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A three-dimensional computational fluid dynamics (CFD) study was carried out for drilling fluid flow with drill cuttings in open channels. The flow is similar to the return flow when drilling, stream containing drilling fluid, and drill cuttings. The computational model is under the framework of the Eulerian multifluid volume of the fluid model. The Herschel–Bulkley rheological model was used to describe the non-Newtonian rheology of the drilling fluid, and the computational model was validated with experimental results for two-phase flow in the literature. The effect of flow depth and flow velocity in an open channel was studied for drill cutting size of up to 5 mm and for a solid volume fraction of up to 10%. For constant cross section and short open channels, the effect of drill cuttings on flow depth and mean velocity was found to be small for particle sizes less than 5 mm and solid volume fractions less than 10%. High momentum force in the downward direction can carry the solid-liquid mixture at higher velocities than a lower density mixture. Higher inclination angles mean that the gravity effect upon the flow direction is more significant than the particle friction for short channels.

Open Venturi channel flow measurement might be an alternative to expensive Coriolis flow meters in measuring well return flows while drilling [

The open channel is located between the choke valve and the mud tank.

Several studies have been carried out on sediment flow in an open channel. The particle sizes in these studies were, however, in the 1

According to the Muste et al.’s [

Drill cuttings have a size range from clay-sized particles to coarse gravel, 2

An Eulerian multifluid volume of the fluid model (multifluid VOF) was used for the simulation of the granular particles. Each phase is a continuous phase. Three phases are considered in this study. The governing continuity equation for the

There are three equations similar to equation (

There are, one for each phase, three momentum equations from equation (

Figure

Computing cycle of transient multifluid VOF model for three-phase flow.

A rectangular channel was used for the 3D CFD simulations. The channel length was 1 m, width 0.3 m, and height 0.2 m. The mesh had 0.7 million structured hexahedral elements including inflation near the walls (see Figure

3D section of meshed open channel geometry. The rectangular channel height, width, and length are, respectively, 0.2 m, 0.3 m, and 1 m.

The inflation layers were added for accurately capturing the flow effects near the walls. The average mesh size was 25 mm, which is 5 times larger than the largest particle size used in the study. This avoids particles spanning the many fluid cells. Edge sizing was implemented to improve the resolution of the mesh. The mesh had low skewness (<0.8) and high orthogonality (>0.9). To optimize the grid sizes until the results become independent of grid size, a grid independence study was conducted. The inlet drill cutting mass flow rate was 1.12599 kg/s. The outlet drill cutting mass flow rate was monitored for different mesh sizes in the test. The results were taken after reaching the steady state. Table

Different mesh for mesh independency check.

Mesh 1 | Mesh 2 | Mesh 3 | Mesh 4 | Mesh 5 | Mesh 6 | |
---|---|---|---|---|---|---|

Hexahedral cells | 0.342 | 0.487 | 0.7 | 1.02 | 1.35 | 1.93 |

Solid mass flow rate comparison for different meshes. The number of elements in each mesh is given in Table

The drilling fluid used in this study was taken from Kelessidis et al.’ study [

Simulation flow parameters. Case 1 is used in this study. Case 2 is used for model validation.

Case 1 | Case 2 | |
---|---|---|

Fluid and solid | Water-bentonite suspension [ |
10% v/v Kaolin slurry [ |

Fluid density (kg/m^{3}) |
1165 | 1303 |

Particle density (kg/m^{3}) |
2650 | — |

Mean particle diameter (mm) | 5, 1 | — |

Inlet solid volume fraction (%) | 5, 10 | — |

Inlet velocity (m/s) | 1 | 0.567 |

Shape of the channel | Rectangular | Rectangular |

Channel inclination | 3 | 2 |

Yield stress |
11.3025 | 21.311 |

Flow consistency index ^{n}) |
5.9115 | 0.524 |

Flow behavior index |
0.2645 | 0.468 |

Based on the maximum Courant number, the time step is refined near the free surface in VOF calculations. The maximum allowed Courant number is 0.25 in this study. The global Courant number depends on the mesh size, velocity field, and time step size used for the transport equations. Volume fraction values are computed at the previous time step in the explicit approach of the multifluid VOF model, and the standard finite-difference interpolation scheme is used in ANSYS Fluent [

The computational method is due to the lack of experimental results for heavy particle non-Newtonian open channel flow and high computation cost, validated for an experimental case of two-phase non-Newtonian flow in open channel. Haldenwang’s [

The two-phase CFD model was validated using the experimental results published by Haldenwang [

Case 2: (a) a comparison between the 3D CFD result and the Haldenwang [

Open channel length should be considerably longer if a fully developed flow profile is to be achieved [

Figure

3D CFD results of flow depth along the channel for different drill cuttings sizes and volume fraction at steady state. The inlet velocity is 0.5665 m/s for all cases, and the total inlet volume flow rate value is equal for each case.

In all cases, the flow depth reduces along the channel length, which is due to the increase in velocity in the gravity flow. The highest cutting concentration gives the lowest flow depth due to the largest momentum.

Streamwise velocity with particles and without particles is shown in Figure

Steamwise velocity distribution with particle and without particle for the same inlet volume flow rate. The inlet velocity is 0.5665 m/s. The velocity is measured 0.7 m to the downstream from inlet of the channel.

Very high wall friction applies to particle flow because of higher particle concentrations (^{−6} s). This, however, requires a computational time that is unrealistic. The channel used in this study is 1 m long with a low solid concentration. The short channel helped to reduce the computational time by reducing the number of computational cells. The settling distance is greater than the channel length. Particle settling is therefore considerably smaller in the channel used in this study than a long channel. Therefore, the results from this study mainly apply on to not fully developed flow. Figure

Particle settling bottom wall, the flow direction indicates by the arrow. Drill cutting size is 5 mm and inlet volume fraction is 0.05. (a) The solid volume fraction of drill cuttings on the bottom of the open channel at steady state,

Drilling well return flow is a multiphase non-Newtonian flow of mainly drilling mud and drill cuttings. The effect of drill cuttings on open channel flow was studied, with the results being presented in this paper. This can be used for well return flow estimation. The multifluid VOF model 3D CFD simulations were carried out for drilling fluid flow with drill cuttings in open channels. The CFD model was validated using experiment results published in the literature. The effect of drill cutting size on flow depth was found to be small compared to the effect of the cuttings fraction. The drill cuttings volume fraction doubled from 5% to 10% in open channel flow, with the average variation of the flow depth being 2.5%. The effect of cuttings on flow depth in well return flow modeling for a short, prismatic (constant cross section) open channel was found to be small. The conclusion might be different for long and nonprismatic channels. The increase in particle friction due to the rise of the total particle volume is also small, and energy loss is negligible. The liquid level decreases for a higher solid fraction. Higher concentration acts as a higher net density. Thus, the higher density and approximately the same friction will yield a lower flow depth.

Lift force of

Virtual mass force of

Gravity vector (m/s^{2}), gas phase

Flow depth (m)

Turbulence kinetic energy (m^{2}/s^{2})

Liquid phase

Pressure shared by all phases (Pa)

Solid phase

Temperature of gas phase (K)

Temperature of liquid phase (K)

Temperature of solid phase (K)

Three-dimensional velocity components of

Average velocity (m/s)

Volume fraction of

Volume fraction of liquid phase

Volume fraction of gas phase

Volume fraction of solid phase

Interphase momentum exchange coefficient

Turbulence dissipation rate (m^{2}/s^{3})

Density of ^{3})

Stress-strain tensor of

The CFD and experiment data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

The economic support provided by the Research Council of Norway and Equinor ASA through project no. 255348/E30 “Sensors and models for improved kick/loss detection in drilling (Semi-kidd)” is gratefully acknowledged. The authors thank Per Morten Hansen and Andre Vagner Gaathaug for their assistance.