Analysis on Erosion of Pipe Bends Induced by Liquidsolid Twophase Flow
Abstract:
The effect of particleparameters of a liquidsolid two phase flow on the erosion rate of different sections for pipe bends was analyzed by means of computational fluid dynamics (CFD) in terms of flow rate, particle size and particle velocity etc., while the trajectories of particles were calculated by Lagrange method. Then the relevant erosion mechanism of pipe wall may be acquired by considering the known particle collision model. The results show that: (1) the vulnerable areas mainly exist on the sidewall, as well as the outermost side of the junction of downstream straight pipe and elbow; (2) the change of Stokes number can cause shift of the serious erosion area, whilst not the entire sidewall of the junction of downstream straight pipe and elbow will be subjected to serious erosion. 
Key words: pipe bends erosion solid particle trajectory Stokes number 
Wenshan PENG,Xuewen CAO 
1 Introduction
Erosion erosion generally refers to a phenomenon in which fluid or solid particles impinge on the surface of an object at a certain speed and angle, resulting in material loss [1, 2]. Pipeline erosion is a very complicated process, and it is related to many factors such as pipeline flow, pipe geometry, pipe wall material, fluid properties, sand transport rate, sand grain shape, sand particle size, etc. [3]. Abrupt changes in the direction of oil and gas flow during production or particle collisions due to restricted flow are all important causes of erosion and destruction of components. The liquid/solid twophase flow conditions during the development of oil and gas fields bring serious difficulties to multiphase flow delivery. At present, with the extension of oilfield exploitation time, the content of water and sand in crude oil gradually increases, the crude oil content decreases relatively, and the corrosion rate of oil pipelines gradually increases. During the mining process, there are numerous bend pipes that come in contact with the sandcontaining fluid. The sand particles collide with the pipe components such as the inner wall of the pipe and elbows for a long time, which eventually causes erosion and damage to the pipe system. The life of the sand pipe is significantly shortened, and there are hidden safety problems. Dangerous accidents and huge economic losses.
Domestic and foreign scholars have done a lot of research on erosion erosion of pipes. The research contents mainly focused on computational fluid dynamics (CFD) simulations for the erosion parameters of elbows and the elbow erosion corrosion experiments [7, 8] and Erosion model prediction [912] and so on. In the experiments involving erosion erosion of solid particles, researchers [13–15] studied the effects of changes in particle scouring parameters on erosion through a dynamic rotary scouring device. In addition, Zeng et al [16,17] designed realistic tube flow scour experiments to study the interaction of wall erosion and erosion under specific conditions. In terms of CFD numerical calculations, Wang Kai et al. [18] proposed the concept of relative erosion rate, studied the effect of Stokes number on erosion rate, and analyzed the erosion of particles of a certain particle size at a given flow rate for a given flow rate. Most of the above studies on elbow erosion are based on quantitative studies under specific erosion conditions. The study on the mechanism of elbow erosion under solid particle parameter variation conditions is not perfect. This paper establishes the same numerical model as the shallow sea pipeline fluid direction and gravity direction, analyzes the changes of different particle parameters in the liquid/solid twophase fluid and the influence of different particle trajectories on the elbow erosion, and the relevant conclusions can be obtained for the elbow pipe. Structural optimization and prevention of elbow erosion during offshore oil and gas field development provide some guidance.
2 Calculation Model
2.1 Medium flow model
CFDbased erosion studies have become another powerful tool for studying erosion after the experimental method. This method is based on continuous phase flow field calculation. Through the tracking of the solid particle motion trajectory, the wear equation is used to complete the erosion prediction and the calculation of the wear amount. The continuous phase is characterized by threedimensional, incompressible and turbulent flow. The control equations include continuous equations, momentum equations and kε turbulence models.
2.2 Discrete phase control equations
Solid particles in the fluid are represented by:
Dup dt = FD (u – up ) + gy (ρ p – ρ ) ρ p + F y FD = 18 μ ρ pdp 2 C d R ep 24 R ep = ρ dp  up – u  μ C d = a 1 + a 2 R ep + a 3 R ep 2 (1)
Where: u is the velocity of the water flow, m/s; up is the speed of the sand, m/s; ρp is the sand density, kg/m3; ρ is the density of the continuous phase gas, kg/m3; dp is the sand diameter, m; μ is the gas viscosity, Pa·s; Rep is the relative Reynolds number; Cd is the drag coefficient; gy is the gravitational acceleration in the y direction, m/s2; Fy is the other acting force in the y direction: including the virtual mass force, pressure gradient force And Saffman lift; for spherical particles, a1, a2, and a3 are constants within a certain range of Reynolds numbers [19], see Table 1 for specific values.
Table 1 Relationship between Re and Cd
2.3 Erosion wear model
There are many factors that affect particle erosion, such as pipe shape, fluid velocity, particle characteristics, particle content, and impact angle. According to this paper, the parameters involved in the liquid/solid twophase flow elbow erosion include particle velocity, particle mass flow and particle size. Given that the model proposed by Huser et al. [20] is used by the CFD model and numerous erosion experience models, this paper will This model is applied to CFD software to complete the erosion calculation:
R erosion = ∑ n = 1 N m p C (d p ) f ( θ ) u p b ( v ) A face (2)
In the formula, Rerosion is the wall wear rate, kg/(m2·s); N is the number of collision particles; mp is the mass flow of particles, kg/s; C(dp) is a function of particle diameter; θ is the collision of particles against the wall Angle, (°); f (θ) is a function of the angle of intrusion; up is the velocity of the particle with respect to the wall surface, m/s; b(v) is a function of this relative velocity, taken as 2.6; Aface is the calculation unit of the wall Area, m2.
f ( θ ) = 2.69 θ + 1.61 θ 2 – 8.84 θ 3 + 7.33 θ 4 – 1.85 θ 5 (3)
C (d p ) = 1.8 × 10 – 9 (4)
2.4 Wall collision recovery equation
There is energy transfer and energy loss when a solid particle collides with a wall surface, which mainly manifests in the change of the velocity component before and after the collision [18]. The loss of energy is usually measured as the ratio of the velocity component before and after the collision, and this ratio is defined as the coefficient of restitution. This paper uses the Grant and Tabakoff recovery coefficients [21], which are more commonly used in calculations. The equation is:
ε N = 0.993 – 1.76 θ + 1.56 θ 2 – 0.49 θ 3 ε T = 0.988 – 1.66 θ + 2.11 θ 2 – 0.67 θ 3 (5)
In the formula, T and N represent the tangential and normal directions, respectively.
3 Inpipe particle erosion numerical model
3.1 Pipeline parameters
The model consists of an upstream inlet section L1, an elbow section, and a downstream outlet section L2, as shown in FIG. 1 . The diameter of the elbow pipe is D = 40 mm, and the ratio of the radius of curvature R/D = 1.5. At room temperature, with water as the continuous phase medium, the inlet velocity is 20 m/s, and it flows in from the upstream horizontal straight pipe inlet and flows straight out from the downstream straight pipe. The discrete phase sand density is 2650 kg/m3 and the particle size is 200 μm. Assuming that the initial velocity of the sand is the same as that of water, the mass flow rate is 0.2 kg/s.
Fig.1 Geometric model of pipe elbow and griddivision
3.2 Boundary Conditions and Grid Division
Fluid phase: The standard kε turbulence model was used for the calculation, and the normal wall function was used for the near wall area. Three types of boundary types are set: the inlet uses the velocity inlet boundary, the outlet uses the free flow boundary, the tube wall is the wall boundary, and the boundary layer is set near the tube wall surface. The speed entrance uses the “boundary normal” approach; the specified turbulence description is “turbulence intensity” and “hydraulic diameter”; and the wall boundary is set to “stationary wall” and “nonsliding wall”.
Discrete phase: In the DPM model, Escape conditions are adopted at the inlet and outlet, and Reflect conditions are adopted at the wall surface. It is assumed that the incident particles are mutually independent and uniform spheres, and the combination and fragmentation caused by collisions between particles are ignored. It should be noted that solid particles do not rotate and ignore the collision between particles [22]. Particle trajectories are solved using Lagrangian equations. Due to the small concentration of solid particles in the flow field, the fluid velocity of the continuous phase is large, and there is a large density difference between the continuous phase and the discrete phase. Therefore, the virtual mass force, the pressure gradient force, and the Saffman lift effect of the solid particles are affected. Force will not be considered [23].
The multiphase model uses a discretephase model. The pressure and velocity coupling uses the SIMPLE algorithm. The momentum, turbulent kinetic energy, and turbulent dissipation rate are discretized using the secondorder upwind style. The discrete phase is calculated using bidirectional coupling. Before the calculation starts, the discrete phase model is opened by adding discrete phase particles, the flow field is initialized, and the phasetophase coupling is set. After each fivestep continuous phase, discrete phase orbit calculations are performed, and then the updated discrete phase momentum and energy are added. The next step in the calculation of the continuous phase equation. In the calculation process, the residual and the wallweighted average wear amount are used as the evaluation basis for the calculation of convergence.
When meshing, in order to improve the calculation accuracy, a boundary layer treatment is performed near the pipe wall, as shown in FIG. 1 .
3.3 Grid and Elbow Length Settings
The grid type and size relate to the calculation accuracy and the total amount of calculations. Gridindependent analysis can get the density of the mesh suitable for this problem and guarantee the accuracy of numerical simulation results. Assuming that the upstream and downstream lengths are 5 times the diameter (5D), the relationship between the erosion rate and the grid is shown in Figure 2. It can be seen that with a smaller number of meshes, the corrosion rate exhibits irregular wavelike changes with the increase in the number of meshes. When the number of meshes reaches 3.2×105, the corrosion rate tends to be stable. Therefore, in the premise that the calculation amount is allowed, in order to minimize the calculation error, a grid division method with a grid number of 3.2×105 is used when dividing the grid.
Fig.2 Erosion rate vs grid curve
Because the tube is turbulent and the flow distribution is not uniform, the upstream and downstream lengths in the liquid/solid twophase flow process also have a large effect on the erosion rate. When the fluid flows in a steady state in a circular straight tube, the flow velocity distribution and flow pattern in each section in the tube remain unchanged. However, in numerical calculations, when a velocity inlet uniformly distributed along the cross section is provided, a long straight tube is required to achieve the flow velocity and flow pattern in the steady flow in the straight tube. In order to ensure the full development of the liquid/solid twophase flow in the pipe, the erosion rates of the same length of the upstream and downstream pipes, the lengths of different upstream pipes, and the lengths of different downstream pipes were analyzed, respectively. When the lengths of the upstream and downstream pipelines are the same, the erosion rate increases as the length of the upstream and downstream pipelines increases. When the upstream and downstream pipeline lengths reach 18D, the erosion rate tends to be stable, indicating that when the upstream and downstream pipeline reaches this length, the turbulence rate As the pipe erosion tends to be stable, 18D is determined to be the maximum length of the upstream and downstream pipe erosion. When the length of the downstream pipeline remains unchanged at 18D, the erosion rate increases slowly with the increase in the length of the upstream pipeline; when the length of the upstream pipeline remains 18D, the erosion rate gradually increases as the length of the downstream pipeline increases. increase. From the figure, we can see that with the increase of the length of the upstream pipeline, the erosion rate caused by the increase in the length of the downstream pipeline is greater, indicating that changing the upstream pipeline length has a greater impact on the erosion rate.
Fig.3 Erosion rate vs upstream and downstream lengthcurves
Based on the above analysis results, the length of the pipe upstream of the bend pipe is 18D and the length of the downstream pipe is 16D.
4 Results and Discussion
4.1 Effect of particle flow rate on elbow erosion
Because of the special role of maximum erosion rate in engineering safety production, it is of great significance to analyze the relationship between the change of particle parameters and the maximum erosion rate. The relationship between the particle flow rate and the maximum erosion rate is shown in Fig. 4 at a particle size of 200 μm and a particle flow rate of 0.2 kg/s. It can be seen from Fig. 4a that the maximum erosion rate increases with the increase of the particle flow rate, showing an exponential relationship, indicating that the speed factor has a greater influence on the maximum erosion rate. The maximum erosion rate of particles at each section in the bend is shown in Figure 4b. It can be seen that, at the same crosssection, the maximum erosion rate also increases with the increase of the particle velocity, and the faster the erosion rate increases with increasing velocity; at different crosssections, at the same velocity, along the crosssection of the elbow In the direction of flow, the erosion rate gradually increases, and the erosion rate increases at high flow rates. It can be seen that within a certain range of flow velocity, the greater the velocity in the elbow, the greater the erosion rate and the faster the increase in the elbow along the flow direction.
Fig.4 Maximum erosion rate as functions of particle velocity (a) and bend section position (b)
4.2 Effect of Particle Flow on Elbow Scour
The relationship between the different particle flow rates and the maximum erosion rate is shown in Fig. 5 for a particle size of 200 μm and a particle flow rate of 20 m/s. Figure 5a shows that there is a positive relationship between the particle flow rate and the maximum erosion rate. With the increase of the particle flow rate, the maximum erosion rate gradually increases, indicating that the increase of the particle flow rate exacerbates the wear of the elbow. It can be seen from Figure 5b that, at the same crosssection, the erosion rate increases as the particle flow increases, but the erosion rate increases more evenly. At the same flow rate, the eroding rate of the crosssection increases gradually along the flow direction, but the increase rate is small. Therefore, the effect of the particle flow rate on the erosion rate is not significant. The literature [24] proposes that the erosion rate no longer increases when the particle flow increases to a certain amount.
Fig.5 Maximum erosion rate as functions of particle flow rate (a) and bends ection position (b)
4.3 Effect of particle size on elbow erosion
The relationship between the particle size and the maximum erosion rate is shown in Fig. 6 at a particle flow rate of 20 m/s and a particle flow rate of 0.2 kg/s. Figure 6a shows that the maximum erosion rate increases with the increase of the particle size in the 100250 μm particle size range, while the maximum erosion rate is smaller than the particle size of 100 μm when the particle size is 50 μm. There is an increase, mainly because the fluid has a better carrying effect on the particles with smaller particle size, and the collision between the particles and the wall surface is more adequate, and the secondary flow in the elbow tube has a more obvious influence on the smaller particle size particles, resulting in a more obvious Large erosion rate. When the particle size is large, the inertial force plays a dominant role. The larger the particles, the greater the inertial force and the greater the collision energy. The colliding of the particles along the flow direction with the tube wall results in a larger erosion rate of the elbow.
Fig.6 Maximum erosion rate as functions of particle diameter (a) and bend section position (b)
The maximum erosion rate for different bend sections is shown in Figure 6b. The particle size is in the range of 100250 μm. Due to the inertial force, the particles collide with the direction of the incoming flow, so the erosion rate is larger at the larger cross section. The particle size of 50 μm, due to the smaller particle size, is significantly affected by the secondary flow at the elbow, so the erosion rate at the inner side of the elbow is greater, but at the 90° cross section, there is no larger front cross section.
4.4 Analysis of Relationship between Particle Trajectory and Erosion
In order to study the effect of the interaction of solid particle size, velocity and flow rate on erosion erosion of the elbow, the Stokes number was used to analyze the mechanism of the above factors affecting erosion. The Stokes number expression is:
St = ρ p d p 2 u 18 μD (6)
In the formula, St is the ratio of particle relaxation time and fluid characteristic time, represents the relative size of particle inertia force and drag force, and is a dimensionless parameter that characterizes the motion of the particle curve. When the Stokes number is close to 0, the particles can move with the streamline; with the increase of the Stokes number, the particles can no longer completely change its direction of movement with the streamline. When St<1, the particles follow the fluid better; when St≫1, the particle motion is affected by the change of the fluid velocity relatively small.
Figure 7 shows the particle motion trajectories obtained using the Lagrangian tracking method. The square marks in the figure indicate that there are two areas with more severe erosion: (1) the sidewalls of the downstream straight pipe section and the elbow joint, and (2) the outside of the downstream straight pipe section and the elbow joint. As can be seen from the figure, severe erosion does not occur in all cases where the downstream straight pipe section and the elbow joint are in the sidewall region. In order to study the relation between particle trajectory and erosion, the particle trajectory and erosion rate under different Stokes numbers were analyzed.
Fig.7 Schematic illustrations of particle trajectory and erosion rate under different conditions of particle velocity (a), particle flow rate (b) and particle diameter (c)
The relationship between particle trajectory and erosion rate at different particle flow rates is shown in Figure 7a. With the increase of the Stokes number, the erosion rate of the inner area of the outlet straight pipe section and the elbow joint is getting smaller and smaller. On the contrary, the erosion rate of the outer area of the straight pipe section and the elbow joint is increasing, which is mainly due to the particles. The larger the particle size, the less influence of the secondary flow on the particles, and the erosion of the inside of the joint between the downstream straight pipe section and the elbow is mainly caused by the rebound effect of the wall facing the particles, resulting in the frequent collision of the particles at that location. Not significant; larger particle sizes make the inertial force dominant, combined with increased flow velocity at the elbow, more collisions between the particle and the downstream straight pipe section and the elbow, collision energy increases, erosion rate increases The bigger.
The relationship between particle trajectory and erosion rate under different particle flow rates is shown in Figure 7b. Since only the flow of particles was changed while the other parameters remained unchanged, the Stokes number of the particles was unchanged at 2.915. When the particles reach the elbow, the flow velocity of the particles increases due to the action of centrifugal force, and the erosion at the outer tube wall of the elbow is more serious. As the particle flow increases, the number of collisions between the particles and the wall increases, so the erosion area and erosion The rate also gradually increases.
The relationship between particle trajectory and erosion rate under different particle size is shown in Figure 7c. With the increase of Stokes number, the erosion area of the downstream straight pipe section becomes smaller and smaller. This is mainly due to the fact that the drag force plays a major role when the particle size is small. The particles move along the flow line and the particles do not easily impact through the streamline. The wall surface, therefore, makes the erosion area of the pipe wall of the downstream vertical pipe section larger; furthermore, the sidewall region of the connection between the outlet straight pipe section and the elbow gradually changes from severe erosion to light erosion, and on the contrary, the connection between the straight pipe section and the elbow. The erosion rate of the area gradually changes from slight erosion to severe erosion. This is mainly due to the fact that the erosion of the sidewalls at the junction between the downstream straight section and the elbow is mainly caused by secondary flow. Secondary flow occurs when the grain size is small. The effect on the particles is significant, and the resultant velocity at this point is rushed toward the tube wall, thus making the erosion rate inside the downstream straight tube section and the elbow joint larger. With the increase of particle size, the inertial force dominates, the secondary flow becomes less and less obvious to the particles, and the flow velocity at the elbow increases. The number of collisions between the particle and the downstream straight pipe section and the elbow joint is more and collision occurs. The increase can make the erosion rate of the side wall of the joint decrease, and the erosion rate of the outer side of the joint increases.
5 Conclusion
(1) In a certain range, the maximum erosion rate of the elbow increases with the increase of the particle flow rate and the particle flow rate, but does not increase with the increase of the particle size. When the particle size is small, the maximum erosion rate of the elbow may be greater than the erosion rate when the particle size is larger.
(2) Areas prone to erosion damage are the outer area where the elbow is connected with the downstream straight pipe and the side wall area of the straight pipe section near the outlet of the elbow. The severity of the corrosion in these two areas changes with the Stokes number. Changed. With the increase of the Stokes number, the secondary flow has insufficient effect on the particle carrying, resulting in gradual erosion of the sidewall area at the junction between the outlet straight pipe and the elbow, until there is no serious erosion; and the outlet straight pipe and As the Stokes number increases in the outer region of the elbow joint, the degree of erosion gradually increases due to the inertial force and the number of collisions.
The authors have declared that no competing interests exist.
Source: Network Arrangement – China Pipe Bends Manufacturer – Yaang Pipe Industry (www.metallicsteel.com)
(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless steel products, including Super Duplex Stainless Steel Flanges, Stainless Steel Flanges, Stainless Steel Pipe Fittings, Stainless Steel Pipe. Yaang products are widely used in Shipbuilding, Nuclear power, Marine engineering, Petroleum, Chemical, Mining, Sewage treatment, Natural gas and Pressure vessels and other industries.)
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