Comparison of computed and measured particle velocities and erosion in water and air flows

Wear263(2007)330–338Comparison of computed and measured particle velocitiesand erosion in water and airflowsY.Zhang∗,E.P.Reuterfors,B.S.McLaury,S.A.Shirazi,E.F.RybickiThe University of Tulsa,Department of Mechanical Engineering,600South College Avenue,Tulsa,OK74104,USAReceived15August2006;received in revised form7December2006;accepted8December2006Available online23May2007AbstractErosion equations are usually obtained from controlled experimental tests for solid particles carried in a gas or liquidflow.These equations are then applied to estimate the erosion damage resulting from solid particle impacts for cases of practical interest.It is well known that the particle impact speed and impact angle affect the erosion process and are used as parameters in most erosion equations.For a simple geometry with gas as the carrierfluid,the particle impact speed and impact angle can be accurately estimated,since the particles do not deviate greatly from their initial path.However,for complex geometries,very small particles with liquid as the carrierfluid,the particle trajectories can change significantly and determining the impact velocities can be more challenging.Furthermore,a lot of work has addressed solid particle erosion in gasflows.Many important applications in the oil and gas industry are liquidflows in complex geometries.There is a need for(1)erosion equations for liquidflow with sand and(2)a methodology for predicting erosion for complexflow geometries with liquid and putational Fluid Dynamics(CFD), particle tracking programs and erosion equations are often used together as a tool to help predict erosion damage.However,the accuracy of the CFD based erosion modeling is yet to be determined.In the present work,the velocities of particles entrained in water approaching a target are measured using a laser Doppler velocimeter(LDV).CFD simulations of the experiments were then carried out and the predicted particle velocities match the data very well,implying that CFD is a practical way to estimate the particle impact information.In this work,erosion damage offlat specimens in water or airflow and90◦standard elbows in airflow is also measured using a sensitive electrical-resistance(ER)probe under varying flow conditions.An erosion equation generated from data and several other erosion equations from the literature are applied in the CFD simulations. Predicted erosion rates from the simulations were then compared with the ER probe data.Good agreement between data and CFD predictions is demonstrated by applying a newly generated erosion equation as well as another published equation.©2007Elsevier B.V.All rights reserved.Keywords:CFD;Erosion;Erosion modeling;Erosion equation;LDV;Particle velocity1.IntroductionIn the oil and gas production industry,sand is commonly entrained in thefluid produced from the well.These sand par-ticles,though only150microns in size,can impinge the inner walls of piping,chokes,valves,and otherfixtures and cause extensive erosion damage.Erosion of oil and gasfield piping and equipment is very complex and many factors,such as produc-tionflow rates,multiphaseflow regimes,fluid properties,sand production rates,sand properties,sand shape,sand size distri-bution,equipment and piping wall materials,and geometry of the equipment,can determine the severity of erosion damage.∗Corresponding author.Tel.:+19186312755;fax:+19186312397.E-mail address:yongli-zhang@(Y.Zhang).In order to determine pipe size and allowable wellflow rates,an erosion prediction method accounting for these main factors is needed.This will help optimize the production rate while keep-ing the piping system operating safely and minimize the loss caused by solid particle erosion.A wide variety of erosion equations or models has been devel-oped by many investigators.Meng and Ludema[1]examined various erosion models and equations in the literature.They con-cluded that no single erosion model is general and accurate for practical and general use.Based on the literature survey,they concluded that there are four primary mechanisms for which solid particle erosion occurs.These mechanisms are,namely, (1)cuttings wear(which is defined as indentation of a mate-rial surface by a sharp solid particle and followed by fracture of materials)and plastic deformation(perhaps referring to defor-mation beyond the elastic deformation and followed by fracture0043-1648/$–see front matter©2007Elsevier B.V.All rights reserved. doi:10.1016/j.wear.2006.12.048Y.Zhang et al./Wear263(2007)330–338331of materials),(2)cyclic fatigue,(3)brittle fracture(“non-cyclic failure”)and(4)melting of the materials.Obviously,the ero-sion equations discussed above do not consider all factors that contribute to solid particle erosion in oil/gasfield piping and equipment.Besides variations of solid particle erosion mechanisms, many investigators,including the present authors,found that particle velocity at impact instead offlow stream or slurry velocity should be used to determine erosion characteristics. Investigators also observed that the slurry“velocity exponent”in erosion equations can vary significantly with particle size when continuousflows of liquid containing sand or slugs of liquid and sand were studied in erosion tests.One major rea-son for the variation of the“velocity exponent”with particle size is that when particles are entrained in liquids,the particle impact velocity with a target or a pipe wall can be significantly different from the carrierfluid velocity.Thus,it is very impor-tant to clearly identify experimental conditions when particle erosion data are considered.For example,carrierfluid proper-ties affect particle impact velocity and also can affect frictional forces between particles and the material surface.In addition,fluid density and viscosity may also affect particle rebound and energy dissipation characteristics.The effects of these factors are yet to be determined in a quantitative manner.Besides all these complex factors,many investigators agree that the severity of erosion highly depends on the speed and incoming angle of the impacting particles.Many erosion equa-tions,which take into account these two parameters as well as some other effects,have been proposed in the literature[2–10]. In order to develop an impact angle dependence function,ero-sion tests are usually conducted with particles entrained in gas flow impacting a target wall,since the impact speed and angle are similar to the values in theflow stream.However,in liq-uidflow,the paths of entrained particles can deviate greatly from their carrierfluid path,with impact angles varying greatly. In addition,most erosion experiments are conducted with rel-atively large particles at high velocities and very little erosion data is available forfine particles at low velocities.For some applications with particles moving in liquid,the particle impact speed is commonly very small compared to theflow speed.In addition,sand particles encountered in some applications in oil and gas industries could have average size as low as20␮m.All of the uncertainties discussed above in erosion mech-anisms and erosion models have not stopped engineers from using these tools in predicting erosion in a variety of applica-tions.The present authors,as well as many other investigators, have used Computational Fluid Dynamics(CFD)along with erosion equations to examine erosion in a variety of geometries [11–14].At the University of Tulsa,CFD erosion modeling as well as an extensive erosion database has been used to develop simplified models for predicting erosion in practical geometries, such as elbows,plugged tees,sudden contractions and sudden expansions,for gas,liquid and even multi-phaseflows.CFD based erosion modeling consists of three primary steps:flow modeling,particle tracking and applying erosion equations. In these types of calculations,it is assumed that the solid par-ticle concentration is very low and solid particles do not affect the velocity of thefluids.To determine particle impact velocity at the pipe wall,the particle trajectory is determined by integrat-ing the force balance on the particle.This force balance equates the particle inertia with the forces acting on the particle(New-ton’s Second Law).In order to obtain a reasonable statistical distribution and to reduce scatter in erosion predictions,a large number of particles are normally required to perform the particle tracking.During particle trajectory calculations,the particle-wall interaction information such as impact speed,impact angle, impact location,and impact intensity are stored.This informa-tion is then applied to the appropriate erosion equations,which predict the amount of erosion at the specific location.Although the CFD based erosion modeling is very powerful and can be applied to predict erosion in many complex geome-tries,its accuracy has been questionable for many applications. In the present work,CFD,particle velocity measurements and erosion test data are used to validate and determine if CFD based erosion modeling is a viable and accurate method for predicting solid particle ser Doppler velocimeter(LDV)data are used to validate thefluid velocityfield predicted by the CFD soft-ware for a direct impact test section.The benefits of using LDV measurements,which do not interfere with theflow,include the ability to obtain localizedflow measurements,and the abil-ity to measure a wide range of velocities.In addition tofluid velocity,the LDV is also used to measure particle velocities in the direct impact test section and thus to validate the particle tracking procedure in CFD erosion modeling.High sensitivity electrical-resistance(ER)probes are used to measure erosion rates in addition to traditional weight loss measurements.The LDV and erosion experiments are conducted using sand parti-cles carried in streams of air and waterflow impacting target specimens.Additionalflow geometries(90◦standard elbows) are then simulated to verify and further examine the accuracy of CFD based erosion modeling.2.Description of the experimental facilityA direct impact test facility has been designed for obtaining experimental erosion data for particles traveling at low velocities (<30m/s).The constructed facility makes it possible to measure particle velocities leaving a nozzle and approaching a target in both liquid and gas mediums.This is done using the LDV.For the same measured nozzle exit velocity,erosion measurements can be made in the same facility using an electrical-resistance(ER) probe.A schematic of the test section is shown in Fig.1.The tank is made of acrylic to permit LDV measurements.In addition,the test section was designed so that both LDV measurements and ER probe erosion measurements could be made under identi-cal conditions during the tests.This is done by incorporating two targets into the tank;one for LDV measurements and one for the ER probe measurements.The ER probe is imbedded in a piece of acrylic to imitate the target used for LDV velocity measurements.The nozzle is installed on a pair of tracks so that it can move from the LDV target to the ER probe target and rotate from15to90◦relative to the target surface or to the ER probe.For liquid-sandflow,sand and liquid are mixed in a reser-voir tank and pumped through the nozzle,which is submerged332Y.Zhang et al./Wear263(2007)330–338Fig.1.Schematic of direct impact test.in the liquid/sand mixture in the test tank.For gas–sandflow, however,a special nozzle was designed that incorporates a con-traction followed by a sudden expansion.Suction is created near the expansion that draws in the sand particles from a feeder and injects them into the nozzle.In order to make LDV measurements,it is necessary to have impurities present in theflow.To measure the velocity of the carrierfluid(water or air),silicon carbide(SiC)particles pro-vided by TSI Inc.,Shoreview,MN,USA are used to seed the flow.These particles have a mean diameter of2␮m,density of3200kg/m3,and a high reflectivity which results in a very high data mercially available am625aluminum par-ticles with high reflectivity have been chosen to represent the erodent during LDV measurements.The am625aluminum par-ticles were provided by Ampal Inc.,Flemington,NJ,USA and have a density of2700kg/m3and mean diameter of120␮m, close to that of sand in oil and gas production.The LDV measurement locations are all on the symmetrical plane and are shown in Fig.2.In the direct impact test,the nozzle inner diameter is8mm and the distance from the nozzle exit to the target is12.7mm.The measurement locations are arranged in a matrix,with r=0,1,2,3,4,6,8,10,12mm and d=1,2,4, 6,8,9,10,11,11.4,11.8,12,12.2,12.3mm,where r is the radial distance from the nozzle center line and d is the axial distance from the nozzle exit.Both axial and radial velocity components offluid and sand particles are measured at all117positions.In this study,a Cormon Ltd.ER probe with diameter equal-ing25.4mm(Fig.3)is used to measure the erosion on the target wall.The probe is composed of two electrically conductive ele-ments namely the sample element and reference element,both of which are made of Inconel625which has Vickers hardness of3.43GPa and density of8200kg/m3.The coil-shaped sample element is exposed to theflow and a reference element that sits behind the sample element is protected from theflow by anepoxyFig.2.LDV measurement locations.coating.As particles impact the sample element,the element experiences metal loss and the electrical resistance is changed. Erosion on the probe surface is then determined by comparing the sample element resistance with the reference element resis-tance.These ER probes have high sensitivity and are capable of measuring erosion in the range of nanometers.In addition to metal loss readings,the probes also measure temperature,a useful process parameter which is also used when compensat-ing for the effects of temperature change on the measurement. The calculation and compensation are performed automatically in the instrumentation.This capability prevents the reporting of false erosion events caused by temperature changes in the process stream and is far more efficient and effective than the use of separate temperature sensor information.The tempera-ture value forms part of the instrument output and serves the additional purpose of providing a health check on the probe.A series of direct impact tests were carried out under differ-entflow conditions,including four slurry(sand/water)and two air-borne(sand/air)erosion tests.In addition to the directimpact Fig.3.Surface of the electrical resistance probe(diameter25.4mm).Y.Zhang et al./Wear263(2007)330–338333Fig.4.ER probe installed on the elbow.test,some air-borne(sand/air)erosion data on elbows with ID equaling50.8mm have also been collected using an ER probe [15].The ER probe isflush installed in the middle of the outer bend of the elbow at45◦,as shown in Fig.4.Some key parame-ters,such asfluid type,flow velocity,sand average size and sand volume fraction for each case are listed in Table1.Silicaflour with average size of25␮m,density of2650kg/m3,and angular shape was used in Case4,while OK#1sand with average size of150␮m,density of2650kg/m3,and semi-rounded shape was used in the other eight cases.The silicaflour and OK#1sand were provided by Halliburton Energy Services,Duncan,OK, USA.3.Validation of CFDflow simulationIn order to validate theflow simulations using CFD,bothfluid and sand velocities are obtained using LDV and the direct impact test facility.The mixture of water and silicon carbide particles with a mean diameter of2␮mflows through the nozzle at an average axial velocity of12m/s.The silicon carbide is veryfine so that there is almost no slip between the particle andfluid and the particle velocity can be used to represent thefluid velocity.A commercially available CFD code,FLUENT6[16],is then used to simulate theflow.In the CFD simulations,a3D submerged jetflow with a wall placed12.7mm away from the nozzle exit represents theflow in the testing tank.The LDV measuredfluid velocity profile at the exit of the nozzle is applied as the boundary condition in the simulation.The simulated geometry consists of about400,000hexahedral elements,with most of the elements in the jetflow region,generating a meshfine enough to numerically resolve theflowfield.The second order Reynolds stress turbulent model is employed.Several rebound models including the Grant and Tabakoff[17]and Forder et al.[18]rebound models were implemented into FLUENT6and examined in this work.Both axial and radial velocity components of thefluid at the positions shown in Fig.2are extracted after the simulation is converged. The measured and predictedfluid velocityfield is plotted in a contour form shown in Figs.5and6,for axial and radial components,respectively.For this case,the average velocity of water at the inlet is approximately12m/s.In thesefigures, the upper portion is the contour of the velocity created from the LDV data while the lower portion is the CFD result.Very good agreement between the LDV data and the CFD simulation results was obtained for the axialfluid velocity,as shown in Fig.5.For the radialfluid velocity,the simulation also provides accurate predictions in most areas,especially in the region close to the target surface.In other regions,the actual geometry of the confined tank that is not considered in the simulations may be contributing to the differences between the predictions and the measurements.In addition tofluid velocity,particle velocity components are also collected at the same locations as the velocity measure-ments discussed above using LDV.The sameflow conditions are maintained.Instead of the2␮m silicon carbide particles,am625 aluminum particles with a mean diameter of120␮m are used toTable1Erosion testing conditions and comparison of measured and predicted erosionFluid Flow velocity(m/s)Sand size(␮m)Sand volumefraction(%)ER probe data(m/kg)Erosion predicted using CFD(m/kg)E/CRC erosion model Oka et al.[9]erosion modelDirect impact tests(ER probe at12.7mm away from the nozzle exit)Case1Water101500.59.3×10−8 4.8×10−8 6.8×10−8Case2Water51500.5 1.8×10−87.3×10−9 1.2×10−8Case3Water 2.51500.5 1.3×10−9 1.5×10−9 2.3×10−9Case4Water10250.5 3.4×10−8 1.7×10−8 2.0×10−8Case5Air24.81500.0026 1.1×10−6 1.7×10−6 2.6×10−6Case6Air10.21500.013 1.1×10−7 2.0×10−7 3.0×10−7Elbow erosion tests(ER probeflush installed on the elbow,see Fig.4)Case7Air281500.000617.7×10−7 6.2×10−79.4×10−7Case8Air191500.00051 3.5×10−7 2.4×10−7 3.6×10−7Case9Air121500.00026 1.2×10−78.4×10−8 1.3×10−7Notes:The unit of erosion in this table is m/kg,representing the average thickness loss in meters over the ER probe surface per kilogram of sand impacting the probe surface.The sensing element of ER probe used in all nine cases is Inconel625,which has Vickers hardness of3.43GPa and density of8200kg/m3.Silicaflour with angular shape is used in Case4and OK#1sand with semi-rounded shape is used in the other cases.Both have density of2650kg/m3.Water and air in all cases are nearly at standard conditions.Theflow velocity is the average value at the nozzle exit for Cases1–6and in the elbow for Cases7–9.334Y.Zhang et al./Wear 263(2007)330–338Fig.5.Axial fluid velocity,LDV data vs.CFD result.seed the flow.In the CFD simulations,am625aluminum parti-cles are introduced into the flow field after the flow simulation,assuming dilute flow without particle interaction.The measured and predicted particle velocity components in axial and radial directions are plotted in a contour form shown in Figs.7and 8,respectively.The CFD results match the LDV data very well,in both axial and radial directions.In solid particle erosion prediction,the particle impact speed and impact angle are important parameters.The measured and predicted particle velocity components at positionswithFig.6.Radial fluid velocity,LDV data vs.CFDresult.Fig.7.Axial particle velocity,LDV data vs.CFD result.d =12.3mm,namely 0.4mm away from the target surface,are manipulated to give the particle speed and particle incident angle relative to the target surface.The comparison of particle speed and particle incident angle between LDV data and CFD results are shown in Figs.9and 10,respectively.Since the data points are very close the target surface,they are referred to as impact speed and impact angle in these figures.Fig.9indicates that the predicted particle impact speed matches the data very well.Both LDV data and CFD predic-tions follow the same trend and show that particles neartheFig.8.Radial particle velocity,LDV data vs.CFD result.Y.Zhang et al./Wear 263(2007)330–338335Fig.9.Particle impact speed,LDV data vs.CFD result.center line impact the target surface at the lowest speed due to thestagnant fluid in this region.The highest particle impact speed occurs about 6–8mm from the center line.The CFD simulation also shows excellent agreement of the particle impact angle as shown in Fig.10.Again,because of the stagnation zone around the center line,the particle impact angle is close to 90◦in this region and decreases away from the center line.The comparison of fluid and particle velocities between LDV data and CFD results states clearly that the CFD simulation in this case is reliable and accurate.It is then reasonable to apply the particle impact information to calculate erosion using ero-sion equations.Therefore,erosion equations can be validated by comparing predicted erosion with erosion data collected using the ER probe.4.Validation of erosion equationsSeveral erosion equations were examined during this inves-tigation,including Finne erosion model [4],Hashish and Bitter erosion model [3,6],the Erosion–Corrosion Research Center (E/CRC)erosion model for carbon steel with dry or wet surface [7],E/CRC erosion model for Inconel 718and the Oka et al.erosion model [9,10].In the off-the-shelf version of FLUENT 6,only one erosion equation can be used to calculate erosion when particles hit the wall.In this study,another User Defined Func-tion (UDF)is developed to account for several erosion equations.Therefore,the erosion values calculated by differenterosionFig.10.Particle impact angle,LDV data vs.CFD result.Table 2Values of A i in Eq.(2)A 1A 2A 3A 4A 55.40−10.1110.93−6.331.42equations are based on the same set of particle impingements on the wall.All cases listed in Table 1are then simulated.By comparing the predicted erosion with the ER probe erosion data,it turns out that the E/CRC erosion model and the Oka et al.erosion model give very good results.These two erosion models are discussed below.The E/CRC erosion model is given in Eqs.(1)and (2),ER =C (BH)−0.59F s V np F (θ)(1)F (θ)=5 i =1A i θi(2)where ER is the erosion ratio,defined as the amount of mass lostby the wall material due to particle impacts divided by the mass of particles impacting;BH is the Brinell hardness of the wall material;F s is the particle shape coefficient;F s =1.0for sharp (angular),0.53for semi-rounded,or 0.2for fully rounded sand particles;V p is the particle impact speed in m/s;θis the impact angle in radians;n =2.41and C =2.17×10−7are empirical constants.Values of A i for i =1–5are listed in Table 2.In this model,Eq.(2)is based on a series of direct impact tests of Inconel 718conducted by researchers at the E/CRC and Baker Oil Tools (BOT)[19].In these tests,sand particles with a mean size of 150␮m are injected into high velocity airflows at different incident angles relative to the target.Erosion data are collected for one impact speed,which was measured to be 68m/s using the LDV .The velocity exponent,n,is determined based on published work in the literature (see,for example,Forder et al.[18]and Oka et al.[9,10]).The hardness dependent function in Eq.(1)was determined based on earlier studies conducted by investigators at the E/CRC.The erosion model of Oka et al.[9,10]is presented below:E (θ)=g (θ)E 90(3)g (θ)=(sin θ)n 1(1+Hv(1−sin θ))n 2(4)E 90=K (Hv)k 1V p V k 2 D pD k 3(5)n 1=s 1(Hv)q 1,n 2=s 2(Hv)q 2,k 2=2.3(Hv)0.038(6)where E (θ)is the erosion damage (mm 3/kg)at an arbitraryimpact angle θ;E90is the erosion damage at normal impact angle;Hv is the Vickers number in GPa,indicating the wall material hardness;V p and V (m/s)are the particle impact speed and the reference impact speed,respectively;D p and D (␮m)are the particle diameter and the reference diameter,respectively;for336Y.Zhang et al./Wear 263(2007)330–338Fig.11.Impact angle functions.sand particle,s 1=0.71,s 2=2.4,q 1=0.14,q 2=−0.94,K =65,k 1=−0.12,k 3=0.19,V =104m/s and D =326␮m.In order to compare these two erosion models,the erosion damage given by the Oka et al.erosion model is converted to erosion ratio by multiplying the wall material density ρw (kg/m 3),ER (Oka)=1.0×10−9ρw E (θ)(7)Fig.11shows a comparison of impact angle functions F (θ)and g (θ)for Inconel 718(Hv =3.43GPa).Values of these two func-tions are very close to each other and both indicate that the maximum erosion occurs for an impact angle of about 50◦.The wall material dependence functions of these two erosion models are also compared over a wide range of wall material hardness values (BH =110–750,Hv =1.15–8.04GPa)and plot-ted in Fig.12.In this figure,the wall material hardness effect in g (θ)of the Oka et al.erosion model is not considered.For this range of wall material hardness values,the value of k 2ranges from 2.31to 2.49.Since V p can be any reasonable value and k 2resides in a relatively narrow range,the particle impact speedterm (V k 2p)is also not considered in the comparison.Fig.12shows that the trend of these two functions have almost the same shape,differing by a constant factor about 2778which is balanced by the empirical constant coefficients in both models.For all nine cases listed in Table 1,the ER probe erosion data,as well as the erosion predicted by using the present E/CRC erosion model and the Oka et al.erosion model are providedinFig.12.Wall material hardness dependence (C =2778in f(Hv)).the same table.Both erosion models predict erosion very well for all cases,with the ratio of prediction to data ranging from 0.6to 2.7for the Oka et al.erosion model and 0.4–1.8for the E/CRC erosion model.5.DiscussionFor all cases studied in this work,CFD erosion modeling results are comparable to data for a wide range of erosion data changing from 1.3×10−9to 1.1×10−6m/kg sand.This shows that CFD based erosion modeling can be used to predict solid particle erosion in flow systems.In order to apply this erosion prediction method successfully,experience has shown that many factors have to be considered.Some of these factors are discussed below.5.1.Flow modelingIn CFD erosion modeling,reliable results can only be obtained if accurate results are obtained during the first step,flow modeling.Solid particles cannot be accurately tracked in a poorly resolved flow field.Without accurate calculation of parti-cle trajectories and particle impact information,it is not possible to produce a reasonable erosion prediction.Just like other CFD applications,great care must be taken in modeling the flow field.First of all,a high quality mesh is necessary,especially for complex geometries.In CFD erosion modeling,computational mesh in the boundary layers have to be treated carefully and several layers of hexahedral or prism elements are recommended to be placed next to the wall.Tetrahe-dral elements are commonly used everywhere to mesh complex geometries,however it is advisable to use a hexahedral element near the walls to provide a more accurate numerical solution near wall.This is important because regions next to wall are where particle impingements occur.Secondly,the turbulence model and turbulence boundary conditions should be set-up wisely in simulations.In certain cases,the turbulence field may have sig-nificant influence on particle trajectory calculations and thus erosion prediction.5.2.Particle trackingIn order to obtain a reasonable statistical distribution and to reduce scatter in erosion predictions,a large number of par-ticles are normally required to perform the particle tracking.Particle–particle interactions are usually neglected in practical CFD applications since it’s unreasonable to capture all inter-particle collisions with the large number of particles present in the flow field with current computational capabilities.At low solid particle concentrations,the presence of the solid particles does not have a significant effect on the continuous phase so that particle tracking can be performed after flow modeling.How-ever,for high solid particle concentration flows,the influence of phase coupling must be considered so the flow modeling and particle tracking are performed simultaneously.During solid particle–wall interaction,the particle’s momen-tum is changed and this change is usually accounted for by。