A MECHANISTIC MODEL TO PREDICT EROSION IN MULTIPHASE FLOW IN VERTICAL PIPES
Quamrul H. Mazumder, Siamack A. Shirazi, and Brenton S. McLaury
The University of Tulsa
600 S. College Ave.
Tulsa, OK 74104
Erosion in multiphase flow is a complex Erosion caused by entrained solid particles is a phenomenon due to existence of different flow major problem in fluid handling equipments used in patterns. The presence of sand adds another several industries. In oil and gas industry, the sand dimension to the complexity of erosion in multiphase production from the oil and gas wells may cause flow. Earlier models for predicting erosion in considerable erosional damage in the well tubing, multiphase flow were based on empirical data and the piping, fittings, and other equipments. The accuracy of those models was limited to the flow momentum of the solid particles carried by the conditions of the experiments. A mechanistic model production fluid impinges on the inner surfaces of the has been developed for predicting erosion in pipes, fittings and valves resulting material loss from multiphase flow in vertical pipes considering the the surface that leads to production loss, operating effects of particle distribution and particle velocities problems and lower reliability of the system. In coal in gas and liquid phases of the flow. As the new gasification, erosion problems are added to corrosion model is based on physics of multiphase flow, it is causing severe erosion to valves and pipe fittings expected to be more general than the empirical [Glasser, 1977]. Erosion of slurry pipelines in erosion prediction models. The mechanistic model transportation of raw solid materials, such as iron ore, predictions for an elbow geometry were compared coal and potash is significant problem in the mining with annular, slug/churn and bubble flow erosion industry [Postleth, 1974].
experiments showing good agreement. Solid particle erosion is a process by which Keywords: erosion, multiphase flow, three-phase material is removed from a solid surface due to flow, sand erosion, mechanical effects such as impingement of solid
particles on the surface [Shirazi, 1995]. The erosion
phenomenon is highly complicated and a wide range
of parameters affect the erosion severity, such as Although a number of erosion prediction models production flow rate, sand rate, fluid properties, flow are currently available, most of them are based on regime and solid particle properties, wall material of empirical data [5,6]. These models can be applied to the equipment, and geometry of the equipment [Chen operating conditions that are similar to the X, 2002]. To prevent process equipment failure and experimental conditions and can not be generalized to downtime, it is critical to predict damages that may other flow conditions. The Erosion/Corrosion occur due to erosion in the process equipment and Research Center (E/CRC) at The University of Tulsa piping. has developed a simplified procedure to predict
Erosion prediction is a complex problem due to erosion in elbows and tees. The E/CRC model was lack of understanding of the spatial distribution of initially developed for single-phase flow based on the solid particles in the flow and their corresponding empirical data and computational fluid dynamics impact forces that causes erosion to the metal (CFD) based erosion model that uses flow modeling, surfaces. The solid particle impact velocity depends particle tracking, and empirical erosion equations. upon the geometry of the pipe or fitting, carrying Generalized models such as the computational fluid velocity, flow pattern, inclination angles, solid fluid dynamics (CFD) based erosion models  that concentration, particle shape, size and distributions in take into account details of flow effects and pipe the flow. Most of the erosion prediction models are geometries require significant effort in computation based on single-phase liquid and gas as the carrying using CFD codes for simulating particle impingement fluid. In oil and gas wells, the fluid is a mixture of angle and speed. Thus a mechanistic model was gas, liquid and sand that requires a multiphase developed for predicting the maximum penetration erosion prediction model. The complexity of erosion rate in geometries such as elbows and tees that was prediction increases significantly for multiphase flow based on a CFD erosion model. The mechanistic when gas, liquid and solids are present in the flow. In model was based on extensive empirical information contrast to single-phase flow, multiphase flow has gathered at E/CRC, Texas A&M University, Harwell different flow patterns depending upon the gas, liquid, and DNV for calculating erosion in multiphase flow solid flow rates, pipe size, inclination angles, and . The model uses a characteristic impact velocity fluid properties. Among the different flow patterns, of the particles taking into account factors such as the severity of erosion damage is higher in vertical pipe geometry and size, sand size and density, flow annular flows with high gas velocity and low liquid regime, velocity, and fluid properties. The model velocities. Currently, no simple mechanistic models also can be used to determine the threshold velocity available for erosion prediction in vertical flow. A that could indicate a maximum allowable penetration mechanistic model to predict erosion in multiphase rate. The model for calculating a maximum flow in vertical pipes is presented in this paper. penetration rate for a simple geometry such as elbows
and tees can be written as 1.73BACKGROUND WVLh，FFFF (1) MSPr/D 2(D/D)0
where: model assumes movement in one direction with linear
h = penetration rate in mm/year fluid velocity. Initial particle velocity was assumed
F , F = empirical factors for material and sand to be the same as the flowstream velocity. This is MS
sharpness valid for single-phase flow assuming no slip between
F = penetration factor for steel based in 1” pipe the particles and fluid. This approach is graphically P
diameter, (m/kg) displayed in Figure 1.
Equivalent Stagnation LengthStagnationF = penetration factor for long radius elbows r/DZone
W = sand production rate, (kg/s) LV = characteristic particle impact velocity, (m/s) LParticle InitialPositionD = pipe diameter, (mm)
TeeD = 25.4 mm 0StagnationZone vo
xFor a given geometry, material, sand sharpness
and sand rate, all the terms in equation (1) become
Elbow constant except the characteristic impact velocity, V.L
Figure 1: Concept of Equivalent Stagnation Therefore, Equation (1) can be written as Length
1.73 h，KV (2) L
In a two-phase gas-liquid flow the sand particles The term V in the equation represents the L
may be entrained in the liquid phase traveling at a characteristic particle impact velocity of particles,
velocity close to that of the liquid. Figure 2 shows which must be deduced by solving a simplified
the major flow patterns in vertical multiphase flow. particle tracking equation. The investigators 
The characteristic impact velocities may be different developed a method for calculating V, which is L
for different flow patterns. For annular flow, the obtained by creating a simple model of the stagnation
characteristic impact velocity in annular vertical flow layer in pipe geometry.
may depends upon the entrained liquid droplet The stagnation zone is a region where the
velocity and annular liquid film velocities. For slug particles must travel and penetrate to strike the pipe
flow, the chracteristic impact velocity may depends wall for erosion to occur. The severity of erosion in
on the velocity of the liquid slug and the liquid this zone depends on a series of factors such as fitting
holdup in the liquid slug . For churn and bubble flow, geometry, fluid properties and sand properties. It was
the characteristic velocity may depends upon the gas demonstrated that for elbows with different diameters
and liquid velocities. McLaury and Shirazi  the stagnation length varies. A simplified particle-
assumed that impact velocity for two-phase flow tracking model was used to compute the
depends on a representative “flowstream velocity”, characteristic impact velocity of the particles; the
V. They used empirical information to determine V. o.o
Annular Flow Churn Flow Slug Flow Bubble Flow
Figure 2: Flow Patterns in Vertical Multiphase Flow
In the present work, due to unavailability of a
of flow conditions and more accurate for predicting comprehensive mechanistic erosion prediction model erosion in multiphase vertical flow. The new that can be applied to different flow conditions, a mechanistic model for calculating the initial velocity mechanistic model has been developed to predict
of the particles before they reach the stagnation zone, erosion in multiphase flow. The velocity of sand V, is presented in this work. oparticles plays an important role in calculating the
impact velocity and has a strong influence on erosion PRESENT WORK rate. A mechanistic model was developed
Previous erosion prediction models did not (Mazumder, ASME FED03 paper) to predict erosion
consider the complexity of multiphase flow in the in annular flow using entrained liquid droplet velocity, characteristic impact velocity calculations and liquid film velocity and entrained sand particles. The assumed it to be a function of superficial gas and model was compared with experimental erosion
liquid velocities only. This new mechanistic model results and showed good agreement. The previous
uses the physics of multiphase flow, fluid mechanics mechanistic model used entrainment correlation of
and is expected to be more general and as it ANSARI (1994) that underpredicted the entrained
incorporates the important parameters that are liquid fraction in the gas core region.
critical to erosion. As this model is able to predict The new mechanistic model presented in this
erosion in annular, slug, bubble and churn flow paper uses an improved entrainment correlation
regimes in vertical flow, this model is also more proposed by ISHI that was accurate to a wider range comprehensive than the previous models.
Due to complexity and differences in erosion at due to shearing-off roll waves crests by highly different flow regimes, separate models have been turbulent gas flow. Ishi proposed a semi-empirical developed to calculate the characteristic particle correlation that appears to provide accurate impact velocities. These mechanistic models are entrainment predictions over a wide range of flow described in the following sections. conditions. The entrainment model uses
dimensionless Weber number and liquid Reynolds ENTRAINMENT MODEL number. The model is for quasi-equilibrium
Accurate prediction of the liquids entrained in the condition and can be applied to a region away from gas phase is critical for predicting erosion in the entrance region of the flow.
multiphase flows. In vertical annular flow, the sand
MECHANISTIC MODEL FOR ANNULAR particles entrained in the liquid droplets and in the FLOW
gas core impinge on the pipe wall at a higher velocity Annular flow exists at higher gas and lower causing erosion. Although a number of empirical liquid velocities. In vertical annular flow, the liquid entrainment correlations are available in the forms a thin annular film inside the pipe wall and literatures, the accuracy is limited to the particular partially entrained as droplets in the gas core region. flow conditions that were used to develop the The gas in the core region flows at a higher velocity correlation. Wallis (1969) proposed an entrainment carrying the entrained liquid droplets and sand correlation using superficial gas velocity, fluid particles, while the liquid film adjacent to the pipe properties and surface tension. The correlation did not wall flows at a slower velocity. The droplet consider the effect of liquid rate and therefore entrainment from the liquid film by a streaming high underpredicted entrainment at higher liquid velocities. velocity gas flow is of considerable importance as the Asali and Hanratty (1983) described entrainment as a mechanism that causes liquid droplets to be entrained balance between the deposition of droplets entrained can also cause the sand particles entrained in the gas in the gas and atomization of the liquid film flowing core causing erosion. Figure 3 shows a schematic of along the inner wall of the pipe. The correlation the vertical annular flow with entrained sand particles requires liquid film thickness as an input parameter and liquid droplets.
that is not known in most cases. Olimen (1985) The sand particles were assumed to be uniformly proposed a correlation that contains seven different distributed in the liquid phase and it was assumed that input parameters and their corresponding exponents there is no slip between the liquid and sand particles using Harwell well data. The parameter estimates in the flow. The initial particle velocity was were calculated at different Reynolds Numbers. The calculated by using the liquid film velocity and correlation provided good entrainment results that entrained liquid droplet velocities. The were limited to the flow conditions and variables used “characteristic flowstream velocity” (that is assumed in development of the correlation. Ishi (1989) stated to be the same as initial particle velocity before the that for a relatively high liquid Reynolds number particles reach the stagnation zone) is calculated (Re >160), the droplet entrainment mechanism is using mass weighted average of liquid velocities in L
the film and the entrained liquid droplets in the gas MassofLiquidintheGasCoreE， TotalMassofLiquidcore.
The liquid hold-up (mass fraction of liquid) in the
liquid film is (1- Entrainment). Therefore, Equation
The entrainment rate, E, and the annular film
velocity, V are calculated using Ansari  model film
as described below. The liquid film thickness ！ is
assumed to be uniform or the cylindrical gas core to
be of uniform diameter D. Also, the gas core is C
considered to be composed of homogeneous mixture
of gas and tiny liquid droplets with no relative slip
between them. Thus, various geometric parameters
can be easily expressed.
The cross-sectional area of the gas-core:
2 (5) A，(1？2！)ACP
The cross-sectional area of the liquid film:
Where A is the cross-sectional area of the pipe P
and Figure 3: Vertical Annular Flow with Entrained
Liquid Droplets and Sand pipe diameter, D.
Therefore, the characteristic flow stream velocity The velocity of the film can be determined is calculated by from simple mass balance calculations yielding,
V = (Mass fraction of liquid in film x V + ofilm
Mass fraction of liquid in the gas core x V)d21？ED;； (7) V，VfilmSL (3) 4！(D？！)
where Where V SL
V= average liquid film velocity, m/sec film thickness, D is the pipe diameter, and E is the film
V = average liquid droplet velocity in gas dfraction of the total liquid entrained in the gas core. core, m/sec
The film thickness δ was calculated using Ishi  The entrainment, E, is the fraction of liquid entrained
model. Liquid entrainment in the gas core is an in the gas core and is defined as
important parameter and it is calculated from an
explicit correlation given by the Ishi  correlation:
ratio. For annular flow, for superficial liquid
0.25？71.25Reynolds number between 750 and 3000, (8) E=tanh(7.25x10WeRe)L
experimental results of Fore and Dukler  show where,
that the average slip ratio between the droplet and gas 0.332；？；；(；VDLGGSG (9) ~)We，~)core velocities is approximately 0.80. The droplet ，；G??
velocity is calculated by multiplying the average gas and
velocity by the slip ratio between droplet and gas ；VDLSLRe， (10) Lvelocities. ，L
= VS (14) VdgRIn this investigation, a method for calculating the droplet velocity is proposed as in the following Thus, by using V, E, and V, the equivalent filmd section The diameter of the gas core is calculated as: flowstream velocity Vand initial sand velocity are o calculated from Equation (4).
D = D - 2！ (11) c MECHANISTIC MODEL FOR SLUG FLOW
Slug flow occurs over wide range of gas and The average gas core velocity,
liquid flow rates. It is the dominant flow pattern in 2?，D (12) V，V??gsgDupward inclined flow. Slug flow hydrodynamics is c?：
very complex with unique and unsteady flow In annular flow, droplets form from the
behaviors. It is characterized by an alternate flow of a disturbances in the wavy liquid film surfaces near the
gas pocket, named Taylor bubble, and liquid slugs wall, accelerate in the gas core and deposit back on to
that contain numerous small gas bubbles. A thin the film. The droplets represent larger interfacial
liquid film flows downward between the Taylor transfer area than the liquid film and can increase
bubble and the pipe wall in vertical slug flow. mass transport between the phases . The droplet
Assuming the Taylor bubble is symmetric around the and sand velocities in the gas core contributes to
pipe axis for vertical flow, Figure 4 shows a erosion due to high impact velocity of sand particles
schematic description of slug flow in vertical pipe. that are entrained in the droplets. The droplet
The slug body of unit length Lis divided into SU velocities in the gas core are less than the gas velocity
two parts: the Taylor bubble of length L, and the TBdue to interphase slip between the gas and droplets.
liquid slug of length L. The Taylor bubble occupies LSThe mean slip ratio, Sis defined  with the R,
nearly the entire pipe cross-section and propagates droplet velocity, V, as d
downstream with velocity V. The liquid film TBF
flows down with velocity V. The void fraction of VLTBd (13) S，RVgthe bubble section is denoted H. The average GTB
The droplet velocity was calculated by liquid velocity in the liquid slug is V and the LLS
multiplying the gas core velocity by the above slip average velocity of the dispersed bubbles is V GLS.
The liquid holdup of the liquid slug is denoted by comprehensive analysis of slug flow into a unified H. model for horizontal, inclined and vertical flows. LLS
Currently, no data exist to determine the sand
distribution pattern in slug flow. For a preliminary
analysis of slug flow, it is assumed that sand is
distributed in the liquid phase and the uniformly VTBF
mass fraction of sand in the liquid slug is equal
to the mass fraction of liquid in the liquid slug.
Assuming that the mass fraction of sand moving with
Hthe liquid slug causes the erosion in slug flow, the GTB
Taylor initial particle velocity is calculated as: VLTB Bubble
V = Mass fraction of sand in liquid slug x oLTB
Velocity of liquid in the liquid slug (15) VGLS
LSU Thus, by assuming sand is uniformly distributed
in the liquid phase, the characteristic initial particle Liquid
LLS Slug velocity for slug flow can be a calculated as
V= Mass fraction of liquid in the liquid slug x o
Velocity of liquid in the liquid slug (16)
V，VxH (17) oLLSLLS
Where, H is the liquid holdup in the liquid LLS
slug and V is the liquid velocity of the liquid slug. LLS
The liquid holdup in the slug body, H can be LLSFigure 4. Schematic Description of Slug Flow in
calculated using the Gomez et al.  correlation: Vertical Pipe.
Due to unsteady hydrodynamic characteristics -(0.45.( +2.48E-6.Re)H = 1.0 e (18) LLS
of the slug flow, it has a unique velocity, holdup and
pressure distribution. Therefore, the prediction of the where, ( is in radians for pipe inclination angle 0 liquid holdup, 0： ( ： 90 pressure drop, heat and mass transfer are difficult and challenging. Several mechanistic The slug superficial Reynolds number is models have been proposed that enables reasonable calculated as prediction of the liquid holdup in the slug, slug length, slug frequency and velocities of Taylor bubble and
liquid slug. Taitel and Barnea  presented a
； V dLm (19) Re = ， L
where, V = V + V(20)mSGSL
The velocity of liquid in liquid slug can be calculated as :
V？V(1？H)mgssLLS (21) V，LLSHLLS
The calculated initial sand particle velocities
were used in the preliminary mechanistic model for
Figure 5. Schematic Description of Bubble Flow slug flow to calculate erosion and were compared in Vertical Pipe.
with measured erosion from laboratory data.
MECHANISTIC MODEL FOR CHURN FLOW
MECHANISTIC MODEL FOR BUBBLE FLOW
In bubble flow, it is assumed that the gas phase is approximately uniformly distributed in the form of discrete bubbles that move at different velocities in a continuous liquid phase. Bubble flow occurs at low gas rates. Figure 5 shows a schematic description of
a bubbly flow in vertical pipe.
In bubble flow, it is assumed that the sand is uniformly distributed in the liquid phase. The velocities of the liquid and sand in the bubble flow region is assumed to be the same as the mixture velocity. Therefore, the characteristic initial sand
Figure 5. Schematic Description of Churn Flow in particle velocity for bubble flow is assumed to be the Vertical Pipe
mixture velocity and can be calculated as
V = V + V (22) 0SLSG