Wear 259 (2005) 203–207

Short communication

Development and validation of a mechanistic model to predictsolid particle erosion in multiphase flow

Quamrul H. Mazumder∗, Siamack A. Shirazi, Brenton S. McLaury,John R. Shadley, Edmund F. Rybicki

The Erosion/Corrosion Research Center, The University of Tulsa, 600 S. College Avenue, Tulsa, OK 74104, USA

Received 14 September 2004; received in revised form 3 February 2005; accepted 7 February 2005Available online 11 May 2005

Abstract

Prediction of erosion in flow systems requires an understanding of the complex interactions between the fluid and the solids. The complexityof the problem increases significantly in multiphase flow due to the existence of different flow patterns. Earlier predictive methods for erosionin multiphase flow were primarily based on empirical data and the applicability of those models was limited to the flow conditions of thee ultiphasefl ed erosionr for differentfl©

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xperiments. A new mechanistic model for predicting erosion in elbows in multiphase flow is presented. Local fluid velocities in mow are used to calculate erosion rates in multiphase flow using particle tracking and simplified erosion equations. The predictates obtained by the mechanistic model presented here are in good agreement with experimental data available in the literatureow regimes and a wide range of flow velocities.2005 Elsevier B.V. All rights reserved.

eywords:Erosion; Multiphase flow; Solid particle erosion; Annular flow; Slug flow; Elbow

. Introduction

Solid particle erosion is a process by which material isemoved from a metal surface due to impingement of smallolid particles on the metal surface. Many authors, for ex-mple references[1–4] have discussed erosion mechanisms

n ductile and brittle materials and described a number ofactors that affect solid particle erosion. Various industriesre concerned about erosion damage. For example, in theil and gas industry, the oil and gas produced from theells can also include entrained sand. Being able to predictrosion wear is important to design engineers for properelection of pipe size, flow system configuration, and sandontrol equipment. Therefore, it is important to have theapability to calculate erosion damage in flow systems.urrent choices are to either calculate erosion based on

∗ Corresponding author. Tel.: +1 918 459 8210; fax: +1 918 631 2397.E-mail address:q mazumder@yahoo.com (Q.H. Mazumder).

empirical information or to model erosion accountingseveral physical parameters and mechanisms in a “mnistic model.” Obviously, the model development requmany simplifying assumptions to conduct engineecalculations. The work presented here shows a frameas to how various factors can be incorporated intoa model.

While there are models based on computational fluidnamics (CFD) for calculating erosion in single-phaseconditions[5–7], these models still require many simplifyiassumptions for calculating erosion in multiphase flow[8].In addition, the CFD-based erosion calculation procedare generally too complicated for practical use by designgineers at the present time.

One of the simple methods used previously by enginto calculate a maximum allowable threshold velocity to li“erosion” is published by the American Petroleum Insti(API) and called Recommended Practice (RP) 14E[9]. How-ever, this guideline does not consider sand and is not sufor situations involving sand or other solid particles.

043-1648/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.wear.2005.02.109

204 Q.H. Mazumder et al. / Wear 259 (2005) 203–207

account for factors such as solid particle size and gas–liquidmixture velocity, several empirical procedures to predicterosion have been proposed[3,4,10]. However, empiricalprocedures may be valid only near the conditions forwhich experiments were conducted. To overcome previousshortcomings of erosion prediction models and correlations,McLaury and Shirazi[11] developed a semi-empiricalprocedure to predict erosion. The model was an extension ofa model that was originally developed for single-phase flowand based on computational fluid dynamics modeling anddata[4]. The model for calculating the maximum penetrationrate for a simple geometries such as elbows and tees, can bewritten as[4,11]:

h = FMFSFPFr/DWVn

L

(D/D0)2(1)

whereh is the penetration rate in mm/year;n, FM, FS theempirical factors for material and sand sharpness;FP thepenetration factor for material based in 1 in. pipe diameter;Fr/D the penetration factor for long radius elbows;W thesand production rate;VL the characteristic particle impactvelocity; D the pipe diameter andD0 is the referencediameter.

The main difference between this model and earlier mod-els in the literature is that a representative solid particle tom in-sot ayerr a re-g pipew nea ch asfi ate-r icle-t pactv nt ino a-t nec pact-i ata thes .T loc-i rep-r , isas parti-c ibles thee travela ties.T andc ulti-p

Fig. 1. Flow patterns in vertical multiphase flow.

2. Present work

Fig. 1 schematically depicts the major flow patterns thatare observed in vertical multiphase flow. An earlier semi-empirical erosion prediction model[11] did not consider thecomplexities of multiphase flow in the characteristic impactvelocity calculation. The characteristic impact velocity wasassumed to be a simple function of the superficial gas and liq-uid velocities only. To improve the previous model, a prelimi-nary model for calculating the representative or characteristicparticle velocity in multiphase flow was developed[12]. Inthe work described here, earlier models are further improvedand a more realistic mechanistic model is presented for thefollowing four flow regimes encountered in vertical flow.

2.1. Annular flow

Santos[13] used a pitot-type probe to collect sand and liq-uid and determined the sand and liquid distributions in a crosssection of a pipe for annular multiphase flow. He observedthat the distribution of sand that was collected in annular flowclosely resembled the distribution of liquid that is entrained inannular flow. To model the characteristic velocity of particlesin annular flow, based on the work carried out by Santos[13],the sand particles were assumed to be uniformly distributedi slipb fore,t uidfi

itiesi

V

V

wd

etal impact velocity,VL, is used to calculate erosiontead of the flowstream velocity. The investigators[4] devel-ped a simplified method for calculatingVL, which is ob-

ained by creating a simple model of the stagnation lepresenting the pipe geometry. The stagnation zone ision that the particles must travel through to strike theall for erosion to occur. The particle velocity in this zond resulting erosion depend on a series of factors sutting geometry, fluid properties, flow regimes, pipe mial properties, and sand properties. A simplified partracking model is used to compute the characteristic imelocity of the particles; the model assumes movemene direction with linear fluid velocity within the stagn

ion zone. Reference[4] describes how the stagnation zohanges with pipe size and how the characteristic imng velocity is computed. For example, for air flowing

velocity of about 30 m/s in a 50 mm diameter pipe,tagnation zone at a 90◦ elbow is approximately 52 mmhe particle impact velocity depends on the particle ve

ty before the particle reaches the stagnation zone. Aesentative initial particle velocity, for single-phase flowssumed to be the same as the flowstream velocity[4]. Foringle-phase flow, this assumes no slip between theles and fluid. In multiphase flow, assuming a negliglip between the small particles and the carrier fluid,ntrained sand particles in the liquid and gas phasest velocities similar to their corresponding phase velociherefore, it is important to understand the distributionharacteristic behavior of the liquid and gas phases in mhase flow.

n the liquid phase and it was assumed that there is noetween the liquid and sand particles in the flow. There

he initial particle velocity was calculated by using the liqlm velocity and the entrained liquid droplet velocities.

Therefore, the characteristic initial sand particle velocn liquid, V0L, and gas,V0G, phases are calculated as:

0L = Vfilm (2)

0G = Vd (3)

hereVfilm is the liquid film velocity andVd is the liquidroplet velocity in annular flow. The entrainment rate,E, is

Q.H. Mazumder et al. / Wear 259 (2005) 203–207 205

the fraction of liquid entrained in the gas core and is definedas:

E = mass of liquid in the gas core

total mass of liquid

Assuming sand is uniformly distributed in the liquid phase,E can be written as:

E = mass of sand in the gas core

total mass of sand

The fraction of sand entrained in the liquid film is:

1 − E = mass of sand in the liquid film

total mass of sand

The erosion rate due to sand particles in the liquid phasewas calculated by usingV0L and the fraction of sand entrainedin the liquid film (1−E). The erosion rate due to sand par-ticles in the gas phase was calculated by usingV0G and thefraction of sand entrained in the gas core,E. The total ero-sion rate is calculated by adding the erosion rates due to sandparticles in the liquid and gas phases. Details of calculatingliquid film velocities, droplet velocities, and erosion rates arediscussed in references[14,17].

2.2. Slug flow

slugfl thel ovingw ore,t bec

V )

T frac-t

fs ow.T d bya

2

prox-i lest flowo otict ixedt thes n, iti quidp andc turev ve-l -slip

mixture velocity and can be calculated as:

V0 = VSL + VSG (5)

whereVSL andVSG are the superficial liquid and gas veloci-ties, respectively.

3. Results and validation of the mechanistic model

3.1. Validation of droplet velocity and film velocitycalculations

In the present mechanistic model, it is assumed that thesand particles are carried by the annular liquid film near thewall and by the liquid droplets entrained in the gas core.Therefore, the sand particle velocities are similar to the liquidfilm velocity and the liquid droplet velocity in the gas core.Fig. 2shows a comparison of the calculated mean droplet ve-locity and the measured droplet velocity by Fore and Dukler[15] at different superficial gas velocities. Details of calcu-lation procedure are described in reference[12]. The calcu-lated maximum droplet velocity agrees well with the exper-imental data although a simplified approach was used forthe calculation. (Rel shown inFig. 2is the Reynolds numberbased on superficial liquid velocity, liquid properties and pipes

lara itya con-d weent wasc uredfi -d

lossd isticm -p g the

F ta ofF

In the absence of any data for sand distribution inow, it is assumed that sand is uniformly distributed iniquid phase. Also, it is assumed that the mass of sand mith the liquid slug causes the erosion in slug flow. Theref

he characteristic initial particle velocity for slug flow canalculated as:

0 = VLLS = velocity of liquid in the liquid slug (4

he erosion rate for slug flow was calculated using theion of sand particles in the liquid slug andV0.

Reference[12] describes howVLLS and the amount oand moving with the liquid slug are estimated for slug flhe erosion penetration rate due to slug flow is calculatemethod described in reference[17].

.3. Bubble and churn flows

In bubble flow, it is assumed that the gas phase is apmately uniformly distributed in the form of discrete bubbhat are entrained in a continuous liquid phase. Bubbleccurs at low gas rates. Churn flow is much more cha

han other flow regimes with the gas and liquid phases mogether. In bubble and churn flows, information aboutand distribution is not available and as an approximatios assumed that the sand is uniformly distributed in the lihase. The velocities of the liquid and sand in bubblehurn flows are assumed to be equal to the no-slip mixelocity. Therefore, the characteristic initial sand particleocity for bubble and churn flow is assumed to be the no

ize.)Adsani [16] measured film velocity in upward annu

ir–water flow at 0.06–0.37 m/s superficial liquid velocnd at 13.7–44.8 m/s superficial gas velocities using twouctance probes. By measuring the time difference bet

he conductance spikes, the average liquid film velocityalculated.Fig. 3shows a comparison between the measlm velocities and the predicted film velocities[12]. The preicted film velocities agree well with measured values.

Table 1shows a comparison of measured thicknessue to erosion/kg of sand in mm/kg with the mechanodel predictions for annular flow.Table 2shows a comarison of measured thickness loss/kg of sand in mm/k

ig. 2. Comparison of calculated droplet velocity with experimental daore and Dukler[15].

206 Q.H. Mazumder et al. / Wear 259 (2005) 203–207

Table 1Comparison of measured erosion with the mechanistic model predictions (annular flow)

VSL

(m/s)VSG

(m/s)Elbow diameter(mm)

Droplet velocity(m/s)

Entrainmentfraction

Sand size(�m)

Flowpattern

Measurederosion (mm/kg)

Mechanistic modelprediction (mm/kg)

Note

1.0 30.0 49 24.8 0.814 150 ANNUL 5.25E−04 6.40E−4 10.5 30.0 49 24.7 0.713 150 ANNUL 2.46E−03 8.82E−4 15.8 20.0 49 18.1 0.565 150 ANNUL 5.19E−05 6.66E−5 13.1 20.0 49 18.0 0.501 150 ANNUL 6.93E−05 1.12E−04 11.0 15.0 49 14.3 0.198 150 ANNUL 1.47E−04 4.58E−5 11.5 14.4 26.5 13.9 0.248 250 ANNUL 2.30E−04 3.05E−4 21.5 14.6 26.5 14.0 0.257 250 ANNUL 4.20E−04 3.17E−04 22.1 34.4 26.5 27.4 0.982 250 ANNUL 2.83E−03 3.08E−03 21.0 35.0 26.5 28.2 0.971 250 ANNUL 6.56E−03 4.40E−3 20.5 34.3 26.5 27.7 0.935 250 ANNUL 7.20E−03 4.79E−3 20.7 37.0 26.5 29.9 0.977 250 ANNUL 8.03E−03 5.38E−3 20.5 38.5 26.5 30.9 0.979 250 ANNUL 8.03E−03 6.15E−3 21.5 44.0 26.5 35.2 0.985 250 ANNUL 1.05E−02 6.28E−3 20.6 51.0 26.5 40.8 0.989 250 ANNUL 1.34E−02 1.03E−2 2

Notes:(1) Data from Salama[3], air and water at 2 bar, material: carbon steel (BHN 160). (2) Data from Salama[3], nitrogen and water at 7 bar, material:duplex stainless steel.

Fig. 3. Comparison of calculated film velocity with experimental data[13].

mechanistic model predictions for slug/churn (calculated val-ues are actually for churn flow based on observation of flowregime by Mazumder[17]) and bubble flows.Tables 1 and 2indicate that the erosion data used for comparison with themodel encompasses a wide range of liquid and gas veloci-ties.Fig. 4shows the mechanistic model predictions to be ina good agreement with the measured erosion data for a widerange of measure rates of penetration rates.

Fig. 4. Comparison of measured erosion with mechanistic model predic-tions.

4. Summary and conclusion

A mechanistic erosion prediction model has been devel-oped for multiphase flow considering the effects of particlevelocities in multiphase flow. Comparison of the mechanisticmodel predictions with the measured erosion data for annu-lar, slug/churn and bubble flows shows good agreement fora wide range of velocities and erosion rates. The calculated

Table 2Comparison of measured erosion with mechanistic model predictions (slug/churn, bubble flows)

VSL

(m/s)VSG

(m/s)Elbow diameter(mm)

Impact velocity,Vo (m/s)

Sand size(�m)

Flow pattern calculated/exp.observation

Measured erosion(mm/kg)

Mechanistic modelprediction (mm/kg)

Note

5.0 15.0 49 2.3 150 SLUG/CHURN 6.38E−05 2.41E−05 15.0 10.0 49 1.2 150 SLUG/CHURN 1.35E−05 7.08E−06 10.7 10.0 49 4.2 150 SLUG/CHURN 7.01E−05 8.18E−05 10.2 8.0 49 5.3 150 SLUG/CHURN 1.23E−04 2.33E−04 16.2 9.0 26.5 3.06 250 SLUG/CHURN 1.80E−04 9.59E−05 24.0 3.5 49 0.22 150 BUBBLE 4.60E−06 3.12E−07 1

Notes:(1) Data from Salama[3], air and water at 2 bar, material: carbon steel (BHN 160). (2) Data from Salama[3], nitrogen and water at 7 bar, material:duplex stainless steel.

Q.H. Mazumder et al. / Wear 259 (2005) 203–207 207

droplet and film velocities also agree well with the experi-mental data. Due to the limited availability of experimentalerosion data for bubble, slug, and churn flows, additionalverification and modification of this model is required. Thispaper demonstrates a framework for addressing how variousfactors can be accounted for in predicting erosion in complexmultiphase flows, and as new information is available it canbe incorporated into the mechanistic model.

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