advanced multiphase modeling - cadfamily.com · erosion modeling approach in fluent . ... •...

1 © 2013 ANSYS, Inc. May 2, 2014 ANSYS Confidential

15.0 Release

Optional Lecture 2:

Erosion Modelling

Advanced Multiphase Modeling


Agenda

• Introduction to Erosion

• Challenges in Erosion Predications

• Erosion Modeling Approaches

• Recap of Particulate Flow Modeling

• Erosion Modeling in Standard ANSYS Fluent

• Erosion Module

• Examples of Erosion Modeling


Erosion

• Erosion is recognized as a major problems in oil and gas production systems

• A number of dangerous elbow failures occurred in UK waters on production platforms and drilling units between 1993 and 2001

Sand Erosion in a bend

• Erosion is a complex process that is affected by numerous factors and small changes in operational conditions can significantly affect the damage it causes

• Erosion leads to a reduction in expected life time of piping systems, and is therefore vital in risk management studies


Erosion Process

• Hydrocarbon wells produce a complex multiphase mixture of components including • Hydrocarbon liquids – oil, condensate, bitumen • Hydrocarbon solids – waxes, hydrates • Hydrocarbon gases (natural gas) • Other gases – hydrogen sulphide, carbon dioxide, nitrogen • Water with dilute salts • Sand and proppant particles

• Potential mechanisms that could cause significant erosion damage are: • Particulate erosion • Liquid droplet erosion • Erosion-corrosion • Cavitation

• It is generally accepted that particulates (sand and proppant) are the most common source of erosion problems in hydrocarbon systems


Sand and Particulate Erosion

• Factors the determine the rate of particle erosion include:

• The flow rate of sand and the manner in which it is transported through the pipework

• The velocity, viscosity and density of the fluid through the component

• The size, shape and hardness of the particles

• Material



• Sand production and flow rate

• Gas systems generally run at high velocities making them more prone to erosion than liquid systems. However, in wet gas systems sand particles can be trapped and carried in the liquid phase

• Slugging can generate periodically high velocities that may significantly enhance the erosion rate

• If the flow is unsteady or operational conditions change, sand may accumulate at times of low flow, only to be flushed through the system when high flows occur



• The velocity, viscosity and density of the fluid

• The particle erosion rate is highly dependent on the particle impact velocity. It is generally accepted that the erosion rate is proportional to the particle impact velocity raised to a power, n (typically n ranges between 2 and 3 for steels)

• In dense viscous fluids particles tend to be carried around obstructions by the flow rather than impacting on them

• In contrast, in low viscosity, low density fluids particles tend to travel in straight lines, impacting with the walls when the flow direction changes. Particulate erosion is therefore more likely to occur in gas flows, partly because gas has a low viscosity and density and partly because gas systems operate at higher velocities



• Sand shape, size and hardness

• Particle size mostly influences erosion by determining how many particles impact on a surface.

• Very small particles (~10 microns) are carried with the fluid and rarely hit walls

• Larger particles tend to travel in straight lines and bounce off surfaces.

• Very large particles (~ 1mm+) tend to move slowly or settle out of the carrying fluid and therefore they are unlikely to do much harm

• Hard particles cause more erosion than soft particles. There is also evidence to show that sharp particles do more damage than rounded particles


Droplet Erosion

• Droplet erosion is confined to wet gas and multiphase flows in which droplets can form.

• The erosion rate is dependent on a number of factors including the droplet size, impact velocity, impact frequency, and liquid and gas density and viscosity.

• Many of these values are unknown for field situations, and it is difficult to predict the rate of droplet erosion

• Salama & Venkatesh have indicated that droplet erosion only occurs at very high velocities. They define an acceptable velocity limit to avoid significant liquid impingement erosion to be:

𝑽 =𝟑𝟎𝟎

𝝆

• For water this give a rather conservative figure of 11.6 m/s


Cavitation

• When liquid passes through a restriction and pressure is reduced below the vapour pressure of the liquid, bubbles are formed.

• These bubbles then collapse generating shock waves. These shock waves can be of sufficient amplitude to damage pipework

• Cavitation erosion is not well understood, and the most practical approach is to identify whether it is an issue or not. The onset of cavitation in equipment or components with flow constrictions can be predicted by calculating a cavitation number K:

• Cavitation number less than 1.5 indicates that cavitation may occur

𝐾 =2 𝑃𝑚𝑖𝑛 − 𝑃𝑣𝑎𝑝

𝜌𝑣2


• Particle trajectories are calculated using coupled DPM simulation

• Particle-wall interaction are defined through coefficient of restitutions for normal and tangential directions

• When individual particles impact on a wall the damage done is calculated using a impact damage model (default erosion model)

• Computational Fluid Dynamics (CFD) are good at predicting erosion locations and erosion scar shapes. They are particularly advantageous in complex geometries such as valves, in which particle trajectories are very convoluted and complicated

Erosion Modeling Approach in Fluent


• Typical variables affecting Erosion rate • Angle of impingement

• Impact velocity

• Particle diameter

• Particle mass

• Collision frequency between particles and solid walls

• Material properties for particle and solid surface

• Coefficients of restitution for particle-wall collision

• Customize erosion rate expression using User Defined Function “DEFINE_DPM_EROSION”

m : Particle Mass flow rate

f(α): Impact angle function

V : Particle impact velocity

n : Velocity exponent

Cd : Particle diameter function

ER: mass of material loss per

unit area per unit time

Erosion Rate caused by particle impact

Erosion Rate Expression

particlesN

p face

nd

A

mfVCER

1

.


Particle Tracking: Restitution Coefficients Incoming particle

32

32

00000356.0000643.0029.0988.0

00000261.0000475.00307.0993.0

t

n

R

R α is particle impact angle

• At impact, the reflected velocity of the particle is lower than the incoming velocity due to energy transfer. This impact signature is described by the momentum based coefficient of restitution

• Restitution coefficient is generally a function of the impact angle, which depends on pipe surface and particle surface properties (roughness, hardness, sharpness, etc)

• Tangential coefficient is lower at higher angle,

while normal coefficient is lowest around 400 impact angle


• The dependence on the impact angle of erosion damage caused by solid particle impact was characterized on several kinds of material, as expressed by a function of both impact angle and material hardness

• Ductile materials normally attain maximum erosion attacks for impact angles in the range 200 - 300, while brittle materials normally attain maximum erosion attacks for normal angle.

Erosion Rate: Impact Angle Function

Angle (deg) Erosion Ratio

0 0

20 0.8

30 1

45 0.5

90 0.4

Piecewise Linear Function for Ductile Material

The “behavior” for typical brittle and ductile materials


Erosion Modeling: Important Steps

• Erosion Analysis is a Post Processing exercise during Fluent simulation • Ensure proper convergence of flow field with proper turbulence

model and near wall treatments

– Finer mesh resolution near wall helps in better erosion predictions

• Erosion analysis depends on particle information

– Collect details of particle properties – particle diameter distribution, particle mass flow rate, particle density, sphericity, hardness, roughness, etc.

• Good estimates for erosion model parameters

– Impact angle function, diameter function, velocity exponents, restitution coefficients, etc.



Discrete Phase Model Settings:

Interaction with Continuous phase is important to access particle mas flow rate for erosion calculation, keep this iteration as 1

Max number of steps has to large enough for most particles to leave escape out of domain

Hook Erosion UDF here if you are using any customized erosion rate expression

Switch ON Erosion/Accretion option here



DPM Particle Injections:

Particle Release Location

Particle Diameter

Particle Velocity at Injection

Total Mass Flow rate of particles

Particle velocity normal to injection plane

Scale particle mass flow rate based on face area

Important to define large number of stochastic tries to resolve turbulence properly for particle tracking

Choose appropriate drag law to include effect of non-spherical particles on drag (if applicable)



DPM Boundary Conditions for Walls

Velocity Exponent for Erosion Rate Expression

Diameter Function for Erosion Rate Expression



Don’t forget to define correct density for the inert particle used in injection setup

This URF for DPM sources can be reduced to very low as we are not interested in transferring momentum from DPM phase to continuous phase for erosion analysis



Display Contours of Erosion Rate under Discrete Phase Variables Drop Down List

Perform Particle Tracking to compute erosion rate

Unit for Erosion Rate is kg/m2-s (mass loss per unit area per sec)


15.0 Release

Examples of Erosion Modeling


Example – Control and Delay Erosion in Choke Valves

Courtesy of DNV

Area of high erosion

Particle trajectories

colored by velocity and

associated erosion area

for two chokes

Flow Inlet

Problem • Particle impact at the small area with high

velocity causing excessive erosion

Solution • Modify exit flow from chock without causing

additional pressure drop. • ANSYS multiphase flow solutions to understand

and change particulate flow patterns

Result • Modified chock geometry leads to flow

streamlines parallel to exit pipe. • Increase particle impact area while reducing

particle impact velocity • Reduce chock maintenance and replacement cost


• Double Elbow Geometry

• Relatively Low solid loading (~8% volume loading)

• DPM vs DDPM Simulation and same Erosion Settings

• Particle shielding effect captured in multiphase simulation

• Single phase predicts conservative erosion

Example: Single Phase vs Multiphase Erosion

Single Phase Erosion Multiphase Erosion Sand Volume Fraction


Example: Erosion in Gas-Liquid-Solid System

Liquid Volume Fraction Contours

Solid Volume Fraction Contours

Vapor Velocity Contours Contours of Erosion Rate

Courtesy of Suncor

Low Erosion due to liquid cushion and particle shielding


• CFD Simulation to analyze flow field and erosion pattern in frac pack tools

• Calibration of erosion model based on lab tests and Erosion pattern compared with large scale tests.

Example: Tool Erosion in Gravel Pack

Erosion pattern on the inside surface of upper extension sleeve

Fluid Velocity Proppant VOF • Turbulent Slurry flow with high proppant concentrations

• Non-newtonian fluids • Calibration of Impact angle

function

Li, J., Hamid, S., & Oneal, D. (2005, January 1). Prediction Of Tool Erosion In Gravel-Pack and Frac-Pack Applications Using Computational Fluid Dynamics (CFD) Simulation. Offshore Technology Conference. doi:10.4043/17452-MS


Example: Erosion – MDM Coupling

Contour of Erosion Rate

Contour of Total Eroded Distance


Example: Erosion – MDM Coupling

Plots of erosion contours in a 4 inch test case

FLOW

Larger ID After 42 hr

Eroded Material is Removed -> Better Material Thickness Prediction


• It is important to predict erosion rate accurately

• Erosion is a complex phenomena • Semi-empirical models and correlations are not enough

• Need for CFD in erosion modeling

• CFD can provide valuable information for erosion predictions • Multiphase flow modeling for dense slurry

• Erosion-MDM coupling

• ANSYS CFD equipped with all required modeling needs

• ANSYS CFD - Proven approach for many erosion studies for oil & gas industries

Summary: Erosion Modeling


15.0 Release

Erosion Module

Appendix


Erosion Module

• Easy to use template to perform an erosion simulation through a single GUI Panel

• User inputs drive the UDF and journal file in the background

• Multiple Erosion Models to choose

• Built-in defaults for DPM settings

• Customized post processing for erosion rate

• Allow comparison between different erosion models

• Complete Automation of Erosion-MDM coupled simulation • Including post processing and animation

• Allows for multiphase erosion simulations • Choose secondary phase or mixture phase velocity field and fluid properties for particle tracking


• Wide Varieties of Erosion Models are available in ANSYS FLUENT

• FLUENT’s Default Erosion Model

• Mclaury et. Al Erosion Model

• Salama & Venkatesh Erosion Model

• Finnie Erosion Model

• DNV Erosion Model

• Oka Erosion Model

• Zhang (ECRC) Erosion Model

• Grant and Tabakoff Erosion Model

• Erosion Model based on Wall Shear Stress

Erosion Module: Selection of Erosion models

Contours of Erosion Rate on a Choke Valve


k = Empirical Constant

n = Velocity Exponent

f(α) = Impact Angle Function

2

2

.

sin32sin

cos3

1

(

f

f

fkVER n

m

Erosion Module: Erosion Models

if tanα > 1/3

if tanα ≤ 1/3

Mechanical and metallurgical aspects of the erosion of

metals, Hutchings, I.M., Proc. Conf. on Corrosion-Erosion

of Coal Conversion System Materials, NACE (1979) 393

Finnie Erosion Model

k1 = Empirical Constant





α0 = Impact Angle for Maximum Erosion (Deg)

43

4

2

0

122

22

1

.

sin

sin1

sin1

1cos

VkVg

VkR

kkf

VgRVfkmER

T

T

n

k2=1 if α ≤ 2α0

k2=0 if α > 2α0

Grant and Tabakoff Erosion Model

Erosion prediction in turbo machinery resulting from environmental solid

particles, G. Grant and W. Tabakoff, Journal of Aircraft 12 (1975) pp. 471-478


a f b c 2

a

.

59.0 mfVABER n

h

zywxf 22 sinsincos

a, b, c, w, x, y, z are constant for the impact

angle function

A = Empirical constant

Bh = Brinnel Hardness

n = Velocity exponent

McLaury, B.S. ., Shirazi, S.A., Shadley, J.R. and Rybicki, E.F., 1996

“Modeling Erosion in Chokes” Proceeding of ASME Fluids Engg

Summer Meeting, San Diego, California, pp 773-781.


McLaury et al Erosion Model

A = Geometry dependent constant

Dpipe = Pipe diameter (inches)


V = Fluid velocity (ft/s)

P = Material Hardness (psi)

m = Sand Flow rate (bbl/month)

f(2

.

pipe

n

PD

mAVER

Salama, M.M. and Venkatesh, E.S. 1983, “Evaluation of API-RP-14E

Erosion Velocity Limitation for offshore gas wells”. OTC paper

12531, OTC, Houston, Feb 1983.

Salama & Venkatesh Erosion Model


a f b c 2

a

.

59.0 mfVABER n

h

zywxf 22 sinsincos

a, b, c, w, x, y, z are constant for the impact

angle function

A = Empirical constant

Bh = Brinnel Hardness

n = Velocity exponent

McLaury, B.S. ., Shirazi, S.A., Shadley, J.R. and Rybicki, E.F., 1996

“Modeling Erosion in Chokes” Proceeding of ASME Fluids Engg

Summer Meeting, San Diego, California, pp 773-781.


McLaury et al Erosion Model

A = Empirical Constant

Dpipe = Diameter of the Pipe (inches)


V = Particle Impact Velocity (ft/s)

P = Material Hardness (psi)

m = Sand Flow rate (bbl/month)

f(2

.

pipe

n

PD

mAVER

Salama, M.M. and Venkatesh, E.S. 1983, “Evaluation of API-RP-14E

Erosion Velocity Limitation for offshore gas wells”. OTC paper

12531, OTC, Houston, Feb 1983.

Salama & Venkatesh Erosion Model


Cd = Empirical Constant

Fs = Sharpness Factor


B = Brinnel Hardness

Comparison of computed and measured particle velocities and

erosion in water and air flows Y. Zhang, E.P. Reuterfors, B.S.

McLaury, S.A. Shirazi, E.F. Rybicki


.

59.0 mfVBFCER nsd

93.1011.1041.5 2f

Zhang ECRC Erosion Model (Tulsa Model)

E90 = Reference Erosion Ratio

n1, n2 = Constants for angle function

Hv = Vicker Hardness (Gpa)

k2 = Velocity Exponent

k3 = Diameter Exponent

Uref = Reference Velocity (m/s)

Dref = Reference Particle Diameter (microns)

D = Particle Diameter

.

32

90 mfD

D

U

VEER

k

ref

k

ref

21sin11sin

n

v

nHf

Practical estimation of erosion damage caused by solid particle impact:

Effects of impact parameters on a predictive equation, Y.I Oka, K.

Okamura, T. Yoshida, (2005), Wear, 259, p.102-109

Oka Erosion Model


K = Empirical Constant


K. Haugen, O. Kvernvold, A. Ronold and R. Sandberg Sand erosion of wear resistant materials: Erosion in choke valves” Wear 186-

187 (1995) 179-188

Erosion Module: DNV Erosion Model

.

mfKVER n

8762 11.4211.31398.98137.70804.175864.110295.4237.9 f

2f

For Ductile Material

For Brittle Material


Comparison of Erosion Predictions for Elbows

• Predictions for the sand-methane mixture

• Gas Density = 4.82 kg/m3

• Gas Viscosity = 1.1 x 10-5 Pas

• Sand particle size = 150 microns

• Sand density = 2650 kg/m3

• Elbow diameter = 55 mm

• Elbow r/D = 1.5

• Elbow material steel grade (Brinnell Hardness = 210)

• Sand concentration = 21.6

ppmw

Erosion of a 2” elbow in methane-sand flow


Comparison of Erosion Predictions for Elbows

• Predictions for the sand-liquid mixture

• Liquid Density = 769 kg/m3

• Liquid Viscosity = 1.08 x 10-3

Pas

• Sand particle size = 150 microns

• Sand density = 2650 kg/m3

• Elbow diameter = 55 mm

• Elbow r/D = 1.5

• Elbow material steel grade (Brinnell Hardness = 210)

• Sand concentration = 0.1 ppmw

Erosion of a 2” elbow in liquid-sand flow


Summary

• This last two slides demonstrate the inconsistency of modern elbow erosion prediction methods.

• Most of the methods do account for factors such as changes in fluid viscosity and density in some degree

• However the predictions can be orders of magnitude different.


Erosion Module: Erosion Model for Dense System

• Particle-particle interaction and volume fraction of solid phase are important to include in particle tracking and impact erosion

• Eulerian Granular or Dense DDPM simulation to take into account particle-particle interaction

• DPM tracking in mixture phase or solid phase flow field to include particle shielding effect for erosion rate predication.

• ABRASIVE EROSION: Erosive due to relative motion of solid particles moving nearly parallel to a solid surface

• Impact based erosion models can not capture the abrasive erosion

• Abrasive erosion depends on solid phase wall shear stress and solid phase velocity near the wall


Abrasive Erosion Model Based on Wall Shear Stress:

sp

sws

n

sabrasive AVER

A = Empirical Constant


τws= Solid Phase Wall Shear Stress

Vs = Solid Phase Velocity

ERsp= Single Phase Impact Erosion

αs = Volume Fraction of Solid Phase

αsp = Packing Volume Fraction

Erosion Module: Erosion Model for Dense System

spssp

sp

impact ERER

1

Impact Erosion Rate for Dense System:

Total Erosion Rate: impactabrasiveTotal ERERER


Option to start a new Erosion-MDM

simulation or restart from the existing data

file at previous time interval

Opens panel to read the case file for the

flow field

Opens DPM injection panel to define

particle injections

Opens boundary condition panel to set

DPM BCs for wall zones

Opens DPM panel to set parameters for

particle tracking

Opens panel to read the data file for the

flow field

Display erosion rate on wall zones

Display cumulative eroded distance at

wall zones

Perform particle tracks to calculate

erosion rate

Option to run erosion-only

or erosion-MDM coupled

simulation

List of erosion models to

choose from

Option to choose secondary

phase or mixture phase

flow field and properties

for particle tracking

Opens panel to define

required parameters for

Erosion-MDM coupling

Opens panel to start erosion-

MDM simulation Main Panel

Opens panel to define density of particle

material Open Panel to Define

erosion model parameters

Option to add wall shear

stress based abrasive erosion


Erosion Module: Erosion-MDM Coupling • Erosion Module allows dynamically change the solid wall surface based on

an erosion rate at regular time intervals.

• Using the UDF, wall face nodes are moved by a distance calculated from the erosion rate.

• For each node, the user-defined-averaged value of the erosion rate of all faces connected to that node within a user-defined radius is obtained in order to smooth out the new wall surface.

• Then each node is moved normal to face by a distance calculated as average erosion rate divided by area of wall face and wall density.

• User Define Macro, DEFINE_GRID_MOTION, was used to set the desired motion to the surface nodes.


Maximum (as a fraction of

cell length) node move

allowed at each MDM

calculation

Radius of region to define

the area for smoothing

erosion rate at each node

Specify the rate of decay

with distance from the

node center

Selection of participating

walls for the moving

mesh

Prefix for the case and data files

which will be saved at each mesh

motion step

Specify Density for the wall

material

Specify time interval between

each mesh motion

Define number of steps for MDM

calculations at each mesh motion

step

Select surfaces for erosion

module to save images of

contours of eroded distance in

this view at every mesh motion

step. These images can later be

used to create movie.

Erosion Module: Erosion-MDM Coupling

advanced multiphase modeling - cadfamily.com · erosion modeling approach in fluent . ... •...

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