A Numerical Simulation of the Effect of Drilling Fluid Rheology on Cutting Migration in Horizontal Wells at Different Drilling Fluid Temperatures

Abstract

In recent years, significant breakthroughs have been made in the exploration of deep to ultra-deep oil and gas reserves onshore in China. These conventional deep to ultra-deep reservoirs are typically buried at depths exceeding 4500 m, with bottom-hole temperatures surpassing 150 °C. The high temperatures at the bottom of the well are more likely to cause deterioration in drilling fluid properties, altering its rheological properties and reducing cutting transport efficiency, which can lead to wellbore cleaning issues. In this paper, the numerical simulation method is used to analyze the influence of cutting particle size, drilling fluid flow rate, drill pipe rotation speed, and drill pipe eccentricity on the annular cutting concentration under different wellbore drilling fluid temperature conditions. The results show that at the same cutting particle size, as the drilling fluid temperature increases, the cutting concentration in the annulus increases sharply. The increase is the largest when the particle size is 3 mm, and when the drilling fluid temperature is 220 °C, the cutting concentration increases by 79.7% compared to at 200 °C and by 279% compared to at 180 °C. When the flow rate increases from 0.5 m/s to 1.0 m/s, the annular cutting concentration at drilling fluid temperatures of 220 °C and 200 °C decreases by 70.5% and 50.4%, respectively. The higher the drilling fluid temperature, the better the cutting removal effect when increasing the drill pipe rotation speed. However, when the rotation speed exceeds 120 rpm, the change in cutting concentration with increasing rotation speed becomes insignificant. When the drill pipe eccentricity is small, an increase in drilling fluid temperature leads to a significant rise in annular cutting concentration. However, when the drill pipe eccentricity is large, changes in drilling fluid temperature have a smaller impact on cutting concentration. The research findings can provide engineering guidance and theoretical support for the design of drilling fluid hydraulic parameters for cutting transport and rheological parameters in high-temperature wellbores.

1. Introduction

As energy demand continues to rise and drilling technology rapidly advances, it has become increasingly difficult to discover large, resource-rich oil and gas fields in shallow to intermediate depths. Consequently, deep to ultra-deep well drilling has become the primary focus for fossil energy development in China and around the world [1,2]. However, the exploration and development of deep to ultra-deep oil and gas resources are extremely challenging due to factors such as significant burial depths, high temperatures, high pressures, and complex geological conditions. This challenge is especially pronounced during drilling, where the geothermal gradient causes wellbore temperatures to increase with depth [3,4,5,6]. Under the influence of high temperature for a long time in the well, the drilling fluid may degrade, disperse, and flocculate, which will deteriorate the rheology and stability of the drilling fluid, resulting in the poor ability of the drilling fluid to protect the stability of the well wall and suspend and carry cuttings and weighting materials. Consequently, cuttings are more likely to settle under gravity, accumulating at the bottom of the well to form cutting beds or around the drill bit, which can decrease the rate of penetration, increase the risk of stuck pipe incidents, and raise drilling costs [7,8]. Therefore, as drilling depth increases, the ability to measure the rheology of drilling fluid in real-time becomes critically important. Liu et al. [9] summarized four methods for real-time rheology measurement: online rotary Couette viscometers, pipeline viscometers, mathematical and physical models or artificial intelligence models based on the Marsh funnel, and acoustic techniques. The principles, advantages, limitations, and applications of each method are discussed.

To improve the drilling efficiency of deep and ultra-deep wells and ensure the drilling quality, researchers have not only studied various drilling fluids with excellent high-temperature resistance (water-based, oil-based, foam, etc.) but also carried out relevant research on the impact of temperature on cutting transportation. Zhou et al. [10] experimentally studied the effect of different temperatures on the law of cutting transportation and proposed a new hydraulic mechanics model of aerated mud that can accurately predict the friction pressure loss in the annular flow field. Chen et al. [11] used experimental methods to study the effects of foam properties, temperature, and pressure on cutting migration. The results show that when the temperature increases, the cutting concentration does not increase significantly, so they believe that the effect of temperature on the cutting transport efficiency of foam may not be significant in actual drilling operations. Akhshik et al. [12] used a computational fluid dynamics discrete element method to study the cutting transportation law during inclined annulus aerated mud drilling and found that factors such as liquid flow rate, air injection volume, temperature, and annulus inclination all have an impact on the cutting transportation efficiency.

Scholars have also studied drilling fluid rheology’s impact on cutting transport. Pereira et al. [13] analyzed the influence of factors such as flow rate, drilling fluid rheology, wellbore size, and well inclination on cutting transportation, and believed that flow rate and drilling fluid rheology have good controllability and are the preferred adjustment parameters on site. Ytrehus et al. [14] experimentally studied the effects of well inclination, drill pipe rotation, and flow rate on cutting transport efficiency in water-based and oil-based drilling fluids with different rheological properties. The results showed that at a wellbore inclination angle of 60°, the oil-based fluid was more efficient at a flow rate of 0.7 m/s, while at 48°, the water-based fluid was more efficient at the same flow rate. Al-Yasiri et al. [15] used CFD (computational fluid dynamics) simulations to study the effects of parameters such as drilling fluid rheology, flow rate, cutting density, and shape on cutting transport in vertical wells when using nanoparticle-based drilling fluids. The results indicated that adding nanoparticles to the fluid can significantly enhance drilling fluid viscosity and cutting transport efficiency.

It is evident that previous research typically examines drilling fluid rheology’s impact on cutting transport and the effects of temperature on cutting transport separately. However, different formation depths influence drilling fluid temperature, which in turn affects the fluid’s rheological properties. Currently, there are no reports on studies addressing this combined effect. Therefore, this paper uses numerical simulation to investigate the drilling fluid rheology’s impact on cutting transport at various temperatures. Based on the situation of cutting transport, the drilling fluid formula can be adjusted and optimized in real-time, ensuring that the drilling fluid maintains good rheological properties in the high-temperature and high-pressure environment downhole. This helps prevent incidents such as sediment blockages and blowouts, thereby ensuring the efficiency of borehole cleaning and enabling safe and efficient drilling operations [16,17].

2. Cutting-Drilling Fluid Two-Phase Flow Equations

The flow of cuttings and drilling fluid in the wellbore annulus is a typical example of liquid–solid two-phase flow. In numerical simulations, the Euler–Euler model or the Euler–Lagrange model is commonly used to describe two-phase flow. The Euler–Euler model treats each phase in the flow field as a continuous medium, with both cuttings (solid phase) and drilling fluid (liquid phase) filling the entire flow field. Interactions between phases are incorporated as additional terms in the momentum conservation equations. This method is relatively computationally efficient and fast, and its accuracy has been extensively validated in engineering applications. It has been widely applied in current cutting transport studies. For example, Tong et al. used CFD numerical simulation to investigate wellbore cleaning in coiled tubing operations and developed a transient cutting transport model based on a two-layer steady-state assumption. An et al. developed a one-dimensional two-layer model, which employs three correction factors to represent the effects of drill pipe rotation on cutting transport and annular pressure loss. The parameters of the one-dimensional model were calibrated using CFD simulation results to accurately predict cutting transport and annular pressure loss in small-diameter boreholes. Additionally, researchers have also used numerical simulations to develop and optimize cleaning tools. Zhou et al. applied CFD numerical methods to analyze the wellbore cleaning performance of a V-shaped impeller, which helps improve the efficiency and performance of cutting removal in horizontal wells [18,19,20].

2.1. Mass Conservation Equation for Drilling Fluid and Cuttings

During the flow of cuttings in the drilling fluid, there is no mass exchange between the two phases, which complies with the principle of mass conservation.

The mass conservation equation of drilling fluid is as follows:

(1)${\displaystyle \frac{\partial \left({\epsilon }_l{\rho }_1\right)}{\partial t}}+\nabla \cdot \left({\epsilon }_l{\rho }_l{\mathrm{v}}_l\right)=0$

The mass conservation equation of cuttings is as follows:

(2)${\displaystyle \frac{\partial \left({\epsilon }_s{\rho }_s\right)}{\partial t}}+\nabla \cdot \left({\epsilon }_s{\rho }_s{\mathrm{v}}_s\right)=0$

And the sum of the two-phase volume fractions is 1:

(3)${\epsilon }_l+{\epsilon }_s=1$

where ε_l and ε_s represent the volume fractions of the drilling fluid and cuttings, respectively—dimensionless; ρ_l and ρ_s are the densities of the drilling fluid and cuttings, respectively—kg/m³; v_l and vs. are the flow velocities of the drilling fluid and cuttings, respectively—m/s.

2.2. Momentum Equation for Drilling Fluid and Cuttings

The momentum equation for drilling fluid is as follows:

(4)${\displaystyle \frac{\partial \left({\epsilon }_l{\rho }_l{\mathit{v}}_l\right)}{\partial t}}+\nabla \cdot \left({\epsilon }_l{\rho }_l{\mathit{v}}_l{\mathit{v}}_l\right)={\epsilon }_l\nabla \cdot {\tau }_l+{\epsilon }_l{\rho }_l\mathit{g}-{\epsilon }_l\nabla p-\beta \left(v_l-v_s\right)$

The momentum equation for cuttings is as follows:

(5)${\displaystyle \frac{\partial \left({\epsilon }_s{\rho }_s{v}_s\right)}{\partial t}}+\nabla \cdot \left({\epsilon }_s{\rho }_s{\mathit{v}}_s{\mathit{v}}_s\right)={\epsilon }_s\nabla \cdot {\tau }_s+{\epsilon }_s{\rho }_{s}g-{\epsilon }_s\nabla p-\nabla p_s+\beta \left(v_l-v_s\right)$

Among them, the equation for the stress tensor τ_l of the drilling fluid is as follows:

(6)${\tau }_l={\mu }_l\left[\nabla v_l+{\left(\nabla v_l\right)}^T\right]-{\displaystyle \frac{2}{3}}{\mu }_l\left(\nabla \cdot v_l\right)\mathrm{I}$

The stress tensor of the cuttings τs is shown as below:

(7)${\tau }_s={\mu }_s\left\{\left[\nabla v_s+{\left(\nabla v_s\right)}^T\right]-{\displaystyle \frac{2}{3}}\left(\nabla \cdot v_s\right)\mathrm{I}\right\}+{\zeta }_s\nabla \cdot v_s\mathrm{I}$

where g is 9.81 m/s²; p is the pressure between the two phases, Pa; p_s is the solid pressure, Pa; β is the momentum exchange coefficient—dimensionless; μ_l is the shear viscosity of the drilling fluid—Pa‧s; μ_s is the shear viscosity of the cuttings—Pa‧s; I is a unit vector; ζ_s is the volume viscosity of the cuttings—Pa‧s.

p_s, μ_s, and ζ_s [21] are calculated as follows:

(8)$p_s={\epsilon }_s{\rho }_s{\theta }_s+2g_0{\epsilon }_s^2(1+e){\rho }_s{\theta }_s$

(9)${\zeta }_s={\displaystyle \frac{4}{3}}{\epsilon }_s^2{\rho }_s{d}_s{g}_0(1+e)\sqrt{{\displaystyle \frac{{\theta }_s}{\pi }}}$

(10)${\mu }_s={\mu }_{s,col}+{\mu }_{s,kin}+{\mu }_{s,fr}$

The collision viscosity μ_s,col adopts the model proposed by Gidaspow [22]:

(11)${\mu }_{s,col}={\displaystyle \frac{4}{5}}{\epsilon }_s^2{\rho }_s{g}_0{d}_s(1+e)\sqrt{{\displaystyle \frac{{\theta }_s}{\pi }}}$

The dynamic viscosity μ_s,kin also uses the model proposed by Gidaspow, and the expression is as follows:

(12)${\mu }_{s,kin}={\displaystyle \frac{10{\rho }_s{d}_s{\epsilon }_s\sqrt{\pi {\theta }_s}}{96(1+\lambda )g_0}}{\left[1+{\displaystyle \frac{4}{5}}{g}_0{\epsilon }_s(1+e)\right]}^2$

The friction viscosity μ_s,fr adopts the model proposed by Schaeffer [23]:

(13)${\mu }_{s,fr}={\displaystyle \frac{p_{fr}\sin \phi }{2\sqrt{I_{2D}}}}$

where d_s is the diameter of the cutting particle—m; λ is the collision recovery coefficient between the cutting particles; p_fr is the friction pressure—Pa; φ is the internal friction angle—°; I_2D is the second invariant of the deviatoric stress tensor—N/m²; g₀ is the radial distribution function of the cutting particles; θ_s is the pseudo-temperature of the cuttings—m²/s².

The pseudo-temperature is used to reflect the strength of the pulsating motion of the cutting particles. The formulas for g₀ and θ_s are shown as follows:

(14)$g_0={\left[1-{\left({\displaystyle \frac{{\epsilon }_s}{{\epsilon }_{s\max }}}\right)}^{{\displaystyle \frac{1}{3}}}\right]}^{-1}$

(15)${\theta }_s={\displaystyle \frac{v_{(s,i)}{v}_{(s,i)}}{3}}$

where v_(s,i) is the pulsating velocity of the cutting particles, caused by interactions between collisions among cutting particles and the turbulent pulsations of the drilling fluid.

2.3. Drag Model

Momentum transfer between the drilling fluid and cuttings is achieved through inter-phase interactions, including drag force, lift force, buoyancy force, Brownian force, etc. However, except for the drag force, the influence of other forces on the cutting particles is small and can be ignored. Previous researchers found that the Huilin–Gidaspow drag model is the most widely used in the study of liquid–solid two-phase flow [24]. This model is a combination of the Wen–Yu drag model and the Ergun drag model and is suitable for most fluidization calculations [25,26]. Therefore, this study uses the Huilin–Gidaspow drag force model:

(16)${\beta }_{Huilin-Gidaspow}=\left\{\begin{array}{ll}{\beta }_{Wen\&Yu}={\displaystyle \frac{3C_{\mathrm{D}}{\epsilon }_s{\epsilon }_l{\rho }_l\left|v_l-v_s\right|}{4d_{\mathrm{s}}}}{\epsilon }_l^{-2.65}& \left({\epsilon }_l>0.8\right)\\ {\beta }_{E\mathrm{rgun}}={\displaystyle \frac{150{\epsilon }_s\left(1-{\epsilon }_l\right){\mu }_1}{{\epsilon }_l{d}_s^2}}+{\displaystyle \frac{1.75{\rho }_l{\alpha }_s\left|v_l-v_s\right|}{d_s}}& \left({\epsilon }_l⩽0.8\right)\end{array}\right.$

where C_D is the drag coefficient, which is expressed as follows:

(17)$C_{\mathrm{D}}==\left\{\begin{array}{ll}{\displaystyle \frac{24}{R{e}_{\mathrm{s}}}}\left(1+0.15R{e}_{\mathrm{s}}^{0.687}\right)& \left(R{e}_{\mathrm{s}}⩽1000\right)\\ 0.44& \left(R{e}_{\mathrm{s}}>1000\right)\end{array}\right.$

where Re_s is the Reynolds number of cutting particles, and its expression is as follows:

(18)$R{e}_s={\displaystyle \frac{{\epsilon }_l{\rho }_l{d}_s\left|v_l-v_s\right|}{{\mu }_l}}$

Because this paper mainly focuses on horizontal wells, the drag force exerted by the drilling fluid on the cuttings is in the horizontal direction.

3. Geometric Model and Mesh Used for Simulation

3.1. Geometric Model and Mesh Generation

The numerical simulation model used in this study has the same dimensions as the model used by Han et al. [27] in their experiments, and a structured mesh is employed to divide the annular flow field. The annular flow field model is divided into two parts: the inner wall and the outer wall. The inner wall simulates the drill pipe and the outer wall simulates the wellbore wall. The schematic diagram is shown in Figure 1. Numerical simulation is conducted based on the computing platform of “Fluent 6.3”.The simulation adopts a transient model. When the change value of the cutting volume fraction in the annulus is less than 0.01 within 10 s, the simulation can be considered to be converged. The simulation parameters are shown in Table 1. The rheological parameters of the drilling fluid at different temperatures used in the simulation are based on a novel high-temperature-resistant water-based drilling fluid studied by Hamad et al. [28], with these parameters listed separately in Table 2. A newly synthesized amphoteric polymer PEX is added to the water-based drilling fluid. PEX not only improves the rheological properties and reduces the filtration behavior, but also enhances the thermal stability of the drilling mud formulation. The drilling fluid rheological model used is the Herschel–Bulkley model, and the expression is as follows:

(19)$\tau ={\tau }_0+K{\gamma }^n$

where τ is the shear stress—Pa; τ₀ is the dynamic shear force—Pa; γ is the shear rate—1/s; n is the drilling fluid fluidity index—dimensionless.

3.2. Grid Number and Time Step Independence Verification

For transient numerical simulation, grid independence verification and time independence verification are required [29]. The number of grids will affect the grid quality. Grid-independent verification means that when the grid quality meets the requirements, further refining the grid will have little effect on the results. As shown in Figure 2, when other parameters are the same, even if the number of grids is greater than 89,964, the calculation results will hardly change. The time step will affect the convergence speed. It means that under the premise of meeting the convergence requirement, the speed of convergence has little effect on the result. As shown in Figure 3, the time step of 0.001 s meets the requirement. If the step size is reduced, the calculation cycle will be increased, and if the step size is increased, the calculation accuracy will be affected. Therefore, under the premise of ensuring the accuracy and reliability of the simulation results, to improve the calculation efficiency, this paper selects the number of grids as 89,964 and the time step as 0.001 s.

3.3. Model Validation

To verify the accuracy of the CFD numerical model, the model in this paper was verified based on the experimental data of Han et al. [27]. They studied the solid–liquid two-phase flow law in the annulus of a small borehole by establishing an indoor experimental pipeline. This paper simulated and verified the cutting concentration in the annulus at different flow rates when the well inclination angle was 45°, the drill pipe speed was 200 rpm, the experimental fluid was a sodium carboxymethyl cellulose solution with a mass fraction of 0.4%, and the injected cutting concentration was 4%. The results are shown in Figure 4. By comparison, the average error between the simulation and the experiment is 6.74%, and the two have the same change trend. It is found that the simulation results are lower than the experimental results, which may be because the wellbore wall is smooth in the numerical simulation, thus ignoring the friction between the cuttings and the wellbore wall. However, the error value is within an acceptable range, so it is believed that the CFD simulation model used in this paper is accurate.

4. Simulation Results Analysis and Discussion

4.1. Effect of Cutting Particle Size on Cutting Transport at Different Temperatures

During the drilling process, the cuttings generated by the drill bit are of different sizes, and different diameters of cuttings have different effects on cutting transportation. Figure 5 and Figure 6 show the curve graph and cloud graph of the effect of increasing cutting particle size on cutting concentration in the annulus at different temperatures when v = 0.5 m/s, e = 0, Ω = 0 rpm, and the well inclination angle θ = 90°, respectively. Figure 7 is a cloud graph of cutting concentration distribution at the outlet.

As shown in Figure 5 and Figure 6, for the same cutting particle size, an increase in temperature leads to a higher cutting concentration in the annulus. For example, with a cutting particle size of 3 mm, the cutting concentration at a drilling fluid temperature of 220 °C is 2.79 times higher than that at 180 °C, and the concentration at 200 °C is 1.11 times higher than at 180 °C. Because the temperature rises, the properties of the drilling fluid are changed. The hydraulic energy required by the drilling fluid to clean the cuttings is reduced, and the ability to suspend the cuttings is weakened, exacerbating the accumulation of cuttings [30]. As shown in Figure 5, when the cutting particle size increased from 4 mm to 5 mm at 180 °C, the cutting concentration increased fastest, increasing by 74%. At 200 °C, it increased from 3 mm to 4 mm, increasing by 56%. At 220 °C, it increased from 2 mm to 3 mm, increasing by 58%. It can be seen that as the temperature of the drilling fluid increases, the particle size of the cuttings that cause the fastest increase in cutting concentration becomes smaller. Therefore, it is necessary to conduct particle size analysis on the returned cuttings, which is conducive to better optimizing hydraulic parameters and ensuring wellbore cleanliness.

4.2. Effect of Drilling Fluid Velocity on Cutting Transport at Different Temperatures

Drilling fluid flow rate is the drilling variable that has the most significant impact on wellbore cleaning effectiveness. When e = 0, Ω = 0 rpm, d_s = 3 m, and θ = 90°, Figure 8 is a curve diagram showing the effect of increasing drilling fluid flow rate on the cutting concentration in the annulus at different temperatures, Figure 9 is a cloud diagram showing the effect of increasing drilling fluid flow rate on the cutting concentration in the annulus at different temperatures. In the simulated environment of this study, considering the migration characteristics of cutting particles, the rheological properties of the drilling fluid, and the variations in wellbore temperature and pressure, the drilling fluid flow rate required to keep the wellbore clean should be at least 0.7 m/s. This flow rate is derived from numerical simulations and experimental validation within a certain range, ensuring the effective prevention of cutting accumulation in the wellbore, thereby avoiding potential downhole complications such as wellbore instability and stuck pipe. Figure 10 shows a cloud diagram showing the cutting concentration distribution at the outlet.

Combining Figure 8 and Figure 9, it can be seen that when the drilling fluid flow rate increases to 1.0 m/s at 220 °C and 200 °C, the annular cutting concentration decreases by 70.5% and 50.4%, respectively, compared with the cutting concentration at 0.5 m/s, while the drilling fluid flow rate increases at 180 °C, and the annular cutting concentration remains almost unchanged. This is because, at 220 °C and 200 °C, the drilling fluid is affected by the increase in temperature, the rheology changes, and the viscosity decreases. Low-viscosity drilling fluid is more likely to have turbulence when the flow rate increases, and has a better cutting-carrying effect than high-viscosity drilling fluid [31].

Combining Figure 9 and Figure 10, when the drilling fluid carries cuttings at a low speed, the cuttings tend to accumulate and form a cutting bed. This accumulation becomes more pronounced at higher temperatures, with the accumulation area moving closer to the wellbore outlet. As the drilling fluid flow rate increases, the distribution of cuttings becomes more uniform, making it easier for the cuttings to move from the cutting bed at the bottom of the annulus to the high-velocity flow region in the upper annulus. Consequently, the cutting concentration in the annulus decreases. However, in actual operations, factors such as wellbore erosion, circulation pressure losses, and pump pressure must be considered, to ensure that the drilling fluid flow rate remains within a reasonable range.

4.3. Effect of Drill Pipe Rotation Speed on Cutting Transport at Different Temperatures

Drill pipe rotation is an important factor in improving the efficiency of cutting transport. To explore the effect of drill pipe rotation speed changes on cutting concentration in the annulus at different temperatures, the change in cutting concentration when the drill pipe rotation speed increases from 0 rpm to 180 rpm under the conditions of e = 0, d_s = 3 mm, and θ = 90° was simulated. Figure 11 is a curve graph, Figure 12 is a cloud graph, and Figure 13 is a cloud graph of the cutting concentration distribution at the outlet.

As shown in Figure 11, when the drill pipe rotation speed increases to 60 rpm at 220 °C, the annular cutting concentration is only 31.8% of that when the drill pipe is not rotating. When the drill pipe rotation speed increases to 60 rpm at 200 °C, the annular cutting concentration is only 49.1% of that when the drill pipe is not rotating. The decrease is obvious. At 180 °C, the cutting concentration only decreases by 0.71%, and the change is not obvious.

Combining Figure 12 and Figure 13, it can be seen that the rheology of the drilling fluid is relatively good at 180 °C, and most of the cuttings are suspended in the drilling fluid. However, when the temperature rises to 200 °C and 220 °C, the rheology of the drilling fluid deteriorates, most of the cuttings are deposited on the lower well wall, and the quantity of suspended cuttings decreases. At this time, the increase in the drill pipe rotation speed causes the cuttings fixed into the cutting bed to move to the suspended layer and the moving bed layer, and the cutting bed layer is significantly reduced. In addition, as the drill pipe rotation speed increases, the centrifugal force applied to the drilling fluid also increases, and the ability of drilling fluid to carry cuttings has also been improved, making the cutting bed loose, thereby achieving the effect of destroying the cutting bed [32]. However, there is an upper limit to the improvement of the cutting cleaning effect by increasing the drill pipe rotation speed. As shown in Figure 11, at three different temperatures, when the rotation speed exceeds 120 rpm, even if the drill pipe rotation speed is increased, the improvement in the cutting cleaning effect is small.

4.4. Effect of Drill Pipe Eccentricity on Cutting Transport at Different Temperatures

In extended-reach wells or long horizontal wells, the drill pipe will form an eccentricity near the borehole wall under the action of its gravity. Figure 14 and Figure 15 show the curve and cloud diagram of the effect of increased drill pipe eccentricity on the cutting concentration in the annulus at different temperatures when v = 0.5 m/s, Ω = 0 rpm, d_s = 3 mm, and θ = 90°, respectively. Figure 16 is a cloud diagram of the cutting concentration distribution at the outlet.

As shown in Figure 14, when the eccentricity is the same, the cutting concentration increases with the increase in temperature. The increase is very obvious when e = 0.1. The cutting concentration in the annulus at 220 °C increases by 1.8 times compared with 180 °C and 1.2 times compared with 200 °C. This once again proves that the rheological properties of drilling fluid under high-temperature conditions are crucial to wellbore cleaning. If its high-temperature resistance is poor, the cutting concentration will increase significantly. However, when e = 0.5, the temperature increases, and the cutting concentration does not increase significantly. The cutting concentration at 220 °C only increases by 1.21% and 2.58% compared with 200 °C and 180 °C, respectively.

Combining Figure 15 and Figure 16, it can be seen that due to the eccentricity of the drill pipe, the flow space in the lower area of the annulus is reduced, and only a small part of the cuttings can flow out of the wellbore under the drag of the drilling fluid, while the other large part of the cuttings are continuously deposited at the bottom under their gravity, further reducing the flow space at the bottom. When the eccentricity is serious, a large amount of cuttings accumulate at the bottom, and the drilling fluid can only flow on the wide side of the annulus [33]. Therefore, in addition to improving the high-temperature resistance of the drilling fluid, one should try to ensure that the drill pipe can be located in the center.

5. Conclusions

In this study, the Eulerian two-fluid model was used to numerically simulate the effects of cutting size, drilling fluid velocity, drill pipe rotation, and drill pipe eccentricity on cutting transport under different temperature conditions. Based on the simulation results, the following conclusions were drawn:

• (1). When the cutting particle size is the same, the cutting concentration in the annulus will increase sharply due to the increase in drilling fluid temperature. The increase was the largest when the particle size was 3 mm, and the cutting concentration increased by 2.79 times and 1.11 times when the drilling fluid temperature was 220 °C and 200 °C, respectively, compared with 180 °C. As the drilling fluid temperature increases, the smaller the cutting particle size is, the faster the increase in cutting concentration is.

• (2). The higher the drilling fluid temperature, the more obvious the decrease in cutting concentration as the drilling fluid flow rate increases. When the flow rate increases from 0.5 m/s to 1.0 m/s, the cutting concentration in the annulus decreases by 70.5% at 220 °C and 50.4% at 200 °C. Moreover, as the flow rate increases, the cutting distribution in the annulus becomes more uniform than at low flow rates. Therefore, under the premise of ensuring the stability of the wellbore, the drilling fluid flow rate should be increased as much as possible.

• (3). Under certain conditions, an increase in drill string rotational speed leads to a decrease in the annular cutting concentration, and the reduction in cutting concentration becomes more pronounced as the drilling fluid temperature rises. However, there is an upper limit to the improvement in cleaning efficiency with increasing rotational speed. When the speed exceeds 120 rpm, further increases in speed result in less noticeable changes in cutting concentration compared to lower speeds, and the cleaning efficiency declines.

• (4). When the eccentricity of the drill pipe is small, the temperature of the drilling fluid increases, and the concentration of cuttings in the annulus increases significantly. However, when the eccentricity is larger, the cutting concentration shows little change with temperature variations. Therefore, during the drilling process of horizontal wells, stabilizers should be installed at appropriate locations or the number of stabilizers should be increased to reduce the degree of eccentricity of the drill string, thereby minimizing the accumulation of cuttings.

Author Contributions

Data curation, X.W. (Xiumei Wan); investigation, W.L.; methodology, Y.C.; software, X.W. (Xudong Wang) and Z.W.; validation, P.W.; writing—original draft, Y.C. and J.L.; writing—review and editing, X.S. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Conflicts of Interest

The authors Ye Chen, Wenzhe Li, Xudong Wang, Pengcheng Wu, Xiumei Wan and Zhiqiang Wang were employed by the PetroChina Southwest Oil & Gasfield Company. The authors declare that this study received funding from PetroChina Southwest Oil & Gasfield Company. The funder was not involved in the study design; the collection, analysis, and interpretation of the data; the writing of this article; or the decision to submit it for publication.

Footnotes

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Figures and Tables

Figure 1. Schematic diagram of mesh division of annulus model.

Figure 2. Verification of grid number independence.

Figure 3. Verification of time step independence.

Figure 4. Comparison between numerical simulation and experiment.

Figure 5. A curve diagram of the change in CVT with cutting size at different temperatures.

Figure 6. A cloud diagram of the change in CVT with cutting size at different temperatures.

Figure 7. Cloud diagram of cutting concentration distribution at the outlet.

Figure 8. A curve diagram of the change in CVT with flow rate at different temperatures.

Figure 9. A cloud diagram of the change in CVT with flow rate at different temperatures.

Figure 10. Cloud diagram of cutting concentration distribution at the outlet.

Figure 11. A curve diagram of the change in CVT with drill pipe rotation at different temperatures.

Figure 12. A cloud diagram of the change in CVT with drill pipe rotation at different temperatures.

Figure 13. Cloud diagram of cutting concentration distribution at the outlet.

Figure 14. A curve diagram of the change in CVT with eccentricity at different temperatures.

Figure 15. A cloud diagram of the change in CVT with eccentricity at different temperatures.

Figure 16. A cloud diagram of cutting concentration distribution at the outlet.

Table 1

Numerical simulation parameter data.

Symbol	Parameter	Value	Unit
Dw	Wellbore diameter	44	mm
Dp	Drill pipe diameter	30	mm
Lw	Wellbore length	1.8	m
ds	Cutting diameter	2, 3, 4, 5, 6	mm
v	Drilling fluid flow rate	0.5, 0.6, 0.7, 0.8, 0.9, 1.0	m/s
Ω	Drill pipe speed	0, 60, 120, 180	rpm
e	Eccentricity	0, 0.1, 0.3, 0.5	Dimensionless

Table 2

Rheological parameters of drilling fluid at different temperatures.

Temperature (°C)	Dynamic Shear Force τ (Pa)	Consistency Coefficient K (Pa‧sn)	Flow Index
180	2.112	0.627	0.713
200	2.33	0.378	0.738
220	2.098	0.338	0.707

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