Erosion Analysis for the Carcass of Unbonded Flexible Pipes

At present, unbonded ﬂexible pipes (UFPs) are widely used in ocean engineering for oil exploitation. In practice, erosion will lead to premature failure of pipelines. There is a lack of researches on the erosion of interlock carcass of UFPs. As the authority in the ﬁeld of offshore engineering, DET NORSKE VERITAS(DNV) suggested a way to estimate the erosion rate of pipes, however, it does not study the erosion mechanism of UFPs in detail and the relevant parameters are not speciﬁed. This paper modiﬁes erosion prediction of UFPs based on a user deﬁned Fortran subroutine. A series of CFD simulations have been conducted, and three widely used erosion models were used for comparative veriﬁcation. The effect of geometric shape on erosion rate has been carefully studied. and the effect of velocity, particle size, and concentration are also studied to verify the reliability of the improved model.


Introduction
Flexible pipes are important components of offshore platforms, especially in offshore oil engineering and deep-sea mining industry. As the depletion of offshore and shallow onshore oil resources, it becomes more and more important to explore the deep sea in which submarine pipelines as the foundation of marine engineering have been more widely used 1 . Among them, UFPs play an increasingly important role due to the excellent tensile and compression performance brought by their multilayer composite structures 2 . The typical structural is shown in Figure 1. UFPs usually consist of eight layers. They are polymeric layers, including anti-wear tapes, fluid barriers and outer sheath, provide leak-proof capacity in respect. In the meantime, they can reduce the friction abrasion between metallic layers and protect pipes against seawater ingress in the annulus 3 . The sealing is provided by the concentric polymeric layers. And the internal and external pressure is resisted by the interlocked metallic layers when the axial loads and torsion are carried by the helically wound tensile armour wire layers 4 . Generally, the curvature of the buoyancy segment is smaller than typical riser structures. The comparison results of the two forms are shown in the Figure 2. Erosion in pipes with smooth surface has been studied a lot for more than 50 years, especially of 90-degree bends and T-branch pipes. Finnie 5 was the first to propose erosion model and Oka erosion model was proposed 6 later. In recent years, Homicz 7 performed simulations of flow in a constant radius smooth 90°bend. Yang 8 investigated the relationship between slurry flow velocity and confirmed the effects of impact angle on electrode surface status and E-C rate. Then Cheng 9-12 discussed erosion-accelerated in flow systems. Arun 13,14 investigated the fluid dynamics and wall erosion characteristics in 90-degree circular bends. Wang [15][16][17] developed an erosion equation with the consideration of applied stress for the first time and simulated the erosion of high-pressure pipe bends considering fluid-induced stress. Peng and Cao 18-20 analysed the erosion profile and explained the erosion mechanism through an experimental facility and CFD simulation. Kumar 21 studied the erosion of AISI 316 pipe bend and the optimal distance of pacing the vane under different angles and velocities. Liu and Zhang [22][23][24] derived a theoretical solution to the movement and erosion of solid particles in a bend and proposed a simplified CFD-based erosion prediction procedure to calculate the erosion rates in elbows for annular flow. Kannojiya 25 simulated erosion using ANSYS CFX and the results can be employed in industrial flow applications.
From previous research 26 , erosion in pipes with smooth inner surfaces can be easily predicted with industry-standard prediction methodologies. However, there is little information available on erosion of UFPs 27 which has interlock carcasses existing on the inner surface. Not all bending pipes have smooth inner wall, and there is a lack of research on erosion of single-ply bellows such as flexible pipes. To date, few works have addressed the erosion of the carcass. For example, DET NORSKE VERITAS has not given the specific value of GF in the assessment of UFPs. Only a minimum of GF for the leading edge of the interlock carcass was proposed and the specific erosion mechanism is not clear.
The present work shows that the value of erosion calculated by the DNV theory is too small, which may cause serious safety problems in practical projects. Therefore, a series of numerical simulations were done to develop an improved model in this paper, and the predicted value was compared with the numerical simulation results. Finally, the variation of erosion rate with geometric shape was investigated to determine function value of the improved model.

Results
In this paper, the erosion rate for the carcass of UFPs has been firstly analyzed and results have been compared with pipes with smooth inner surface using several erosion models. In order to verify new model, the effects of velocity of particles, size of particle and the concentration of particles have been studied. In the end, modification of the convex parameters is provided. It can be concluded that: The simulation results of the new model under various conditions are more accurate than those of DNV specification. It has been found that erosion rate increases with fluid velocity increasing, concentration and size of particles. In all cases, the erosion rate of DNV model is slightly greater than that of Tabakoff model. When the velocity is low, the predicted results of Finnie model are in good agreement with other groups. As the velocity increases, the erosion difference increases significantly.
As the roughness of convex structure increases, the erosion rate increases firstly. When the length of pits is close to radius of arcs, the erosion rate comes to maximum and then decreases. The improved model was summarized.

Discussion
To validate the presently adopted DNV standard, a separate numerical study was carried out on smooth pipes, which was compared with each other. The CFD analysis results of erosion rate density, streamlines and particles tracking of the smooth pipes and UFPs are shown in Figure 3. In smooth-faced pipes, the erosion rate distribution varies between 4.156*10 −8 kg/(m 2 * s) and 8.2671 −6 kg/(m 2 * s). The erosion rate by using Finnie and Tabakoff model have been calculated from 1.537 * 10 −8 kg/(m 2 * s) to 1.254 * 10 −4 kg/(m 2 * s). The maximum erosion is near the outside profile the same as a standard 90°bend. The velocity of initial particles are perpendicular to the inlet surface which are uniformly distributed. From the statistical conclusion of the experiment, the maximum erosion area is strip equidistant distribution and is located outside pipes. For UFPs, an obvious conclusion is that the site of erosion is located at the innermost part of the carcass and velocity of particles near pipes decreases as shown in Figure 3.

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Effect of Pressure These four sets of graphs are the erosion results at 20m/s. As the blue darkens, the erosion rate decreases. The most severe corrosion occurs in the pit, which is the result of multiple rebound particles in it. According to the particle trajectory graphs, we can find that the number of particle collisions in UFPs is significantly greater than that in the smooth pipes, which explains the large erosion rate of UFPs. The pressure distribution of the four models when the speed is adjusted to 20m/s is shown in Figure 4, which depicts the pressure distribution in UFPs. It is shown that pressure in outer-side elbow is higher than that in the inner-side elbow.   For the new computation model, different geometry parameters will be discussed in this section. From figures above, it can be found that the main eroded part of UFPs is the pit.

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In this part, its length has been changed to decrease value of erosion. As shown in Fig.11, when the length of pits is less than 11mm, the erosion rate increases with the increase of length. However, when the length of pits is greater than 11mm, the erosion rate decreases with the increase of it. When the length is small enough, the outer length is larger and the inner surface is smoother. Similarly, when its large enough, inner surface is rougher. It is easy to find that when its value between 10mm and 35mm, the probability of particle collision is the highest, leading to the most erosion rate. Therefore, the optimal length of pit should be evaluated at both ends of the curve.
In the meantime, Figure 6 illustrates f(Le/r) is an unimodal function. The sensitivity analysis in the following part will also prove this point.

Effect of impact velocity
Impact velocity is compared to pipes with a smooth inner surface, the maximum erosion result of UFPs is greater. And the difference increases as the velocity increases. The erosion results under four conditions were compared as shown in Figure 7.
In the legend, 'DNV', 'Tabakoff' and 'Finnie' means that the result is obtained by 'DNV', 'Tabakoff' and 'Finnie' models. In the legend, '0.5 Improved' means erosion results of pipes with smooth surfaces with improved model and the number in front of it represents coefficient of f(Le/r).  Conclusions can be drawn that the erosion results of DNV model is about equal to that of the improved model. When the velocity increases, the difference of erosion rate between DNV model and 1.5 improved model is not significant. It is safe to use only when its value is greater than the specification value.Referring to the conversion of DNV formula, we found that when the velocity was 10-60m/s,only the erosion rate of '1.5 Improved model' meets the specification.

Effect of Particle Concentration
With the increase of particle concentration, the erosion rate increases almost linearly. Consistent with the above conclusions 28 , the erosion rate of DNV model at various concentrations was slightly higher than Tabakoff model. A conclusion can be drawn from Figure 9 that improved model is applicable to the erosion rate prediction under various particle size gradients and the value of f ( Le r ) is 1.4. Based on the discussion above, f ( Le r ) should take the maximum of a reasonable value in order to make the rapid prediction more accurate under the circumstance of ensuring safety.

Effect of Particle Size
Erosion rate density increases to a maximum value when the value of particle diameter is 500µm. The rate rises with the increase of particle size as shown in Figure 10.
Consistent with the above results, the erosion rate of UFPs is higher than that of pipes with smooth surfaces. Among three parameters, The maximum value is obtained under the condition that DNV model is used. Only when the value is lower than the standard value can it operate safely and pass the institution inspection .The coincidence rate between '1 Improved' model and DNV curves is very high, ans some of the lower values are danger points. Hence, the most appropriate value of f ( Le r ) is 1.75.

Modification of the Convex Parameters
Considering all cases, the following conclusion can be reached. Because the inner wall of UFPs is uneven, the number of collisions between particles and walls increases significantly. With the number of collisions increases, the erosion rate will increase significantly. Therefore, the erosion rate of UFPs is higher than that of smooth pipes.  In order to satisfy the needs of accuracy and safety at the same time, considering all cases above, the value of convex parameters should take the minimal maximum. Therefore, it is suggested that the value of Le r should be modified to 1.75.

Methods
Due to the entrainment of a large number of particles in the multiphase flow, the innermost interlock carcass will be eroded. Erosion depends on surface, granular flow properties and erodent. In general, the curvature radius of UFPs are greater than pipes with smooth inner surfaces. Up to now, most of the researches are focused on tubes with smooth inner surfaces. The curved area of interlock carcass inside the flexible pipes is cratering, which will have a completely different erosion result from the previous studies.
The sand particles are mixed with petroleum, making the solution more viscous. The oil slurry is usually transported to FPSO (Floating Production, Storage and Offloading Unit) or the desired place using pipelines 29,30 . A schematic of particle erosion is shown in Figure 11. If angles between 0-18.42°, sliding wear dominates, otherwise, impact wear dominates 31 . And for most of the curved made by the standard cast iron, if angles between 40-45°, impact wear dominates 32 . Figure 11. Erosion Sketch of UFPs and Conventional Pipes.

Interlock Carcass Physical Parameters
The configuration of carcass profiles is shown in Figure 12. Since we only focus on the internal flow field in this paper, its outer profile was simplified by taking the centre line as the axis and the inner side as the edge line. The simplified edges are highlighted in Figure 12. The comparison results of the two pipes are shown in the Figure 13. According to the API specification 33 , the model parameters are shown in Table 1 represents the influence of the convex structure of the skeleton layer on the erosion results. Le means the length of pit in Figure 12, r represents the radius is the radius of the arcs,G 1 G 2 G 3 are convex parameters related to convex 8/11 Figure 13. Comparison of Two Kinds of Pipes.
structures, K represents the material erosion constant, F(α) is the function characterizing ductility of material,U P represents the particle impact velocity, G represents corrections function for particle diameter, C 1 represents geometry factor, M P is the mass of sand, ρ t means the density of target material, A t is the impact area of particles, some relevant properties are shown in Table 2.

Parameters
Symbols Values The Model Geometry Factor C 1 2.5 The Unit Conversion Factor C unit 3.15 * 10 10 The Geometry Factor GF 2 Table 2. Parameters of DNV Model.
In this paper, Finnie and Tabakoff erosion models were used to derived the improved model, both of which are widely used in industry. Detailed information of these two models are shown as follows: where n = 2, V p is the particle impact velocity, α is the particle impact angle. In the Ansys CFX, we use V 0 = ( n 1 k ) to simulate different materials.

Tabakoff model
Relative parameters are made to be tally with the actual situation [43]. In this model, the erosion rate is determined from the following relation: where R T = 1 − V P V 3 sinγ and the value of k 12 k 2 V 1 V 2 and V 3 are shown in Table 3 Particles tracking model In order to predict the trajectory of particles in UFPs and to figure out the erosion path, integrating the solution of force balance equation is needed. The equation is shown in the following: where F D represents the drag force, v L means the velocity of liquid, v L means the velocity of solid, F represents the force per unit paticle mass, g means gravity, rho s and rho L are the density of solids and fluids.