Narrow annular drilling such as casing-while-drilling technique is gaining popularity due to its ability to mitigate nonproductive time during oil and gas drilling operations. However, very little is known about the flow dynamics in narrow annular drilling. In this study, the Eulerian-Eulerian two-fluid model was used to examine the influence of Yield Power Law fluid rheological properties on cuttings transport in eccentric horizontal narrow annulus. The flow was assumed as fully developed, laminar, and transient state. The present simulation model was validated against experimental data, where a mean percent error of −1.2% was recorded. Results revealed an increase in the radial distribution of cuttings transport velocity in the wide annular region as the consistency index,

Drilling fluid rheological properties are important parameters which contribute to effective hole cleaning. Adari et al. [

In literature, most experimental studies on drilling fluids observed that the drilling fluid rheological curves (rheogram) conformed best to that of YPL fluid model. Ahmed and Miska [

Several experimental and numerical studies have also evaluated the effects of drilling fluid rheological properties on cuttings transport. Cho et al. [

In addition, other authors have utilized CFD approach to model YPL fluid through pipes and annuli. Bui [

It is evident that very rare or few studies on cuttings transport using YPL fluids exist in literature. As the oil and gas industries are developing the interest in the use of YPL fluids in drilling operations, there is need to conduct more research to understand the behavior of this fluid of interest on cuttings transport.

Several studies [

The present study adopts the inhomogeneous Eulerian-Eulerian two-fluid model to analyze the effect of fluid rheological properties on cuttings-YPL flow in eccentric narrow horizontal annulus. A finite volume method is used to solve the continuity and momentum equations. CFD methods have been proven to be very effective for multiphase flow problems due to their ability in handling unlimited number of physical and operational conditions as well as eliminating the need for expensive experimental and materials setups.

Within the context of this study, the radial distributions of cuttings transport velocity were observed in both wide and narrow annular regions. The wide region (sector A-A) is the gap between the top of the drillpipe and hole, while the gap between the bottom of the drillpipe and hole represents the narrow region (sector B-B) as shown in Figure

2D and 3D meshed sections of eccentric horizontal annular geometry.

The inhomogeneous (Eulerian-Eulerian) two-fluid model in ANSYS CFX 14.0, where both the liquid and solid phases are considered interpenetrating continua, is adopted in this study. Other models such as Eulerian-Lagrangian model, however, simulate the solid phase as a discrete phase and allows for particle tracking. The Eulerian-Eulerian model is preferred to the Eulerian-Lagrangian model due to its ability to handle high solid volume fractions. Furthermore, it accounts for particle-particle interaction and includes turbulence automatically. A drawback of this model is, however, the need for complex closure relations. The commercial software package ANSYS CFX 14.0 consists of the following five

The solid-liquid flow is assumed as (a) isothermal and (b) laminar and transient state.

The governing continuity equations for both liquid and solid phases could be expressed, respectively, as [

The forces acting on each phase and interphase momentum transfer term that models the interaction between each phase are given below [

For liquid phase,

Considering spherical particles, the drag force per unit volume is given as

For large solid volume fraction,

For spherical solid particles, ANSYS CFX employs the lift force model by Saffman [

Solid particles suspended in a liquid phase are affected by shear rate redistribution. The solid phase viscosity,

Equations (

There is singularity problem associated with the classical YPL viscosity model at vanishing shear rate. To alleviate this, the proposed YPL viscosity function by Mendes and Dutra [

At the inlet, a mass flow rate is specified, while a zero-gauge pressure is specified at the outlet boundary. At the pipe walls, different boundary conditions were used for both liquid and solids. The usual no-slip condition was imposed at the walls for the liquid phase, while for the solid phase, the free-slip condition was assumed at the walls to prevent the solid phase from adhering to the walls. This is consistent with real flow behavior of solid particles flowing near a solid boundary. The solid volume fraction in the domain was specified at the beginning of each simulation to correspond to the desired solid loading.

The annular 3D geometry of diameter ratio

Grid independent study.

The simulation of the two-phase solid-liquid flow was set up in three dimensions using ANSYS CFX 14.0 with the transport equations solved using CFX-Solver. The geometry dimensions, fluid rheological properties, solid properties, and operating parameters are presented in Table

CFD simulation matrix.

Simulation data | Diameter ratio |
---|---|

Flow behavior index |
0.31–0.75 |

Consistency index ( |
1.7–6.3 |

Yield stress ( |
2–8 |

Zero shear rate viscosity ( |
1100 |

Fluid density ( |
1020 |

Bulk fluid velocity ( |
0.50 |

Inner pipe rotation speed ( |
0 |

Outer diameter ( |
50.8 |

Inner diameter ( |
45.7 |

Eccentricity |
0.50 |

Cuttings density ( |
2650 |

Avg. cuttings size (mm) | 1.0 & 4.0 |

Rate of penetration, ROP (m/s) | 0.00508 |

The CFX-Solver is based on a finite volume method in which the flow equations are integrated over each control volume. The advection scheme is set to high resolution to satisfy both accuracy and boundedness, where the blend factor,

It should be noted that the complexity of the transport equations could not permit numerical convergence under steady state. However, all simulations were run in transient state. It is usually recommended that simulation of such steady state nature should first be run under transient state when it is difficult to attain convergence [

There is scarcity of data for cuttings transport study using YPL fluids. The most recent and only experimental cuttings transport study is conducted by Taghipour et al., where annular pressure losses were measured for cuttings-YPL fluid flow in inclined (30°) eccentric wellbore and are used to validate the two-phase CFD model. To validate the present model, the author simulated the experimental condition as presented by Taghipour et al. [

Experimental setup and operating conditions [

Inner diameter of casing, |
101.6 |

Outer diameter of pipe, |
50.8 |

Length of test section, |
12 |

Fluid density, |
1020 |

Cutting density, |
2400 |

Avg. cutting diameter, |
1.25 |

Cutting injection rate, |
0.05 |

Flow behaviour index, |
0.61 |

Fluid consistency index, |
0.09 |

Fluid yield stress, |
1.3 |

Avg. fluid velocity, |
0.54–1.3 |

Drillpipe rotation speed, |
0 |

Experimental and simulation comparison of pressure loss data.

The simulation results reported here include the effects of yield stress, consistency index, and flow behavior index on cuttings transport velocity in YPL fluid in eccentric horizontal narrow annulus. Measurements of the radial distributions of the cuttings velocity profiles were taken along sectors A-A and B-B or at the positions 0° and 180° (see Figure

Studies have shown that YPL fluids used in the field have a wide range of values of rheological properties. These rheological properties could include the following range of values [^{
n}, and flow behavior index,

The yield stress value evaluates the ability of the drilling fluid to suspend drilled cuttings during circulation. A high yield stress fluid is believed to transport cuttings better than fluid with low yield stress having similar density values. Figures

Effect of yield stress on cuttings transport velocity: (a) wide annular region and (b) narrow annular region.

The consistency index of a drilling fluid is a rheological property related to the cohesion of the individual particles of the fluid, its ability to deform, and its resistance to flow. Figures

Effect of consistency index on cuttings transport velocity: (a) wide region and (b) narrow region.

It should be noted that

On the contrary, due to the flow restriction induced by the narrow annular region, cuttings travelling in high ^{
n} leads to ~11.0% increment in the maximum cuttings velocity in the wide annular region (sector A-A), whereas ~37.7% reduction in cuttings velocity was recorded as ^{
n} in the narrow annular region (sector B-B).

The flow behavior index,

Effect of flow behavior index on cuttings transport velocity: (a) wide region and (b) narrow region.

Figure

3D profiles for ^{
n},

Accurate estimation of annular pressure losses is very vital when designing drilling hydraulic programs, particularly the equivalent circulating densities (ECD) required for efficient transport of drilled cuttings from the wellbore to the surface. Figure ^{
n} with approximately 132.6% increase in pressure loss. Last but not the least, increase in

Effect of rheology on annular pressure loss: (a) flow behavior index,

A study on the effect of rheological parameters on cuttings transport velocity in YPL fluid flowing in eccentric narrow horizontal annulus is analyzed using Eulerian-Eulerian two-fluid CFD model. The proposed viscosity model for YPL fluid by Mendes and Dutra [

Within the context of this study, the radial distributions of cuttings transport velocity were observed in both wide and narrow annular regions. The increase in yield stress of the carrier fluid from 2 to 8 Pa did not have much influence on the cuttings transport velocity in the wide region especially in the core region. However, there was much improvement in the cuttings transport velocity at the vicinity of the walls, indicating less cuttings bed accumulation. In the narrow gap, cuttings travelled much faster in low yield stress fluids as a result of their low resistance to flow compared to high yield stress fluids.

The study also revealed that carrier fluids with high consistency index value enhanced more cuttings transport especially in the wide annular region due to the fluid’s cuttings lifting ability. At the vicinity of the walls, cuttings travelled faster in low consistency index fluids due to the fluid’s tendency to high shearing and, hence, resulted in less cuttings bed formation. In the narrow region, however, cuttings travelled faster in low consistency index fluids due to their less resistance to flow.

Increasing the flow behavior index of the carrier fluid also showed much improvement in the cuttings transport velocity, especially in the core region of the wide annular gap. Meanwhile, carrier fluid with low flow behavior index transported cuttings better at the vicinity of the walls, an indication of less formation of cuttings bed. A reverse trend was, however, observed in the narrow annular gap, where there was significant cuttings transport in the carrier fluid with low flow behavior index. Three-dimensional flow distribution profiles have shown the actual dynamics of cuttings travelling in the eccentric annulus, where most of the cuttings were inclined to travel in the wide margin with less stress.

The YPL fluid model has been shown to fit much better rheological data of drilling fluids in the oil and gas industry compared to the Bingham plastic and power law fluid models. Furthermore, YPL fluids with high yield stress values reduce convective heat loss in most especially high temperature wellbores, thus possessing the very rheological properties which are important for an insulating fluid to perform well. It is noteworthy that YPL fluids have viscosities that increase significantly as shear-strain rate diminishes; hence, by increasing the viscosity of the fluid, the drilling engineer can gain partial control over convection heat loss. More importantly, YPL fluids tend to have relatively low viscosity at high shear rates (shear-thinning), making them easier to place initially, to bleed off pressure that may build up in the annulus equipped with venting capability, and to displace the drilling fluid in the event of well intervention. This study provides a guide to the drilling engineer on the selection of YPL fluid rheological properties which would enhance efficient transport of drilled cuttings in narrow horizontal wellbores.

It was further observed that the rheology of YPL fluids has significant effect on the annular pressure losses. Proper caution must be taken in selecting the fluid rheology to ensure efficient cuttings transport while maintaining a bottomhole pressure which will not fracture the formation.

Drag coefficient (—)

Solid particle mean diameter (m)

Outer diameter of inner pipe (m)

Inner diameter of outer pipe (m)

Hydraulic diameter,

Offset distance (m)

Gravity vector (m/s^{2})

Liquid phase volume fraction (—)

Solid phase volume fraction (—)

Consistency index (Pa·s^{
n})

Annular geometry length (m)

Hydrodynamic length (m)

Interphase momentum transfer

Drag force per unit volume (N/m^{3})

Lift force per unit volume (N/m^{3})

Flow behavior index (—)

Fluid Reynolds number (—)

Solid particles Reynolds number (—)

Vorticity Reynolds number (—)

Solid particle pressure (Pa)

Radial direction

Normalized radial distance

Rate of penetration (m/s)

Cuttings velocity at any radial distance (m/s)

Bulk fluid velocity (m/s)

Fluid phase velocity vector (m/s)

Solid phase velocity vector (m/s)

Axial direction.

Eccentricity

Fluid phase density (kg/m^{3})

Solid phase density (kg/m^{3})

Viscous stress tensor (Pa)

Diameter ratio

Zero shear rate viscosity (Pa·s)

Viscosity defined in (14) (Pa·s)

Liquid viscosity (Pa·s)

Apparent viscosity (Pa·s)

Relative viscosity

Solid viscosity (Pa·s)

Suspension viscosity (Pa·s)

Specific volume (m^{3}/kg)

Angular velocity (1/min)

Shear rate (1/s)

Rotation vector (1/min)

Circumferential direction.

The author declares that there are no competing interests regarding the publication of this paper.