CFD Study of Cuttings Transport through Vertical Wellbore يدومع رئب للاخ ةلقتنملا روخصلا عطقل ةيباسحلا عئاملا تايكرح ةسارد

Cuttings transportation from the bit up the annulus to the surface is one the essential functions that are performed by drilling fluid. Predication of drilling fluid efficiency to transport cuttings in the annulus is very complicated due to numerous parameters that have affected drilling operations. Computational Fluid Dynamics (CFD) is widely used as a numerical technique in handling complex multiphase flow problems in different operational conditions. The present work has taken the advancement of CFD to computationally analyse the influence of the effects of various parameters like drilling fluid rheology, flow rate, pipe rotation, cuttings density, shape, concentration and drilling fluidcuttings particle coupling regimes on the cuttings transport in a vertical wellbore. The CFD simulation was carried out by using transient solver of ANSYS-FLUENT CFD commercial code. The dense discrete phase model (DDPM) is suggested in this work to overcome the main shortcomings of Eulerian–Eulerian and CFD-DEM approaches in simulating drilling fluid-cuttings flow. Also, some of the experimental investigations were involved in determining the fluid physical properties and essential input data to perform the CFD simulations. Regarding the results validation and verification, well agreement has been achieved between results obtained in this study with those reported in other studies.


Introduction
The drilling fluid cycle is rising from the bottom of the wellbore to transport the cuttings to the surface. The circulating speed of the drilling fluid should rapidly enough to overcome cuttings tend to overwhelm through the rookie fluid due to the gravitational force. Other

No.20 Journal of Petroleum Research & Studies (JPR&S)
159 factors are also affecting the cuttings removal involve drilling mud density, rheology, hole angle, angular velocity, drilled cuttings size and their shape [1].
A great effort has been devoted to analyse the main parameters effect on cutting transport behaviour through experimental studies [2][3][4]. The researchers have arrived at the conclusion that cuttings transport is controlled by a number of factors including the drilling fluid rheology, cutting characterizations (size, density, shape, and concentration), fluid velocity, and etc. Using of CFD technique can lead to better observe for cuttings transportation process inasmuch as measurement and visualization of downhole drilling fluid parameters during the drilling operation is not easily possible. Furthermore, the most existing theoretical relations are not having the ability of considering most parameters simultaneously.
CFD equips a qualitative analysis beside quantitative prediction of fluid flows as well as an insight into flow patterns that are hard, costly or difficult to consideration using experimental methods. Moreover, CFD does not displace the experimental technique entirely but the number of experimentation and the overall cost can be remarkably reduced.
The simulation of communication between the drilling fluid and the cuttings is particularly useful. As, the cuttings removal is advantageous since it decreases fluid loss and mechanical pipe sticking [5]. Nevertheless, if the cuttings cannot be removed from the wellbore, they will soon impede drilling. Therefore, it is important computationally analysed the influence of the effects of various parameters like drilling fluid rheology, flow rate, pipe rotation, cuttings density, shape, concentration and drilling fluid-cuttings particle coupling regimes on the cuttings transport in a vertical wellbore.
The cutting-drilling fluid flow can simulate as solid-liquid flow; the cutting as solid particles while the drilling fluid as non-Newtown fluid. The literature on cuttings transportation shows a variety of modelling approaches. The choosing of the suitable model is a real serious concern. Drilling fluid-cuttings flow modelling is a challenging responsibility, but it is a handy tool to infer more about these flows. Recently, several authors have proposed a Eulerian-Eulerian approach to model drilling fluid-cuttings flow [6,7]. This strategy usually requires much less computational resources corresponded to Eulerian-Lagrangian schemes. Thus, it can be employed to model pilot scale [8,9].
However, the discrete nature of the solid phase is missed in the Eulerian-Eulerian strategy due to the continuous representation of the dispersed phase. This weakness can be

No.20 Journal of Petroleum Research & Studies (JPR&S)
surmounted with discrete element method [10][11][12], in this approach, the solid particles are tracked separately based on Newton's laws of motion besides particle-particle and particlewall collisions. Not only Eulerian approach has limitations, but also Lagrangian approach has, one of the main shortcomings of DEM technique is the cost computational demands that reduce its applications to small-scale [13].
Discrete phase model was used in the simulation of cuttings to eliminate the previous restrictions [1], which is two ways coupling between the cutting and fluid. As a result of using DPM, the volume fraction of the discrete phase should not be exceeded 10%.
Otherwise weak accurate predictions will be obtained. To avert all previous approaches limitation, the dense discrete phase model (DDPM) has been established in which the details of particle-particle and particle-wall collisions are not overtly tracked anymore; as an alternative, a force is employed to represent these collisions [14]. Moreover, the hypothesis of the parcel is utilised to lessen the amounts of particles included in the computations, resulting in an essential acceleration of the speed of simulations. Therefore, the DDPM looks promising considering the advantages of Lagrangian methods and applies to large scales.
The DDPM model is suggested in this work to overcome the main shortcomings of Eulerian-Eulerian and CFD-DEM approaches. DDPM has the powers of smooth implementation of realistic particle size distribution and tracking the discrete character of particles. It's also less computational cost than Eulerian-Eulerian approach [15] since coarse grid can be employed to perform grid-size-independent simulations and the application of the idea of the parcel.
Although several studies have been done in recent years, no attention has been paid to the effect of cuttings concentration and coupling way. Nonetheless, it is possible to account the impact of these parameters with propose approach. With this goal, this work seeks to investigate the impact of cuttings concentration and coupling way as well as the drilling fluid rheology, cutting characterisations (size, density, shape, and concentration), fluid velocity.

Experimental work
In general, the preliminary investigations are complementary to the numerical simulations. Lastly, the other ingredients were added to the mixture and mixed until all solid particulates disappear.

Computational Simulation Methodology:
The present work is using fluent (Ansys 15) to simulate the drilling fluid process. The fluent consists of Five consecutive steps; geometry, mesh, setup, solution and results. pre-processor. Three different sizes of meshes have been used to eliminate the dependency on the mesh size (see Table (2)). Figure (2) displays a good agreement between the grids in term of velocity magnitude, turbulent kinetic energy (k), wall shear stress, and turbulence intensity. The refined medium grid has been selected for the further simulation to make a balance between the computational time and the accuracy of the prediction. The three meshes size and characteristics are presented in Table (2).  Where: The general form of mass conservation or continuity equation for multiphase incompressible flows can be written as follows: The conservation of momentum or (Newton's Second Law) can be written as follows: In Lagrangian approach, Ansys Fluent predict the trajectory of particles by integrating the force balance on the particles. The force balance equates the particle inertia with forces applying on particles like drag force, gravity force, etc. (FLUENT, 2013). Particle force balance can be written as follows: Where F is an additional acceleration (force/unit particle mass), is the drag  Table 3. The cuttings material has been assumed to be Sandstone rock.

Effects of Cuttings Shape on the Cuttings Transport
As the drilling bit encroaches through the earth layers and crushing rocks starts, nonuniform cuttings shapes are produced. The proportion of particular shape relies on the formation type, and penetration rate and method. Three shape factors have been employed, namely 1, 0.9, and 0.8, with total cuttings concentration about 38 wt. %. The analysis result reveals the transportation of spherical cuttings is more than the transportation of the nonspherical cuttings, as shown in figure (7). As the cutting particle shape approaching spherical shape, the cuttings transport likely to be improved.

Fig. (7) Effects of cuttings shape on the cuttings transport at 600rpm
This trend can be explained according to Haider and Levenspiel correlation for calculating drag coefficient for non-spherical particles [16]. This correlation points out that increasing the shape factor of particle reduces the drag coefficient and drag force. Hence, the resistance to particles transport in the wellbore more likely to be lower. In terms of the

No.20 Journal of Petroleum Research & Studies (JPR&S)
170 results validation,  investigated the effects of particle shape on the hole cleaning process using CFD-DEM model. They found that the in-situ concentration of particles in the wellbore decreases with fluid flow rate. Also, the transportation of the spherical particle is better than the non-spherical ones for particular fluid velocity. Well agreement, regarding the concept, is obtained between the present results and Akhshik et al. results [17].
Effects of Cuttings Density on the Cuttings Transport The effects of particle density on the cuttings distribution and fluid carrying capacity have been studied. Three more particle true densities: 1500, 3000, and 4000 kg/m 3 , besides the case base particle density (2300 kg/m 3 ) have been employed. The volume fraction of cuttings in the effluent fluid outside the annular is inversely changed with a density of cuttings, as illustrated in Figure (8).
The higher density, the heavier cutting particles are released. Hence the fluid carrying capacity becomes weaker. Pronounced drag force dominates even the micro-sized particles of density above 3000 kg/m3. Furthermore, the cuttings distribution directly dominated by a density of cuttings. Where, the heavier the cuttings, the higher in-situ quantitative concentration can be obtained. In contrast, low-density particles can be carried by the fluid easier than others. Figure 8 reveals the distribution of cuttings volume fraction in the annular space with different particle densities under static condition. These results agree with Hussaini and Azar results; they suggested that mud annular velocity decreases in-situ cuttings concentration [18]. However, increasing the mud flow rate needs to be restricted to control the pressure drop, pumping cost, and wellbore stability. As the cutting particle shape approaching spherical shape, the cuttings transport likely to be improved. Similarly, the cuttings outlet volume fraction increases with inlet fluid velocity, as illustrated in figure (10) Also, the figure shows that the particles with higher sphericity can be smoothly transported during the hole cleaning process.

Effect of Drilling Stem Speed on the Cuttings Transport
Cuttings distribution within a wellbore space for different rotational speeds is illustrated in figure (11). The cuttings transport with 36% in-situ concentration has been enhanced as the rotational speed increases. 173 transportation of the non-spherical cuttings, as shown in figure (12). As the cutting particle shape approaching spherical shape, the cuttings transport likely to be improved. phase. Employing four-way coupling regime fulfils a realistic and robust interaction between the two phases. On the other hand, particle movement will be restricted due to collision with an adjacent particle or solid surface. Where, this collision can lead to a loss of particle kinetic energy, and hence reducing cuttings transport. Figure (13) content supports this argument, where pronounced variation between volume fraction from twoway and four-way coupling methods. As the cutting particle in two-way coupling (DDPM) does not affect contact dynamics, the particle accessible to transports to a surface.
Therefore, the quantity of drilling cuttings leaving the wellbore in DDPM case is greater than that in DDPM+DEM case. Longitudinal sectional contours of cuttings volume fraction depict a frivolous difference in cuttings distribution between DDPM and DDPM+DEM cases, as shown in figure (14).