International Journal of Chemical Engineering

Volume 2019, Article ID 7068989, 17 pages

https://doi.org/10.1155/2019/7068989

## CFD Analysis of Pressure Losses and Deposition Velocities in Horizontal Annuli

^{1}BID Group Technologies LTD., Deltech Manufacturing Division, Prince George, BC, Canada^{2}Texas A&M University at Qatar, Doha, Qatar^{3}King Faisal University, Al Ahsa, Saudi Arabia^{4}Memorial University of Newfoundland, St. John’s, NL, Canada^{5}Petroleum Institute, Abu Dhabi, UAE

Correspondence should be addressed to Rasel A. Sultan; ac.num@083sar

Received 31 October 2018; Accepted 5 January 2019; Published 3 February 2019

Academic Editor: Evangelos Tsotsas

Copyright © 2019 Rasel A. Sultan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Estimation of pressure losses and deposition velocities is vital in the hydraulic design of annular drill holes in the petroleum industry. The present study investigates the effects of fluid velocity, fluid type, particle size, particle concentration, drill string rotational speed, and eccentricity on pressure losses and settling conditions using computational fluid dynamics (CFD). Eccentricity of the drill pipe is varied in the range of 0–75%, and it rotates about its own axis at 0–150 rpm. The diameter ratio of the simulated drill hole is 0.56. Experimental data confirmed the validity of current CFD model developed using ANSYS 16.2 platform.

#### 1. Introduction

In the petroleum industry, predicting frictional pressure losses and settling conditions for the transportation of drilling fluids in the annuli are important for drilling operations. Inaccurate predictions can lead to a number of costly drilling problems. A few examples of such problems are loss of circulation, kicks, blockage, wear, abrasion, and improper rig power selection. The existing empirical models become less accurate as those involve many simplified assumptions. CFD simulations help to minimize such assumptions by using the physics-based Navier–Stokes equations to model the hydrodynamics of the flow system. Current work is focused on developing a comprehensive CFD model which is capable of considering the effects of all important drilling parameters, such as fluid velocity, fluid type, particle size, particle concentration, drill pipe rotation speed, and drill pipe eccentricity.

#### 2. Literature Review

The estimation of pressure loss in an annulus is more difficult compared with pipe flow due to the complexities in hydraulics resulting from the complex geometry [1, 2]. From an empirical perspective, the issue is usually addressed by replacing pipe diameter in the pipe flow models with an “effective diameter” of annulus. A number of definitions of “effective diameter” have been proposed till date. However, it is difficult to select a definition for a field application as those were developed and/or applied empirically. A comparison of multiple definitions in predicting pressure losses is presented by Anifowoshe and Osisanya [3]. Other issues that make the estimation of pressure losses in drilling holes difficult are the eccentricity and the rotational speed of inner drill pipe. Many studies have been done on the flow of non-Newtonian fluids in annuli to introduce empirical/analytical models which allow to take these effects into account [1, 3–10]. The results of the previous studies show that the annular pressure losses for non-Newtonian (power law) fluids flowing in a drill hole depend on drill pipe rotation speed, fluid properties, flow regimes (laminar/transitional/turbulent), diameter ratio, eccentricity, and equivalent hydrodynamic roughness.

Using commercially available CFD packages like ANSYS FLUENT to predict pressure losses for the annular transportation of drilling fluids is comparatively a new approach. Sorgun and Ozbayoglu [9] demonstrated the better performance of CFD model compared with the existing empirical models in predicting frictional pressure losses. Sorgun [8] investigated the effect of pipe eccentricity on pressure loss, tangential velocity, axial velocity, and effective viscosity by using CFD. Erge et al. [6] presented a CFD modeling approach which is applicable to estimate frictional pressure losses in an eccentric annulus with inner pipe rotation while circulating yield power law fluids. However, most of these CFD studies were limited to the laminar flow of a single phase in hydro dynamically smooth annuli.

Annular flow of drilling fluids containing cuttings, i.e., slurry, has not been studied in sufficient detail. Examples of works in the field of annular slurry flow are available in references [11–14]. The focus of these studies was to understand the hydrodynamics of the slurry flow in annulus from real-time experiments and to produce empirical models based on data analysis. Recently, different researchers [15–17] have used CFD in studying the transportation of slurry in annuli. Ofei [15] examined the effect of the rheological parameters of the carrying fluids on the velocity of solid. Sorgun and Ulker [16] compared the predictions of pressure losses obtained using artificial neural network (ANN) and CFD. Both methods produced comparable results. Sun et al. [17] studied the effects of inclination, rotational speed, and flow rate on the distribution of solid concentration and the frictional pressure loss. Similar to the single-phase annular flow works, most of these CFD studies were limited to the laminar slurry flow conditions.

#### 3. Methods

##### 3.1. CFD Simulation

In the current work, the CFD simulation model of the annular slurry flow is developed using ANSYS Fluent 16.2 platform. Following previous works [18–20], a multi-fluid granular model is used to describe the flow behavior of a fluid-solid mixture. The granular version of Eulerian model is selected as the multiphase model (Appendix C). This is because high solid volume fraction is expected to be used for this study and the granular version captures the hydrodynamics of high concentration slurries consisting of varying grain sizes. It allows modeling of multiple separate but interacting phases. The phases can be liquids, gases, or solids in nearly any combination. The Eulerian treatment is used for each phase, in contrast to the Eulerian–Lagrangian treatment that is used for the discrete phase model.

The description of multiphase flow as interpenetrating continua incorporates the concept of phasic volume fractions, which represent the space occupied by each phase. Each phase satisfies the laws of conservation of mass and momentum individually. The conservation equations are modified by averaging the local instantaneous balance for each of the phases [21] or by using the mixture theory approach [22]. A detailed description is available in Appendix A.

For Eulerian multiphase calculations, the phase-coupled SIMPLE (PC-SIMPLE) algorithm is used for the pressure-velocity coupling. PC-SIMPLE is an extension of the SIMPLE algorithm to multiphase flows [23, 24]. The velocities coupled by phases are solved in a segregated fashion. The block algebraic multigrid scheme used by the density-based solver is used to solve a vector equation formed by the velocity components of all phases simultaneously [25]. Then, a pressure correction equation is built based on the total volume continuity. Pressure and velocities are then corrected so as to satisfy the continuity constraints.

To ensure stability and convergence of iterative process, a second-order upwind discretization was used for momentum equation, and first upwind discretization was employed for volume fraction, turbulent kinetic energy, and its dissipation. Upwinding refers to the face value derived from quantities in the cell upstream, or “upwind,” relative to the direction of the normal velocity. When first-order accuracy is desired, quantities at cell faces are determined by assuming that the cell-center values of any field variable represent a cell-average value and hold throughout the entire cell; the face quantities are identical to the cell quantities. Thus, the face value is set equal to the cell-center value of the upstream cell when first-order upwinding is selected. In contrast, when second-order accuracy or second-order upwinding is desired, quantities at cell faces are computed using a multidimensional linear reconstruction approach [26]. In this approach, higher order accuracy is achieved at cell faces through a Taylor series expansion of the cell-centered solution about the cell centroid. The total simulation process is shown in Figure 1.