Journal of Petroleum Engineering

Volume 2016, Article ID 5743471, 10 pages

http://dx.doi.org/10.1155/2016/5743471

## Eulerian-Eulerian Simulation of Particle-Liquid Slurry Flow in Horizontal Pipe

Petroleum Engineering Department, Universiti Teknologi PETRONAS, 32610 Bandar Seri Iskandar, Malaysia

Received 25 July 2016; Accepted 14 August 2016

Academic Editor: Alireza Bahadori

Copyright © 2016 Titus Ntow Ofei and Aidil Yunus Ismail. 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

In this study, a computational fluid dynamics (CFD) simulation which adopts the inhomogeneous Eulerian-Eulerian two-fluid model in ANSYS CFX-15 was used to examine the influence of particle size (90 *μ*m to 270 *μ*m) and in situ particle volume fraction (10% to 40%) on the radial distribution of particle concentration and velocity and frictional pressure loss. The robustness of various turbulence models such as the -epsilon , -omega , SSG Reynolds stress, shear stress transport, and eddy viscosity transport was tested in predicting experimental data of particle concentration profiles. The -epsilon model closely matched the experimental data better than the other turbulence models. Results showed a decrease in frictional pressure loss as particle size increased at constant particle volume fraction. Furthermore, for a constant particle volume fraction, the radial distribution of particle concentration increased with increasing particle size, where high concentration of particles occurred at the bottom of the pipe. Particles of size 90 *μ*m were nearly buoyant especially for high particle volume fraction of 40%. The CFD study shows that knowledge of the variation of these parameters with pipe position is very crucial if the understanding of pipeline wear, particle attrition, or agglomeration is to be advanced.

#### 1. Introduction

Conveyance of slurries through pipelines is common throughout the worlds. Over the decades, the flow of slurries through pipelines had been a common practice for various industries such as the oil and gas, food, pharmaceutical, solid handling, tailing, and even power generation. Many factors affect slurry flow behaviour in pipelines. These include particle size, velocity profile, frictional pressure loss, and concentration profile [1–4]. Past studies have suggested many empirical correlations to predict slurry flow behaviour; nonetheless, the capability of these correlations is limited to some data range and experimental setup.

In the oil and gas industry, applications of horizontal well have increased especially in cementing operations and hydraulic fracturing treatment. Furthermore, in unconsolidated formations, oil is usually produced along with sand particles and transported through horizontal pipes. To have an efficient design, accurate prediction of the transport of slurry properties in horizontal pipe is required. Recently, CFD has become an effective tool for modelling complex multiphase flow behaviours as it has the capability to tackle unlimited number of physical and operation conditions.

Ekambara et al. [3] used CFD simulation to investigate the effect of in situ solids volume concentration, particle size, mixture velocity, and particle diameter on local time-averaged solids concentration profiles, particle and liquid velocity profiles, and frictional pressure loss. The simulated results were compared to experimental data from published literature with good agreement. The study revealed that particles were asymmetrically distributed in the vertical plane with the degree of asymmetry increasing with increasing particle size.

Nabil et al. [4] examined the effect of particle size on frictional pressure loss in a horizontal pipeline using both experimental setup and CFD technique. They observed that fine particle size recorded the least pressure loss, whereas coarse particle size recorded the highest pressure loss for each constant particle volume fraction (5% to 30%). CFD prediction of pressure loss was in agreement with measured experimental data especially at low particle volume fraction and fine particle size. Furthermore, the study revealed that the particle velocity profiles were asymmetric in nature and dependent on particle size. The degree of asymmetry was observed to be directly proportional to the particle size due to the gravitational effect and inversely proportional to the mixture velocity at constant volume fraction.

An approach related to slurry flow modelling started where one-dimensional (1D) Schmidt-Rouse equation [5] or equivalent to Hunt [6] was developed to relate the particle sedimentation rate to the turbulence exchange rate, as represented by solid eddy diffusivity. Based on this formulation, Karabelas [7] built an empirical model to predict the profile of particle concentration. Work done by him was then continued by Kaushal and coworkers [8–12] in developing a diffusion model. The model proposed a modification for solid diffusivity for coarse slurry flows and their functions show that the increase in solid concentration is due to the increase in the solid diffusivity. However, the model was formulated without taking into consideration solid diffusivity on both particle size and pipe Reynold number [13]. By comparing their pressure loss data with modified Wasp model, they found a match at higher fluid velocity; however, significant deviation shows at flow velocities near the deposition velocity [14].

A 1D two-layer model considering coarse particle slurry was developed by Wilson [15]. The author considered each layer with a uniform velocity and particle concentration because he assumes the particles to be very coarse. Doron et al. [16] developed a 2D model to predict flow patterns and pressure loss which is similar to Wilson’s model, where the authors assumed the lower layer as stationary. Wilson and Pugh [17] expanded the dispersive force model by accounting for particles suspended by fluid turbulence and contact-load (Columbic) friction. Their model prediction of particle concentration and velocity profile was in a good agreement with measured experimental data.

Doron and Barnea [18] extended their study to a three-layer model of slurry fluid flow in horizontal pipeline which consists of a suspended layer, a bed layer, and a dispersive layer which lies in between the suspended and bed layers. They assumed the dispersive layer to be high in concentration gradient where a no-slip condition was imposed between fluid and solid particles. The model prediction successfully showed assent with experimental data. Ramadan et al. [19] also proposed a three-layer model. The model predictions were then compared with experimental data where satisfactory agreement was achieved.

Messa and Malavasi [20] proposed a new two-fluid model for the simulation of fully suspended liquid-solid slurry flows in horizontal pipes. The model is claimed to address wall boundary conditions for solid phase, viscosity of the slurry mixture which incorporates particle shape, and a solution algorithm which reduces computational burden. The authors emphasised that the new model increased the accuracy of the pressure gradient predictions without affecting the model’s capability in reproducing other engineering features such as solid volume fraction and velocity distributions. Ma et al. [21] conducted a CFD study for calculating erodent particle trajectories in slurry flow. It involves the capturing of the movement of erodent particles using the discrete phase method (DPM) and calculating the interfaces between fluid phase and gas phase using the volume of fluid (VOF) method. The authors revealed that their model results were in reasonable agreement with experimental observations in terms of normal impact velocity on the specimen surface. Recently, Miedema [22] proposed a framework for predicting head loss and limit deposit velocity in slurry flow. The framework is based on constant spatial volumetric concentration curves and uniform sand or gravels for five flow regimes in Newtonian fluid, namely, the stationary or fixed bed regime, the sliding bed regime, the heterogeneous regime, the homogeneous regime, and the sliding flow regime. The author concluded that the new framework explained the behaviour of very small particles in terms of the mobilisation of the lubrication effect of the particle poor viscous sublayer.

In this study, the effects of particle size ( to ) and volume fraction (10% to 40%) which are typical of slurry conditions in the oil and gas industry are analysed on the radial distribution of particle concentration and velocity and frictional pressure loss in horizontal pipe using CFD method. The findings are helpful to understand slurry transport behaviour on pipeline wear, particle attrition, or agglomeration.

#### 2. Materials and Method

A commercial CFD software ANSYS-CFX 15.0 is implemented in this study. The inhomogeneous Eulerian-Eulerian model, sometimes called the two-fluid model, which regards both continuous (liquid) and dispersed (solid) phases as interpenetrating continuum is used to model the slurry flow. The Eulerian-Eulerian model is best suited for high volume fractions of the dispersed phase which is averaged over each control volume. Each phase is governed by similar conservation equations and modelling is needed for interaction between the phases, turbulent dispersion of particles, and collision of particle with walls. A drawback of this model is, however, that complex closure relations are required. The following continuity and momentum equations representing the two-phase flow model are described for the sake of brevity.

##### 2.1. Continuity Equations

The volume-averaged, incompressible, isothermal, and transient Navier-Stokes continuity equations for both liquid and solid phases are, respectively, given by [23, 24]where and are the volume fraction of liquid and solid, respectively, and and are the velocity vector of liquid and solid, respectively. The mass exchange between the liquid and solid phases due to reaction or combustion is not considered.

##### 2.2. Momentum Equations

The momentum balance for the liquid and solid phases which includes the interphase momentum transfer term that models the interaction between each phase is given by the Navier-Stokes equations as [23, 24]where is the gravity term, is the thermodynamic pressure, and are density of liquid and solid, respectively, is the sum of interfacial forces including drag force and lift force, and and are the shear stress tensor for both liquid and solid, respectively.

The liquid phase and solid phase stress tensors can be represented, respectively, aswhere and are the shear liquid and solid viscosity, respectively, and is the bulk solid viscosity which accounts for the resistance of the granular particles to compress and expand and has the form [25]Similarly, is the solid pressure that represents the solids phase normal forces caused by particle-particle interactions and takes the form [26]The first term represents the particle velocity fluctuations and the second term represents the particle collisions.

The shear solid viscosity can be represented as the sum of the kinetic and collisional contributions asThe kinetic and collisional component of the solids viscosity are modelled, respectively, as [26]

##### 2.3. Interphase Models

###### 2.3.1. Drag Force

For spherical particles, the drag force per unit volume is given asFor densely distributed solid particles, where the solid volume fraction , the Wen and Yu [27] drag coefficient, , model may be utilised. This model is modified and implemented in ANSYS-CFX to ensure the correct limiting behaviour in the inertial regime aswhere and .

For large solid volume fraction, , the Gidaspow drag model may be used with the interphase drag force per unit volume defined as [26]In this study, both Wen and Yu and Gidaspow drag models were employed depending on the computed solid volume fraction.

###### 2.3.2. Lift Force Model

For spherical solid particles, ANSYS-CFX employs the Saffman and Mei lift force model asSaffman [28, 29] correlated the lift force for low Reynolds number past a spherical solid particle where and . For higher range of solid particle Reynolds number, Saffman’s correlation was generalised by Lun et al. [25] as follows:where

###### 2.3.3. Turbulence Model

The turbulence model offers a good compromise in terms of accuracy and robustness for general purpose simulations. It is a semiempirical model based on transport equation for the estimation of turbulent length scale and velocity scale from the turbulent kinetic energy and dissipation rate [30]. In multiphase flow, the transport equations for and are phase dependent and assume a similar form to the single-phase transport equations, respectively, aswhere , , , , and are standard constants. and are the interphase transfer for and , respectively.

Diffusion of momentum in phase is governed by an effective viscosity asThe model assumes that the turbulence viscosity is linked to the turbulence kinetic energy and dissipation by the relationThe governing sets of partial differential equations were discretised using finite volume technique. The discretised equations together with initial and boundary conditions are solved iteratively for each control volume of pressure drop and cuttings concentration using ANSYS-CFX 15.0 solver.

##### 2.4. Geometry Modelling and Meshing

The three-dimensional (3D) horizontal pipe geometry was modelled using ANSYS 15.0 Workbench Design Modeller. The dimensions of the geometry were taken from literature [31]. In order to ensure a fully developed flow, a hydrodynamic entrance length was computed using the following expression: where is the Reynolds number of the liquids and is the hydraulic diameter.

The geometry was meshed into small grid cell using unstructured tetrahedral mesh type with inflation layers created at the boundary of the pipe to accurately capture the flow effect in that region [32]. Figure 1 presents the meshed 3D geometry. The number of elements were optimised until the results were no longer affected. In this study, the optimised number of elements used was 801,848.