Study on hydrodynamic characteristics of oil-water annular flow in 90° elbow

Journal Pre-proof Study on Hydrodynamic Characteristics of Oil-Water Annular Flow in 90◦ Elbow Junqiang Wu Wenming Jiang Yang Liu Yi He Jianan Chen Liang qiao Tianyu Wang

PII:

S0263-8762(19)30531-3

DOI:

https://doi.org/doi:10.1016/j.cherd.2019.11.013

Reference:

CHERD 3896

To appear in:

Chemical Engineering Research and Design

Received Date:

20 June 2019

Revised Date:

10 October 2019

Accepted Date:

11 November 2019

Please cite this article as: Wu, J., Jiang, W., Liu, Y., He, Y., Chen, J., qiao, L., Wang, T.,Study on Hydrodynamic Characteristics of Oil-Water Annular Flow in 90circ Elbow, Chemical Engineering Research and Design (2019), doi: https://doi.org/10.1016/j.cherd.2019.11.013

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Study on Hydrodynamic Characteristics of Oil-Water Annular Flow in 90° Elbow Junqiang Wu 1,2, Wenming Jiang1,2,*, Yang Liu 1,2, Yi He3, Jianan Chen1,2, Liang qiao1,2, Tianyu Wang1,2 1

College of Pipeline and Civil Engineering, China University of Petroleum (East China),

Qingdao 266580, China 2

Shandong Key Laboratory of Oil & Gas Storage and Transportation Safety, Qingdao

266580, China

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Petrochina Changqing Oilfield Company Oilfield Development Division, Xi’an 710061,

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China

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Abstract: The transportation of heavy oil surrounded by water annular can significantly reduce the resistance and reduce energy consumption. In the process of conveying high

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viscosity oil, it will inevitably pass through elbow components. In the present study, the stability in the development of core annular flow (CAF) by the influence of the elbow was

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investigated by computational fluid dynamics (CFD). The simulated data matched well with the previous experimental data and empirical correlation, which indicates the reliability and practicability of the model. The effects of inlet water fraction, the oil-water property (density

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ratio, viscosity ratio), and the geometric parameters (diameter ratio, curvature ratio) on

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hydrodynamic performance, eccentricity and oil transportation efficiency were analyzed, and the results could provide a reference for the design of 90° elbow structures and the

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optimization of flow parameters. Keywords: Elbow; Core-annular flow (CAF); Heavy oil transportation; Eccentricity; Oil transportation efficiency 1. Introduction

With the development of light oil exploitation, the oilfield has entered the stage of heavy oil exploitation. However, due to its high viscosity and excessive resistance, heavy oil is less likely to be directly piped (Vanegas and Bannwart, 2001; Li et al., 2012; Ko et al., 2002). Among the many conveying methods, water lubricated transportation is considered to be an Corresponding Author Phone: +8615053255692; E-mail: [email protected] Page 1 of 23

energy-efficient conveying technology, which confines the core oil flow to the center of the pipeline, and low-viscous water layer flows along the wall of the pipeline. In the past few decades, several studies on CAF have been observed. Isaac and Speed (1904) first proposed in their patent that water can be used to wrap core oil in pipelines to reduce resistance during transportation. After that, a series of experimental studies were carried out on CAF transportation. Charles et al. (1961) conducted experiments in a pipe with a diameter of 1 inch. It was found that when the oil-water density is equal and the oil-water

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velocity ratio is 4.54, the oil-water core annular flow can be observed. Joseph et al. (1996) proposed an effective viscosity standard for stable annular gas-liquid and liquid-liquid flows.

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The annular flow is stable when a liquid having a higher effective viscosity occupies the core region and the annular region is a liquid of lower viscosity. Subsequently, the problem of

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restarting CAF transportation was introduced by Joseph et al. (1997). The experiment shows that when the pipeline was stopped and restarted, the oil flow adheres to the pipeline, which

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causes difficulty in restarting. Lum et al. (2006) carried out an experimental study on oil-water annular flow in inclined pipelines. By changing the volume fraction of oil, the law of pressure gradient, velocity ratio, mixing speed, and friction in annular flow was obtained.

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Rodriguez and Bannwart (2006) analyzed the experimental data of the velocity, wavelength,

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amplitude and waveform curve of the interface wave of the core flow of heavy oil and water in a vertical glass pipe. The results showed that the measured wavelength was lower than two

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pipe diameters in all cases, and the shorter the wavelength, the higher the wave peak. Silva (2006) studied the variation of wettability of heavy oil on the inner surface of pipeline in heavy oil-water annular flow. The results showed that hydrophilic or oleophobic materials can be used as the inner coating of the pipe wall to reduce scaling. Rodriguez et al. (2009) carried out in-situ CAF experiments in a pipeline with a length of 274 m and a diameter of 7.7 cm. The pressure loss of CAF transportation was four times lower than that of single-phase oil flow. Sharma et al. (2011) conducted a hydrodynamic study on the CAF through a 180° U-tube, it was found that the flow direction of the two-phase flow through the bend has a significant influence on the phase distribution of the downstream oil and water,

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while the bending geometry could be neglected. In addition, some theoretical studies have been proposed for CAF. Bannwart (1998) applied the theory of motion wave to study the propagation velocity of interface wave in oil-water annular flow and proposed a general correlation, and the interfacial tension played a vital role in forming a stable CAF was proposed by Bannwart (2001). Ooms and Poesio (2003) have payed attention to the buoyancy on the core caused by the density difference between the core and the annular layer. Rodriguez and Bannwart (2006) analyzed the analytical model of the core-annular flow in the

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vertical pipeline and derived the differential equation of the liquid-liquid interface shape, and after explored the stability of the core annular flow by comparing the theoretical results with

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the experimental data, a general stability criterion was proposed by Rodriguez and Bannwart (2007). Goldstein et al. (2017) gave an exact solution of the eccentric CAF in the inclined

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pipe, which proved that the upward inclined pipe was not conducive to CAF transport and was independent of the density of the annular layer fluid. Babakhani Dehkordi et al. (2019)

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studied the effect of oil core eccentricity and flow characteristics of oil-water annular flow through abruptly variable cross-section, which provided a theoretical guidance for water annular flow through irregular pipe.

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In recent years, with the development of computational fluid dynamics (CFD), some

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commercial software has begun to be applied to the study of CAF, which has accelerated the research of CAF to some extent. Ghosh et al. (2010) used Fluent software to simulate vertical

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CAF downflow, the study shows that the frictional pressure gradient increases with the increase of the apparent velocity of oil and water, and the pressure gradient increases more obviously when the oil velocity increases. Subsequently, the flow characteristics of CAF in 180° elbow was studied by Ghosh et al. (2011), it has been found that with the increase of curvature radius, the pressure drop of two-phase flow approaches that of single-phase oil, and the drag reduction effect of CAF transportation decreased. Jiang et al. (2014a) simulated the flow of CAF in U-shaped elbow based on Euler model and concluded that Euler model was suitable for simulating oil-water annular flow through U-shaped elbow, and the results are similar to VOF model. After that, Jiang et al. (2014b) simulated CAF through a Π pipe. The

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results revealed the velocity distribution and interfacial structure of CAF when passing through Π pipe, which provides a reference for optimizing operation . Babakhani Dehkordi et al. (2017a) used high-speed camera image processing technology to obtain detailed information of the flow field when oil-water two-phase flow passed through a sudden expansion. After that, to obtain the characteristics of two-phase flow, CFD technology was used to study the oil-water flow through the sudden expansion by Babakhani Dehkordi et al. (2018), it was found that the simulated results and experimental data were in good agreement.

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Subsequently, Ooms et al. (2015) and Park et al. (2015) have begun to focus on the flow of CAF in 90° elbows, they have studied the effects of interfacial tension and secondary flow

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on the flow characteristics of the CAF in the elbow. However, there are few studies on the flow characteristics of CAF in 90° elbows concerning flow parameters and pipe geometry

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parameters. The purpose of this study was to investigate the flow characteristics of CAF flowing through 90° elbow, and the effects of inlet water fraction, oil viscosity, oil density,

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diameter ratio, curvature ratio on hydrodynamic performance, eccentricity and pressure drop. 2. Model development

Due to the influence of centrifugal force, in order to fully reflect the internal flow field

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of the elbow, the three-dimensional model was used in this study. The specific structure of the

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elbow is shown in Fig. 1. The oil inlet diameter is 7.44 mm and the water inlet is an annular inlet, the diameter of the pipe is 9.52 mm, the curvature radius of the pipe is 28.56 mm, the

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curvature ratio is 1/6, and the length of the straight pipe is 20 mm (Park et al., 2015).

Fig.1-The structure of curve pipeline

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2.1 Governing equation The common two-phase flow calculation models include VOF model, Eulerian model and Mixture model. Choosing the right model is the key to success. It is considered

that

high viscosity oil and water are two kinds of liquids which are incompressible and immiscible with each other. And in order to fully reflect the characteristics of the fluid interface.

the

VOF model is applied for numerical calculation (Ingen Housz et al., 2014; Kaushik et al., 2012).

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The continuity equation is as follows:

(  )    (  U)  0 t

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where, ρ U, t are density, velocity and time, respectively.

(1)

In the VOF algorithm, FLUENT solves only one momentum equation for the entire flow

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field region, as shown in Equation (2) below. The solution of the momentum equation

of the fluid in each phase.

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depends on parameters such as density ρ and viscosity μ determined by the volume fraction

 (  U)    (  U U)   P    [  ( U   UT )]  (  g )  F t

(2)

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where P, g, F, and μ are the pressure in the flow field, the acceleration of gravity, the force

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acting on the system, and the viscosity of the flow system, respectively. 2.2 Turbulence model

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Due to the fact that the heavy oil always maintains a laminar flow during the process of water lubricated transportation, the water layer always maintains a turbulent state. Therefore, the standard k-ε model is selected (Babakhani Dehkordi et al., 2017b; Tripathi et al., 2015; Duran et al., 2009).

The equation for the standard k-ε model is: ( k t )    (  k t U)   ( t   k t )  2 t Eij Eij   t t k

 (  t )   2   (  t U)  ( t    t )  C1 t 2  t Eij Eij  C2  t t  kt kt

(3)

(4)

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t  C 

kt2 t

(5)

1 U U j Eij  ( t  ) 2 X j X i

(6)

where, kt, εt, μ t, are the turbulent kinetic energy, dissipation rate and eddy viscosity respectively. The constant are taken as Cμ=0.09, σk=1, σε=1.3, C1ε=1.44, C2ε=1.92. 2.3 Surface tension and wall adhesion

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The interfacial tension model used in FLUENT is the continuous interfacial tension model (CSF). The model takes the interfacial tension as the source phase processing of

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momentum equation in VOF model (Beerens et al., 2014; Ghosh et al., 2009). In the CSF model, the normal vector of n is defined as the gradient of the volume fraction of the q phase

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at the interface:

n   q

(7)

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Defining the curvature К as the divergence of the unit normal vector n:

   n

(8)

 n n n

(9)

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The expression of the interfacial tension is: Fovi   ij

 ki   i 1/ 2( i   j )

(10)

where ρ is the average density obtained by calculation. The above equation shows that the source phase of the surface tension in the grid is proportional to the average density of the grid. 2.4 Evaluation Parameters 2.4.1 Eccentricity Due to the different properties of the core and the liquid annular, the core portion will inevitably float or fall, and the core portion will deviate from the center of the pipe and become an eccentric CAF, which will eventually affect the stability of the CAF. For this

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purpose, the effects of fluid parameters and pipe geometry parameters on eccentricity are studied in this paper. For this, the eccentricity e is defined as follow (as shown in Fig. 2): e

h R1  R2

(11)

where h is the distance between oil core and pipeline center, R1 and R2 are the radius of pipeline and the radius of oil core, respectively, and in the following sections, all we

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discussed is the eccentricity of the oil core at the exit of the elbow.

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Fig.2-Schematic diagram of eccentric CAF

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2.4.2 Average Volume Fraction of Oil

In order to fully reflect the distribution of the oil phase varies in 90° elbow, the oil

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volume fraction (α0) in the elbow was studied.

0 

1 n   oi Ai A i 1

(12)

where Ai and A are the area occupied by oil and the area of cross-section, respectively. The empirical formula of α0 proposed by Arney et al. (1993) is:

 0  1   [1  0.35(1   )]

(13)

β is the volume fraction of water at the inlet and defined as follows:



Qw Qw  Qo

(14)

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where Qo and Qw are volumetric flow rates of oil and water, respectively. 2.4.3 Pressure drop and Oil transportation efficiency Compared with the conventional oil transportation method, the CAF transportation reduces the oil delivery capacity even though the resistance decreases under the same conditions. Therefore, we use the concept of "oil transportation efficiency (q)" to discuss the benefits of CAF transportation, which is defined as "average oil delivery per unit friction

Qh P / l

(15)

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q

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pressure drop gradient".

where Qh is average oil delivery and ΔP/Δl is unit friction pressure drop gradient.

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3. Numerical simulation 3.1 Meshing of the model

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In this paper, the mesh generation in computational domain is accomplished by software ICEM. The mesh independence test has been carried out, and the results are shown in Fig. 3.

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It confirms that when the number of meshes increases from 240653 to 451254, the volume fraction of oil at different locations does not change much, in order to ensure that the

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oil-water interface is clear enough, the final number of selected meshes is 240653.

Fig.3-Mesh independency 3.2 Solution strategy and convergence criterion In order to understand the flow characteristics of oil-water two-phase flow, the oil phase

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was used as the primary phase and the water phase as the secondary phase, the transient simulation with a time step of 0.0001s was carried out. The PISO scheme was adopted to solve the pressure-velocity coupling. The first-order upwind method is selected to discretize the momentum, turbulent energy, and dissipation rate equations. When the residuals are reduced by five orders of magnitude, all calculated variables are considered convergent. 3.3 Boundary condition Both oil and water inlets are velocity inlet boundary conditions, the initial conditions

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are : at 0
pipeline wall is set to 27° (Jiang et al., 2014b).

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4. Validation

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no-penetration boundary conditions. In addition, the contact angle between water and

Due to the fact that there are few experimental studies on the CAF in the 90° elbow in

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the literature, the numerical results of this paper are compared with the 180° elbow to verify the accuracy of the numerical method (Sharma et al., 2011). Experimental photograph and simulated contour of CAF through 180° elbow at Vso=0.15 m/s and Vsw=0.3 m/s are shown

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in Fig. 4a, and the comparison between numerical results and empirical values of the 90°

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elbow in present study is shown in Fig. 4b. It can be seen that the numerical results are in

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good agreement with the experimental and empirical values.

Fig.4a-Comparison of experimental and numerical result during CAF through the 180° elbow

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Fig.4b-Comparison of numerical and empirical values 5. Results and discussion

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After verification, the model is used to obtain useful information on CAF through 90° elbow. In the following section , the development of CAF are reported. Next, the

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hydrodynamic of oil-water core flow are discussed about inlet water fraction, the oil-water property (density ratio, viscosity ratio), and the geometric parameters (diameter ratio,

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curvature ratio). Subsequently, the pressure drop and oil transportation efficiency of the CAF through the 90° elbow are analyzed.

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5.1 Development of water-oil core annular flow Fig. 5 is a cross-sectional contour of oil phase volume distribution at different locations

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at different times. Fig. 6 is the oil phase distribution curve at different positions in the elbow at t=0.4s. As can be seen from Fig. 5 and Fig. 6, the oil core gradually moves toward to the outer-side of the curved pipe as it passes through the curved portion, and the core deforms under the action of centrifugal force, but it never contaminated the inner wall.

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Fig.5-Annular flow image developed over time; Vso=0.31 m/s and Vsw=0.19 m/s. (O: outer

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curve, I: inner curve)

Fig.6-Different position of oil core inside the pipe

5.2 Hydrodynamic study The numerical simulation method can well predict the internal flow field. Fig. 7 and Fig.

8 show velocity, pressure and secondary flow contours at different locations of the CAF passing through the 90° elbow at Vso=0.31 m/s and Vsw=0.19 m/s. Fig. 7 depicts the velocity and pressure contour of the CAF as it passes through the elbow. At an angle of θ=0, the velocity in the elbow is uniform, and the velocity in the central region is higher than the velocity in the annular region. However, with the increase of the

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angle, at an angle of θ=π/2, under the action of centrifugal force, the velocity of the outer-side of the elbow is significantly higher than that of the inner-side of the elbow. At the same time, as the angle of the elbow increases, the pressure near the outer side of the elbow increases, and the pressure build-up in the outer annular region pushes the oil core out of the pipe wall, which is also the reason why the oil core passes through the elbow and still does not touch the

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pipe wall.

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Fig.7-Velocity and pressure contour during core annular flow through the elbow; Vso=0.31 m/s, Vsw=0.19 m/s

The left side of Fig. 8 is the secondary flows at different locations in the elbow, and the

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right side is an enlarged view of the secondary flow at the position of θ=π/4. It can be seen

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from the figure that there is no secondary flow at the entrance of the elbow (θ=0), but with the increase of the angle, the secondary flow is observed at θ=π/8, θ=π/4 and θ=3π/8 positions,

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while the secondary flow almost disappears at θ=π/2 positions. From the enlarged view, we can clearly see that the secondary flow occurs in the water area, and the circulating flow in the water layer is upward along the oil-water interface and downward along the pipe wall, which can better explain why the oil core does not contact the pipe wall when the CAF passes through the elbow.

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f

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Fig.8-Secondary flows in elbow at different locations; Vso=0.31 m/s, Vsw=0.19 m/s To fully understand the oil-water distribution in the elbow, the effects of different inlet

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water fraction, oil density, oil viscosity, oil inlet diameter and curvature ratio on the volume distribution of the two fluids and eccentricity of oil core were studied. The oil-water

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hydrodynamic effects are described by the eccentricity E (eq 11) and the area-weighted average of the oil volume fraction α0 (eq 12). Where E represents the eccentricity of the oil

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core at the exit of the elbow (As mentioned in section 2.4.1), and α0 represents the average volume fraction of the oil phase in the entire elbow (As mentioned in section 2.4.2).

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Fig. 9 is the oil core eccentricity and oil phase volume fraction at Vso=0.31m/s with different inlet water fraction. As can be seen from the figure, the volume fraction of oil phase

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decreases with the increase of inlet water fraction, while the eccentricity increases first and then decreases. Although the eccentricity is low when the inlet water fraction is about 0.7, the

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volume fraction of the oil phase in the pipeline is also low at this time. Therefore, in order to maintain the eccentricity at a lower value and the oil phase fraction at a higher value, the inlet water fraction should be maintained at 0.2-0.3 when the CAF is transported in the elbow.

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Fig.9-Eccentricity and volume fraction of oil phase at different inlet water fraction

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5.2.1 Effect of oil density

Fig. 10a shows the effect of different oil density on eccentricity and volume fraction of

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oil in the elbow at Vso=0.31 m/s and Vsw=0.19 m/s. It indicates that the density of the oil has little effect on the oil phase fraction in the elbow, and as the density of the oil increases, the

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eccentricity of the oil core increases, but in the horizontal pipe, the density of the oil increases, the eccentricity of the oil core decreases.

Because the density of the oil in the elbow pipe is

increased, which leads to an increase of centrifugal force, and eventually leads to an increase

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in the eccentricity of the oil core.

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5.2.2 Effect of oil viscosity

The effect of different oil phase viscosities on oil core eccentricity and oil volume

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fraction is shown in Fig. 10b. It is evident that the viscosity of the oil still has little effect on the volume fraction of the oil phase in the elbow, and as the viscosity of the oil increases, the eccentricity of the oil core decreases. Therefore, when the CAF passes through the elbow, the higher the viscosity of the oil, the less likely the oil core will pollute the wall of the pipe. 5.2.3 Effect of oil inlet diameter Fig. 10c depicts the effect of oil inlet diameter (D1) on eccentricity and volume fraction of the oil phase. It can be clearly found that the volume fraction of the oil phase in elbow increases with the increase of the diameter of oil inlet, and the eccentricity decreases with the increase of the diameter of oil inlet. Because as D1/D increase, the effect of secondary flow

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on oil core is more obvious, which pushes the core away from the inner wall. Therefore, in the actual conveying process, the smaller the annular area of the CAF, the larger the volume fraction of the oil phase in the elbow, and the less likely the oil core is to contaminate the pipe wall. 5.2.4 Effect of curvature Fig. 10d represents the relationship between curvature ratio and volume fraction of oil, curvature ratio and eccentricity. It can be observed that the curvature ratio of the elbow has

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little effect on the volume fraction of the oil phase, but it has a more significant impact on the eccentricity. The eccentricity of the core fluctuates with the increase of the curvature. When

b

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a

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R/D=2.5 or 4, the eccentricity is the smallest, which is most conducive to CAF transportation.

c

d

Fig.10-Eccentricity and volume fraction of oil phase at different operating conditions 5.3 Pressure drop and Oil transportation efficiency As mentioned in Section 2.4.3 above, when evaluating the process of conveying heavy

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oil by CAF, it is necessary to consider both important parameters of oil delivery capacity and energy consumption. It is worthwhile to study the methods of oil transportation that can increase oil delivery or reduce energy consumption. Therefore, "oil transportation efficiency" is used to discuss the benefits of CAF conveying at 90° elbow. Fig. 11 reflects the effect of inlet water fraction on pressure drop and oil transportation efficiency at Vso=0.31 m/s. It can be seen from the figure that the pressure drop increases with the increase of the inlet water fraction, but at this time, the oil transportation efficiency

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decreases, and it is known from the previous section 5.2 that if the eccentricity is small, the water fraction should be maintained at a lower value. Therefore, in this study, when using the

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CAF to transport heavy oil, the inlet water fraction should be maintained at a low value of

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around 0.2-0.3.

Fig.11-Variation of pressure drop and oil transportation efficiency with inlet water fraction 5.3.1 Effect of oil density The effect of density on the pressure drop and oil transportation efficiency is shown in

Fig. 12a. It can be observed that as the oil density increases, the pressure drop of the CAF in the elbow increases, but oil transportation efficiency decreases. Therefore, to ensure that the oil transportation efficiency maintained at a high value, the lower density oil should be transported as much as possible, which is also consistent with the conclusion in the previous section 5.2.1 that in order to reduce the eccentricity, the density should be maintained at a low value.

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5.3.2 Effect of oil viscosity Fig. 12b depicts the effect of oil viscosity on pressure drop and oil transportation efficiency in a 90° elbow. It can be clearly seen from the curve that as the viscosity of the oil phase increases, the pressure drop increases, and the oil transportation efficiency decreases. Therefore, to maintain a high oil transportation efficiency in a specific range, the oil viscosity should be lower. However, the lower the viscosity of the oil, the higher the eccentricity (as

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oil transportation efficiency should be considered comprehensively.

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discussed previously). In the actual transportation process, the influence of eccentricity and

5.3.3 Effect of oil inlet diameter

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The effect of the oil inlet diameter (D1) on the pressure drop and the oil transportation efficiency is shown in Fig. 12c. Although the pressure drop increases as D1 increases, oil

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transportation efficiency also increases. Moreover, the volume fraction of oil increases with the increase of D1, and the eccentricity decreases as D1 increases. In summary, the thinner

5.3.4 Effect of curvature

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the water layer, the more favorable the CAF passes through the 90° elbow.

Finally, the influence of curvature of the elbow on pressure drop and oil transportation

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efficiency is studied. As shown in Fig. 12d, the pressure drop decreases with the increase of

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curvature ratio. When R/D increases to 3.5, the pressure drop has basically remained unchanged; on the contrary, oil transportation efficiency increases with the increase of

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curvature ratio. When the curvature ratio increases to 3.5, the change is not apparent. At the same time, when R/D=2.5 or 4, the eccentricity is the smallest. Considering the parameters such as eccentricity and oil transportation efficiency, the R/D is preferably taken as 4 when CAF transports the heavy oil.

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b

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a

d

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Fig.12-Pressure drop and oil transportation efficiency at different operating conditions 6. Conclusion

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In the present work, FLUENT 15.0 software is used to study the flow of CAF in 90°

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elbow under different working conditions, and eccentricity, oil transportation efficiency and the distribution of volume fraction in the 90° elbow is obtained. From the study, the main

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conclusions are summarized as follows: The density of oil will affect the stability of CAF in the elbow. In order to ensure high

oil transportation efficiency and low eccentricity of oil core, the density of oil should be maintained at a low value. When the viscosity of the oil is high, the eccentricity of the oil core after CAF passes through the curved pipe is low, and it is not easy to pollute the pipe wall surface, but the oil transportation efficiency is low at this time. Therefore, the influence of eccentricity and oil transportation efficiency should be considered comprehensively in actual transportation. The increase in the diameter of the oil inlet will increase oil transportation efficiency

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while reducing the eccentricity. The diameter of the oil inlet should be increased as much as possible when CAF is used in 90° elbow. Under this condition, D1/D is most suitable at around 0.9. The oil transportation efficiency will increase with the increase of curvature ratio. When it increases to 3.5, the oil transportation efficiency has remained unchanged, while the eccentricity is the smallest when R/D=4. Therefore, considering comprehensively, R/D=4 is most suitable for CAF conveying in 90° elbow.

characteristics of core-annular flow to a satisfactory level.

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Notes

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This analysis also shows that the CFD model can forecast the hydrodynamic

The authors declare no competing financial interest.

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Acknowledgements

This work was supported by the Natural Science Foundation of Shandong Province

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(Grant No. ZR2019MEE105 and No. ZR2019MEE011), the Science and Technology Plan Projects of QingDao (Grant No. 17-1-1-88-jch), the Fundamental Research Funds for the Central Universities (Grant No. 18CX02082A and No. 17CX02064 and No. 14CX02211A

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and No. 12CX04070A), and the Open Research Fund Program of Shandong Provincial Key

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Laboratory of Oilfield Produced Water Treatment and Environmental Pollution Control (Sinopec Petroleum Engineering Corporation)

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Nomenclature

α0=oil phase fraction C1ε=constant C2ε=constant Cμ=constant

e=eccentricity of oil core F=body force, kg/m3 g=gravitational constant, m/s2 kt=turbulent kinetic energy, m2/s2

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P=pressure in the flow field, Pa q=average oil delivery per unit friction pressure drop gradient Qw=the volumetric flow rates of water, m3/s Qo=the volumetric flow rates of oil, m3/s t=time, s U=velocity, m/s μt=eddy viscosity, Pa.s

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Vso=superficial oil velocity, m/s Vsw=superficial water velocity,m/s Greek letters

εt=dissipation rate, m2/s3 σ=surface tension coefficient, N/m

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σk=constant

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ρ=density, kg/m3

σε=constant References

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application to heavy oil production. J. Energy Resour. Technol. 123, 194−199.

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CFD models are developed for core annular flow through 90° elbow. The simulation model has been verified by experimental and empirical values.

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The effects of inlet water fraction, the oil-water property (density ratio, viscosity ratio), and the geometrical parameters (diameter ratio, curvature ratio) on hydrodynamic

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performance, eccentricity and oil transportation efficiency are predicted.

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The results could provide a reference for the design of 90° elbow structures and the optimization of flow parameters.

Graphical abstract

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