computational fluid dynamic analysis for investigating the ...computational fluid dynamics (cfd) is...

[email protected]

Computational fluid dynamic analysis for investigating the influence of pipe curvature on erosion rate prediction during crude oil production

Chukwugozie Jekwu Ejeh1 (), Evans Annan Boah1, Gbemisola Precious Akhabue2, Chigozirim Cyprian Onyekperem3, Josiah Ikechukwu Anachuna1, Isaac Agyebi1

1. All Nations University College, Eastern Region, Ghana 2. Presbyterian University College, Eastern Region, Ghana 3. Centre of Excellence in Marine Engineering, Rivers State, Nigeria Abstract The flow dynamics in pipes is a very complex system because it is largely affected by flow

conditions. The transport of crude oil in pipelines within unconsolidated petroleum reservoirs is associated with presence of solid particles. These particles are often transported as dispersed phases during crude oil production and are therefore detrimental to the pipe surface integrity. This

could lead to the occurrences of crevice corrosion due to pipe erosion. In relation to the above discussion, this paper is aimed at analyzing crude oil dynamics during flow through pipeline and identifying erosion hotspot for different pipe elbow curvatures. Reynolds Averaging Navier–Stokes

(RANS) and Particle Tracing Modeling (PTM) approach were used. The focus is to simulate fluid dynamics and particle tracing, respectively. Post-processed results revealed that the fluid velocity magnitude was relatively high at the region with minimum curvature radius. The maximum static

pressure and turbulence dissipation rate were experienced in areas with low-velocity magnitude. Also, the rate of erosive wear was relatively high at the elbow and the hotspot varied with pipe curvature. The particle flow rate, mass, and size were varied and it was found that erosion rate

increased with an increase in particle properties.

Keywords rate of erosion

pipe curvature

pipe elbow

computational fluid dynamics

presence of solid particles

Article History Received: 14 September 2019

Revised: 23 October 2019

Accepted: 23 October 2019

Research Article © Tsinghua University Press 2019

1 Introduction

The increasing demand for energy from fossil fuel has led to an extensive search for hydrocarbon resource subsurface. Pipelines are widely used in the petroleum industry in the extraction and transportation of crude oil and natural gas from the reservoir, through the wellhead, to its depot site for storage (Sanni et al., 2015; Al-Baghdadi et al., 2017). The flow of fluid (crude oil) through a pipe is unsteady and associated with turbulence. The intensity of turbulence experienced during this flow can be estimated from the Reynolds number. In the past, analysis of fluid flow behavior was investigated from experimental and theoretical point of view. It showed to be capital intensive and hence requires an efficient, cost-effective, and reliable computational tool (Al-Baghdadi et al., 2017).

Computational Fluid Dynamics (CFD) is now commonly applied in the industry to analyze exterior and interior fluid flow. The extensive application of the approach is based on

its success to solve real-life problems and the reliability of solver predictions.

The Navier–Stokes (N–S) equation for incompressible flow is derived from the conservation of mass, energy, and momentum. In the modeling of the N–S equation, critical flow parameters such as velocity vectors, pressure, and Reynolds number, a function of turbulence intensity, are fundamental to its application in CFD simulations. These variables form the basic concept governing external and internal flows (Bazilevs et al., 2015; Egerer et al., 2016; Takizawa et al., 2017; Yan et al., 2017).

In this study, the two-equation, k ω- turbulent model, a type of the Reynolds Averaging Navier–Stokes (RANS) turbulent models, was used to model turbulent flow of the continuous phase through the pipe. The flow model was selected over the k ε- turbulent model and others, because of its accuracy in predicting flow features around region with strong streamline curvature and relatively low computational time (Yan et al., 2017).

Vol. 2, No. 4, 2020, 255–272Experimental and Computational Multiphase Flow https://doi.org/10.1007/s42757-019-0055-5

C. J. Ejeh, E. A. Boah, G. P. Akhabue, et al.

256

Peng and Cao (2016) predicted the velocity distribution in a 45°, 90°, and 180° pipe bend. From the study, the fluid flow velocity profile was largely influenced by the shape of the pipe. Furthermore, the velocity magnitude was relatively high in regions with minimum curvature radius.

Crude oil is a complex mixture of hydrocarbons and other substances which exist as contaminants. When crude oil is extracted from a petroleum reservoir, it is associated with solid particles sourced from the unconsolidated nature of some sandstone formation (Islam and Farhat, 2014; Parsi et al., 2014). These contaminant particles are identified to be sand particles, wax, insoluble scale and/or mineral, solid residue from production enhancement implementation, and many more (Sanni et al., 2015; Al-Baghdadi et al., 2017). Amongst these list of potential hazardous solids, the presence of sand particles is dominant and possesses greater concern (Veritas, 2007; Agrawal et al., 2019). The problem associated with the presence of sand particles transported as the dispersed phase in crude oil is associated with the degradation, fracture, and deformation of the pipe surface (Murrill, 2016; Agrawal et al., 2019). The resultant effect of this is most experienced at the pipe surface exposed to maximum particle–wall contact. This region has been identified by a number of researchers including Abdulla (2011) as the local mixing point where recirculation of the moving fluid and static pressure prevail. This type of problem is technically referred to as a flow assurance problem, and calls for the identification and mitigation of the effect of contaminant particles present during crude oil transportation (Saniere et al., 2004; Murrill, 2016).

When solid particles are transported through a curved pipe, it collides in-elastically with the pipe wall. This phenomenon is most experienced at the elbow junction (Abdulla, 2011; Bonelli and Marot, 2011; Parsi et al., 2014; Sanni et al., 2015; Al-Baghdadi et al., 2017). When this happens, the dispersed phase exerts a significant amount of pressure force at the contact points. Most times, wall lift-off in viscous unit, pipe deformation and failure is experienced in the process. The resultant effect of this phenomenon causes the particle to deform and impinge on the pipe wall, thereby stripping away corrosion-resistant layer with time (Okonkwo and Mohamed, 2014; Eliyan et al., 2017). This can be referred to as pipe surface erosion and the synergy effect resulting from chemical interaction between corrosive fluid and eroded pipe surface is termed erosion-corrosion (Veritas, 2007; Abdulla, 2011; Parsi et al., 2014; Agrawal et al., 2019).

The continuous occurrence of particle–wall collision will yield constant depletion of the corrosion-resistant layers, and expose the pipe surface to chemical interaction with the corrosive fluid (crude oil). Hence, pitting corrosion is experienced (Okonkwo and Mohamed, 2014; Eliyan et al., 2017).

Regions with high erosion rates are identified to be the erosion hotspot (Abdulla, 2011; Agrawal et al., 2019; Ejeh et al., 2019). These areas are susceptible to pipe surface deterioration, fatigue, deformation, and leakage. If not properly identified, mitigated, and/or prevented, pipe failure is likely to occur. In the long run, this will call for production shut down, and unplanned cost of maintenance (Saniere et al., 2004; Murrill, 2016). Therefore, it is crucial to identify this susceptible region. Notwithstanding, the identification of the erosion hotspot is largely dependent on the pipe bend angle. Analysis of predicting erosion hotspots for different pipe bend is important (Peng and Cao, 2016).

Computational Fluid Dynamics (CFD) has shown to be reliable in solving real-life problems and is now extensively used for industrial applications to provide a cost-effective approach for the design and analysis of engineering systems (Abdulla, 2011; Okonkwo and Mohamed, 2014; Sanni et al., 2015; Al-Baghdadi et al., 2017; Ejeh et al., 2019). CFD has been applied in recent years using a number of software or computer programs. Selected examples are the STAR C++ code, ALGOR code, ANSYS Fluent software. CFD analysis with COMSOL Multiphysics software was considered in this study as the computational tool. This choice of computational program was made based on its availability and reliability to properly solve the problem related to particle trajectories and erosion rate prediction (Sanni et al., 2015; Al-Baghdadi et al., 2017; Ejeh et al., 2019).

Abdulla (2011) showed that the rate of erosion is high at right angle in pipes. In his investigation, gas, oil, and water were transported through the pipe in the presence of solid particles. Al-Baghdadi et al. (2017) performed a similar study on erosion severity in a 90° pipe elbow due to the presence of solid particles during transportation of crude oil and found that erosion rate was more pronounced at right angle. However, the pipe bend angle was not varied. Also, Parsi et al. (2014), Wong et al. (2014, 2016), Qi et al. (2017), Bonelli and Marot (2011), Ejeh et al. (2019), Islam and Farhat (2014), Najmi et al. (2015), Kesana et al. (2014), and Sanni et al. (2015) investigated on erosion rate prediction using crude oil as the case fluid and achieved similar findings.

These publications have made significant contributions to solve this problem, but the influence of pipe elbow curvature for number of cases was not taken into consideration in the cited publications. Adding to the above citations, Abdulla (2011) conducted a sensitivity study on the influence of fluid density, velocity, particle size, and angle to erosion prediction along a 90° pipe elbow, but never the less, the elbow curvature was not varied to have a better understanding about the possible variations in the erosion hotspot.

Banakermani et al. (2018) performed a very interesting work in this area where they considered different pipe bends with angle 15°, 45°, and 90° elbows by numerical simulation

Computational fluid dynamic analysis for investigating the influence of pipe curvature on erosion rate prediction during...

257

of gas–solid flow. The difference between their publication and this paper is the extension in the pipe curvature angle up to 135° and 180°. Also, crude oil was used as the continuous phase instead of gas, as published by Banakermani et al. (2018) and sensitivity studies on the influence of fluid–particle size and flow rate were considered in the research objectives. These considerations bridge the research gap in Banakermani et al. (2018) work and further their findings.

Successful achievement of the set objectives will provide critical information on the erosion hotspot for specified pipe bend angle considered in the design of pipelines for crude oil transport. This study seeks to build on the established theory postulated in literature. The implementation of fluid–particle, particle–particle interaction, and particle–wall integration is considered in this study and was not case in Badr et al. (2002), Abdulla (2011), Wong et al. (2016), Veritas (2007), Bounaouara et al. (2015), and Parsi et al. (2014) work. Therefore, it is expected that the successful achievement of objective results will bridge the scientific gap and lay strong foundation for further investigation.

Despite the use of Computational Fluid Dynamics for simulation of erosion rate prediction in pipe bends, the use of Reynolds Averaging Navier–Stokes (RANS) and Particle Tracing Modeling (PTM) approach is very rare in literature. This study focuses on using Reynolds Averaging Navier– Stokes (RANS) method coupled with the Particle Tracing Modeling (PTM) approach to evaluate the influence of pipe elbow curvature on flow variables and erosion rate prediction. Fluid–particle and particle–particle interactions were con-sidered in the modeling process. Also, sensitivity studies are performed to evaluate the effect of variable particle flow rate, mass, and size on erosion rate prediction. The case fluid used in this investigation is Bonny Light crude, a type of Nigeria light crude. COMSOL Multiphysics version 5.4 software was used as the computational platform to achieve the set goals and objectives of this research.

2 Simulation methodology

Two CFD simulations, that is, static and transient simulations, were conducted. The static simulation was aimed at analyzing fluid flow dynamics, assuming that the chemical composition of the fluid remains unchanged. At the end of the simulation, the fluid velocity magnitude, static pressure, turbulent dissipation rate, cell Reynold’s number, and wall viscosity predictions were obtained. The segregated solver which functions similar to the pressure-based solver in ANSYS Fluent was used to perform the numerical computation.

The time-dependent or transient simulation enabled analysis of particle tracing with time from which regions with maximum erosion rate can be identified. In addition,

it was applied to perform sensitivity studies on the effect of particle size and mass flow rate variations. Here, a time- dependent solver which works based on Jacobian iterative processes was used. These predictions were performed for Finnie, E/CRC, Oka et al. and DNV erosion models. Figure 1 is a flowchart which summarizes the procedure adopted to achieve research objectives.

2.1 Model design, meshing and sensitivity study

The pipe model geometry was made up of two (2) cylindrical straight pipe sections connected by a local geometry (elbow). The choice of pipe design was inspired by the geometric complexity involved in pipeline installation at offshore oil and gas production sites in-line with the terrain. Four (4) 3D pipe models were created in COMSOL platform using the CAD Kernel module. The pipe designs are shown in Fig. 2. The dimensions used in creating the pipe geometries are the same, but the major difference between each design is the curvature angle. The pipe’s horizontal length is 25 m and radius 5 m.

Table 1 is a summary of all parameters considered in creating the pipe geometry. The four (4) pipe designs were named design-1, design-2, design-3, and design-4. Their individual curvature angles are 45°, 90°, 135°, and 180° respectively. A straight pipe geometry was not considered since it has no bend section and the erosion rate at longitudinal sections will be very minimal.

The decision on model structural shape was informed by the topology of the geographic terrain on which crude oil pipelines are frequently installed. To by-pass this obstruction,

Fig. 1 Simulation methodology flowchart.


258

Table 1 Pipe model design parameters

Parameter Input

Material Steel

Normalized pipe radius 5 m

Normalized horizontal length 25 m

Curvature angle

45° (Design-1) 90° (Design-2) 135° (Design-3) 180° (Design-4)

Table 2 Summary of mesh design parameters

Parameter Input

Meshing method Hybrid

Growth formula Arithmetic sequence

Face meshing method Quadrilateral (general hexahedra)

Maximum element size 0.65 m

Minimum element size 0.123 m

Element growth rate 1.13

Element ratio 100

Number of boundary layer 20

Layer thickness 0.2 m

Curvature factor 0.5

Total number of elements 91,979

the piping route is structured so as to deviate from any discontinuity. This is done by introducing a curved local geometry.

Geometry discretization is an important part of CFD studies. This involves dividing the geometry into smaller elements, to create a flow domain. There are basically three (3) types of meshing strategies commonly used in CFD. These are unstructured, structured, and hybrid meshing. An unstructured mesh is easier to generate, but there exists a compromise in the accuracy of its solution. Structured meshing is more reliable than unstructured in terms of accuracy and prediction of solution variables at sensitive regions or curvatures, most especially at the wall boundary.

A structured mesh was created to reduce the com-putational cost and processing time required by the solver and to increase the accuracy of the solution. Boundary layers were created at the wall boundaries, to accurately resolve flow in a pipe with streamline curvatures. This strategy bridges the disadvantages and limitations of using an unstructured mesh, hence making it a suitable meshing strategy for various CFD applications to reproduce a reliable solution.

The model mesh for design-4 is demonstrated in Fig. 3. The mesh was made fine at wall boundaries and erosion rate due to drag force is obtained. The described meshing strategy was used to discretize all four (4) pipe designs. The meshing process involves splitting the face by using a

Fig. 2 Pipe model design for different curvature angles.


259

Fig. 3 Mesh sensitivity plot relating velocity and pressure pre-dictions with element size.

circle of radius 4 m from the primitive toolbar. This was done to create extreme edge points from which a structured mesh can be distributed along the wall boundaries. A total of 20 elements with element ratio of 100 were considered when distributing hexahedra mesh at the wall boundary and mapped at equal distance between each element. The separation between the boundary layers had thickness of 0.2 m and a total of 20 boundary layers were generated. The Sweep option was used to create quadrilateral dominant mesh at the remaining domain.

Mesh sensitivity analysis is very important in CFD simulations. This analysis is aimed at observing how the grid sizes affect the solution accuracy. The best choice of mesh design depends on this analysis and can be obtained from the convergence zone. The plot in Fig. 3 describes the relationship between maximum velocities and static pressures against number of elements.

The mesh sensitivity analysis was conducted to observe how the solver prediction for velocity and pressure variables is affected by refinement in mesh size. This is a verification process performed to ensure that the choice of mesh design will yield an accurate prediction for the simulation setup.

The plot in Fig. 3 informs that the solver solution con-verged after 32,000 elements. Hence, the choice of an adequate mesh strategy was obtained from this confidence interval.

The mesh sensitivity study was performed using the model design-4 only to save time and computational cost, reason being that the meshing technique used to discretize the domain, created fundamental basis for meshing the remaining three (3) pipe models. The model mesh can be seen in Fig. 4.

2.2 Turbulent flow and particle tracing modeling for erosion prediction

In computational fluid dynamic analysis, flow of the continuous is modeled using the Reynolds Averaging Navier–

Fig. 4 Model meshing for design-4 showing surface, interior, and lateral view.

Stokes (RANS) equation. This equation works based on the principle of mass, momentum, and energy (Ejeh et al., 2019). In this study, liquid hydrocarbon (n-octane) flows through the pipe as the continuous phase. It was assumed that the petroleum reservoir was under-saturated, meaning that gas and oil flows as a single phase. The continuous phase was treated as an incompressible fluid, assuming that the change in the physical properties (density) of the fluid is insignificant.

The Reynolds number of magnitude 222,857.14 (2.22×105) was computed from the pipe hydraulic size (Eq. (1)), fluid density, initial velocity, and viscosity. This informs that, the flow is turbulent and requires a suitable flow physics. The choice of turbulent model depends on the objective function of the simulation study (Egerer et al., 2016). Since the erosion rate is estimated from the wall contacts, it is important to select a turbulent model that can provide reliable predictions of sensitive parameters at the wall boundary. The estimated turbulence intensity calculated from Eq. (2) below was 3.43%. This value is significant and signifies medium to high turbulence intensity. Because the fluid flow is unsteady, it is expected that the Reynolds number will change along with the fluid stream. This hypothesis was proven in Section 3.1.4.

The two-equation k ω- turbulent model, which is a type of the RANS model, was used in this simulation study as the flow physics to model turbulent flow of the continuous phase. This flow model was selected over the k ε- turbulent model because of its accuracy in predicting flow features around region with strong streamline curvature. Since the pipe curvature was made steep, prediction of objective parameters around this area is critical.


260

DDuρR

μ= (1)

18

D0.16I R -= ´ (2)

Particle tracing is governed by the Newtonian formulation. This formulation differs from the Navier–Stokes equation because it deals with the motion of solid objects and not fluids as applied to the Navier–Stokes theorem. The Newtonian formulation is expressed in Eq. (3) (Ejeh et al., 2019).

pD g ext

d( )dm V

F F Ft = + + (3)

Given that, t is the time factor, extF , gF , and DF are the unbalanced external force, gravitational force, and drag force measured in Newton respectively. V and pm are the particle initial velocity in meter per second and mass in kilogram respectively (Ejeh et al., 2019).

The drag force acting between the particle–wall interfaces from which erosion rate can be estimated is modeled using Eq. (4). Equations (5) and (6) provide detail formulation from which the parameters in Eq. (4) can be computed (Ejeh et al., 2019).

D pp

1 ( )F m V Uτ= - (4)

2

p pp 18

ρ dτ

μ= (5)

ΔV u u= + , where 2Δ3ku δ= (6)

where V, u, and Δu are the instantaneous, initial, and change in particle velocity in the drag force, measured in meter per second respectively, k is the turbulent kinetic energy, pτ is the particle response time in motion measured in second and δ is the vector uncorrelated Gaussian numbers with unit variance (Ejeh et al., 2019).

Table 3 is a summary of the input parameters used in the setting-up of the particle tracing physics. Different types of erosion rate models have been used in the literature, to compute erosion wear at the particle–wall contacts. These models are empirically derived based on certain fundamental concepts and objective functions, and they differ in application.

The commonly used erosion rate models in COMSOL Multiphysics software are the Finnie, E/CRC, Oka et al. and DNV. As mentioned previously, these models were developed based on different empirical constants and variables used. The listed erosion models were used in this study, to perform the erosion rate prediction and identify potential leak points on the pipe surfaces. It is difficult to say which model is preferred over the other since they operate independently. From the

Table 3 Particle tracing with fluid flow modeling parameters

Parameter Input

Formulation Newtonian

Turbulent dissipation model Discrete random walk

Drag law Stokes

Maximum number of secondary particles 30,000

Wall condition Freeze

Particle density 2200 kg/m3

Particle size 1 μm

Environment temperature 323.15 K

Number of particles per release 3000

Mass flow rate 0.9 kg/s

literature, the Finnie and Oka et al. erosion models are widely recommended because of their similarities, accuracy in erosion rate prediction and the number of variables considered when developing the model equation (Abdulla, 2011; Sanni et al., 2015; Al-Baghdadi et al., 2017; Ejeh et al., 2019). It is assumed that the higher the number of variables used by the model, the higher its reliability. However, it is important to consider the use of the DNV and E/CRC erosion model, for comparative purposes.

The erosion rate equations used by the particle tracing physics are shown below. Tables 3.1, 3.2, and 3.3 provide a summary of the variables description and empirical values for the Finnie, E/CRC and Oka et al. model equations respectively.

Table 3.1 Variables and emperical constant for Finnie model

Parameter Input

The fraction of particles cutting in an idealized manner, ci

0.1

The ratio of normal and tangential force, K 2

Surface hardness, Hv 2 GPa

Mass density of surface, ρ 7.5×103 kg/m3

Moment of inertia calculation Isotropic sphere

Table 3.2 Variables and emperical constant for E/CRC model

Parameter Input

E/CRC model coefficient, C 2.17×10-7

Brinell hardness of surface material, BH 200

Particle shape coefficient, Fs 0.2

E/CRC model exponent, n 2.41

Table 3.3 Variables and emperical constant for Oka et al. model

Parameter Input

Oka et al. model coefficient, K 65 mm3/kg

Reference size, dref 326×10-6 m


261

(Continued)

Parameter Input

Surface hardness, Hv 2 GPa

The mass density of surface, ρ 7.5×103 kg/m3

Reference velocity, Vref 104 m/s

Oka et al. model coefficient, k1 -0.12

Oka et al. model coefficient, k3 0.19

Oka et al. model coefficient, q1 0.14

Oka et al. model coefficient, q2 -0.94

Oka et al. model coefficient, s1 0.71

Oka et al. model coefficient, s2 2.4

Finnie erosion model

M M, jj

E E=å (7.0)

( ) ( )2

i p rel i 2M, i i2

p p

p

cos ,tan2

4 1j

c ρm f v pE α αm r

Hv I

= >æ ö÷ç + ÷ç ÷÷çè ø

(7.1)

( ) ( ) ( )2

i p rel i 2M, i i i2

p p

p

2 2sin 2 sin ,tan2

4 1j

c ρm f v pE α α αm r p p

Hv I

é ù= - £ê ú

æ ö ê úë û÷ç + ÷ç ÷÷çè ø

(7.2)

2p p

p1

kpm r

I

=æ ö÷ç + ÷ç ÷÷çè ø

(7.3)

2p p p

25

I m r= (7.4)

where pm is the particle mass in kilogram, and pr is the particle size in the micrometer.

E/CRC erosion model

M M, jj

E E=å (8.0)

( )0.59M, s i

ref( )

n

jj

VE CF BH F αV

- æ ö÷ç= ÷ç ÷çè øå (8.1)

( )5

i i1

kk

k

F α A α=

=å (8.1.1)

Oka et al. erosion model

M M, i( )jj

E E α=å (9.0)

( )[ ]

1 2M, i i i M,

π(sin ) 1 (1 sin )

1 GPa 2n n

j j

HvE α α α E

é æ ö æ ö÷ ÷ç ç= +ù

ê -÷ ÷ç ç ÷ç÷ç èøê úë øú

è û

(9.1)

[ ]

31 2p

M,ref ref

π2 1 GPa

kk k

j

dH VE K

V dv æ öæ öæ ö æ ö ÷÷ ç÷ ÷çç ç= ÷÷÷ ÷ ççç ç ÷÷ ÷ç ç÷ç ÷çè ø è øè ø è ø

(9.1.1)

[ ] [ ]

[ ]

1 2

1 1 2 2

0.038

2

; ;1 GPa 1 GPa

2.31 GPa

q qHv Hv

n s n s

Hvk

æ ö æ ö÷ ÷ç ç= =÷ ÷ç ç÷ ÷ç çè ø è ø

æ ö÷ç= ÷ç ÷çè ø (9.1.1.1)

DNV erosion model

M M, jj

E E=å (10.0)

M, m1 s

n

jvE K

-æ ö÷ç ÷ç ÷ç ÷= ç ÷ç ÷é ùç ÷÷ç ê ú ÷çè øë û

( )iF α (10.1)

( )8

1i i

1( 1)k k

kk

F α A α+

=

= -å (10.1.1)

where K = 2×10-9 is the DNV model coefficient and n = 2.6 is the DNV model exponent.

2.3 Computational error analysis

Computational solver error analysis is very important to ascertain the accuracy of the solver solution. The commonly used solver in COMSOL Multiphysics is the segregated solver. This solver solves for velocity, pressure, and turbulent variables separately. It works by decoupling the momentum equation and solves the variables separately. It works in a similar manner as the Pressure based solver in ANSYS- Fluent.

The plot for velocity, pressure, and turbulent variables for every iterative value is shown in Fig. 5. The segregated solver convergence or error analysis plot shows that the error of estimation of these variables converges within the 1×10–2 and 1×10–4 error limit. It informs that the solver error of

Fig. 5 Segregated solver convergence plot.


262

estimation lies within the acceptable error margin (Ejeh et al., 2019). It can be summarised that the solution to the pressure, velocity, and turbulence variables is of the 4th order accuracy after 60 iterations.

An average of 2.01-hour computational time was used by the solver to solve the variables that constitute the momentum equation.

3 Results and discussion

The concept of fluid dynamics, specifically RANS and PTM approaches has been applied to evaluate the effect of particle size, mass, and flow rate on erosion rate. More importantly, it provides the platform to identify erosion hotspots in pipelines to prevent failure. Most times, the fluid processing facility is located miles away from the production system. As such, the fluid loses its kinetic energy with time due to the unsteadiness in the flow characteristics. This phenomenon is accompanied with constant depreciation in fluid pressure. The pressure drop or loss of kinetic energy prevails at the pipe curvatures. Achievement of this will provide good information on the flow property characteristics across the flow media. This is possible using computational fluid dynamics.

3.1.1 Velocity magnitude

In CFD studies, analysis of fluid velocity distribution across

the flow domain is critical. This is because it provides critical insight about the fluid dynamic behavior under prevailing ambient conditions. By definition, the velocity of a fluid is influenced by directional displacement of the fluid molecules and the geometric shape of the transport media.

In this study, the fluid velocity distribution for the different model designs was investigated. Recall that, the initial fluid velocity at pipe inlet was 40 m/s. It was noticed that the solver predicted higher values of velocity magnitude at the pipe local areas with minimum curvature radius. This was the case for all design considerations.

From in-depth observation of Fig. 6, it was observed that the predicted velocity magnitude at sharp curvatures was relatively high and minimal along the straight pipe sections. This phenomenon can be explained based on the theory that when fluid moves through a curved path, it attaches itself to the curved surface preferentially and causes the fluid to flow faster than expected. This hypothesis confirms the Coanda principle (López-López et al., 2019). This phenomenon was more pronounced for model design-4, which can be seen in Fig. 6(d).

A maximum of 57.4, 64.9, 65.1, and 65.2 m/s velocity magnitude was obtained for model design-1, design-2, design-3, and design-4 respectively.

From detailed look of results shown in Fig. 6, flow separation was observed at adjacent part of the pipe elbow (region with maximum curvature radius). In this region, fluid

Fig. 6 Flow profile of velocity magnitude for all model design.


263

static pressure is maximum and hence, the velocity magnitude is minimal. The reduction in the velocity magnitude around this re-circulation region was estimated to be 20 m/s.

To confirm the statement made in Section 3.1, the pre-dicted fluid velocity at the pipe outlet was less than that from the inlet section (40 m/s) by an average of 6 m/s. It can be said that the flow pressure dropped, and it is expected to prevail with time.

3.1.2 Fluid static pressure

Fluid pressure is another important flow variable that aids in the critical analysis of fluid dynamics. In fluid dynamics, there exist two main types of pressures, namely dynamic and static pressure. Comparatively, the difference between these two classes of pressure lies on the kinematics of the transported fluid. Dynamic pressure deals with pressure exerted by the fluid in maximum displacement, while static from its name is concerned with the pressure exerted by the fluid around the re-circulation zone. These two (2) pressures are experienced during fluid flow through a pipe (López-López et al., 2019).

From detail observation of results shown in Fig. 7, it can be deduced that the fluid pressure is high around areas with minimum flow velocity predictions. This was the case for the four (4) model designs and was more prevailing for design-4 shown in Fig. 7(d). The maximum pressure value recorded was 6.28×105 Pa. This pressure value is high and may cause local deformation or fatigue of the pipe elbow.

From a theoretical point of view, when fluid flows through a confined path and encounters an immediate curve

path, the fluid bulk collides with the curved surface exposed to its path. By so doing, it exerts or transfers momentum energy in the form of stress at the contact point. This is due to the fact that recirculation of the fluid is dominant at areas with maximum static pressure and as such, an increase in the turbulence dissipation rate is expected. This theory is further discussed in Section 3.1.3.

In addition, the results obtained agree well with Peng and Cao (2016) result for velocity magnitude profile.

3.1.3 Turbulent dissipation rate

This analysis was conducted to confirm the hypothesis made in Section 3.1.2. The turbulent dissipation rate is calculated from the k parameter in the k ω- turbulent model for-mulation. Turbulent dissipation rate is the rate at which turbulent energy is absorbed when large flow eddies are broken down into smaller eddies. It is associated with the dissipation of kinetic energy of the fluid molecule in the form of eddies during flow.

Comparing Figs. 8(a)–8(d), the turbulence dissipation rate and flow curvature are relatively high at the pipe section closest to the elbow outlet. The contour plot from Fig. 8 informs that the fluid turbulent dissipation is relatvely high at the pipe curvature, and spreads out through the wall boundary. Comparatively, Fig. 8(d) predicted a higher value of turbulent dissipation rate with magnitude 35 m2/s2. The lowest prediction with magnitude 8.38 m2/s2 was achieved for design-1 with minimal pipe curvature, shown in Fig. 8(a).

It can be deduced that pipelines with steep curvatures are expected to experience an increasing turbulent dissipation

Fig. 7 Flow profile of hydrostatic pressure for all model design.


264

rate and formation of large eddies. From critical observation of Fig. 9(d) in Section 3.1.4, large eddies are formed during fluid flow and its occurrence is dominant compared to other geometries.

Also, since crude oil flows unsteadily with associated suspended phases (solid particles), the rate of particle–wall contact will be high where the turbulent dissipation of kinetic energy is maximum. Hence, severe erosive wear and fluid shear will be experienced

3.1.4 Cell Reynolds number

The cell Reynolds number was also considered to observe the formation of small and large flow eddies due to turbulence. From a detailed analysis of Fig. 9 below, the formation of small flow eddies was dominant for model design-1 and its influence is reduced with an increase in the pipe curvature. An eddy can be defined as the swirling of fluid in multiple directions and creates a reverse current during a typical turbulent flow regime. This is usually experienced behind rocks inflowing rivers. Therefore, the formation of eddies is affected by the speed of fluid and turbulence intensity.

Comparing Figs. 9(a)–9(d), the inertia forces that con-tribute to turbulent flow are dominant over viscous force in Fig. 9(d) than others. This can be measured from the unit-less parameter known as the Reynolds number. The cell Reynolds number was maximum for design-4 compared to the other geometries.

It can also be deduced that the Reynolds number at each cell exceeds 2000 implying that turbulent flow prevails and its intensity is non-linearly correlated with pipe distance.

3.1.5 Wall resolution analysis

During turbulent flow of fluids through a confined media, multiple fluid–wall contacts are experienced. At contact areas, the fluid and pipe walls are in relative motion. In this case, the pipe is fixed whilst the fluid is in continuous motion. Frictional force is generated at contact areas causing the fluid to be viscous at fluid–wall interfaces. Interfacial tension existing between two immiscible phases develops molecular attraction between the fluid and wall surface. From this, the wall tends to offer a significant amount of flow resistance to the fluid. This phenomenon is termed wall viscosity and is measured in parts per million (ppm) or viscous units.

Comparing the contour plot in Fig. 10, the wall viscosity is dominant where the fluid makes maximum contacts with the pipe wall. The maximum observed wall viscosity pre-diction had magnitude 1.19×10−4 viscous unit and prevails for the 90° curved pipe. This area can be identified using the red color band.

In addition, the shear rate is high at areas with high wall viscosity and informs that, the pipe interior surface protective layers will deteriorate with time, and may eventually induce fatigue in the pipe structure. For industrial application, it is important to use orthotropic materials (material property

Fig. 8 Flow profile of the turbulent dissipation rate for all model design.


265

vary with direction) than isotropic materials, in the design of crude oil pipelines. Its application enhances the resistance of the pipe material to damage.

3.2 Analysis of erosion rate due to presence of con-taminant particles

This section is aimed at addressing the third objective of this research. It elaborates on particle tracing, predicting erosion rate at particle–wall contacts during flow, and identification of potential leak point. Sensitive parameters such as particle size, mass, and flow rate are varied.

In the numerical simulation of erosion rate, base para-meters were kept constant. The selected base parameters are tabulated in Table 4.

The simulation was set to run for about 6000-time step in seconds, and objective results were archived after 5000-time step in seconds with an average computational time of 3.3 hours.

The rate of erosion is computed from the drag force at the wall boundary. As a result, it is required that the mesh size at the wall boundary should be fine to better resolve flow properties at contact points and provide a reliable prediction. This was done by introducing boundary layers with minimum

Fig. 9 Cell Reynolds number describing turbulence dissipation during flow.

Fig. 10 Effect of fluid–wall interaction on the interior pipe surface.


266

Table 4 Base parameters for erosive wear sensitivity analysis

Parameter Input

Fluid density 848 kg/m3

Fluid dynamic viscosity 0.056 Pa·s

Particle density 2200 kg/m3

Particle size 1×10−6 in

Temperature 323.15 K

Particle mass flow rate 0.9 kg/s

Particle shape Isotropic sphere

first layer thickness so that the y-plus value is approximately equal to 1 ( 1).y+»

3.2.1 Verification of pipe leak point with computational model

The simulation model was verified with a typical real-life pipe leak which occurred as a result of pipe erosion. From Fig. 11 below, it is evident that the model result for erosion hotspot using design-2 correlates well with that achieved in an actual real-life case scenario. The erosion hotspot or leak point is located at the same position. Hence, it can be said that the simulation model is valid and verified for its accuracy in the prediction of potential erosion hotspot.

3.2.2 Particle tracing analysis

Particle tracing is aimed at determining the particle velocity in terms of magnitude and direction from the inlet through the fluid domain, and also at particle–wall contact areas. The impact velocity is important for the modeling of erosion rate and particle trajectory in its course of motion.

In the particle tracing modeling, it was considered that the particle interacts with each other and the effect of fluid path to particle trajectory was taken into consideration. Both the fluid–particle and particle–particle interaction was activated. This was not the case with Badr et al. (2002), Abdulla (2011), Wong et al. (2016), Veritas (2007), Bounaouara et al. (2015), and Parsi et al. (2014). Also, the fluid flow field influenced the particle trajectory. This was achieved by allowing the flow turbulent model used in governing fluid flow, to influence the particle motion. By using the keywords turbulent kinetic energy (spf) and turbulent dissipation rate (spf/fp1) at the boundary condition for the drag force modeling, the particles were forced to interact with the fluid and neighboring solid phase.

From detail observation of Figs. 12(a) and 12(b), the trajectory of the particle in the fluid is influenced by the fluid velocity, density, and pipe shape. The result shows presence of particles dispersed randomly within the fluid domain.

Fig. 11 Verification of pipe leak point with the computational model.

Fig. 12 Contour plot showing variations in particle angle and position at t = 2 seconds.


267

This was achieved by implementing the keywords velocity field (spf), dynamic viscosity (spf/fp1), and density (spf/fp1) in the drag law formulation section of the boundary condition.

In real-life cases, solid particles transported along with produced crude oil, are angular in shape. From critical review of literature, it was commonly assumed that the shape of the particles remains unchanged, by assuming that the particles do not interact with each other. This assumption is crucial and may introduce uncertainties in the solution.

In this study, the particles interacted with each other. By so doing, the shape and size of the transported particles change with colliding frequency. At colliding areas, the particle size, shape, and kinetic energy are altered.

This is based on the inelastic collision theory. This explains that the momentum energy of the object before collision is not the same after collision. Hence, the conservation law of momentum is not conserved. In addition, solid particles possess low elasticity and will easily observe plastic behavior under the influence of external load. In the long run, it disintegrates and reduces in size and shape. Figures 12(a) and 12(b) show particle angle varying between 3.83° to 89.8° for model design-2 and design-3. This validates the implementation of particle–particle interaction in the particle tracing modeling.

Figures 13(a)–13(d) are contour plots showing erosion hotspots. From critical observation, the erosive wear hotspot

or leak point varies in each model design. This validates the hypothesis made in the introductory section of this paper. At his stage, the first and second objective of this work was achieved. The maximum erosion rate obtained for the four case pipe designs has magnitude 2.14×10−9, 3.93×10−7, 7.21×10−7, and 6.13×10−4 kg/(m2·s), respectively. This informs that, erosion rate is affected by the curvature angle of the pipe elbow and is intense for higher curvature angles. The pipe model design obtained the highest erosion rate and is expected to fail at an earlier date compared to the other designs considered in this work.

In addition, due to the unsteadiness in the flow direction, the erosion hotspot is seen to be unevenly distributed and is concentrated at the section with flow curvatures and turbulence intensity (Njobuenwu and Fairweather, 2012).

3.2.3 Influence of particle size to erosion rate

It is right to say that, the size of each solid particle dispersed in the fluid does not have a fixed size. In the previous section, it was discussed that the resultant effect of the particle–particle and particle–wall interaction caused constant reduction in the size of the particle. This factor was considered in this sensitivity study, where the size of the particle was varied between 1×10−6 and 1×10−4 m. This analysis was performed using different erosion models.

The results obtained in Fig. 13, show that the larger the

Fig. 13 Contour plot showing potential leak points for all case pipe models.


268

Fig. 14 Effect of particle size to maximum erosion rate.


269

particle size, the lower the erosion rate (Badr et al., 2002; Abdulla, 2011; Bonelli and Marot, 2011; Njobuenwu and Fairweather, 2012; Islam and Farhat, 2014; Okonkwo and Mohamed, 2014; Parsi et al., 2014; Bounaouara et al., 2015; Wong et al., 2016; Al-Baghdadi et al., 2017; Eliyan et al., 2017; Qi et al., 2017; Banakermani et al., 2018; López-López et al., 2019). This is true because large-sized particles possess reduced kinetic energy and velocity during flow. Therefore, the impact of particles with the wall is less severe compared to smaller particles with higher momentum and kinetic energy. Adding to these, the computation of the drag force at particle–wall contact depends on the particle velocity. Therefore, the larger the particle size, the lower its velocity, drag force, and erosive wear rate.

Comparing results obtained for the case designs, pipe design-4 obtained the highest erosion rate prediction. Note that the vertical primary axis at the left shows erosion rate prediction results for design-2 and design-4, while the secondary axis at the right of the plot shows results for pipe design-1 and design-3.

3.2.4 Influence of particle mass/density to erosion rate

The particle mass is directly related to particle density from the mathematical expression of density. Besides the fact that the particle size changes with time during flow, the density of the particle is also affected. This is because particle size and density are directly related. The higher the particle size, the more pronounced its volume.

In the petroleum reservoir, insoluble scales, sand particles, proppants, and other associated solid substances present in the fluid have different densities. Based on this, the density of the solid particles in terms of mass was varied in the range 0.003 to 0.13 kg for a unit volume. Here, the mass is translated to density for a unit particle volume.

The results shown in Fig. 15 provide critical informa-tion on the effect of particle mass on erosion rate. Detail analysis of Fig. 15 shows that an increase in the density of the dispersed phase yielded a proportional increase in the rate of erosive wear (Badr et al., 2002; Abdulla, 2011; Njobuenwu and Fairweather, 2012; Islam and Farhat, 2014; Banakermani et al., 2018; López-López et al., 2019). It can be explained based on the theory that soft particles disintegrate faster than dense particles during inelastic collision. In this case, the soft particles will disintegrate faster into smaller elements and become absorbed by the dense crude oil. Therefore, the particle loses its feel and the pipe erosion will be less pronounced with time. The reverse statement is true dense particles. Therefore, the results obtained in this analysis are realistic and have strong scientific basis.

Comparing results obtained for the four (4) case designs

in Fig. 15, pipe design-4 obtained the highest erosion rate prediction for all erosion models considered. It should be noted that the vertical primary axis at the left, shows erosion rate prediction results for design-2 and design-4, while the secondary axis at the right of the plot shows results for pipe design-1 and design-3.

3.2.5 Influence of particle flow rate to erosion rate

In addition to the effect of particle mass and size on erosion rate, the particle flow rate was also considered. The flow of crude oil in the reservoir pore spaces and pipelines are unsteady. This is due to certain prevailing conditions in the petroleum reservoir settings. Technically, most petroleum reservoirs are heterogonous in nature, meaning that the petrophysical properties of the rock and fluid vary along the vertical, radial, and lateral direction with time and distance from the reservoir boundaries. This heterogeneity causes the reservoir flow pressure to change unsteadily with time. Therefore, the flow rate of the crude oil and associated phases through the pipeline is affected. Adding to this, the kinetic energy possessed by the dispersed phase (solid particles) is directly affected by the speed of the flowing fluid. Therefore, the slower the fluid movement, the lesser the particle velocity, and hence the less intense the rate of erosion.

With respect to the underlined theory, the particle flow rate was varied and its effect on erosion rate was observed. The results of this consideration can be seen in Fig. 16. The particle mass flow rate was varied in the interval 0.9–2.2 kg/s. the choice of values used in this study is hypothetical for analytic purposes. It can be said that the rate of erosion increases with particle or fluid flow rate.

As stated in Sections 3.2.3 and 3.2.4, the vertical primary axis at the left, shows erosion rate prediction results for design-2 and design-4, while the secondary axis at the right of the plot shows results for pipe design-1 and design-3. Comparatively, the erosion rate was dominant for pipe model design-4 and was less intense for design-1.

4 Conclusions and further study

The application of RANS and PTM to investigate pipe erosion showed to be positive in predicting fluid flow features and erosive wear hotspot. The erosion rate was found to increase with an increase in pipe curvature angle. The sensitivity study conducted depicts that the rate of erosion is influenced by the particle flow rate, mass, and density. The greater the particle flow rate, mass, and density, the higher the erosion rate predicted at the identified erosion hotspot. It could be recommended that the pipe design material properties should be selected to offer a higher resistance to surface wear at the identified leak possible points.


270

Fig. 15 Effect of particle mass to maximum erosion rate.


271

Fig. 16 Effect of particle flow rate to maximum erosion rate.


272

References

Abdulla, A. 2011. Estimating erosion in oil and gas pipeline due to sand presence.

Agrawal, M., Khanna, S., Kopliku, A., Lockett, T. 2019. Prediction of sand erosion in CFD with dynamically deforming pipe geometry and implementing proper treatment of turbulence dispersion in particle tracking. Wear, 426–427: 596–604.

Al-Baghdadi, M. A., Resan, K. K., Al-Wail, M. 2017. CFD investigation of the erosion severity in 3D flow elbow during crude oil contaminated sand transportation. Engineering and Technology Journal, 35: 930–935.

Badr, H. M., Habib, M. A., Ben-Mansour, R., Said, S. A. M. 2002. Effect of flow velocity and particle size on erosion in a pipe with sudden contraction. In: Proceedings of the 6th Saudi Engineering Conference, 5: 79–88.

Banakermani, M. R., Naderan, H., Saffar-Avval, M. 2018. An investigation of erosion prediction for 15° to 90° elbows by numerical simulation of gas-solid flow. Powder Technol, 334: 9–26.

Bazilevs, Y., Takizawa, K., Tezduyar, T. E. 2015. New directions and challenging computations in fluid dynamics modeling with stabilized and multiscale methods. Math Mod Meth Appl S, 25: 2217–2226.

Bonelli, S., Marot, D. 2011. Micromechanical modelling of internal erosion. Eur J Environ Civ En, 15: 1207–1224.

Bounaouara, H., Ettouati, H., Ticha, H., Mhimid, A., Sautet, J. 2015. Numerical simulation of gas–particles two phase flow in pipe of complex geometry: Pneumatic conveying of olive cake particles toward a dust burner. Int J Heat Technol, 33: 99–106.

Egerer, C. P., Schmidt, S. J., Hickel, S., Adams, N. A. 2016. Efficient implicit LES method for the simulation of turbulent cavitating flows. J Comput Phys, 316: 453–469.

Ejeh, C. J., Akhabue, G. P., Onyekperem, C. C., Annan, E. B., Tandoh, K. K. 2019. Evaluating the impact of unsteady viscous flow and presence of solid particles on pipeline surfaces during crude oil transport using computational fluid dynamics analysis. Acta Mechanica Malaysia, 2: 20–27.

Eliyan, F. F., Kish, J. R., Alfantazi, A. 2017. Corrosion of new-generation steel in outer oil pipeline environments. J Mater Eng Perform, 26: 214–220.

Islam, M. A., Farhat, Z. N. 2014. Effect of impact angle and velocity on erosion of API X42 pipeline steel under high abrasive feed rate. Wear, 311: 180–190.

Kesana, N. R., Throneberry, J. M., McLaury, B. S., Shirazi, S. A., Rybicki, E. F. 2014. Effect of particle size and liquid viscosity on erosion in annular and slug flow. J Energy Resour Technol, 136: 012901.

López-López, J. C., Salinas-Vázquez, M., Verma, M. P., Vicente, W., Galindo-García, I. F. 2019. Computational fluid dynamic modeling to determine the resistance coefficient of a saturated steam flow

in 90 degree elbows for high Reynolds number. J Fluids Eng, 141: 111103.

Murrill, B. J. 2016. Pipeline Transportation of Natural Gas and Crude Oil: Federal and State Regulatory Authority. Congressional Research Service.

Najmi, K., Hill, A. L., McLaury, B. S., Shirazi, S. A., Cremaschi, S. 2015. Experimental study of low concentration sand transport in multiphase air–water horizontal pipelines. J Energy Resour Technol, 137: 032908

Njobuenwu, D. O., Fairweather, M. 2012. Modelling of pipe bend erosion by dilute particle suspensions. Comput Chem Eng, 42: 235–247.

Okonkwo, P. C., Mohamed, A. M. A. 2014. Erosion-corrosion in the oil and gas industry: A review. Int J Metall Mater Sci Eng, 4: 7–28.

Parsi, M., Najmi, K., Najafifard, F., Hassani, S., McLaury, B. S., Shirazi, S. A. 2014. A comprehensive review of solid particle erosion modeling for oil and gas Wells and pipelines applications. J Nat Gas Sci Eng, 21: 850–873.

Peng, W., Cao, X. 2016. Numerical simulation of solid particle erosion in pipe bends for liquid–solid flow. Powder Technol, 294: 266–279.

Qi, H., Wen, D., Yuan, Q., Zhang, L., Chen, Z. 2017. Numerical investigation on particle impact erosion in ultrasonic-assisted abrasive slurry jet micro-machining of glasses. Powder Technol, 314: 627–634.

Saniere, A., Hénaut, I., Argillier, J. F. 2004. Pipeline transportation of heavy oils, a strategic, economic and technological challenge. Oil Gas Sci Technol, 59: 455–466.

Sanni, S. E., Olawale, A. S., Adefila, S. S. 2015. Modeling of sand and crude oil flow in horizontal pipes during crude oil transportation. J Eng, 2015: 1–7.

Takizawa, K., Tezduyar, T. E., Kanai, T. 2017. Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity. Math Mod Meth Appl S, 27: 771–806.

Veritas, D. N. 2007. Recommended practice RP O501 erosive wear in piping systems. Available at http://shaghool.ir/Files/EROSIVE- WEAR-IN-PIPING-SYSTEMS-RP-O501.pdf.

Wong, C. Y., Boulanger, J., Feng, Y., Wu, B. 2016. Experimental and discrete particle modelling of solid particle transportation and deposition in pipelines. In: Proceedings of the SPE Asia Pacific Oil & Gas Conference and Exhibition: SPE-182407-MS.

Wong, C. Y., Boulanger, J., Zamberi, M. S. A., Shaffee, S. N. A., Johar, Z., Jadid, M. 2014. CFD simulations and experimental validation of sand erosion on a cylindrical rod in wet gas conditions. In: Proceedings of the Offshore Technology Conference-Asia: OTC-24761-MS.

Yan, J., Korobenko, A., Tejada-Martínez, A. E., Golshan, R., Bazilevs, Y. 2017. A new variational multiscale formulation for stratified incompressible turbulent flows. Comput Fluids, 158: 150–156.

computational fluid dynamic analysis for investigating the ...computational fluid dynamics (cfd) is...

Documents