential

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velocities and streamlines of cuttings at four instantaneous moments of a drill pipe orbital period are

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illustrated in Fig. 10. As shown, the secondary flow exists at the inner wall of the casing. The

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cuttings and drilling fluids possess a large tangential velocity component and the secondary flow

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exists because of the stirring effect of the orbital motion. In the secondary flow regime, the direction

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of tangential velocity is opposite to that of the mainstream. Furthermore, it can also be observed

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from the four instantaneous results that the regime of high tangential velocity and secondary flow

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rotates with the orbital motion of drill pipe.

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5.2. Effect of motion state of drill pipe on cuttings transport

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The motion states of drill pipe were summarized in Table 3, and the flow in the horizontal well

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with these motion states of drill pipe was simulated respectively. Fig. 11 illustrates cuttings

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concentration in the horizontal well with a motionless pipe, a self-rotating pipe, or an orbiting pipe. 13

ACCEPTED MANUSCRIPT In the annulus with a motionless pipe, the cuttings accumulation is extremely severe. In more than

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half the volume of the annulus, the concentration of cuttings exceeds 50%. Extremely dense

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cuttings bed is formed in lower wall of the well, which is to the disadvantage of hole cleaning.

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While in the annulus with a self-rotating pipe, the tangential force introduced by the rotating pipe

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improves hole cleaning. The volume fraction of retained cuttings is significantly reduced. Moreover,

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in the annulus with an orbiting pipe, the cuttings concentration is even lower. The orbiting drill pipe

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enhances the spiral flow of drilling fluid and periodically scrapes the cuttings bed at the lower side

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of the annulus, which causes more cuttings to be carried out of the wellbore. The delamination

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phenomena of cuttings concentration are obvious, especially in the annulus with a motionless pipe

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or a self-rotating pipe. According to the distribution of solid concentration, three flow zones can be

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defined, namely the cuttings suspension zone in the upper side of the wellbore, the fixed bed zone

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in the lower side of the wellbore and the moving bed zone between them, similar to the

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experimental findings (Doron and Barnea, 1996).

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The detailed cross-section profiles of cuttings concentration are shown in Fig. 12 respectively.

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In the annulus with a motionless pipe, the distribution of cuttings is almost symmetrical, with X = 0

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as the axis of symmetry. However, the swaying phenomena of cuttings core zone are observed in

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the annulus with drill pipe rotation. It can also be concluded that in the annulus with the drill pipe

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making self-rotation and orbital motion simultaneously, the swaying direction of cuttings

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accumulation is the same as that of the orbital motion. The orbital motion plays a leading role in the

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tangential flow in the annulus.

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For different rotation states of drill pipe, the lateral forces exerted by liquid-solid mixture on

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the inner pipe were calculated and analyzed. The time history of the drag coefficient in the X and Y

23

directions for flow around a self-rotating pipe or an orbiting pipe is shown in Fig. 13. When the drill 14

ACCEPTED MANUSCRIPT pipe merely rotates counterclockwise around its own axis, the force exerted by the fluid is always

2

positive in the X direction. There is a tendency for the drill pipe to shift to the right and to orbit

3

along the same direction as its self-rotation (counterclockwise). From the positive value of the force

4

in the Y direction, we can see that at this eccentricity, the fluid forces have the effect of pushing the

5

pipe inwardly. It can be concluded that if the drill pipe is not concentric, there must be lateral

6

movement when it rotates.

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1

When the drill pipe is orbiting, the lateral resistance on the drill pipe is much greater than that

8

when it merely rotates around its own axis. Moreover, the force periodically changes with the

9

orbital rotation of the drill pipe. Each time domain is labeled as

SC

7

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,

,

and

respectively in the

figures when the drill pipe axis is in the first, second, third, and fourth quadrants of the wellbore.

11

When both the self-rotation direction and the orbital motion direction of drill pipe are

12

counterclockwise (Orbital motion 1), in the X direction, the drill pipe is subjected to the rightward

13

force of the fluid in the upper half of the annulus (ie, quadrant

14

force in the lower half of the annulus. In the Y direction, the drill pipe is subjected to the upward

15

force of the fluid in the left half of the annulus (ie, quadrant

16

force in the right half of the annulus. Similarly, when the drill pipe self-rotates counterclockwise

17

and orbits clockwise (Orbital motion 2), the resistance to the drill pipe also periodically changes

18

over time. The direction of resistance is dominated by orbital motion. However, it can also be seen

19

that the change of the direction of the force on the drill pipe does not occur exactly at the

20

intersection of the quadrants, which is due to the combined effects of the self-rotation and orbital

21

motion of the drill pipe.

and quadrant

and quadrant

) and the leftward

) and the downward

AC C

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10

22

During the rotation of the drill pipe, the resultant moment exerted by fluid were calculated.

23

The time history of the moment coefficient for flow around a self-rotating pipe or an orbiting pipe is 15

ACCEPTED MANUSCRIPT shown in Fig. 14. When the drill pipe only self-rotates counterclockwise, the resultant moment is in

2

the direction of clockwise and its magnitude slightly fluctuates with time. When the drill pipe is

3

orbiting, the resultant moment is much greater than that when the drill pipe self-rotates only.

4

Moreover, the magnitude of the resultant moment changes periodically with the orbital motion of

5

the drill pipe. When the drill pipe orbits counterclockwise (Orbital motion 1), the direction of the

6

moment is clockwise, and the maximum value of the resultant moment appears in the left part of the

7

annulus. When the drill pipe orbits clockwise (Orbital motion 2), the direction of the moment is

8

counterclockwise, and the maximum value of the resultant moment appears in the right part of the

9

annulus. Furthermore, when the self-rotation and the orbital motion are in the opposite direction, the

10

magnitude of resultant moment on the drill pipe is lower than that when the self-rotation and the

11

orbital motion are in the same direction.

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1

Fig. 15 depicts profiles of cuttings axial velocities in horizontal annuli with the four motion

13

states of drill pipe. In the annulus with a motionless pipe, the axial velocity in the lower part of the

14

annulus is very low. The velocity difference between wide gap and narrow gap of the annulus is

15

very large. While in the annulus with a self-rotating pipe, the cuttings concentration is reduced and

16

the axial velocity in the lower part of the annulus is increased. Furthermore, in the annulus with an

17

orbiting pipe, the axial velocity core zone rotates following the orbital motion, and lagging behind

18

that. The cuttings transport is relatively uniform in the radial direction.

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12

19

Fig. 16 depicts profiles of cuttings tangential velocities in annuli with the four motion states of

20

drill pipe. In the annulus with a motionless pipe, the annulus is packed with dense cuttings bed and

21

the cutting particles are barely flowing in the tangential direction. In the annulus with the inner pipe

22

merely rotating around its own axis, the tangential velocity reaches the maximum near the wall of

23

drill pipe and it is gradually reduced along the radial direction. And, the eccentric rotation of drill 16

ACCEPTED MANUSCRIPT pipe generates recirculation eddies in the annulus. In the annulus with the drill pipe making orbital

2

motion in the same direction as that for its self-rotation, high tangential velocities are induced and

3

more particles are lifted from the fixed bed to the suspension zone. Comparing with the flow in the

4

annulus with a self-rotating pipe, the area of the recirculation eddy is suppressed, moving to the

5

lower part of the narrow gap, similar to the earlier findings (Feng et al., 2007). When the inner pipe

6

makes orbital motion in the opposite direction to its self-rotation, the tangential flow in the annulus

7

is divided into two eddies, which are in the opposite direction. The tangential velocities in narrow

8

gap of the annulus are positive and the ones in wide gap are negative. The direction of the eddy in

9

wide gap of the annulus is clockwise and is the same as the direction of the orbital motion of inner

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1

10

pipe. While the direction of the eddy in narrow gap is the opposite.

11

5.3. Effect of rotation speed of drill pipe on cuttings transport

Fig. 17 depicts profiles of cuttings concentration in the horizontal annulus with the drill pipe

13

orbiting at different rotation speeds. As shown, regardless of the direction of self-rotation and

14

orbital motion, along with the increase of drill pipe rotation speed, the cuttings concentration in the

15

annulus decreases and the swaying phenomenon of cuttings bed is more remarkable. Higher

16

tangential force caused by the rotating pipe is exerted on the drilling fluids and cutting particles.

17

The cuttings bed becomes loose and the spiral flow carries more cutting particles out of the

18

wellbore.

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19

The histograms of cuttings transport ratio and pressure drop as a function of drill pipe rotation

20

speed are shown in Fig. 18. As shown, along with the increase of drill pipe rotation speed, there is a

21

certain improvement in cuttings transport ratio. The increased rotation speed increases the scraping

22

frequency of the orbiting pipe to the cuttings bed. However, the additional contribution of orbital

23

motion of drill pipe on cuttings transport is small when the rotation speed is large enough. In the 17

ACCEPTED MANUSCRIPT annulus with the drill pipe orbiting in the same direction as that for its self-rotation, the increase of

2

the rotation speed from 25 rpm to 50 rpm resulted in 22.3 % increase in the cuttings transport ratio.

3

However, as the rotation speed was increased from 100 rpm to 200 rpm, the CTR only increased by

4

4.4%. With the increase of drill pipe rotation speed, the pressure drop through the annulus drops

5

slightly and then increases. The decreased bed height increases the effective area of flow section.

6

The increased shear rate near the surface of the rotating pipe reduces the local apparent viscosity of

7

the drilling fluid because of the shear thinning property of the pseudo-plastic fluid. As a result, the

8

pressure drop through the annulus is reduced. However, as the rotation speed continues to increase,

9

the pressure loss increases due to the increased friction between the pipe wall and the liquid-solid

10

mixture. Furthermore, at high rotation speeds, the pressure loss increases more when the drill pipe

11

makes orbital motion in the opposite direction to its self-rotation.

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Fig. 19 plots axial velocities of drilling fluids and cuttings along radial direction of the annulus

13

with the drill pipe orbiting at different rotation speeds. As can be seen, the velocity distributions of

14

drilling fluids and cutting particles in the annulus are very close. Regardless of the direction of

15

self-rotation and orbital motion, the maximum axial velocity decreases with the increasing rotation

16

speed of drill pipe. As the rotation speed increases, the axial velocities of drilling fluids and cuttings

17

are increased in narrow gap of the annulus and are reduced in wide gap. A higher rotation speed of

18

drill pipe reduces the velocity difference between wide gap and narrow gap of the annulus. This can

19

be interpreted by the fact that for higher rotation speeds, the height of cuttings bed is reduced, and

20

then, the flow resistance is reduced. The axial flow tends to be more uniform due to the increase of

21

the effective area of the flow in the annulus.

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22

Fig. 20 plots tangential velocities of drilling fluids and cuttings along radial direction of the

23

annulus with the drill pipe orbiting at different rotation speeds. In the annulus with the drill pipe 18

ACCEPTED MANUSCRIPT orbiting in the same direction as that for its self-rotation (ωd = Ωd), the maximum tangential velocity

2

increases with the increase of the rotation speed of drill pipe. At high rotation speeds, the

3

recirculation eddy appears near the casing wall, especially in lower side of the annulus. Moreover,

4

when the direction of orbital motion is opposite to that of self-rotation (ωd = -Ωd), the area of the

5

recirculation eddy is significantly expanded. The tangential flow in the annulus is divided into two

6

eddies, which are in the opposite rotation direction. As the rotation speed of drill pipe increases, the

7

magnitude of tangential velocity within both eddies increase, which indicates that the secondary

8

flow in the annulus becomes more considerable.

9

5.4. Effect of orbital radius of drill pipe on cuttings transport

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Fig. 21 depicts profiles of cuttings volume fraction in the annulus with the drill pipe orbiting at

11

different drill pipe eccentricity ratios, 0.3, 0.5 and 0.7. As shown, regardless of the direction of

12

self-rotation and orbital motion, as the drill pipe eccentricity increases, the volume fraction of

13

cuttings decreases and the swaying phenomenon is more remarkable. The increase of orbiting radius

14

enlarges the scope of agitation of the drill string against the flow field. The cuttings bed near the

15

lower wall of the well is effectively cleaned and transported out of the wellbore.

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10

The histograms of cuttings transport ratio and pressure drop as a function of eccentricity ratio

17

of drill pipe are shown in Fig. 22. Simulations show that the cuttings transport ratio increases with

18

the increase of the eccentricity of the orbiting pipe. This is because as the orbital radius of drill pipe

19

increases, the contact area between the drill pipe and the cuttings bed increases, and the effect of

20

tangential force on particles increases, which leads to more cutting particles escaping from the

21

cuttings bed. The pressure drop in the annulus reduces with the increase of drill pipe eccentricity,

22

consistent with experimental measurements (Bicalho et al., 2016). On one hand, the increase of

23

orbital radius enlarges the scope of agitation of the drill string against the flow field, which leads to

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16

19

ACCEPTED MANUSCRIPT an increase in the area of effective flow section. On the other hand, the increase of eccentricity

2

results in the formation of axial preferential flow zones, therefore decreasing the friction factors.

3

Furthermore, simulations show the pressure drop in the annulus with the drill pipe orbiting in the

4

same direction as that for its self-rotation is slightly lower than that in the annulus with the drill pipe

5

orbiting in the opposite direction.

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1

Fig. 23 plots axial velocities of drilling fluids and cuttings along radial direction of the annulus

7

with the drill pipe orbiting at different drill pipe eccentricity ratios. The axial velocities of drilling

8

fluids and cuttings in the lower part of the annulus are low due to the formation of cuttings bed, and

9

they are high in the upper part. Regardless of the direction of self-rotation and orbital motion, as the

10

drill pipe eccentricity increases, the axial velocity decreases in the lower part of the annulus and it

11

increases in the upper part. The asymmetry of axial flow in the annulus is enhanced.

M AN U

SC

6

Fig. 24 plots tangential velocities of drilling fluids and cuttings along radial direction of the

13

annulus with the drill pipe orbiting at different drill pipe eccentricity ratios. When the drill pipe

14

orbits in the same direction as that for its self-rotation (ωd = Ωd), the direction of tangential flow of

15

the vast majority of drilling fluids and cuttings is the same as that of the rotation of drill pipe. As the

16

eccentricity of drill pipe increases, the tangential velocity in the upper part of the annulus increases,

17

and the eddy whose direction is opposite to the mainstream appears in the lower part of the annulus.

18

While in the annulus with the drill pipe orbiting in the opposite direction to its self-rotation (ωd =

19

-Ωd), the tangential flow in the annulus is divided into two eddies, which are in the opposite rotation

20

direction. Furthermore, as the eccentricity of drill pipe increases, the magnitude of tangential

21

velocity within both eddies increase.

22

5.5. Additional moment of torque experienced by the orbiting drill pipe

23

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As mentioned above, the orbital motion of the drill pipe is favorable for hole cleaning. 20

ACCEPTED MANUSCRIPT However, another more generally accepted fact is the negative effect that the orbital motion can be

2

detrimental to drilling equipment, especially in the case of backward whirling motion. The orbital

3

motion of the drill pipe is usually accompanied by strong lateral vibration and eccentric wear, which

4

results in frictional resistance between the drill pipe and the casing wall and the lateral force exerted

5

by the liquid-solid mixture. The additional torque experienced by the rotating drill string increases

6

the shear stress on each section of the drill pipe, accelerating the wear and fatigue damage of the

7

drill pipe and casing. Within the studyable scope of the computational fluid dynamics model in this

8

work, the resultant moment exerted by the liquid-solid mixture on the drill pipe due to the orbital

9

motion of drill pipe is discussed in this section.

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M AN U

10

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1

The moments along the axis, also known as torques, are defined as (FLUENT, 2011):

ur uuur M z = ez ⋅ M a ,

11

ur

(4)

uuur

where e z is a unit vector in the axial direction, and M a is the total moment around the center of

13

the axis. The direction of the torque is anticlockwise when Mz is positive, and it is clockwise when

14

Mz is negative. The total moment M a is computed by summing the cross products of the pressure

15

and viscous force vectors for each face element of drill pipe wall with the moment vector ra :

TE D

12

EP

uuur

16

uur

uuur ur uur ur uur M a = ra × F p + ra × Fv ,

ur

(5)

uur

where F p is the pressure force vector and Fv is the viscous force vector. The direction of the

18

total moment M a follows the right hand rule for cross products.

AC C

17

uuur

19

Fig. 25 shows the histograms of cuttings transport ratio and maximum torque in the horizontal

20

annulus with a motionless pipe, a self-rotating pipe, or an orbiting pipe, in which the maximum

21

value of the torque is compared in scalar form. The positive and negative effects of the orbital

22

motion of the drill pipe are obvious. The positive effect is that the orbital motion increases the

23

cuttings transport ratio, which improves the hole cleaning. While the negative effect is that the 21

ACCEPTED MANUSCRIPT

1

orbital motion causes the torque exerted by the liquid-solid mixture on the drill pipe to increase

2

sharply. Compared to the annulus where the drill pipe only self-rotates, the orbital motion increases

3

the maximum torque exerted by the fluid nearly ten times, which does not include the friction

4

generated by the eccentric wear between the drill pipe and the casing wall. Fig. 26 shows the histograms of the maximum value of the resultant moment on the orbiting

6

pipe as a function of rotation speed. As shown, with the increase of the rotating speed of the orbiting

7

pipe, the resultant moment on the pipe increases. The increased rotating speed increases the relative

8

speed between drill pipe and fluid, which in turn increases the instantaneous resistance in the

9

upwind direction. When the direction of self-rotation is the same as the direction of orbital motion

10

(ωd = Ωd), the magnitude of the resultant moment on the drill pipe is higher than that when the drill

11

pipe orbits in the opposite direction (ωd = -Ωd). Simulations also indicate that the increase in the

12

resultant moment on the drill pipe is more pronounced in the high rotation speed range. As the

13

rotation speed increases, the difference in the resultant moment between cases where the drill pipe

14

orbits in the same direction as that of its self-rotation and in the opposite direction is also increased.

TE D

M AN U

SC

RI PT

5

The histograms of the maximum value of the resultant moment on the orbiting pipe as a

16

function of drill pipe eccentricity ratio are shown in Fig. 27. The increase in the eccentricity of the

17

drill pipe directly increases the moment arm, which significantly increases the magnitude of the

18

resultant moment on the drill pipe during rotation. At a higher eccentricity ratio of the drill pipe, the

19

difference in the resultant moment between cases where the drill pipe orbits in the same direction as

20

that of its self-rotation and in the opposite direction is reduced. Moreover, the higher the

21

eccentricity ratio of the drill pipe, the greater the rate of increase of the resultant moment. When the

22

eccentricity ratio of drill pipe increased from 0.3 to 0.5 and from 0.5 to 0.7, the resultant moment

23

increased by 1.54 times and 2.21 times respectively, which indicates that high rotational speed and

AC C

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15

22

ACCEPTED MANUSCRIPT high eccentricity put forward higher requirements on the torsional strength of the drill pipe.

2

Therefore, it should be noted that the purpose of this paper is not to encourage artificially reinforce

3

the orbital motion of the drill pipe to improve the cuttings transport ratio, but to draw attentions of

4

researchers on the overestimation of cuttings deposition in the horizontal annulus due to the neglect

5

of the orbital motion of the drill pipe.

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1

6

6. Conclusions

SC

7

Cuttings transportation through the horizontal annulus considering the effect of orbital motion

9

of drill pipe was deeply investigated using a CFD model based on kinetic theory of granular flow.

10

Effects of rotational state, rotational speed and eccentricity of the orbiting pipe on cuttings transport

11

ratio, pressure drop, axial and tangential flow, and resultant moment on the drill pipe in the annulus

12

were analyzed in detail.

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8

Comparing with self-rotation, the orbital motion of drill pipe improves hole cleaning

14

significantly due to its periodical stirring and entrainment effect on cutting particles. Instead of

15

the self-rotation, the orbital motion of drill pipe plays the dominant role in the tangential flow

16

in the annulus. The direction of cuttings bed swaying phenomenon is the same as that of the

17

orbital motion. The core zone of axial velocity rotates following the orbital motion, and lagging

18

behind that. When the drill pipe makes orbital motion in the opposite direction to its

19

self-rotation, the tangential flow is divided into two distinct eddies, which are in the opposite

20

direction. The direction of the eddy in wide gap of the annulus is the same as the direction of

21

the orbital motion, while the direction of the eddy in narrow gap is the opposite.

22

With the increase of the rotating speed of drill pipe, the tangential flow is enhanced and the

23

axial velocity difference between wide gap and narrow gap of the annulus is reduced. Within a

AC C

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23

ACCEPTED MANUSCRIPT certain rotating speed range, the cuttings transport ratio increases, and the annular pressure drop

2

decreases.

3

With the increase of the orbital radius of drill pipe, the hole cleaning is improved and the

4

pressure drop is reduced persistently. The increase of orbiting radius enlarges the scope of

5

agitation of the drill string against the flow field, which results in the formation of axial

6

preferential flow zones and more considerable secondary flow.

7

Negative effects of the drill pipe orbital motion have also been analyzed. The lateral resistance

8

and the torque exerted by liquid-solid mixture on the orbiting drill pipe is much greater than

9

that when the drill pipe merely rotates around its own axis. The increase in the rotating speed

10

and eccentricity of the orbiting drill pipe significantly increases the torque exerted by the

11

liquid-sold mixture. Furthermore, an excessive rotating speed causes a sharp increase in the

12

pressure drop especially when the drill pipe orbits in the opposite direction to its self-rotation.

13

It should be noted that some important parameters including hole and pipe size, flow rate and

14

rheology of drilling fluid, cuttings size, etc. are maintained constant in the present work, taking into

15

account impacts of which will draw broader conclusions.

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18 19

Acknowledgements

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Financial support of this work by the National Natural Science Foundation of China under the grants Nos. 11472093 and 91752115 is gratefully acknowledged.

20 21 22

Reference

23

Aadnøy, B.S., Andersen, K. 2001. Design of oil wells using analytical friction models. J. Pet. Sci.

24

Eng. 32 (1), 53-71. https://doi.org/10.1016/S0920-4105(01)00147-4. 24

Aarsnes, U. J. F., Busch, A. 2018. Transient modeling of one-dimensional solid-liquid flow in

2

conduits.

3

https://doi.org/10.1016/j.ijmultiphaseflow.2018.03.023.

J.

Multiphas.

105,

102-111.

Akhshik, S., Behzad, M., Rajabi, M. 2015. CFD-DEM approach to investigate the effect of drill

5

pipe

6

http://dx.doi.org/10.1016/j.petrol.2015.01.017.

7

Flow.

rotation

on

cuttings

transport

behavior.

J.

Pet.

RI PT

4

Int.

Sci.

Eng.

127,

229-244.

Akhshik, S., Behzad, M., Rajabi, M. 2016. CFD-DEM simulation of the hole cleaning process in a

8

deviated

9

https://doi.org/10.1016/j.partic.2015.02.008.

drilling:

The

effects

of

particle

shape.

Particuology,

25,

72-82.

M AN U

well

SC

1

ACCEPTED MANUSCRIPT

10

Avila, R.J., Pereira, E.J., Miska, S.Z., Takach, N.E. 2008. Correlations and analysis of cuttings

11

transport with aerated fluids in deviated wells. SPE Drill. Complet. 23 (2), 132-141.

12

https://doi.org/10.2118/87180-PA.

14

Baranyi, L., 2004. Numerical simulation of flow past a cylinder in orbital motion. J. Comput. Appl. Mech. 5 (2), 209-222.

TE D

13

Bicalho, I.C., dos Santos, D.B.L., Ataíde, C.H., Duarte, C.R.; 2016. Fluid-dynamic behavior of flow

16

in partially obstructed concentric and eccentric annuli with orbital motion. J. Pet. Sci. Eng. 137,

17

202-213. https://doi.org/10.1016/j.petrol.2015.11.029.

19 20 21

AC C

18

EP

15

Cunha, J.C., 2004. Buckling of tubulars inside wellbores: a review on recent theoretical and experimental works. SPE Drill. Complet. 19 (1), 13-19. DOI: 10.2118/87895-PA. Ding, J., Gidaspow, D. 1990. A bubbling fluidization model using kinetic theory of granular flow. AIChE J. 36 (4), 523-538. DOI: 10.1002/aic.690360404.

22

Ding, J., Lyczkowski, R. W., SHA, W.T. 1995. Modeling of concentrated Liquid-solids flow in

23

pipes displaying shear-thinning phenomena. Chem. Eng. Commun. 138(1), 145-155. 25

4 5 6 7 8 9 10 11

Flow. 22 (22), 273-283. http://dx.doi.org/10.1016/0301-9322(95)00071-2. Drew, D.A., Lahey, R.T., 1993. Analytical modelling of multiphase flow. In Particulate two-phase

RI PT

3

Doron, P., Barnea, D., 1996. Flow pattern maps for solid-liquid flow in pipes. Int. J. Multiphase.

flow. Boston, MA: Butterworth-Heinemann.

Feng, S., Li, Q., Fu, S. 2007. On the orbital motion of a rotating inner cylinder in annular flow. Int. J. Multiphase. Flow. 54 (2), 155-173. DOI: 10.1002/fld.1388.

SC

2

https://doi.org/10.1080/00986449508936386.

FLUENT, 2011. ANSYS FLUENT User’s Guide. ANSYS, Inc. Release 14.0, Southpointe, 275 Technology Drive, Canonsburg, PA 15317, November.

M AN U

1

ACCEPTED MANUSCRIPT

Gidaspow, D. 1994. Multiphase flow and fluidization: continuum and kinetic theory descriptions. Academic press.

Gulyaev, B.I., Lugovoi, P.Z., Andrusenko. Å.N., 2014. Numerical modeling of the elastic bending

13

of a drill string in a curved superdeep borehole. Int. Appl. Mech. 50, 412-420. DOI:

14

10.1007/s10778-014-0645-7.

TE D

12

Gulyayev, V.I., Hudoly, S.N., Glovach, L.V., 2011. The computer simulation of drill column

16

dragging in inclined bore-holes with geometrical imperfections. Int. J. Solids. Struct. 48 (1),

17

110-118. https://doi.org/10.1016/j.ijsolstr.2010.09.009.

AC C

18

EP

15

Guo, X.L, Wang, Z.M, Long, Z.H., 2010. Study on three-layer unsteady model of cuttings transport

19

for

20

http://dx.doi.org/10.1016/j.petrol.2010.05.020.

21 22

extended-reach

well.

J.

Pet.

Sci.

Eng.

73

(1-2),

171-180.

Guskov, O.B. 2012. The virtual mass of a sphere in a suspension of spherical particles. J. Appl. Math. Mec. 76(1), 93-97. https://doi.org/10.1016/j.jappmathmech.2012.03.007.

26

1 2

ACCEPTED MANUSCRIPT Han, S. M., Hwang, Y. K., Woo, N. S., Kim, Y. J. 2010. Solid-liquid hydrodynamics in a slim hole drilling annulus. J. Pet. Sci. Eng. 70 (3-4), 308-319. https://doi.org/10.1016/j.petrol.2009.12.002. Huilin, L., Gidaspow, D., Bouillard, J., Wentie, L., 2003. Hydrodynamic simulation of gas–solid

4

flow in a riser using kinetic theory of granular flow. Chem. Eng. J. 95 (1-3), 1-13.

5

https://doi.org/10.1016/S1385-8947(03)00062-7.

Johnson, P.C., Jackson, R., 1987. Frictional-collisional constitutive relations for granular materials,

7

with

8

https://doi.org/10.1017/S0022112087000570.

application

to

plane

shearing.

J.

Fluid

Mech.

176,

67-93.

SC

6

RI PT

3

Kelessidis, V.C., Maglione, R., Tsamantaki, C., Aspirtakis, Y., 2006. Optimal determination of

10

rheological parameters for Herschel-Bulkley drilling fluids and impact on pressure drop, velocity

11

profiles and penetration rates during drilling. J. Pet. Sci. Eng. 53 (3-4), 203–224.

12

http://dx.doi.org/10.1016/j.petrol.2006.06.004.

M AN U

9

Kendoush, A. A., Sulaymon, A. H., Mohammed, S. A. M. 2007. Experimental evaluation of the

14

virtual mass of two solid spheres accelerating in fluids. Exp. Therm. Fluid Sci. 31(7), 813-823.

15

https://doi.org/10.1016/j.expthermflusci.2006.08.007.

EP

16

TE D

13

Lim, C.W., 2003. A spiral model for bending of non-linearly pretwisted helicoidal structures with

17

lateral

18

https://doi.org/10.1016/S0020-7683(03)00198-7.

20 21

Int.

AC C

19

loading.

J.

Solids

Struct.

40

(16),

4257-4279.

Menter, F.R., 1994. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32 (8), 1598-1605. https://doi.org/10.2514/3.12149. Naganawa, S., Nomura, T., 2006. Simulating transient behavior of cuttings transport over whole

22

trajectory

23

https://doi.org/10.2118/103923-MS.

of

extended

reach

well.

27

Society

of

Petroleum

Engineers.

ACCEPTED MANUSCRIPT

1

Ozbayoglu, M.E., Saasen, A., Sorgun, M., Svanes, K. 2008. Effect of pipe rotation on hole cleaning

2

for water-based drilling fluids in horizontal and deviated wells. In IADC/SPE Asia Pacific

3

Drilling Technology Conference and Exhibition. Society of Petroleum Engineers. Pang, B., Wang, S., Liu, G., Jiang, X., Lu, H., Li, Z., 2018a. Numerical prediction of flow behavior

5

of cuttings carried by Herschel-Bulkley fluids in horizontal well using kinetic theory of granular

6

flow. Powder Technol. 329, 386–398. https://doi.org/10.1016/j.powtec.2018.01.065.

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Pang, B., Wang, S., Wang, Q., Yang, K., Lu, H., Hassan, M., Jiang, X., 2018b. Numerical prediction

8

of cuttings transport behavior in well drilling using kinetic theory of granular flow. J. Pet. Sci.

9

Eng. 161, 190-203. https://doi.org/10.1016/j.petrol.2017.11.028.

Sanchez, R.A., Azar, J.J., Bassal, A.A., Martins, A.L. 1997. The effect of drill pipe rotation on hole

11

cleaning

12

https://doi.org/10.2118/37626-MS.

16 17 18 19 20 21 22 23

well

drilling.

Society

of

Petroleum

Engineers.

Sheppard, M.C., Wick, C., Burgess, T., 1987. Designing well paths to reduce drag and torque. SPE

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15

directional

Drill. Eng. 2, 344-350. DOI: 10.2118/15463-PA. Sifferman, T.R., Myers, G.M., Haden, E.L., Wahl, H.A., 1974. Drill cutting transport in full scale

EP

14

during

vertical annuli. J. Petrol. Technol. 26 (11), 1295-1302. DOI: 10.2118/4514-PA. Sorgun, M., 2010. Modeling of Newtonian fluids and cuttings transport analysis in high inclination

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10

SC

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wellbores with pipe rotation. (Ph.D. thesis). Middle East Technical University. Stansby, P.K., Rainey, R.C.T. 2001. On the orbital response of a rotating cylinder in a current. J. Fluid Mech. 439, 87-108. https://doi.org/10.1017/S0022112001004578. Tomren, P.H., Iyoho, A.W., Azar, J.J., 1986. Experimental study of cuttings transport in directional well. SPE Drill. Eng. 1 (1), 43–56. DOI: 10.2118/12123-PA. van der Heijden, G.H.M., Champneys, A.R., Thompson, J.M.T., 2002. Spatially complex 28

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localisation in twisted elastic rods constrained to a cylinder. Int. J. Solids Struct. 39 (7),

2

1863-1883. https://doi.org/10.1016/S0020-7683(01)00234-7. Wang, S., Jiang, X., Wang, R., Wang, X., Yang, S., Zhao, J., Liu, Y. 2017. Numerical simulation of

4

flow behavior of particles in a liquid-solid stirred vessel with baffles. Adv. Powder Technol. 28(6),

5

1611-1624. https://doi.org/10.1016/j.apt.2017.04.004.

Wang, Z.M., Guo, X.L., Li, M., Hong, Y.K., 2009. Effect of drill pipe rotation on borehole cleaning

7

for

8

https://doi.org/10.1016/S1001-6058(08)60158-4.

reach

well.

J.

Hydro.

Ser,

B

21

(3),

366-372.

Wilcox, D. C., 1998. Turbulence modeling for CFD. DCW industries, Inc. La Canada, California.

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Figure captions

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Fig. 1. Sketch of the orbiting drill pipe in the drilling annulus.

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Fig. 2. Meshing scheme and flow zones of the annulus with an orbiting pipe.

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Fig. 3. Time history of the simulated volume fraction of the retained cuttings in annulus as a function of mesh resolutions (E = 15 mm, ωd = Ωd = 50 rpm, εs,in = 4%, uin = 1.016 m/s).

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Fig. 4. Compared cuttings volume fraction between simulations and measurements (Han et al., 2010) at different inlet fluid velocities (5% bentonite solution + 4% sand, ωdrillpipe = 400 rpm).

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Fig. 5. Cuttings deposition along the horizontal annulus with an orbiting pipe at four instantaneous moments of a drill pipe orbital period (e = 0.5, ωd = Ωd = 50 rpm, εs,in = 4%, uin = 1.016 m/s).

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Fig. 6. Profiles of granular temperature and volume fraction of cuttings along axial direction of the annulus (e = 0.5, ωd = Ωd = 50 rpm, εs,in = 4%, uin = 1.016 m/s).

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Fig. 7. Profiles of cuttings volume fraction in the horizontal annulus with an orbiting pipe at four instantaneous moments of a drill pipe orbital period (e = 0.5, ωd = Ωd = 50 rpm, Z = 3.0 m, εs,in = 4%, uin= 1.016 m/s). a) α = 0°; b) α = 90°; c) α = 180°; d) α = 270°.

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Fig. 8. Instantaneous axial and tangential velocities of cuttings along the horizontal annulus with an orbiting pipe (e = 0.5, ωd = Ωd = 50 rpm, εs,in = 4%, uin = 1.016 m/s, α = 0°).

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Fig. 10. Profiles of tangential velocity and streamlines of cuttings in the horizontal annulus with an orbiting pipe at four instantaneous moments of a drill pipe orbital period (e = 0.5, ωd = Ωd = 50 rpm, Z = 3.0 m, εs,in = 4%, uin= 1.016 m/s). a) α = 0°; b) α = 90°; c) α = 180°; d) α = 270°.

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Fig. 11. Cuttings volume fraction along the horizontal well with a motionless pipe, a self-rotating pipe, or an orbiting pipe (e = 0.5, ωd = 100 rpm, Ωd = ±100 rpm, εin = 4%, uin = 1.016 m/s, α = 0°).

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Fig. 12. Profiles of cuttings volume fraction in the horizontal annulus with a motionless pipe, a self-rotating pipe, or an orbiting pipe (e = 0.5, εin = 4%, uin = 1.016 m/s, Z = 3.0 m, α = 0°). a) ωd = Ωd = 0; b) ωd = 100 rpm, Ωd = 0; c) ωd = Ωd = 100 rpm; d) ωd = 100 rpm, Ωd = -100 rpm.

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Fig. 13. Time history of the drag coefficient for flow around a self-rotating pipe or an orbiting pipe in the horizontal annulus (e = 0.5, εin = 4%, uin = 1.016 m/s).

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Fig. 14. Time history of the moment coefficient for flow around a self-rotating pipe or an orbiting pipe in the horizontal annulus (e = 0.5, εin = 4%, uin = 1.016 m/s).

16 17 18

Fig. 15. Profiles of cuttings axial velocity in the horizontal annulus with a motionless pipe, a self-rotating pipe, or an orbiting pipe (e = 0.5, εin = 4%, uin = 1.016 m/s, Z = 3.0 m, α = 0°). a) ωd = Ωd = 0; b) ωd = 100 rpm, Ωd = 0; c) ωd = Ωd = 100 rpm; d) ωd = 100 rpm, Ωd = -100 rpm.

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Fig. 16. Profiles of cuttings tangential velocity in the horizontal annulus with a motionless pipe, a self-rotating pipe, or an orbiting pipe (e = 0.5, εin = 4%, uin = 1.016 m/s, Z = 3.0 m, α = 0°). a) ωd = Ωd = 0; b) ωd = 100 rpm, Ωd = 0; c) ωd = Ωd = 100 rpm; d) ωd = 100 rpm, Ωd = -100 rpm.

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Fig. 17. Profiles of cuttings volume fraction in the horizontal annulus with the drill pipe orbiting at different rotation speeds (e = 0.5, εin = 4%, uin = 1.016 m/s, Z = 3.0 m, α = 0°). a) ωd = Ωd = 25 rpm; b) ωd = Ωd = 50 rpm; c) ωd = Ωd = 100 rpm; d) ωd = Ωd = 200 rpm; e) ωd = -Ωd = 25 rpm; f) ωd = -Ωd = 50 rpm; g) ωd = -Ωd = 100 rpm; h) ωd = -Ωd = 200 rpm.

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Fig. 18. Histograms of cuttings transport ratio and pressure drop as a function of drill pipe rotation speed in the horizontal annulus with an orbiting drill pipe (e = 0.5, εin = 4%, uin = 1.016 m/s).

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Fig. 19. Axial velocities of drilling fluids and cuttings along radial direction of the annulus with the drill pipe orbiting at different rotation speeds (e = 0.5, εin = 4%, uin = 1.016 m/s, Z = 3.0 m, α = 0°). a) Orbital motion 1; b) Orbital motion 2.

31 32 33

Fig. 20. Tangential velocities of drilling fluids and cuttings along radial direction of the annulus with the drill pipe orbiting at different rotation speeds (e = 0.5, εin = 4%, uin = 1.016 m/s, Z = 3.0 m, α = 0°). a) Orbital motion 1; b) Orbital motion 2.

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Fig. 9. Profiles of cuttings axial velocity in the horizontal annulus with an orbiting pipe at four instantaneous moments of a drill pipe orbital period (e = 0.5, ωd = Ωd = 50 rpm, Z = 3.0 m, εs,in = 4%, uin= 1.016 m/s). a) α = 0°; b) α = 90°; c) α = 180°; d) α = 270°.

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Fig. 21. Profiles of cuttings volume fraction in the horizontal annulus with the drill pipe orbiting at different drill pipe eccentricities (εin = 4%, uin = 1.016 m/s, Z = 3.0 m, ωd = 50 rpm, α = 0°). a) e = 0.3, ωd = Ωd; b) e = 0.5, ωd = Ωd; c) e = 0.7, ωd = Ωd; d) e = 0.3, ωd = -Ωd; e) e = 0.5, ωd = -Ωd; f) e = 0.7, ωd = -Ωd.

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Fig. 22. Histograms of cuttings transport ratio and pressure drop as a function of drill pipe eccentricity ratio in the horizontal annulus with an orbiting drill pipe (εin = 4%, uin = 1.016 m/s, ωd = 50 rpm).

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Fig. 23. Axial velocities of drilling fluids and cuttings along radial direction of the annulus with the drill pipe orbiting at different drill pipe eccentricity ratios (εin = 4%, uin = 1.016 m/s, Z = 3.0 m, α = 0°, ωd = 50 rpm). a) Orbital motion 1; b) Orbital motion 2.

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Fig. 24. Tangential velocities of drilling fluids and cuttings along radial direction of the annulus with the drill pipe orbiting at different drill pipe eccentricity ratios (εin = 4%, uin = 1.016 m/s, Z = 3.0 m, α = 0°, ωd = 50 rpm). a) Orbital motion 1; b) Orbital motion 2.

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Fig. 25. Histograms of cuttings transport ratio and maximum torque in the horizontal annulus with a motionless pipe, a self-rotating pipe, or an orbiting pipe (e = 0.5, ωd = 100 rpm, Ωd = ±100 rpm, εin = 4%, uin = 1.016 m/s).

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Fig. 26. Histograms of the maximum value of the resultant moment on the orbiting pipe as a function of drill pipe rotation speed (e = 0.5, εin = 4%, uin = 1.016 m/s).

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Fig. 27. Histograms of the maximum value of the resultant moment on the orbiting pipe as a function of drill pipe eccentricity ratio (εin = 4%, uin = 1.016 m/s, ωd = 50 rpm).

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Table 1. Closure relations for drilling fluids and cuttings

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Table 2. Detailed parameters used in simulations

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Table 3. Summarized motion state of drill pipe in wellbore

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Table 1. Closure relations for drilling fluids and cuttings

∂ (ε i ρ i ) + ∇ ⋅ (ε i ρ i v i ) = 0 ∂t

1.Continuity equation

(T1-1)

2.Momentum conservation equations (T1-2)

∂ (ε s ρs vs ) + ∇ ⋅ (ε s ρs vs vs ) = −ε s∇p + ∇ ⋅ ps I + ∇ ⋅τ s + ε s ρs g + β (vl − vs ) + Fvm,s ∂t

(T1-3)

τ l = η ( D) ⋅ D

3.Stress tensor of non-Newtonian fluid

 ∂v ∂v D =  l j + li  ∂x ∂x j i 

Shear rate

γ=

Apparent viscosity of power-law fluid

1 D: D 2

(T1-8)

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∂ ∂ ∂  ∂ω  ( ρlω ) + ( ρlωvli ) =  Γω  + Gω − Yω + Dω ∂t ∂xi ∂x j  ∂x j 

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 

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ξ s = ε s ρ s d s g 0 (1 + e )

Shear viscosity of solids

µs = ε s ρs g 0 d s (1 + e)

6.Particle pressure 7.Granular temperature equation

 

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τ s = ξs∇ ⋅ vs I + µs [∇vs + (∇vs )T ] − (∇ ⋅ vs ) I 

Bulk viscosity of solids

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θs

π

+

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(T1-10)

(T1-11)

π

θs

(T1-5)

(T1-7)

 ∂k   Γ k  + Gk − Yk  ∂x j 

∂ ∂ ∂ ( ρl k ) + ( ρ l kvli ) = ∂t ∂xi ∂x j

(T1-4)

(T1-6)

η = Kγ n−1

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∂ ( ε l ρ l v l ) + ∇ ⋅ (ε l ρ l v l v l ) = ε l ∇ ⋅ τ l + ε l ρ l g − ε l ∇ p − β ( v l − v s ) + F vm,l ∂t

10 ρs d s πθ s 96(1 + e)ε s g 0

ps = εs ρsθs + 2g0εs2 (1+ e)ρsθs

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(T1-12)

(T1-13)

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(T1-14)

β = ϕβErgun + (1 − ϕ )βWen&Yu arctan [ 262.5(ε s − 0.2)]

β Ergun = 150

β Wen & Yu =

ε s2 µl ε ρ + 1.75 s l | v l − v s | 2 ds ε lds

3Cdε lε s ρ l | vl − vs | −2.65 εl 4d s

d ( v l − v s ) (Fvm,s = - Fvm,l) dt

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9.Virtual mass force

(T1-16)

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(T1-17)

(T1-18)

(T1-19)

Table 2. Detailed parameters used in simulations Input values

Units

Dh

Hole diameter

203.2

mm

Dp

Pipe diameter

101.6

mm

E

Eccentric distance

15, 25, 35

mm

e

Eccentricity ratio (e = E/(Dh/2 - Dp/2))

0.3, 0.5, 0.7

-

ωd

Self-rotation speed of drill pipe

0, 25, 50, 100, 200

rpm

Ωd

Orbital revolution speed of drill pipe

0, ±25, ±50, ±100, ±200

rpm

Consistency factor for drilling fluid

0.9448

Pa·sn

Power-law index for drilling fluid

0.4097

-

Density of liquids

1437.6

kg/m3

uin

Fluid inlet velocity

1.016

m/s

dp

Diameter of cuttings

3.0

mm

ρs

Density of cuttings

2550

kg/m3

εs,in

Feed concentration of cuttings

4

%

n ρf

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Table 3. Summarized motion state of drill pipe in wellbore Orbital revolution

Description

speed (ωd)

speed (Ωd)

Pipe sticking

0

0

The drill pipe is motionless.

Self-rotation

≠0

0

The drill pipe rotates around its own axis.

Orbital motion 1

+

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+

The drill pipe makes orbital motion in the same direction as that for its self-rotation.

Orbital motion 2

+

-

The drill pipe makes orbital motion in the

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Highlights

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Cuttings transport in annuli with four motion states of drill pipe were studied. The orbital motion of drill pipe improves cuttings transport in drilling annulus. Effects of rotation speeds and eccentricity ratios of orbiting pipe were studied.

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Orbital motion of drill pipe plays the dominant role in tangential flow in annulus.

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Orbital motion significantly increases the resultant moment on the drill pipe.