Wear 259 (2005) 203–207
Short communication
Development and validation of a mechanistic model to predict
solid 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 2005
Available 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 complexity
of the problem increases significantly in multiphase flow due to the existence of different flow patterns. Earlier predictive methods for erosion
in multiphase flow were primarily based on empirical data and the applicability of those models was limited to the flow conditions of the
experiments. A new mechanistic model for predicting erosion in elbows in multiphase flow is presented. Local fluid velocities in multiphase
flow are used to calculate erosion rates in multiphase flow using particle tracking and simplified erosion equations. The predicted erosion
rates obtained by the mechanistic model presented here are in good agreement with experimental data available in the literature for different
flow regimes and a wide range of flow velocities.
© 2005 Elsevier B.V. All rights reserved.
Keywords: Erosion; Multiphase flow; Solid particle erosion; Annular flow; Slug flow; Elbow
1. Introduction
Solid particle erosion is a process by which material is
removed from a metal surface due to impingement of small
solid particles on the metal surface. Many authors, for example references [1–4] have discussed erosion mechanisms
in ductile and brittle materials and described a number of
factors that affect solid particle erosion. Various industries
are concerned about erosion damage. For example, in the
oil and gas industry, the oil and gas produced from the
wells can also include entrained sand. Being able to predict
erosion wear is important to design engineers for proper
selection of pipe size, flow system configuration, and sand
control equipment. Therefore, it is important to have the
capability to calculate erosion damage in flow systems.
Current choices are to either calculate erosion based on
∗
Corresponding author. Tel.: +1 918 459 8210; fax: +1 918 631 2397.
E-mail address: q [email protected] (Q.H. Mazumder).
0043-1648/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.wear.2005.02.109
empirical information or to model erosion accounting for
several physical parameters and mechanisms in a “mechanistic model.” Obviously, the model development requires
many simplifying assumptions to conduct engineering
calculations. The work presented here shows a framework
as to how various factors can be incorporated into such
a model.
While there are models based on computational fluid dynamics (CFD) for calculating erosion in single-phase flow
conditions [5–7], these models still require many simplifying
assumptions for calculating erosion in multiphase flow [8].
In addition, the CFD-based erosion calculation procedures
are generally too complicated for practical use by design engineers at the present time.
One of the simple methods used previously by engineers
to calculate a maximum allowable threshold velocity to limit
“erosion” is published by the American Petroleum Institute
(API) and called Recommended Practice (RP) 14E [9]. However, this guideline does not consider sand and is not suitable
for situations involving sand or other solid particles. To
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Q.H. Mazumder et al. / Wear 259 (2005) 203–207
account for factors such as solid particle size and gas–liquid
mixture velocity, several empirical procedures to predict
erosion have been proposed [3,4,10]. However, empirical
procedures may be valid only near the conditions for
which experiments were conducted. To overcome previous
shortcomings of erosion prediction models and correlations,
McLaury and Shirazi [11] developed a semi-empirical
procedure to predict erosion. The model was an extension of
a model that was originally developed for single-phase flow
and based on computational fluid dynamics modeling and
data [4]. The model for calculating the maximum penetration
rate for a simple geometries such as elbows and tees, can be
written as [4,11]:
h = FM FS FP Fr/D
WVLn
(D/D0 )2
(1)
where h is the penetration rate in mm/year; n, FM , FS the
empirical factors for material and sand sharpness; FP the
penetration factor for material based in 1 in. pipe diameter;
Fr/D the penetration factor for long radius elbows; W the
sand production rate; VL the characteristic particle impact
velocity; D the pipe diameter and D0 is the reference
diameter.
The main difference between this model and earlier models in the literature is that a representative solid particle to
metal impact velocity, VL , is used to calculate erosion instead of the flowstream velocity. The investigators [4] developed a simplified method for calculating VL , which is obtained by creating a simple model of the stagnation layer
representing the pipe geometry. The stagnation zone is a region that the particles must travel through to strike the pipe
wall for erosion to occur. The particle velocity in this zone
and resulting erosion depend on a series of factors such as
fitting geometry, fluid properties, flow regimes, pipe material properties, and sand properties. A simplified particletracking model is used to compute the characteristic impact
velocity of the particles; the model assumes movement in
one direction with linear fluid velocity within the stagnation zone. Reference [4] describes how the stagnation zone
changes with pipe size and how the characteristic impacting velocity is computed. For example, for air flowing at
a velocity of about 30 m/s in a 50 mm diameter pipe, the
stagnation zone at a 90◦ elbow is approximately 52 mm.
The particle impact velocity depends on the particle velocity before the particle reaches the stagnation zone. A representative initial particle velocity, for single-phase flow, is
assumed to be the same as the flowstream velocity [4]. For
single-phase flow, this assumes no slip between the particles and fluid. In multiphase flow, assuming a negligible
slip between the small particles and the carrier fluid, the
entrained sand particles in the liquid and gas phases travel
at velocities similar to their corresponding phase velocities.
Therefore, it is important to understand the distribution and
characteristic behavior of the liquid and gas phases in multiphase flow.
Fig. 1. Flow patterns in vertical multiphase flow.
2. Present work
Fig. 1 schematically depicts the major flow patterns that
are observed in vertical multiphase flow. An earlier semiempirical erosion prediction model [11] did not consider the
complexities of multiphase flow in the characteristic impact
velocity calculation. The characteristic impact velocity was
assumed to be a simple function of the superficial gas and liquid velocities only. To improve the previous model, a preliminary model for calculating the representative or characteristic
particle velocity in multiphase flow was developed [12]. In
the work described here, earlier models are further improved
and a more realistic mechanistic model is presented for the
following four flow regimes encountered in vertical flow.
2.1. Annular flow
Santos [13] used a pitot-type probe to collect sand and liquid and determined the sand and liquid distributions in a cross
section of a pipe for annular multiphase flow. He observed
that the distribution of sand that was collected in annular flow
closely resembled the distribution of liquid that is entrained in
annular flow. To model the characteristic velocity of particles
in annular flow, based on the work carried out by Santos [13],
the sand particles were assumed to be uniformly distributed
in the liquid phase and it was assumed that there is no slip
between the liquid and sand particles in the flow. Therefore,
the initial particle velocity was calculated by using the liquid
film velocity and the entrained liquid droplet velocities.
Therefore, the characteristic initial sand particle velocities
in liquid, V0L, and gas, V0G, phases are calculated as:
V0L = Vfilm
(2)
V0G = Vd
(3)
where Vfilm is the liquid film velocity and Vd is the liquid
droplet velocity in annular flow. The entrainment rate, E, is
Q.H. Mazumder et al. / Wear 259 (2005) 203–207
the fraction of liquid entrained in the gas core and is defined
as:
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
V0 = VSL + VSG
(5)
where VSL and VSG are the superficial liquid and gas velocities, respectively.
3.1. Validation of droplet velocity and film velocity
calculations
mass of sand in the liquid film
total mass of sand
The erosion rate due to sand particles in the liquid phase
was calculated by using V0L and the fraction of sand entrained
in the liquid film (1 − E). The erosion rate due to sand particles in the gas phase was calculated by using V0G and the
fraction of sand entrained in the gas core, E. The total erosion rate is calculated by adding the erosion rates due to sand
particles in the liquid and gas phases. Details of calculating
liquid film velocities, droplet velocities, and erosion rates are
discussed in references [14,17].
2.2. Slug flow
In the absence of any data for sand distribution in slug
flow, it is assumed that sand is uniformly distributed in the
liquid phase. Also, it is assumed that the mass of sand moving
with the liquid slug causes the erosion in slug flow. Therefore,
the characteristic initial particle velocity for slug flow can be
calculated as:
V0 = VLLS = velocity of liquid in the liquid slug
mixture velocity and can be calculated as:
3. Results and validation of the mechanistic model
The fraction of sand entrained in the liquid film is:
1−E =
205
(4)
The erosion rate for slug flow was calculated using the fraction of sand particles in the liquid slug and V0 .
Reference [12] describes how VLLS and the amount of
sand moving with the liquid slug are estimated for slug flow.
The erosion penetration rate due to slug flow is calculated by
a method described in reference [17].
In the present mechanistic model, it is assumed that the
sand particles are carried by the annular liquid film near the
wall and by the liquid droplets entrained in the gas core.
Therefore, the sand particle velocities are similar to the liquid
film velocity and the liquid droplet velocity in the gas core.
Fig. 2 shows a comparison of the calculated mean droplet velocity and the measured droplet velocity by Fore and Dukler
[15] at different superficial gas velocities. Details of calculation procedure are described in reference [12]. The calculated maximum droplet velocity agrees well with the experimental data although a simplified approach was used for
the calculation. (Rel shown in Fig. 2 is the Reynolds number
based on superficial liquid velocity, liquid properties and pipe
size.)
Adsani [16] measured film velocity in upward annular
air–water flow at 0.06–0.37 m/s superficial liquid velocity
and at 13.7–44.8 m/s superficial gas velocities using two conductance probes. By measuring the time difference between
the conductance spikes, the average liquid film velocity was
calculated. Fig. 3 shows a comparison between the measured
film velocities and the predicted film velocities [12]. The predicted film velocities agree well with measured values.
Table 1 shows a comparison of measured thickness loss
due to erosion/kg of sand in mm/kg with the mechanistic
model predictions for annular flow. Table 2 shows a comparison of measured thickness loss/kg of sand in mm/kg the
2.3. Bubble and churn flows
In bubble flow, it is assumed that the gas phase is approximately uniformly distributed in the form of discrete bubbles
that are entrained in a continuous liquid phase. Bubble flow
occurs at low gas rates. Churn flow is much more chaotic
than other flow regimes with the gas and liquid phases mixed
together. In bubble and churn flows, information about the
sand distribution is not available and as an approximation, it
is assumed that the sand is uniformly distributed in the liquid
phase. The velocities of the liquid and sand in bubble and
churn flows are assumed to be equal to the no-slip mixture
velocity. Therefore, the characteristic initial sand particle velocity for bubble and churn flow is assumed to be the no-slip
Fig. 2. Comparison of calculated droplet velocity with experimental data of
Fore and Dukler [15].
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Q.H. Mazumder et al. / Wear 259 (2005) 203–207
Table 1
Comparison of measured erosion with the mechanistic model predictions (annular flow)
VSL
(m/s)
VSG
(m/s)
Elbow diameter
(mm)
Droplet velocity
(m/s)
Entrainment
fraction
Sand size
(␮m)
Flow
pattern
Measured
erosion (mm/kg)
Mechanistic model
prediction (mm/kg)
Note
1.0
0.5
5.8
3.1
1.0
1.5
1.5
2.1
1.0
0.5
0.7
0.5
1.5
0.6
30.0
30.0
20.0
20.0
15.0
14.4
14.6
34.4
35.0
34.3
37.0
38.5
44.0
51.0
49
49
49
49
49
26.5
26.5
26.5
26.5
26.5
26.5
26.5
26.5
26.5
24.8
24.7
18.1
18.0
14.3
13.9
14.0
27.4
28.2
27.7
29.9
30.9
35.2
40.8
0.814
0.713
0.565
0.501
0.198
0.248
0.257
0.982
0.971
0.935
0.977
0.979
0.985
0.989
150
150
150
150
150
250
250
250
250
250
250
250
250
250
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
ANNUL
5.25E−04
2.46E−03
5.19E−05
6.93E−05
1.47E−04
2.30E−04
4.20E−04
2.83E−03
6.56E−03
7.20E−03
8.03E−03
8.03E−03
1.05E−02
1.34E−02
6.40E−4
8.82E−4
6.66E−5
1.12E−04
4.58E−5
3.05E−4
3.17E−04
3.08E−03
4.40E−3
4.79E−3
5.38E−3
6.15E−3
6.28E−3
1.03E−2
1
1
1
1
1
2
2
2
2
2
2
2
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].
Fig. 4. Comparison of measured erosion with mechanistic model predictions.
mechanistic model predictions for slug/churn (calculated values are actually for churn flow based on observation of flow
regime by Mazumder [17]) and bubble flows. Tables 1 and 2
indicate that the erosion data used for comparison with the
model encompasses a wide range of liquid and gas velocities. Fig. 4 shows the mechanistic model predictions to be in
a good agreement with the measured erosion data for a wide
range of measure rates of penetration rates.
4. Summary and conclusion
A mechanistic erosion prediction model has been developed for multiphase flow considering the effects of particle
velocities in multiphase flow. Comparison of the mechanistic
model predictions with the measured erosion data for annular, slug/churn and bubble flows shows good agreement for
a wide range of velocities and erosion rates. The calculated
Table 2
Comparison 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 model
prediction (mm/kg)
Note
5.0
5.0
0.7
0.2
6.2
4.0
15.0
10.0
10.0
8.0
9.0
3.5
49
49
49
49
26.5
49
2.3
1.2
4.2
5.3
3.06
0.22
150
150
150
150
250
150
SLUG/CHURN
SLUG/CHURN
SLUG/CHURN
SLUG/CHURN
SLUG/CHURN
BUBBLE
6.38E−05
1.35E−05
7.01E−05
1.23E−04
1.80E−04
4.60E−06
2.41E−05
7.08E−06
8.18E−05
2.33E−04
9.59E−05
3.12E−07
1
1
1
1
2
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
droplet and film velocities also agree well with the experimental data. Due to the limited availability of experimental
erosion data for bubble, slug, and churn flows, additional
verification and modification of this model is required. This
paper demonstrates a framework for addressing how various
factors can be accounted for in predicting erosion in complex
multiphase flows, and as new information is available it can
be incorporated into the mechanistic model.
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