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Sand erosion experiments and modeldevelopment for UNS N06625 claddingand UNS S32750BY GURUPRASAD KULKARNI, RAVINDRA DEVI, BIJU DASAN, PAUL MATHEW /GE GLOBAL RESEARCHYONGLI ZHANG, EMAD GHARAIBAH, JOHN DANIEL FRIEDEMANN /SUBSEA SYSTEMS, GE OIL & GAS

Copyright 2012, Offshore Technology Conference

This paper was prepared for presentation at the Offshore Technology Conference held on 30 April – 3 May2012, Houston, Texas.

AbstractMaterial loss due to sand erosion can cause severe damage to oil and gas production facilities andlead to leaks and ruptures if left undetected. The design of oil and gas production equipment tosafely withstand sand erosion and simultaneously optimize production requires a reliable erosionprediction tool. One of the key requirements for such a tool is that it correctly models both theerosion resistance of the exposed materials and the effects of the particle impact trajectories andvelocities.

Key to this is a full understanding of the individual materials and their impact resistance. This isbecause the impact behavior varies very much between materials and models cannot be simplified to two approaches: ductile or brittle. Model validity must be questioned as the oil industry begins toimplement hardened and high chrome content materials.

UNS N06625 and UNS S32750 are two of the popular alloys in the subsea industry. Despite the popularity of these materials, little erosion data or validated models for either application are found inthe literature. Another significant gap is related to experimental studies aimed at understanding the erosion caused by fines.

To fill this gap and provide verification of the existing models, a series of experiments were conducted and analyzed. Direct impact erosion experiments for UNS N06625 cladding and UNS S32750were conducted using sand particles carried by air at ambient temperature and pressure. The sand particle sizes ranged from 27 µm to 619 µm, sand particle velocities from about 25 m/s to 160m/s, and impact angles from 15° to 90°. An erosion correlation for each material was derived from these experimental data. The erosion correlations were then applied within a CFD (ComputationalFluid Dynamics) model for a typical subsea assembly to demonstrate the applications. A significant contribution is that these experiments and correlations provide an input to the understanding oferosion for the full range of particle size, impact angles and velocities, and how these are related to erosion in modern corrosion resistant alloys (CRAs).

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Introduction

Sand erosion is commonly encountered in the oil and gas industry. Severe damage to the production facilities can occur if the sand is not handled properly. The sandproduced with oil and gas is normally filtered down hole and monitored at various critical locations in the pipeline. The down hole sand screen limits the size and amount ofsand that can move through it. The material of the pipeline and other components is also important for mitigating the sand erosion damage. UNS N06625 and UNS S32750are two of the popular alloys in the subsea industry. Sometimes, the oil and gas production rate has to be limited due to excessive sand erosion. The design of the oil and gasproduction systems to safely withstand sand erosion and simultaneously optimize production requires a reliable sand erosion prediction tool. Tulsa SPPS [1] and DNV RPO501 [2] are the two methods widely applied in the oil and gas industry for predicting sand erosion. One of the key ingredients of these methods is the erosion correlation,which calculates the erosion rate from the parameters that are believed to affect the erosion rate the most. The accuracy of the erosion correlation is thus very importantfor the erosion rate prediction.

A wide variety of erosion correlations have been developed by many investigators. Meng and Ludema [3] examined various erosion correlations in the literature. Theyconcluded that no single erosion correlation is accurate for practical use across the the range of parameters affecting erosion. Based on the literature survey, theyconcluded that there are four primary mechanisms by which solid particle erosion occurs. These mechanisms are:

Cuttings wear (which is defined as indentation of a material surface by a sharp solid particle followed by fracture of the material) and plasticdeformation (perhaps referring to deformation beyond the elastic deformation and followed by fracture of the material)Cyclic fatigueBrittle fracture ("non-cyclic failure")Melting of the materials

These mechanisms were proposed by various investigators to explain the erosion, or in general, the wear process. The real erosion process is much more complex thanwhat can be explained by these mechanisms. Many parameters were investigated and incorporated into the erosion correlations found in the literature. For the sand erosionencountered in the oil and gas industry, the important contributing factors are believed to be the sand particle impact velocity and angle, the pipeline material hardness, andthe sand particle size and sharpness [1, 2, 4, 5].

As discussed above, the existing erosion models do not correctly describe the materials currently in use by the subsea industry. UNS N06625 and UNS S32750 are widelyused in subsea oil and gas pipelines but there is little erosion data in the literature. Another challenge is that there is little erosion data for very small sand particle size (< 50µm). Fine sand was believed to cause insignificant erosion damage. However, some recent evidence shows that these fines can cause severe erosion damage under certainconditions [6]. Fines are almost inevitable in oil and gas production since they can escape through most sand screens.

There are two major objectives of this work. The first one is to generate erosion data using both fine and coarse sand grain sizes. The second is to develop erosioncorrelations for UNS N06625 and UNS S32750 from these data. The ultimate goal is to implement these erosion correlations into various sand erosion prediction tools andprovide more accurate sand erosion prediction for oil and gas production systems.

Figure 1Schematic of the test facility

UNS N06625 UNS S32750Sample Length 76.2 mm 76.2 mm

Sample Width 25.4 mm 25.4 mm

Sample Thickness 10 mm 5 mm

Sample Weight 200 g 80 g

Surface Roughness Ra = 0.2 µm Ra = 0.2 µm

Vickers Hardness 2.26 GPa 2.69 GPa

Sample Cleaning Using acetone in an ultrasonic cleaner for 5 minutes

Table 2Key parameters of the erosion samples

Figure 2Erosion sample and the sample holding assembly

Figure 2aErosion sample before (top) and after (bottom) the test

Description of the experimentsA direct impact test rig has been designed. The experiments were conducted in air-under-room conditions (1 atm,24°C). Figure 1 shows a schematic of the test rig. It consists of the compressor, the sand feeding system, the venturidevice for mixing the sand and air, and the test section. The test section is a transparent acrylic cabin with two ofthe walls made of borosilicate glass to enable velocity measurement using LDV (Laser Doppler Velocimetry). Adouble-disk device can also be put in the test section for measuring the sand particle velocity. The sand feedingsystem consists of a hopper with a pneumatic vibrator that feeds the sand particles onto a slowly rotating disk thatdrops the sand particles into the venturi device. The sand feeding rate is maintained at about 10 g/min for all cases.The volumetric sand concentration varies depending on the airflow rate, with the highest value of about 0.014%.The test duration ranges from about 9 to 16 minutes, depending on the particle velocity. Lower velocities weretested for longer times to achieve measurable erosion. The venturi device creates a relatively low pressure regionand draws the sand particles in. The mixture of sand and air is then accelerated through the nozzle to the requiredvelocities. The erosion samples are mounted at the exit of the nozzle which is designed according to ASTM guidelineG76 [7]. The nozzle is made of stainless steel and has an ID of 5 mm and length of 125 mm. The distance betweenthe nozzle exit and the surface of the erosion samples along the nozzle centerline is maintained at 10 mm. Afterimpacting the erosion sample, the sand particles fall into a collecting hopper that is connected to a dust collector atthe bottom of the test section. The dust collector is filled with water to prevent the fine particles from flying out tothe atmosphere. The airflow is controlled and monitored with a pressure gage that can regulate air pressures to amaximum of 6 bars. The velocity of air and particles is controlled using the pressure gage. The key parameters aresummarized in Table 1.

Carrier Fluid Air under room conditions (1 atm, 24°C)

Line Pressure 6 bars

Sand Feed Rate 10 g/min

Volumetric Sand Concentration < 0.014%

Test Duration 9 to 16 min

Nozzle ID 5 mm

Nozzle Length 125 mm

Nozzle-Coupon Distance 10 mm along the nozzle centerline

Table 1Key parameters of the test rig

Erosion samplesTwo types of materials were tested in this work, the Ni-based alloy UNS N06625 and the highchrome alloy UNS S32750. UNS N06625 is normally used for cladding due to its excellentweldability and erosion/corrosion resistance. UNS S32750 is also widely used in the harshoffshore environment due to its great mechanical strength and corrosion resistance. In thiswork, the erosion samples are rectangular shaped (1 inch by 3 inches). The thickness of theUNS S32750 samples is about 5 mm, with a weight of about 80 g per sample. The UNSN06625 samples are thicker (about 10 mm) since they are a combination of an AISI 4130substrate and the UNS N06625 cladding. The weight of a UNS N06625 sample is about 200 g.The sample surfaces subject to sand impact are polished to Ra = 0.2 µm. The average Vickershardness (Hv) is about 2.26 GPa for the UNS N06625 samples and 2.69 GPa for the UNSS32750 samples. The samples are cleaned in acetone in an ultrasonic cleaner for 5 minutesand weighed. Weight measurements are made before and after each test. Figure 2 shows pictures of a typical erosion sample before and after the test, and the erosionsample holding arrangement. The key parameters of the erosion samples are summarized in Table 2.

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Figure 3Sand particle size distribution.

Figure 4Sand sample SEM pictures

Case No. dP (µm)θ

(degree) VP (m/s)

1 27 15 69.2

2 27 15 161.6

3 78 15 25.7

4 211 15 110.7

5 619 15 44.3

6 619 15 161.3

7 78 25 110.7

8 211 25 41.0

9 211 25 157.2

10 619 25 22.7

11 619 25 71.5

12 619 25 161.3

13 27 35 24.8

14 27 35 161.6

15 211 35 26.3

16 211 35 72.4

17 211 35 157.2

18 619 35 44.3

19 619 35 108.1

20 27 45 24.8

21 211 45 157.2

22 619 45 22.7

23 619 45 108.1

24 27 60 161.6

25 619 60 161.3

26 27 90 69.2

27 211 90 26.3

28 211 90 157.2

29 619 90 22.7

30 619 90 108.1

31 27 60 24.8

32 211 60 72.4

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Sand used for the erosion testFour different size ranges of sand were used in this work. These are naturally occurring sand (Silica, SiO2) from mines (Tumkur mines in Karnataka state, India), washed,crushed and sieved to the required sizes. The D50 sizes of these four types of sand are 27 µm, 78 µm, 211 µm, and 619 µm (). Due to the mechanical crushing, the sandparticles have an angular shape, as seen in the Scanning Electron Microscopy (SEM) pictures ().

Measurement equipmentThe weight of sand and erosion samples is obtained using a high resolution digital balance (Sartorius model CPA 225D). Thisdigital balance has an upper limit of 220 g and a resolution of 0.1 mg.

The air flow is regulated using a digital pressure gauge which has a resolution of 0.1 bar. In addition, a pitot tube is used tomeasure the air velocity at the nozzle exit to ensure consistency of the air flow rate. An anemometer is also used to measurethe air velocity for a lower range, up to 30 m/s.

The sand particle velocity was measured using a double-disk device. The distance is 10 mm between the nozzle exit and thetop disk, and 24 mm from the top to the bottom disk. The width of the four slits on the top disk is 1.5 mm each. Formeasurements, the double-disk device is set at 1000 rpm for the 619 µm sand and about 3000 rpm for the other sand sizesto ensure that a measurable scar is formed on the bottom disk. The double-disk is considered acceptable for measuringparticle velocity in erosion tests according to ASTM G76 [7]. However, the accuracy of the double-disk measurements may bequestionable due to the errors induced due to manual measurement of the scar and also the wide range of sand particlesizes and velocities explored in this work. Laser Doppler Velocimetry (LDV) is scheduled for measuring the sand particlevelocity to achieve better accuracy in the next stage of this work. The sand particle velocities reported in this paper are basedon double-disk measurements.

Design of experiments (DOE)DOE is a systematic way of evaluating the variables within a design space and analyzing the resulting responses in order toquantify the effects of inputs on the responses while using a minimum number of experimental runs. In this work, theexperiments for evaluating the erosion behavior were designed using an optimal DOE method [8, 9] that maximizes theamount of information from a fixed number of experiments.

The experiments were planned for the following three parameters, angle of impact (θ), particle size (dP) and particle velocity(VP). These three parameters define the basic design space for the DOE (Table 3). The hardness of the materials is used insome erosion correlations [1, 4, 5]. However, using the hardness to characterize the material’s erosion resistance isquestionable. In this work, the hardness is not included in the DOE because it is kept constant for each of the two materialsand an erosion correlation will be developed for each of the two materials. The full test matrix, based on a full factorial DOE,would consist of 120 cases for each test material. The number of actual test cases was reduced to 36 by applying the Q-optimal criterion during the DOE. Table 4 lists the tested cases along with the corresponding parameters.

dP (µm, measured D50 values) 27, 78, 211, 619

θ (degree) 15, 25, 35, 45, 60, 90

VP (m/s, nominal values) 25, 40, 70, 110, 160

Table 3Basic Design Space for the DOE

33 78 60 41.234 78 15 158.2

35 78 35 75.5

36 78 45 158.2

Table 4Q-Optimal DOE – Tested Cases and Parameters

Figure 5Experimental results of UNS 06625

Figure 6Experimental results of UNS S32750.

Experimental resultsThere are 36 test cases conducted for each of the two materials. Each test case was repeated three times. Figure 5 and Figure 6 plot the results for all tested cases in theorder of increasing percentage of the standard deviation with respect to the mean erosion rate. The repeatability of the measurements is considered good for most cases.

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Figure 7Effects of impact angle and impact velocity on the erosion rate, according to equations (1) and(2)

Equation 3Tulsa correlation for steels [10]

Equation 4DNV correlation for steels [2]

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Sand erosion correlations and discussion

The erosion correlations for UNS N06625 and UNS 32750The collected erosion data were analyzed and a correlation was developed for each of the two materials, Equation (1) for UNS N06625 and Equation (2) for UNS S32750, asshown below:

– UNS N06625 Correlation (15° ≤ θ ≤ 90°) (1)

– UNS S32750 Correlation (15° ≤ θ ≤ 90°) (2)

where,E – Erosion rate in micrograms of target mass loss per gram of sand (µg/g of sand)θ – Sand particle impact angle (radian, refer to Figure 2)d – Sand particle diameter (µm)V – Sand particle impact velocity (m/s)a to k – parameters derived from experimental results to best model the erosion, all positive values

Note that these two equations are applicable in the design space that is definedby the tested parameters, namely, the sand particle diameter, impact angle andimpact velocity. It must be recognized that these two equations are not valid foran impact angle less than 15°.

The format of the equations is pre-assumed based on a review of publishedsand erosion correlations and on the trend of the experimental data collected inthis work. The R-square value of these two equations is about 97%, whichsuggests that these two equations are a good fit to the experimental data. d andj are the largest parameters in these two equations, indicating that the impactvelocity is the most important parameter affecting the erosion rate. The positivevalue in the exponent indicates that the erosion rate increases with an increaseof the impact velocity. The erosion rate decreases with increasing sand particlesize. The number of small sand particles is greater than that of large sandparticles for the same amount (in terms of mass) of sand. Therefore, the smallsand particles may erode more efficiently. Notice that this trend is opposite tothat observed by some investigators, such as Oka et. al. [4, 5]. This is anindication that some other sand particle properties, such as sharpness and sizedistribution, need to be considered in a more accurate correlation. Designersshould apply caution while assuming that smaller sand causes less erosion, orvice versa. The effect of the impact angle is slightly more complicated since it iscoupled with the impact velocity in these two equations. Figure 7 includes a fewgraphs to show the trend dependence of particle impact angle and impact velocity, according to equations (1) and (2). The erosion rate trends vary as a function of angle andvelocity. Noticeably, the maximum rate of erosion occurs at varying angles with an increase in velocity for the same particle size. One can also find that the erosionresistance of these two tested materials is not vastly different. The erosion rate, especially for UNS S32750, becomes increasingly independent of angle from low to highvelocities.

Comparison with other erosion correlationsThe most-used erosion correlations in the oil and gas industry are the Tulsa correlation [10] and the DNV correlation [2]. These two correlations are cited here for thepurpose of comparison. The Tulsa correlation is shown in Equation (3) and the DNV correlation is shown in Equation (4). In the Tulsa correlation, HB is the Brinell hardnessnumber of the pipeline material; FS is the sand particle sharpness factor and is set to 1.0 since all sand utilized in this work has sharp edges. Other variables are the same asin Equations (1) and (2). Both correlations are applied to common steels, and sometimes to modern CRAs with caution. Notice that the unit of erosion rate had beenconverted to µg/g of sand. Therefore, the constant coefficients in Equations (3) and (4) are different than in the original forms.

Figure 8 shows the comparison of these erosion correlations for several sets of conditions. The comparison is done for only one particle size since the erosion rate isindependent of the particle size in Equations (3) and (4), and is a weak function of particle size in Equations (1) and (2). For low impact velocity (V1) and an impact angle greater

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Figure 8Comparison with other erosion correlations.

than about 25°, the UNS N06625 and UNS S32750 correlations lie between theTulsa and DNV correlations for impact angle greater than about 25°. For highimpact velocity (V4), the UNS N06625 and UNS S32750 correlations give a lowererosion rate, close to the DNV correlation but much lower than the Tulsacorrelation. The impact angle of the maximum erosion rate is about 35° for theDNV correlation and 50° for the Tulsa correlation, but varies for the UNSN06625 and UNS S32750 correlations depending on the impact velocity.

All four erosion correlations are purely derived from experimental data aftermaking some assumptions about the format of the correlations. For instance,the Tulsa and the DNV correlations assume that the erosion rate is a function ofthe impact velocity raised to a constant power and is independent of the particlesize, and that the impact velocity and impact angle dependence are not coupled.Each set of experimental data for deriving these correlations has its own testingconditions. Therefore, each correlation should be applied with caution, ensuringthat the applied conditions of interest are not too far off from the testingconditions. Compared to the Tulsa and the DNV correlations, the correlationsderived in this paper cover a relatively larger range of impact velocity and abroader sand particle size.

Equations (1) and (2) do not cover impact angles less than 15°. These angles canbe included by assuming that the erosion rate is zero at the impact angle ofzero, and then fitting a curve based on the trend at larger impact angles. Thiswas also done when the Tulsa and the DNV correlations were derived. Therewere no sound erosion data for impact angles shallower than 10~15° whenderiving all of these four correlations. The challenge for the UNS N06625 and UNS S32750 correlations is that the maximum erosion rate occurs at 15° under certainconditions, which makes it hard to tell where the maximum erosion rate would be for the full range (0~90°) of the impact angle.

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Figure 9The direct impact geometry and dimensions.

Figure 10Boundary conditions and hexahedral mesh.

Figure 11CFD prediction results in comparison with the UNS 06625 correlation.

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Predicting sand erosion using the correlations

Approximate method: bulk particle impact informationThe simplest way of applying the correlations is to use them directly, without calculating the true particle impact angle and impact velocity. Instead, the bulk flow velocity andthe angle estimated from the flow geometry can be used under certain conditions. For instance, the impact angle can be assumed as 45° and the impact velocity as the fluidvelocity in a standard elbow. This approach is best applied when the inertia of the sand particles is much greater than that of the carrier fluid. The sand particles aretherefore expected to retain their direction and velocity towards the wall. This is also the main reason for conducting the erosion experiments in air rather than in liquid, ifthe final purpose is to derive a correlation through experiments in which the impact angle and impact velocity are well controlled. The DNV RP O501 [2] uses this approach,with a little more adjustment depending on the type of flow geometry. The correlations derived in this work can be used along with the method described in the DNV RPO501, simply by replacing the DNV correlation. This method is easy to apply but can only be used in very limited applications.

Accurate method: CFD with detailed particle impact informationThe most accurate way of applying the erosion correlations is to use them along with CFD. CFD is able to provide detailed information for the whole flow domain, includingthe motion of the sand particles. By modeling the dynamics of a large number of sand particles, the particle impact angles and velocities are calculated and then used in theerosion correlations. This approach can provide a very detailed erosion distribution and help identify erosion hot spots. It is useful when the flow geometry is complex. Themain disadvantages of this approach are that it normally takes much more time and requires CFD expertise.

In this work, the UNS N06625 and UNS S32750 correlations are implemented into ANSYS CFX v12.1. CFD simulations were performed to evaluate the implementation andthe CFD setup. The simulations were carried out to replicate the direct impact experiment setup as shown in Figure 9. The geometry has a nozzle with 5mm diameter and itslength is 25 times the nozzle diameter, 125mm, as per the ASTM [6] recommendation. The length of the nozzle makes the particles injected at the inlet flow through asufficient length to have a fully developed flow at the outlet of the nozzle. The distance from the nozzle center at the exit to the target coupon, along the nozzle axis, is 10 mmaway from the target coupons. The target coupon dimensions were 1 x 3 inch. All flow condition parameters are chosen to reflect the experiments.

The upper nozzle opening was treated as an inlet with uniform velocity/mass flow and the bottom of the chamber as an outlet with constant pressure. A no-slip wallboundary condition was imposed for all other boundaries (Figure 10). A hexahedral mesh was generated and a mesh sensitivity study was carried out. The boundary layer atthe wall is well captured with y+ values less than 5 and an elemental growth ratio of around 1.2 from wall to volume zone. Steady state fluid flow was computed, under theassumption of a smooth wall boundary condition. The SST k-ω turbulence model with automatic wall function was used. The sand particle path was then solved assumingone way coupling, i.e., the sand particles are transported by the fluid but are not affecting the fluid. This is a reasonable assumption for low volume flow rates of particles(volume fraction less than 10 percent) [11]. The perpendicular and parallel restitution coefficients describing the wall-rebound action of the particles are set to 0.8 and 1.0,respectively. The effects of drag (calculated using the Schiller Naumann drag model), pressure, added mass, buoyancy, and the particle dispersion due to turbulence areconsidered in calculating the particle trajectories. For each impact on the wall, the UNS N06625 or the UNS S32750 correlations was applied to calculate the correspondingerosion rate at the impacted location. Figure 11 shows the comparison between the CFD prediction results and the UNS N06625 correlation. The CFD prediction matches thecorrelation.

Practical method: mechanistic model with representative particle impact informationThis approach aims to provide a quick solution like the approximate method, but still captures the most important dynamics of the sand particles like the CFD approach. TheTulsa SPPS tool [1] belongs to this category. The 1D version of SPPS calculates the impact information of one representative sand particle and uses this to estimate the

Nomenclatured Sand particle size, µm

D50 Median sand particle size, µm

E Erosion rate, µg/g of sand

F Particle sharpness factor

HB Brinell hardness

Hv Vickers hardness, GPa

Ra Absolute roughness, µm

V Impact velocity, m/s

θ Impact angle, radian or degree

maximum erosion rate for the given set of conditions. By calculating the representative impact information, it takes into account the effects of fluid properties, sand particleproperties, geometry, and other flow field information. The 2D version of SPPS is just like a 2D CFD, calculating the impact information of a large number of sand particles. Ittakes significantly more time than the 1D version but much less time than a true CFD simulation.

Concluding remarksThe main conclusions drawn from this work are,

1. Direct impact erosion experiments were performed and data was collected, especially for fines.2. Sand erosion correlations were derived for UNS N06625 and UNS S32750.

According to these correlations, the impact velocity is the dominant parameter; the effect of theimpact angle varies depending on the impact velocity; the erosion rate decreases slightly withincreasing sand particle size; and the UNS N06625 and UNS S32750 have comparable erosionresistance.

3. The UNS N06625 and UNS S32750 correlations lie between the Tulsa and the DNV correlations forrelatively low impact velocity. For relatively high impact velocity, however, they give much lowererosion rates in comparison with the Tulsa and the DNV correlations.

4. A revision of the UNS N06625 and UNS S32750 correlations is necessary using more accurateparticle velocity measurements that are scheduled for the next phase of this work.

5. The derived erosion correlations are successfully implemented into ANSYS CFX and can be applied incomplex geometries.

References[1] Tulsa E/CRC, 2011, Sand Production Pipe Saver (SPPS) v4.2.

[2] K. Haugen, O. Kvernvold, A. Ronold, and R. Sandberg, 1995, "Sand Erosion of Wear-ResistantMaterials: Erosion in Choke Valves," Wear vol. 186-187, 179-188.

[3] H.S. Meng, and K.C. Ludema, 1995, "Wear Models and Predictive Equations: Their Form and Content," Wear 181–183 (1995) 443–457.

[4] Y.I. Oka, K. Okamura, and T. Yoshida, 2005, "Practical Estimation of Erosion Damage Caused by Solid Particle Impact. Part 1: Effects of Impact Parameters on a PredictiveEquation," Wear vol. 259, 95–101.

[5] Y.I. Oka, and T. Yoshida, 2005, "Practical Estimation of Erosion Damage Caused by Solid Particle impact. Part 2: Mechanical Properties of Materials Directly Associatedwith Erosion Damage," Wear vol. 259, 102–109.

[6] R. Okita, Y. Zhang, B.S. McLaury, S.A. Shirazi, E.F. Rybicki, 2010, "Experimental and CFD Investigations to Evaluate the Effects of Fluid Viscosity and Particle Size on ErosionDamage in Oil and Gas Production Equpiment," American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM 2010, v 1, Parts A, B and C, 361-374.

[7] ASTM, 2007, "Standard Test Method for Conducting Erosion Tests by Solid Particle Impingement Using Gas Jets," G76-07.

[8] T. Hooks, D. Marx, S. Kachman, and J. Pedersen, 2009, "Optimality Criteria for Models with Random Effects, Criterios de Optimalidad Para los Modelos con EfectosAleatorios," vol 32, no. 1, 17–31.

[9] E. Timothy, and B.O’brien, 1992, "A note on Quadratic Designs for Nonlinear Regression Models," vol. 79, no.4, 847-849.

[10] Y. Zhang, E.P. Reuterfors, B.S. McLaury, S.A. Shirazi, and E.F. Rybicki, 2007, "Comparison of Computed and Measured Particle Velocities and Erosion in Water and AirFlows," Wear vol. 263, 330-338.

[11] ANSYS, 2010, "CFX 12.1 Help Documentation, Chapter 12."

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