Numerical Simulation Study on Cuttings Transport Behavior in Enlarged Wellbores Using the CFD-DEM Coupled Method

Abstract

As global energy demand rises, developing unconventional oil and gas resources has become a strategic priority, with horizontal well technology playing a key role. However, wellbore instability during drilling often leads to irregular geometries, such as enlargement or elliptical deformation, causing issues like increased friction and stuck-pipe incidents. Most studies rely on idealized, regular wellbore models, leaving a gap in understanding cuttings transport in irregular wellbore conditions. To address this limitation, this study employs a coupled CFD-DEM approach to investigate cuttings transport in enlarged wellbores by modeling the two-way interactions between drilling fluid and cuttings. The study analyzes the impact of various factors, including drilling-fluid flow rate, drill pipe rotational speed, rheological parameters, wellbore enlargement ratio, and ellipticity, on wellbore cleaning efficiency. The result indicates that increasing the flow rate in conventional wellbores reduces cuttings volume by 75%, while in wellbores with a 0.7 enlargement ratio, the same flow rate only reduces it by 37.8%, highlighting the limitations of geometric complexity. In conventional wellbores, increasing drill pipe rotation reduces cuttings volume by 42.6%, but in enlarged wellbores, only a 13% reduction is observed, indicating that rotation alone is insufficient in large wellbores. Optimizing drilling fluid rheology, such as by increasing the consistency coefficient from 0.3 to 1.2, reduces cuttings volume by 58.78%, while increasing the flow behavior index from 0.4 to 0.7 results in a 38.17% reduction. Although higher enlargement ratios worsen cuttings deposition, a moderate increase in ellipticity improves annular velocity and enhances transport efficiency. This study offers valuable insights for optimizing drilling parameters in irregular wellbores.

1. Introduction

Petroleum is a critical energy source for social production, playing an indispensable role in driving socioeconomic development and fulfilling human livelihood needs [1,2,3]. However, as the global population grows, energy demand continues to rise. According to the International Energy Agency (IEA), global energy demand is projected to continue rising. Oil demand is expected to increase until at least the 2030s, reaching 103.4 million barrels per day, while natural gas demand is anticipated to grow steadily through to the 2040s. As a result, the extraction of conventional oil and gas resources is increasingly insufficient to meet this growing demand [4,5,6]. To address the imbalance between energy supply and demand, the exploration and development of unconventional oil and gas resources has emerged as a critical strategy. This approach not only significantly enhances oil and gas production but also offers a strategic solution to mitigate global energy pressures [7,8,9].

In oil and gas field development, horizontal well technology has been widely adopted due to its ability to significantly expand the oil drainage area and enhance single-well productivity. Compared with traditional vertical wells, horizontal wells extend both vertically and horizontally, significantly increasing the contact area between the wellbore and the reservoir formation, thereby enabling more efficient extraction of oil and gas. By leveraging horizontal well technology, producers can substantially enhance resource recovery from hydrocarbon-bearing zones, resulting in higher per-well productivity. Statistical data indicate that although the construction cost of horizontal wells is approximately 1.2 to 2 times that of vertical wells, their cumulative production can reach 3 to 8 times greater [10]. Horizontal wells command a dominant share (>70%) of new drilling in major shale plays, highlighting their fundamental role in unconventional resource extraction. During this period, this technology has also experienced rapid advancement in domestic applications [11,12,13]. The development of unconventional oil and gas resources, particularly the extraction of shale gas and tight oil using horizontal well technology, has become a significant trend in the global energy sector [14,15]. However, the drilling of horizontal wells encounters numerous technical challenges, and wellbore cleaning stands out as a critical factor influencing both drilling efficiency and operational safety [16,17,18]. Horizontal wells are highly susceptible to cuttings gravity and drill pipe eccentricity, leading to cuttings bed formation, which can trigger a series of severe drilling issues, including high torque and friction, stuck pipe, and wellbore leakage [19,20]. These issues significantly impair the efficiency and effectiveness of drilling operations, not only increasing the risk of downhole incidents but also complicating subsequent procedures such as cementing and logging and contributing to substantial cost escalations associated with managing complex wellbore conditions. Therefore, a thorough understanding of cuttings transport mechanisms in the annulus of horizontal wells is essential for optimizing drilling parameters and developing effective cleaning strategies. Currently, the primary methods employed to mitigate these issues involve enhancing the drilling fluid velocity and drill pipe rotational speed, along with optimizing the rheological properties of the drilling fluid.

Over the past few decades, numerous scholars worldwide have conducted extensive research on cuttings transport mechanisms. Ma et al. [21] examined the influence of key parameters such as drilling fluid return velocity, drill pipe rotational speed, fluid density, and viscosity on cuttings bed thickness. They also developed a predictive model for the steady-state, dimensionless cuttings bed thickness in horizontal and highly deviated wells.

By introducing a “stirring diffusion factor”, Zhao et al. [22] quantified the impact of drill pipe rotation on cuttings transport, developing its formulation through numerical simulation and nonlinear regression analysis. They further identified the critical conditions governing flow regime transitions and defined the operational envelopes for different transport mechanisms. Sun et al. [23] employed the CFD-DEM coupled method to simulate cuttings transport in rotary drilling, systematically analyzing the effects of conveying velocity, drill pipe rotational speed, and eccentricity on cuttings flow patterns, and determined the critical point of flow pattern transition through the relationship between dimensionless annular pressure drop and total Reynolds number. Mao et al. [24] applied cubic spline interpolation to accurately reconstruct the wellbore trajectory and developed a two-layer dynamic model for cuttings transport in long horizontal wells that incorporates the actual wellbore geometry. They systematically evaluated the effects of flow rate, drilling fluid density, and mechanical drilling rate on drilling fluid performance. A one-dimensional (1D) two-layer model was further developed, incorporating three correction factors to account for the influence of drill pipe rotation on cuttings transport efficiency and annular pressure loss. Pang et al. [25] were the first to apply granular flow dynamics theory to predict three-phase flow behavior of air, mud, and cuttings in underbalanced drilling within a wellbore with a rotating drill pipe, incorporating a comprehensive model for inter-particle collisions. The study investigated the suspension, deposition, and transport of cuttings particles in aerated mud, and further conducted a detailed analysis of how air injection rate and aerated mud velocity influence cuttings concentration, pressure loss, effective viscosity, mud turbulence, and cuttings pulsation. A review of these studies reveals that much of the existing research has primarily focused on cuttings transport in regular wellbores.

However, during actual drilling operations, variations in strata rock properties and drilling practices, among other factors, can lead to wellbore instability issues such as wellbore collapse and diameter enlargement. Chen et al. [26] proposed a collapse pressure model for elliptical vertical wellbores, examining how ellipticity and the presence of weak planes influence the wellbore collapse pressure. Their findings indicate that the collapse pressure rises as the wellbore ellipticity increases, while it decreases with a stronger weak plane. Liu et al. [27] conducted hydraulic fracturing experiments on elliptical boreholes and compared fracture behavior between elliptical and circular borehole configurations. Their results demonstrate that fracture pressure is jointly influenced by horizontal stress difference and borehole shape. Specifically, in the presence of a horizontal stress difference, fracture pressure decreases with increasing minor axis length of the elliptical borehole. Pierdominici et al. [28] determined the in situ stress orientation by analyzing wellbore breakouts observed in the PTA2 borehole on the Island of Hawaii. High-resolution acoustic imaging was conducted in the open-hole interval between 886 m and 1567 m, leading to the identification of 371 wellbore breakout features. Collectively, these studies have demonstrated that wellbore stability is significantly influenced by in situ stress and borehole geometry, as revealed through mechanical modeling, experimental data, and well logging. However, there is still insufficient research on how irregular wellbore geometries, such as enlarged sections and elliptical cross-sections caused by instability, impact cuttings transport efficiency in the annulus.

The traditional two-fluid model or Euler-Euler approach treats the cuttings phase as a continuous medium, which limits its ability to accurately capture discrete particle behaviors—such as collisions and friction among cuttings particles—and the complex interactions between particles and irregular wellbore or drill pipe surfaces. In this context, the coupled computational fluid dynamics and discrete element method (CFD-DEM) has emerged as a powerful numerical tool [29,30,31]. This method is capable of capturing complex mechanical behaviors at the particle scale, including fluid–particle, particle–particle, and particle–wall interactions [32,33,34]. This offers unprecedented opportunities for in-depth investigation of cuttings transport mechanisms under irregular wellbore conditions.

This study employs the CFD-DEM numerical simulation approach to investigate cuttings transport behavior in the annulus of a horizontal well with an enlarged borehole. First, the effects of drilling fluid velocity, drill pipe rotational speed, and drilling fluid rheological properties on wellbore cleaning performance are examined. Building upon this analysis, the influence of borehole enlargement ratio and ellipticity on cuttings transport in enlarged boreholes is further investigated. Although the CFD-DEM method has been widely applied in numerous cuttings transport studies [23,32,35], most existing research has focused on simplified, regular wellbore geometries and has not adequately accounted for the influence of realistic irregular wellbore shapes on cuttings transport. Therefore, this study aims to address this gap by revealing the mechanisms of cuttings transport in the annuli of irregular wellbores, thereby overcoming the limitations of conventional wellbore models in addressing wellbore cleaning challenges. The overall methodology is summarized in Figure 1.

2. CFD-DEM Coupling Methodology

In this study, a coupled computational approach based on computational fluid dynamics (CFD) and the discrete element method (DEM) was employed to accurately simulate solid–liquid two-phase flow. The implementation of this method was carried out using two specialized software packages: ANSYS Fluent 2022 R1 and EDEM 2022. The CFD-DEM framework involves complex interactions between two distinct phases. The continuous fluid phase is treated as a continuum, with its motion governed by the Navier–Stokes equations solved in ANSYS Fluent 2022R1; concurrently, the discrete particle phase is modeled as individual entities, with their trajectories and inter-particle contact forces computed in EDEM 2022. Coupling between the two phases is achieved through a two-way interaction mechanism, enabling data exchange at every computational timestep and thereby fully capturing the fluid–solid coupling behavior.

2.1. Liquid-Phase Governing Equations

The flow of the drilling fluid is governed by the Navier–Stokes equations. Within the Eulerian framework, the continuity equation and momentum equation for the liquid phase are established as follows:

Continuity equation:

$${\displaystyle \frac{\mathsf{\partial }\left({\epsilon }_l{\rho }_l\right)}{\mathsf{\partial }t}}+{\displaystyle \frac{\mathsf{\partial }\left({\epsilon }_l{\rho }_l{u}_j\right)}{\mathsf{\partial }{x}_j}} = 0$$

(1)

Momentum equation:

$${\displaystyle \frac{\mathsf{\partial }\left({\epsilon }_l{\rho }_l{u}_i\right)}{{\mathsf{\partial }}_t}}+{\displaystyle \frac{\mathsf{\partial }\left({\epsilon }_l{\rho }_l{u}_j{u}_i\right)}{\mathsf{\partial }{x}_j}} = -{\epsilon }_l{\displaystyle \frac{\mathsf{\partial }p}{\mathsf{\partial }{x}_i}}+{\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }{x}_j}}\left({\epsilon }_l{\tau }_{ji}\right)-\beta \left(u_i-v_i\right)+{\epsilon }_l{\rho }_{l}g$$

(2)

where ${\rho }_l$ is the liquid density (kg/m³) and ${\tau }_{ji}$ is the viscous stress tensor. The subscript $i$ refers to the coordinate direction, and $j$ refers to the Einstein summation index. The viscous stress tensor is defined as follows:

$${\tau }_{ji} = \left(\begin{array}{c}\mu +{\mu }_t\end{array}\right)\left({\displaystyle \frac{\mathsf{\partial }{u}_j}{\mathsf{\partial }{x}_i}}+{\displaystyle \frac{\mathsf{\partial }{u}_i}{\mathsf{\partial }{x}_j}}\right)$$

(3)

where $\mu$ is the dynamic viscosity coefficient of the liquid and ${\mu }_t$ is the turbulent viscosity coefficient, which is calculated as ${\mu }_t = {\rho }_l{c}_{\mu }{k}^2/\epsilon$.

$${\displaystyle \frac{\mathsf{\partial }\left({\epsilon }_i{\rho }_{i}k\right)}{{\mathsf{\partial }}_i}}+{\displaystyle \frac{\mathsf{\partial }\left({\epsilon }_i{\rho }_i{u}_{j}k\right)}{\mathsf{\partial }{x}_j}}={\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }{x}_j}}\left[{\epsilon }_i\left(\mu +{\displaystyle \frac{{\mu }_i}{{\sigma }_k}}\right){\displaystyle \frac{\mathsf{\partial }k}{\mathsf{\partial }{x}_j}}\right]+{\epsilon }_i{\mu }_i{\displaystyle \frac{\mathsf{\partial }{u}_i}{\mathsf{\partial }{x}_j}}\left({\displaystyle \frac{\mathsf{\partial }{u}_j}{\mathsf{\partial }{x}_i}}+{\displaystyle \frac{\mathsf{\partial }{u}_i}{\mathsf{\partial }{x}_j}}\right)-{\epsilon }_i{\rho }_i\epsilon$$

(4)

$${\displaystyle \frac{\mathsf{\partial }\left({\epsilon }_t{\rho }_t\epsilon \right)}{{\mathsf{\partial }}_t}}+{\displaystyle \frac{\mathsf{\partial }\left({\epsilon }_t{\rho }_t{u}_j\epsilon \right)}{\mathsf{\partial }{x}_j}}={\displaystyle \frac{\mathsf{\partial }}{\mathsf{\partial }{x}_j}}\left[{\epsilon }_t\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_s}}\right){\displaystyle \frac{\mathsf{\partial }\epsilon }{\mathsf{\partial }{x}_j}}\right]+{\displaystyle \frac{{\epsilon }_t{c}_t\epsilon }{k}}{\mu }_t{\displaystyle \frac{\mathsf{\partial }{u}_i}{\mathsf{\partial }{x}_j}}\left({\displaystyle \frac{\mathsf{\partial }{u}_j}{\mathsf{\partial }{x}_i}}+{\displaystyle \frac{\mathsf{\partial }{u}_i}{\mathsf{\partial }{x}_j}}\right)-{\epsilon }_t{c}_2{\rho }_t{\displaystyle \frac{{\epsilon }^2}{k}}$$

(5)

2.2. Solid-Phase Governing Equations

The discrete element method (DEM) has become a prominent approach in numerical analysis and is specifically designed to model granular systems by monitoring the trajectory and contact mechanics of discrete particles [36,37,38]. The translational motion of particles in DEM is governed by Newton’s second law.

$$m_p{\displaystyle \frac{d{v}_p}{dt}}=\sum F_{c,pq}+F_{pf,p}+m_{p}g\left(1-{\displaystyle \frac{{\rho }_f}{{\rho }_p}}\right)$$

(6)

where $m_p$ is the mass of particle $p$;$v_{p }$ denotes the velocity vector of particle $p$; $F_{c,pq }$ represents contact forces between particles and with walls (e.g., Hertz–Mindlin normal and tangential forces); $F_{pf,p}$ signifies fluid–particle interaction forces; g is gravitational acceleration; and ${\rho }_f$ and ${\rho }_p$ denote fluid density and particle density, respectively.

The rotational motion of particles is governed by the angular momentum conservation equation:

$$I_p{\displaystyle \frac{d{\omega }_p}{dt}} = \sum \left(T_{t,pq}+T_{r,pq}\right)+T_{f,p}$$

(7)

where $I_p$ is the moment of inertia of particle p; ${\omega }_p$ denotes the angular velocity vector of particle p; $T_{t,pq }$ and $T_{r,pq }$ represent the torque due to tangential contact force and rolling friction torque, respectively; and $T_{f,p }$ is the torque caused by fluid.

The contact forces during the transport process of cuttings are typically divided into three types: cutting-to-cutting, cutting-to-drillpipe, and cutting-to-wellbore.

The contact force exerted on the cuttings particle p by the cuttings particle q can be expressed as [39]:

$$F_{c,q}^p = F_{n,pq}+F_{n,pq}^d+F_{t,pq}+F_{t,pq}^d$$

(8)

where $F_{n,pq}$, $F_{t,pq}$, $F_{n,pq}^d$, and $F_{t,pq}^d$ represent the normal elastic force, tangential elastic force, normal damping force, and tangential damping force, respectively. According to elastic contact mechanics, the nonlinear relationship between the normal force $F_n$ and the normal overlap ${\delta }_n$ is described by:

$$F_n = {\displaystyle \frac{4}{3}}{E}^{*}\sqrt{R^{*}{\delta }_n^3}$$

(9)

The equivalent elastic modulus $E^{*}$ is defined as $E^{*} = {\left[{\displaystyle \frac{\left(1-v_P^2\right)}{E_P}}+{\displaystyle \frac{\left(1-v_q^2\right)}{E_q}}\right]}^{-1}$, and the equivalent radius $R^{*}$ is given by $R^{*} = {\left[{\displaystyle \frac{2}{d_p}}+{\displaystyle \frac{2}{d_q}}\right]}^{-1}$. In these expressions, $E_P$, $v_{P }$, and $d_p$ represent the Young’s modulus, Poisson’s ratio, and the diameter of particle $p$, while $E_q$, $v_q$, and $d_q$ denote the corresponding properties of particle $q$. The normal damping force $F_{n,pq}^d$ is given by [39]:

$$F_{n,pq}^d = -2\sqrt{{\displaystyle \frac{5}{6}}}{\displaystyle \frac{lne}{\sqrt{l{n}^{2}e+{\pi }^2}}}\sqrt{S_{n,pq}{m}^{*}}{v}_{n,pq}$$

(10)

The equivalent cuttings mass, $m^{*}$, is defined as $m^{*} = {\left[{\displaystyle \frac{2}{m_p}}+{\displaystyle \frac{2}{m_q}}\right]}^{-1}$, where $m_p$ and $m_q$ represent the masses of individual particles in the contact pair; the normal stiffness, $S_{n,pq}$, is given by $S_{n,pq} = 2E^{*}\sqrt{R^{*}{\delta }_{n,pq}}$. Here, $v_{n,pq}$ is the normal component of the relative velocity at the contact point; and $e$ is the restitution coefficient. The tangential contact force ${ F}_{t,pq }$ is given by:

$$F_{t,pq} = \left\{\begin{array}{ll}-{\delta }_{t,pq}{S}_{t,pq}\hfill & \left|F_{t,pq}\right|<{\mu }_s\left|F_{n,pq}\right|\hfill \\ {\mu }_s\left|F_{n,pq}\right|{\displaystyle \frac{v_{t,pq}}{\left|v_{t,pq}\right|}}\hfill & \left|F_{t,pq}\right|\ge {\mu }_s\left|F_{n,pq}\right|\hfill \end{array}\right.$$

(11)

The torques generated by rotational motion during cuttings migration are defined as follows:

The torque due to tangential forces from the collision of cuttings particle q against particle p is given by:

$$T_{t,q}^P = r_{pq}\times \left(F_{t,pq}+F_{t,pq}^d\right)$$

(12)

The friction torque resisting the rolling of particle p induced by the collision with particle q is expressed as:

$$T_{r,q}^P = -{\mu }_r\left|r_{pq}\right|\left|F_{n,pq}\right|{\displaystyle \frac{{\omega }_{pq}}{\left|{\omega }_{pq}\right|}}$$

(13)

Here, $r_{pq}$ is the vector that points from the centroid of the cuttings particle p to the contact point; ${\mu }_r$ denotes the rolling friction coefficient; and ${\omega }_{pq }$ represents the angular velocity of particle p relative to particle q. The torques $T_{t,q}^P$ and $T_{r,q }^P$ correspond to the torque generated by the tangential contact force and the rolling friction torque, respectively.

When particles collide with the wellbore wall or drill pipe, contact forces are computed in the same manner as inter-particle collisions. In such scenarios, the wellbore wall velocity is treated as zero and modeled as a particle with an infinite diameter and mass.

2.3. Solid–Liquid Coupling

The interaction between cuttings particles and the surrounding fluid is crucial in determining the efficiency of the transport process in drilling fluid. Interphase forces mediate the coupling between the solid and liquid phases. In this study, due to the significantly higher density of the solids compared to the fluid, the virtual mass force is considered negligible. The primary forces considered include drag force, lift force (comprising shear-induced and rotation-induced lift), and pressure-gradient force. The drag force refers to the force exerted by the fluid on a moving solid particle and represents the momentum exchange between the two phases. Its specific expression is:

$$F_d = V_p\cdot {\displaystyle \frac{\beta }{1-{\epsilon }_f}}\left(u_f-u_p\right)$$

(14)

Here, $V_p$ denotes the particle volume, ${\epsilon }_{f }$ represents the fluid void fraction, and $u_f$ and $u_p$ denote the fluid and particle velocities, respectively. The drag coefficient $\beta$ is determined piecewise according to the void fraction:

$$\beta = \left\{\begin{array}{ll}\hspace{1em} {\displaystyle \frac{u_f\left(1-{\epsilon }_f\right)}{d_p^2{\epsilon }_f}}\left[150\left(1-{\epsilon }_f\right)+1.75R{e}_p\right]\hfill & \hspace{1em} \left({\epsilon }_f\le 0.8\right)\hfill \\ \hspace{1em} {\displaystyle \frac{3}{4}}{C}_D{\displaystyle \frac{u_f\left(1-{\epsilon }_f\right)}{d_p^2}}{\epsilon }_f^{-2.65}R{e}_p\hfill & \hspace{1em} \left({\epsilon }_f>0.8\right)\hfill \end{array}\right.$$

(15)

The drag coefficient $C_D$ is expressed as follows:

$$C_D = \left\{\begin{array}{ll}\hspace{1em} {\displaystyle \frac{24\left(1+0.15R{e}_p^{0.687}\right)}{R{e}_{p }}}\hfill & \hspace{1em} \left(R{e}_p\le 1000\right)\hfill \\ \hspace{1em} 0.44\hfill & \hspace{1em} \left(R{e}_p>1000\right)\hfill \end{array}\right.$$

(16)

The particle Reynolds number $R{e}_p$ is defined as:

$$R{e}_p = {\displaystyle \frac{{\rho }_f{\epsilon }_f{d}_p\left|u_f-u_p\right|}{{\mu }_f}}$$

(17)

The lift force primarily consists of the Saffman shear lift and the Magnus rotational lift. The Saffman shear lift arises due to the fluid velocity gradient, and its expression is:

$$F_S = C_{LS}{\displaystyle \frac{{\rho }_f\pi }{8}}{d}_p^2\left|u_f-u_p\right|·{\displaystyle \frac{{\omega }_f\times \left(u_f-u_p\right)}{\left|{\omega }_f\right|}}$$

(18)

The fluid angular velocity is expressed as:

$${\omega }_f = \nabla \times u_f$$

(19)

The lift coefficient $C_{LS}$ is computed according to the Mei model [40]

$$C_{LS}={\displaystyle \frac{4.1126}{R{e}_s^{0.5}}}f\left(R{e}_{HB},R{e}_s\right)$$

(20)

The expression of the function $f$ is given by:

$$f\left(R{e}_{HB},R{e}_s\right) = \left\{\begin{array}{ll}\left(1-0.3314{\beta }^{0.5}\right)e^{-{\displaystyle \frac{R{e}_{HB}}{10}}}+0.3314{\beta }^{0.5}\hfill & R{e}_{HB}\le 40\hfill \\ 0.0524{(\beta R{e}_{HB})}^{0.5}\hfill & R{e}_{HB}>40\hfill \end{array}\right.$$

(21)

Here, $\beta = 0.5 R{e}_s/R{e}_{HB}(0.005<\beta <0.4)$, where the relevant Reynolds number is defined as $R{e}_s = {\rho }_f{d}_p^2{\omega }_f/u_f$.

The Magnus lift force arises from the relative rotational velocity between the fluid and the particle, and the corresponding computational expression is provided by Oesterleé [41]:

$$F_{\mathrm{M}} = C_{LM}{\displaystyle \frac{{\rho }_f\pi }{8}}{d}_p^3\left|u_f-u_p\right|{\displaystyle \frac{\left[\mathsf{\Omega }\times \left(u_f-u_p\right)\right]}{\left|\mathsf{\Omega }\right|}}$$

(22)

The rotational lift coefficient $C_{LM}$ is expressed as [40]:

$$C_{LM} = 0.45+\left({\displaystyle \frac{R{e}_r}{R{e}_{HB}}}-0.454\right)e^{-0.5684R{e}_r^{0.4}R{e}_{HB}^{0.3}}$$

(23)

The rotational resistance torque $T_{f,i}$ exerted by the fluid on the particle is given by the following expression [42]:

$$T_{f,i} = {\displaystyle \frac{{\rho }_f}{2}}{\left({\displaystyle \frac{d_p}{2}}\right)}^5{C}_R\left|\mathsf{\Omega }\right|$$

(24)

Here, $C_R$ denotes the rotational resistance coefficient, and $\mathsf{\Omega }$ represents the angular velocity of the particle relative to the fluid. The coefficient $C_R$ is determined piecewise according to the rotational Reynolds number $R{e}_r$ [43]:

$$C_R = \left\{\begin{array}{ll}{\displaystyle \frac{64\pi }{R{e}_r}},\hfill & R{e}_r<32\hfill \\ {\displaystyle \frac{12.9}{R{e}_r^{0.5}}}+{\displaystyle \frac{128.4}{R{e}_r}},\hfill & 32\le R{e}_r\le 1000\hfill \end{array}\right.$$

(25)

3. Calculation Model and Conditions

3.1. Model Geometry and Conditions

In this study, the computational domain (Figure 2) consists of the annular region between the enlarged wellbore and the drill pipe, as well as the conventional wellbore and the drill pipe. The geometry of the enlarged wellbore is derived from the logging data provided by P. Sarmadi et al. [44] and the geometric model suggested by Sun et al. [45]. However, the CFD-DEM method requires bidirectional coupling and data exchange between the fluid and particle phases at every timestep, resulting in a high computational cost. The particle diameter used in the simulation is 2 mm. If a stable state is reached, the total number of particles in the entire annulus will exceed several million, which will result in a very long total simulation time. Given the computational resource constraints described above, essential simplifications were implemented in the simulation model. The model has a total length of 1.25 m, consisting of a central expanded section of 0.25 m and two unexpanded sections of 0.5 m at each end. This relatively short model length was chosen to balance computational efficiency and accuracy, as well as to keep the simulation within reasonable time frames given the high computational cost of coupled CFD-DEM simulations. While this length does not represent a typical horizontal wellbore, it allows us to investigate the fundamental cuttings transport mechanisms in a controlled environment. The wellbore diameter D₁ = 120 mm, and the drill pipe diameter D₀ = 73 mm. The axial cross-section of the enlarged section is elliptical, and it is defined by two dimensionless parameters: the enlargement ratio ε and the ellipticity α. The enlargement ratio ε is defined as (a − r₁)/r₁, where a is the semi-major axis of the ellipse and r₁ is the radius of the conventional wellbore. The ellipticity α is given by the ratio of the semi-major axis to the semi-minor axis, a/b.

3.2. Boundary Conditions and Simulation Conditions

The inlet boundary was applied with a velocity inlet boundary condition, using a power-law fluid as the simulation medium, and the turbulence intensity at the inlet was specified as follows:

$$I = {\displaystyle \frac{u^{\prime }}{u}} = 0.16\times {\left(Re\right)}^{-0.125}$$

(26)

$$Re=\frac{{\rho }_{f}u(D_1-D_0)}{\mu }$$

(27)

The outlet boundary was configured with a pressure outlet boundary condition, with the pressure value set to 0. No-slip boundary conditions were implemented at the wall surfaces; the drill pipe rotates while the wellbore remains stationary. Cuttings were modeled as monodisperse spherical particles and continuously injected into the annulus at a constant volumetric concentration from the inlet. Identical injection velocities were assigned to both the drilling fluid and cuttings.

In this study, the finite volume method was used to discretize the governing equations, and the Phased-coupled SIMPLE algorithm was applied. First-order implicit time integration was employed to solve these equations. Discretization of the momentum, phase volume fraction, and turbulence equations was performed using a first-order upwind scheme. For the discrete element method (DEM) simulations, an explicit time integration scheme was adopted to solve the motion equations of dispersed particles, where the DEM timestep was typically determined by the Rayleigh timestep, expressed as follows:

$${\tau }_R=0.5\pi d_p\sqrt{\frac{{\rho }_p}{G^{*}}}/(0.1631\nu +0.8766)$$

(28)

To ensure the stability of the discrete element method (DEM) simulations, the DEM timestep was set to 1 × 10⁻⁵ s. The computational fluid dynamics (CFD) timestep was configured at 0.0005 s (50 times the DEM timestep) [46,47]. The total duration of the coupled CFD-DEM simulation reached 18 s. Figure 3 illustrates the variation in the residual cuttings in the annulus over time for different consistency coefficients. It can be observed that, in the final 5 s of the simulation, the mass of cuttings in the annular space reached a stable value, confirming the steady-state conditions. All data discussed in the Section 4 were averaged over this time interval. The physical properties of the materials employed in the simulations are presented in

Table 1. Geometric parameters and operating conditions in the numerical simulation.

Variables	Values
Annulus length, L (m)	1.25
Enlarged annulus length, L (m)	0.5
Angle of inclination, θ (deg)	90
Pipe diameter, D0 (mm)	73
Hole diameter, D1 (mm)	120
Fluid density, ρl (kg/m3)	1000
Drilling fluid circulation velocity, v (m/s)	0.6, 0.75, 0.9, 1.05
Drill pipe rotational speed, n0 (rpm)	0, 60, 120, 180
Drill cuttings density, ρ2 (kg/m3)	2500
Flow behavior index, n	0.4, 0.5, 0.6, 0.7
Consistency index, k (Pa·sn)	0.3, 0.6, 0.9, 1.2
Particle diameter, D2 (mm)	2
Eccentricity, e	0.4
Enlargement ratio, ε	0.4, 0.5, 0.6, 0.7
Ovality, α	1, 1.1, 1.2, 1.3
Static friction coefficient	0.6
Rolling friction coefficient	0.01
Collision restitution coefficient	0.45

.

3.3. Model Validation

To validate the accuracy of the CFD-DEM numerical model, the present model was verified against experimental data from Han et al. [48], who conducted laboratory-scale flow-loop experiments to investigate cuttings transport behavior in small-diameter annuli. The simulations were performed at a 45° well inclination angle, with a drill pipe rotation speed of 200 rpm and water as the working fluid. The cuttings concentration in the annulus was evaluated across a range of drilling-fluid velocities. The results are presented in Figure 4. A comparison shows that the numerical results match the experimental data with an average error of 7.29% and exhibit a consistent variation trend. Given that the discrepancy falls within an acceptable range, the model is deemed capable of accurately predicting cuttings transport behavior.

For transient numerical simulations, grid independence verification is essential to achieve an optimal balance between solution accuracy and computational efficiency. Grid independence is achieved when further mesh refinement yields negligible changes in the results, provided that the mesh quality satisfies the required standards. In this study, a grid independence study was conducted using four distinct mesh resolutions comprising 52,467, 105,392, 208,745, and 305,128 elements, respectively. The results of the grid sensitivity analysis are summarized in

Table 2. Grid independence test results.

	Steady-State Annular Cuttings		Steady-State Annular Pressure
Grid Quantity	Residual Mass (kg)	Relative Error (%)	Loss Gradient (Pa/m)	Relative Error(%)
52,467	1.173	(-)	1301.2	(-)
105,392	1.142	2.64	1269.5	2.44
208,745	1.120	1.93	1250.6	1.49
305,128	1.114	0.54	1244.1	0.52

(-) represents the baseline case with no comparative error.

, with values in parentheses indicating the relative error. As shown in Table 2, increasing the number of elements from 208,745 to 305,128 led to a marginal increase in accuracy, with only a 0.54% change in steady-state annular cuttings mass and a 0.52% deviation in annular pressure loss gradient. Further refinement would significantly increase the computational cost, while coarser meshes compromise accuracy. Therefore, considering both accuracy and computational efficiency, the mesh with 208,745 elements was selected for all subsequent simulations in this work (as shown in Figure 5).

4. Results and Discussion

4.1. Effect of Annulus Flow Velocity on Hole Cleaning

As shown in Figure 6, in the enlarged wellbore, when cuttings are transported into the expanded section by the drilling fluid, the sudden increase in cross-sectional area leads to a sharp reduction in the axial flow velocity of the fluid. Consequently, cuttings settle under gravity and accumulate to form a cuttings bed in the annulus. As the drilling fluid circulation velocity increases, the radial height of the cuttings bed decreases significantly, while the velocity of suspended particles increases markedly. This occurs because higher flow velocities enhance the axial drag force exerted by the fluid, promoting greater axial displacement of particles at the cuttings bed surface. At circulation velocities of 0.6 m/s and 0.75 m/s, the drill pipe is partially embedded in the cuttings bed. However, when the velocity increases to 1.05 m/s, the cuttings bed is sufficiently eroded such that it no longer contacts the drill pipe, and the bed gradually disappears in the downstream portion of the wellbore. This observation demonstrates that drilling fluid velocity is a critical parameter governing hole cleaning efficiency in enlarged sections. As the flow rate increases, the enhanced shear stress on the cuttings bed promotes particle suspension and transport, leading to more efficient cuttings removal from the wellbore.

Figure 7 presents the distribution of cuttings volume fraction at a representative cross-section of the annulus under various drilling fluid flow rates. As illustrated, increasing the inlet velocity significantly reduces the cuttings volume fraction in the annular space. For instance, when the flow rate increases from 0.6 m/s to 1.05 m/s, the cuttings volume fraction decreases from 12.2% to 5.7%, a reduction of 53.3%. At low flow rates (0.6 m/s), the fluid’s kinetic energy is insufficient to effectively lift and transport cuttings, weakening its dominant role in particle suspension. Consequently, the circumferential lifting force induced by drill pipe rotation becomes the primary factor governing cuttings behavior. Under the influence of fluid drag forces, particles are progressively transported toward the wellbore wall and accumulate on the lower side relative to the direction of drill pipe rotation, resulting in an asymmetric cuttings bed. This finding is consistent with the theoretical understanding that lower flow rates lack the required kinetic energy to overcome particle inertia, while higher flow rates allow for more efficient particle suspension. As the flow rate increases, however, the axial fluid motion gains sufficient kinetic energy to dominate the transport process, enhancing momentum transfer between the fluid and cuttings and promoting particle suspension. In this regime, the tangential disturbances generated by drill pipe rotation are significantly attenuated relative to the intensified axial flow field. Moreover, higher flow rates provide greater drag forces that enhance the upward transport of cuttings toward the surface, thereby accelerating axial migration of suspended particles and reducing cuttings bed thickness. The reduction of cuttings volume fraction by over 50% when the flow rate increases from 0.6 m/s to 1.05 m/s further underscores the substantial role of flow velocity in improving cuttings transport efficiency. This observation demonstrates that, at a constant rotational speed, increasing the fluid circulation velocity substantially boosts its capacity to transport cuttings, improving the overall cleaning performance in the wellbore.

Figure 8 presents the contour maps of the annular velocity distribution at a constant drill pipe rotational speed (60 rpm) under varying drilling fluid flow rates. It is evident that the flow velocity of the drilling fluid varies significantly across different regions of the eccentric annulus. At low flow rates (0.6 m/s and 0.75 m/s), the fluid velocity is predominantly concentrated in the wide-gap region above the annulus, and the high-velocity core deflects to the right due to the rotation-induced swirling motion of the drill string. As the flow rate increases, however, the flow gradually extends into the narrow-gap region below the annulus, and the overall velocity distribution becomes more symmetric. This transition occurs because the influence of centrifugal forces generated by drill pipe rotation diminishes relative to axial momentum, while higher bulk fluid velocities enhance the axial drag force. In conjunction with Figure 6, it can be observed that the increased axial transport velocity of cuttings reduces bed accumulation, thereby enlarging the effective flow area for the drilling fluid. Consequently, both the magnitude and spatial extent of the high-velocity core increase markedly, which enhances the capacity for particle transport within the annulus.

Figure 9 illustrates the kinetic energy distribution of cuttings in the annular region of an enlarged wellbore. Cuttings at the bottom of the cuttings bed are densely packed, resulting in low kinetic energy and the formation of a static bed zone. As the drilling fluid circulation return velocity increases, the hydrodynamic coupling between the cuttings on the bed surface and the fluid strengthens, enabling these particles to acquire higher kinetic energy. The high-energy cuttings promote the development of a mobile bed layer through continuous rolling and particle-particle collisions, thereby significantly reducing the number of low-kinetic-energy particles within the bed. At lower flow rates (0.6 m/s and 0.75 m/s), the cuttings bed deflects toward the side of the drill pipe rotation due to rotation-induced asymmetry. In contrast, at higher flow rates (0.9 m/s and 1.05 m/s), the bed distribution becomes more uniform and flattened, reflecting a more efficient cuttings transport as the circulation velocity increases.

As illustrated in Figure 10, as the drilling fluid flow rate increases progressively from 0.6 m/s to 1.05 m/s, the initial velocity of cuttings particles correspondingly increases, demonstrating that higher flow rates significantly promote particle initiation and early-stage transport. At low flow rates (0.6 m/s), particle velocity decays rapidly, indicating limited fluid capacity for suspension and transport, leading to faster settling and deceleration under gravity and other resistive forces. In contrast, at high flow rates (1.05 m/s), particles not only exhibit higher initial velocities but also experience a reduced rate of velocity decay, maintaining relatively high motion speeds throughout the observation period. This indicates that elevated flow rates enable more effective transfer of kinetic energy from the fluid to the particles, allowing them to overcome hydrodynamic resistance and sustain stable transport. Increasing the drilling fluid flow rate therefore both enhances the initial mobilization of cuttings and mitigates subsequent velocity attenuation, thereby facilitating continuous cuttings transport in the wellbore and improving overall drilling efficiency and hole-cleaning performance.

Figure 11 illustrates the relationship between the drilling fluid flow rate and the cuttings volume fraction for various wellbore conditions. The results demonstrate that the drilling fluid flow rate exerts a significant influence on cuttings transport efficiency, but this effect diminishes with increasing wellbore enlargement ratio. In a conventional wellbore, raising the flow rate from 0.6 m/s to 1.05 m/s reduces the cuttings volume fraction from 8.4% to 2.1%, representing a substantial decrease of 75%. In contrast, for wellbores with enlargement ratios of 0.4 and 0.7, the same flow rate increase leads to reductions from 12.2% to 5.7% (53.3% decline) and from 18.5% to 11.5% (37.8% decline), respectively. At a low flow rate of 0.6 m/s, the cuttings volume fraction in the 0.7-enlarged wellbore (18.5%) is approximately 2.2 times higher than that in the conventional wellbore (8.4%). These findings indicate that while increasing drilling fluid circulation velocity effectively enhances hole cleaning in conventional wellbores, its effectiveness is considerably limited in enlarged or large-diameter horizontal sections, where cleaning performance deteriorates progressively with greater wellbore enlargement.

4.2. Effect of Drill Pipe Rotational Speed on Hole Cleaning

Figure 12 presents the contour maps of cuttings volume fraction distribution in the annular cross-section of an enlarged wellbore under varying drill pipe rotational speeds. It is evident that rotational speed primarily influences the spatial configuration of cuttings within the eccentric annulus, inducing a progressive deflection of high-concentration zones in the direction of rotation, yet contributes only marginally to overall hole-cleaning efficiency. As the rotational speed increases from 0 rpm to 180 rpm, the region of high cuttings concentration shifts increasingly toward the wide side of the annulus, with the degree of deflection growing proportionally with rotational speed—this behavior is attributed to the centrifugal forces generated by drill string rotation. Despite this redistribution, the total cuttings volume fraction remains largely unchanged. This limited improvement stems from the pronounced geometrical asymmetry of the enlarged annulus, which results in significant flow velocity disparities between the narrow and wide sides. Even at 180 rpm, the hydrodynamic drag force in low-velocity regions—particularly along the wide side—is insufficient to overcome the combined effects of particle gravity and inter-particle cohesive forces, thereby failing to achieve effective cuttings removal.

As shown in Figure 13, under all wellbore conditions, the cuttings volume fraction decreases with increasing drill pipe rotational speed; however, the degree of reduction varies significantly depending on the wellbore geometry. As the rotational speed rises from 0 rpm to 180 rpm, the cuttings volume fraction decreases by approximately 42.6%, 13.4%, and 13.2% in the conventional wellbore, the wellbore with an enlargement ratio of 0.4, and the wellbore with an enlargement ratio of 0.7, respectively, demonstrating that rotational speed enhances hole-cleaning efficiency most effectively in conventional wellbores. At 0 rpm, the cuttings volume fractions in the enlargement wellbores (ratios of 0.4 and 0.7) are approximately 1.35 and 2.02 times higher than that in the conventional wellbore, respectively. Notably, even at 180 rpm, these ratios remain high at approximately 2.04 for both enlargement cases, indicating persistent challenges in cuttings transport. Consequently, wellbore enlargement substantially increases the risk of cuttings accumulation. While elevated rotational speed generally improves cleaning performance, its effectiveness is markedly limited in enlarged wellbores, where cuttings volume fractions remain significantly higher than in standard configurations. Therefore, in enlarged well conditions, achieving efficient hole cleaning requires integrated strategies, such as optimizing drilling fluid rheology and enhancing flow dynamics, in addition to mechanical parameters.

4.3. Effect of Drilling Fluid Rheological Parameters on Hole Cleaning

As illustrated in Figure 14, under a fixed flow index of n = 0.4, the effect of varying consistency coefficients on wellbore cleaning performance is demonstrated. With increasing consistency in coefficient k, the cuttings deposition area in the axial cross-section of the wellbore progressively diminishes. At k = 0.3, the cuttings volume fraction remains relatively high; however, when k increases to 1.2, the cuttings concentration in this section becomes nearly undetectable, indicating that wellbore cleaning efficiency reaches an optimal level under these conditions. This behavior can be attributed to the fact that, for power-law fluids, an increase in k directly enhances the fluid’s effective viscosity. Higher effective viscosity results in greater internal frictional resistance, which significantly improves the fluid’s capacity to suspend cuttings particles. As particles tend to settle under gravity, they experience stronger hydrodynamic resistance, specifically increased Stokes drag, from the increased viscous fluid, thereby inhibiting their settling toward the wellbore bottom. When k is sufficiently high (k = 1.2), the suspending force exerted by the fluid effectively counteracts the gravitational forces acting on most cuttings, enabling them to remain uniformly distributed within the fluid and be efficiently transported out of the wellbore.

As illustrated in Figure 15, the fluid velocity distribution contour maps at a local annular cross-section under varying drilling fluid consistency coefficients reveal that the flow velocity in the wellbore annulus is inherently non-uniform. A high-speed parabolic velocity core develops centrally within the annulus, whereas the lowest velocities occur near the ends of the elliptical wellbore’s long axis and along its lower side. As the consistency coefficient $k$ increases from 0.3 to 1.2, the extent of the high-velocity core region markedly diminishes, and the velocity field progressively spreads toward the upper and lower extremities of the long axis. This trend indicates a more uniform velocity distribution, which enhances fluid kinetic energy at the wellbore bottom. Consequently, the shear stress and hydrodynamic lift acting on deposited cuttings are strengthened, promoting their entrainment into the main flow stream and facilitating efficient transport out of the wellbore.

As illustrated in Figure 16, with the drilling fluid rheological index fixed at 0.4, increasing the consistency coefficient k from 0.3 to 1.2 progressively slows the velocity decay of cuttings particles, demonstrating that higher k values enhance the fluid’s capacity for particle suspension and transport. At the onset of motion, particle velocities across all cases are nearly identical, approximately 1.05 m/s. However, as time progresses, particles in low-k fluids (k = 0.3) exhibit rapid velocity reduction, indicating insufficient viscous support due to lower fluid viscosity, which leads to gravitational settling and accelerated deceleration. In contrast, when k increases to 1.2, particle velocity attenuation is minimized, and elevated flow speeds are sustained over extended durations. This behavior reflects that high-k fluids possess stronger viscous forces, enabling more effective momentum transfer through the fluid phase and greater resistance to particle settling, thereby enhancing the sustained transport performance of cuttings.

Figure 17 presents the contour map of cuttings volume fraction distribution in the wellbore under varying flow behavior indices. At a drilling fluid velocity of 1.05 m/s and a drill pipe rotational speed of 120 rpm, an increase in the flow behavior index leads to a significant reduction in cuttings accumulation and a marked decrease in cuttings bed thickness. This trend arises because as the power-law index n increases, the fluid’s shear-thinning behavior diminishes. As evidenced by the corresponding fluid velocity distribution contours in Figure 18, while the extent of the high-speed core region decreases, the overall annular velocity field expands, resulting in notably enhanced flow velocities near the bottom of the wellbore. Consequently, the fluid exerts stronger shear forces on deposited cuttings and improves their entrainment and transport capability, thereby more effectively suppressing cuttings bed formation and buildup. The results indicate that, within the studied parameter range, moderately increasing the flow behavior index can enhance wellbore cleaning efficiency.

As illustrated in Figure 19, when the drilling fluid consistency coefficient is fixed at 0.3, increasing the flow index from 0.4 to 0.7 progressively reduces the velocity attenuation of cuttings particles, demonstrating that higher n values contribute to maintaining particle transport efficiency in the annulus. All four cases start with identical initial particle velocities; however, as time progresses, the most pronounced velocity decline occurs under low n conditions (n = 0.4), reflecting the fact that strong shear-thinning behavior results in excessive viscosity reduction in low-shear regions, leading to a rapid deterioration of carrying capacity. In contrast, when n is increased to 0.7, the particles maintain higher velocities throughout the transport process, exhibiting minimal attenuation. This improvement arises because higher-n fluids exhibit weaker shear-thinning characteristics and greater viscosity stability across varying shear rates, enabling them to exert more consistent and uniform drag forces within the annular space. As a result, particle settling is effectively delayed, enhancing both the stability and efficiency of cuttings transport.

4.4. Effect of Enlargement Ratio on Hole Cleaning

Figure 20 shows the cloud map of cuttings distribution in the enlarged section of horizontal wells under different enlargement rates. As shown in the figure, as the enlargement rate increases from 0.4 to 0.7, the cuttings deposition in the enlarged section significantly increases. The annular area of the enlarged section increases with the increase in the enlargement rate. This indicates that the wellbore with a higher ellipticity is more likely to cause a decrease in cuttings transport efficiency during drilling. The reason is that in the wellbore with a large enlargement rate, the flow velocity of the drilling fluid on the long axis side of the large enlargement is greatly reduced (as shown in Figure 21), thereby weakening the drag and lift force of the drilling fluid on the cuttings, making the cuttings more likely to settle from the suspended state.

The variation in cuttings volume fraction at different axial positions along the drill pipe under varying reaming rates is illustrated in Figure 22. The results demonstrate that the effect of the reaming rate on cuttings transport exhibits distinct segmental characteristics. In the upstream non-reamed section (z = 0.25 m), the cuttings volume fraction remains constant at 1.98%, indicating a stable flow field that is unaffected by downstream reaming. In contrast, within the reamed section (z = 0.625 m), the cuttings volume fraction increases significantly with higher reaming rates, rising from 9.1% to 12.9%. This increase is attributed to the reduction in annular flow velocity induced by the enlarged cross-sectional area, which promotes pronounced cuttings accumulation at this location. In the downstream non-reamed section (z = 0.875 m), however, the cuttings volume fraction decreases as the reaming rate increases, declining from 3.72% to 2.76%.

4.5. Effect of Ovality on Hole Cleaning

Figure 23 presents the cloud maps of cuttings distribution in the enlarged section of a horizontal wellbore under varying degrees of ellipticity. As ellipticity increases from 1.0 to 1.3, the minor axis of the enlarged wellbore decreases, leading to a reduction in the cross-sectional area. This geometric change results in a marked decrease in the high-concentration zone of cuttings at the bottom of the annulus—a trend confirmed by quantitative measurements of cuttings volume fraction. Specifically, at an ellipticity (α) of 1.0, the cuttings volume fraction is 5.4%; as ellipticity increases to 1.1, 1.2, and 1.3, the volume fraction progressively declines to 5.2%, 4.9%, and 4.6%, respectively. When considered in conjunction with Figure 24, it becomes evident that, at a constant drilling fluid flow rate, the reduced cross-sectional area increases the average annular flow velocity, thereby diminishing the extent of low-velocity regions. Consequently, a greater proportion of cuttings particles are exposed to sufficient hydrodynamic drag and lift forces, enhancing their suspension and transport efficiency and facilitating effective removal from the wellbore.

Figure 25 clearly illustrates the influence of wellbore ellipticity on the transport velocity of cuttings particles. Initially, particle velocities are identical across different ellipticity conditions; however, as time progresses, the effect of wellbore geometry becomes increasingly evident. In the circular wellbore (α = 1), particle velocity decays most rapidly, eventually stabilizing at approximately 0.30 m/s. As ellipticity increases to α = 1.3, the rate of velocity decay diminishes gradually, and the final steady-state velocity rises to about 0.38 m/s. When considered alongside Figure 24, it is evident that increased ellipticity modifies the annular flow field distribution, thereby enhancing the fluid’s drag and carrying capacity for cuttings. This trend demonstrates that higher wellbore ellipticity helps maintain particle transport efficiency in the annulus.

5. Conclusions

This study employed the CFD-DEM coupled numerical simulation method to investigate the cuttings transport behavior in the annulus of horizontal wells under the influence of drilling fluid flow rate and drill pipe rotation speed, comparing both conventional and enlarged wellbores. Additionally, the effects of drilling fluid rheological parameters, wellbore enlargement ratio, and ellipticity were analyzed. The main conclusions are as follows:

• The flow rate of the drilling fluid is a key factor in determining wellbore cleaning efficiency, but its effectiveness diminishes in enlarged wellbores. Increasing the flow rate enhances the drag force exerted by the fluid on the particles, promoting their suspension and transport, which reduces the thickness of the cuttings bed. However, in the enlarged sections, the increased cross-sectional area leads to a sharp decrease in local fluid velocity, thereby reducing the kinetic energy required for cuttings transport. From a quantitative perspective, increasing the flow rate from 0.6 m/s to 1.05 m/s in conventional wellbores results in a 75% reduction in cuttings volume fraction (from 8.4% to 2.1%). In contrast, in wellbores with an enlargement ratio of 0.7, the same flow rate increase leads to only a 37.8% reduction (from 18.5% to 11.5%). This indicates that geometric complexity fundamentally limits the effectiveness of the primary cleaning mechanism.
• The effect of drill pipe rotation is highly dependent on wellbore geometry. In conventional wellbores, rotation generates strong centrifugal forces that disrupt the cuttings bed, reducing its volume by approximately 42.6% when the rotation speed increases from 0 rpm to 180 rpm. In contrast, in enlarged wellbores (with enlargement ratios of 0.4 and 0.7), the same increase in rotation speed results in only about a 13% improvement. This suggests that in highly enlarged wellbores, relying solely on increased drill pipe rotation is insufficient to mitigate cuttings bed accumulation.
• Optimizing the rheological properties of drilling fluid is an important strategy for enhancing flowability in complex geometries. Increasing the consistency coefficient (k) or flow behavior index (n) raises the effective viscosity and shear stress of the drilling fluid, particularly in low-shear regions near the wellbore bottom. This enhances the fluid’s capacity to suspend particles and promotes a more uniform annular velocity profile, thereby suppressing settling and encouraging a dispersed flow regime. This is crucial for cleaning enlarged regions.
• The enlargement ratio of the wellbore section negatively impacts cuttings transport. As the enlargement ratio increases from 0.4 to 0.7, the cuttings volume fraction in the enlarged section rises from 9.1% to 12.9%. The primary mechanism behind this is that the enlarged flow area reduces the average annular velocity, weakening the drag and lift forces acting on the particles, which hinders their transport.
• Moderate wellbore ellipticity, on the other hand, can improve cleaning efficiency under enlarged conditions. Keeping the enlargement ratio constant, increasing the ellipticity from α = 1.0 to 1.3 lengthens the minor axis, thereby reducing the cross-sectional area. This results in an increase in the average annular velocity and a reduction in the low-velocity regions, making the forces exerted by the fluid on the cuttings more effective. Consequently, the cuttings volume fraction decreases from 5.4% to 4.6%, and the particle transport velocity is better maintained.

6. Future Work

(1)

The section of the wellbore enlargement is limited to a length of 0.25 m. This length was chosen primarily due to considerations of computational resources and simulation accuracy, ensuring that the model could be completed within a reasonable time frame. However, in actual drilling operations, the length of the enlarged section is typically much greater. This limitation may affect the comprehensiveness of the simulation results, particularly in long wellbores or complex wellbore conditions. Therefore, future work could consider extending the length of the enlarged section to better simulate fluid flow and cuttings transport behavior in real-world drilling operations.

(2)

Cuttings are simplified as monodisperse spherical particles (2 mm in diameter) to reduce computational complexity. However, in reality, cuttings are typically angular, polydisperse, and often plate-shaped, which can affect the porosity, frictional forces, and buoyancy behavior of the formation. Therefore, future work could incorporate more complex cuttings models to more accurately reflect the characteristics of cuttings in real-world drilling conditions.

(3)

The virtual mass force was not considered due to the relatively small fluid acceleration and the dominance of drag and lift forces in fluid-particle interactions. However, we acknowledge that, in certain cases, particularly in regions with significant geometric changes, the virtual mass force may have a substantial impact on particle motion. Therefore, future research will incorporate the virtual mass force and provide a more detailed analysis of its effect on fluid-particle coupling.

(4)

The simplified, localized wellbore enlargement model employed in this study facilitates numerical implementation and parametric analysis but differs from the irregular, large-scale, and asymmetric enlargements typically encountered in real formations. This simplification was primarily motivated by computational efficiency. Future models should incorporate irregular, large-scale, and asymmetric geometric features to more accurately represent downhole conditions.

(5)

The model validation in this study focused on standard wellbore geometries. Future work should include experimental studies on cuttings transport in enlarged wellbore sections to further validate the model’s predictions under such conditions.