Modeling Proppant Transport in Fractures Using ANSYS · Modeling Proppant Transport in Fractures...

© 2011 ANSYS, Inc. September 8, 20111

Modeling Proppant Transport in Fractures Using ANSYS

Dr. D. Dakshinamoorthy and Dr. Y. DaiANSYS Inc


Overview of proppant transport in fractures Factors affecting proppant transport

Numerical modeling challenges ‐ANSYS solutions

Present the results for proppant transport simulations

Conclusions and

Future work

Outline: Proppant Transport Using ANSYS


Hydraulic fracturing – Increase the productivity of oil & gas well (1)

Frac‐fluid slurry – Mixture of frac fluid and proppant is injected into the well @ high pressure (2)

Fluid pressure – Generates fractures extending into the rock medium (2)

Width of the fracture is maintained by the transported proppant (2)

Proppant Transport: Overview

Reference: 1. Patankar, N.A., Joseph, D.D., Wang, J., Barree, R.D., Conway, M., Asadi, M., 2002. Power law correlations for sediment transport in

pressure driven channel flows. International Journal of Multiphase Flow. 28. 1269–1292.2. Ouyang, S., Carey, G. F., Yew, C. H., 1997. An adaptive element scheme for hydraulic fracturing with proppant transport. International

Journal of Numerical Methods in Fluids. 24. 645–670.


Where is Proppant Going? Better proppant placement What should be the injection rate? Proppant selection Longer propped fractures – Lateral Spreading Use of high viscous frac‐fluids Height growth – Vertical filling

Concerns in Proppant Transport


Complex multiphase flow problem

Proppant settles to the bottom – Mound develops –Reaches an equilibrium height

Until the equilibrium height – Proppant bed gets higher and then it spreads laterally

Proppant Transport: Overview

Reference: Patankar, N.A., Joseph, D.D., Wang, J., Barree, R.D., Conway, M., Asadi, M., 2002. Power law correlations for sediment transport in pressure driven channel flows. International Journal of Multiphase Flow. 28. 1269–1292.


Various Stages in Proppant Transport (2)

Stage 1: Convection / settling dominated.

Stage 2: Buildup of a proppant bed.

Stage 3: Steady state saltation over bed.

Stage 4: Final settling after flow shutoff.

Proppant Transport: Stages

Reference: 1. Patankar, N.A., Joseph, D.D., Wang, J., Barree, R.D., Conway, M., Asadi, M., 2002. Power law correlations for sediment transport in

pressure driven channel flows. International Journal of Multiphase Flow. 28. 1269–1292.2. Sharma, M.M., Copeland, D., Gadde, B. P., Liu, Y., Norman, J., Bonnecaze, R., 2003. Advanced Fracturing Technology for Tight Gas:

Where is the Proppant Going? COGA Conference.

Stage 1, 2 & 4 ‐ Settling Process Stage 3 – Wash Out process (1)


Settling process is governed by settling laws

Terminal settling velocities ‐ Quantifies the process

Empirical Equations are usually used: Single particle Stokes Law for laminar flow

Allen’s Equation for transition flow

Newton’s Equation for turbulent flow

Proppant Transport: Settling Process

Single particle settling laws are not enough to determine the settling process of the proppant in fractures


Hindered settling – Particle to Particle interaction

Wall effects (or retardation) Leak‐off – Frac‐fluid can leak

Proppant Transport: Settling Process

Reference1. Sharma, M.M., Copeland, D., Gadde, B. P., Liu, Y., Norman, J., Bonnecaze, R., 2003. Advanced Fracturing Technology for Tight Gas:

Where is the Proppant Going? COGA Conference.


Sliding or Slipping – Bed load transport

Advection after fluidization by lift – Suspended loaded transport – Efficient Lift force plays an important role in re‐suspension of

particles Complex physics and requires detailed modeling

Proppant Transport: Washout Process

Reference: Patankar, N.A., Joseph, D.D., Wang, J., Barree, R.D., Conway, M., Asadi, M., 2002. Power law correlations for sediment transport in pressure driven channel flows. International Journal of Multiphase Flow. 28. 1269–1292.


ANSYS: Models for Particulate Flows

Model Numerical approach Particle fluid interaction

Particle‐Particle interaction

Particle size distribution

DPM Fluid – Eulerian Particles – Lagrangian

Empirical models for sub‐grid particles

Particles are treated as points

Easy to include PSD because of Lagrangian description

DDPM ‐ KTGF Fluid – Eulerian Particles – Lagrangian

Empirical; sub‐gridparticles

Approximate P‐P interactions determined by granular models

Easy to include PSD because of Lagrangian description

DDPM ‐ DEM Fluid – Eulerian Particles – Lagrangian

Empirical; sub‐grid particles

Accurate determinationof P‐P interactions.

Can account for all PSD physics accurately including geometric effects

Euler Granular model

Fluid – EulerianParticles – Eulerian

Empirical; sub‐grid particles

P‐P interactions modeled by fluidproperties, such as granular pressure, viscosity, drag etc.

Different phases to account for a PSD; when size change operations happen use population balance models

MacroscopicParticle Model

Fluid – Eulerian Particles – Lagrangian

Interactions determined as part of solution; particles span many fluid cells

Accurate determinationof P‐P interactions.

Easy to include PSD; if particles become smaller than the mesh, uses an empiricial model


The proppant transport process can be analyzed using Lagrangian tracking process

ANSYS FLUENT does offer DEM (Discrete Element Modeling) for analyzing large number of particles Collision and frictional terms are modeled

discretely Understand the extent and limitations of this

approach

DEM Analysis


DEM

DEM modeling of Proppant Transport


ANSYS FLUENT does offer Macro Particle Model (MPM) as a solution for suspended bed transport? Lift and Drag are explicitly calculated or

predicted by the MPM model No empirical correlations are needed

Macro Particle Model


Demonstrate Particle Lift Off from ground using MPM• Geometry of a long narrow channel (200 X 75 microns)• Steady state periodic flow field was solved in the channel

• A 20 microns diameter particle was placed on bottom surface of the channel

• Transient MPM simulation was performed for particle trajectory.

MPM – Lift Force Example

Fine mesh(about 4 fluid cells across particle diameter)

Initial Location of the Particle

Flow Direction


MPM Validation – Lift Force

0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

Axial Distance (microns)

Distance from

Wall (microns) Particle Trajectory

Axial Distance (in microns)

Distance from W

all (in microns)

MPM automatically predicts particle lift force without including any lift force correlation (Saffman etc)


Current Study: Euler‐Granular model is considered for studying settling in fractures Every phase has its own mass, momentum and energy

conservation Conservation equations of different phases are coupled via

interfacial terms – these terms are modeled. Granular model does have intrafacial terms to account for

collision and friction Closeness of these terms to reality determines accuracy of

the model

Proppant Transport: Euler‐Granular


Granular flows are dense so drag coefficients are based on single particle drag + concentration effect – Hindered settling is considered

Collisional and frictional effects (becomes important near packing limit) are considered

Wall effects are also considered

Proppant Transport: Granular Model


Proppant Transport: Solution Domain

Typical Fracture is Considered

300 ft

40 ft

Fracture Width = 0.5 cm


Fracture Geometry

Fluid Properties

Proppant Size and Properties

Injection Rates

Proppant Concentration in Frac Fluid and

Leakoff Rates – Modeled using UDF

Parameters for Proppant Transport Study


Proppant Transport: Boundary Conditions

300 ft

40 ft

Fracture Width = 0.5 cm

Full 3D – Wall Effects and Leak Off – Modeled

Slurry flow: Mixture of Frac‐Fluid and Proppant

0vLv

0v Lv

0V075.0 VVLeak

Leak Off Rates


Fluid density: 998.2 Kg/m3

Particle density: 2500 Kg/m3

Fluid viscosity: 1 cp

Diameter of particle: 100 µm, 300 µm & 500 µm

Particle concentration: 20%

Fluid horizontal velocity: 0.4 m/s

Terminal Settling Velocity = 0.9 cm/s, 7.5 cm/s & 20.5 cm/s

Proppant Transport: Conditions


Typical Results: Contours of Velocity

Frac‐Fluid VelocityVelocity Decreases Due to Leak off

Settled Bed after t‐secs


Typical Results: Contours of Velocity

Proppant Velocity


As state earlier early injected proppant settles and forms a mound and reaches an equilibrium height. The velocity in the gap increases as the mound grows, which allows the later injected proppant to settle and spread laterally.


Typical Results: Contours of Pressure

Pressure drop across the fracture can be calculated during the settling process



Typical Results: Contours of Volume Fraction of Proppant

Settled Proppant Bed after t‐secs

Bed Height

Proppant Volume Fraction

Extent of proppant placement


300 µm Vs 500 µm Settling

300 µm– Proppant 500 µm ‐ Proppant

Settling of Two Different Proppant Sizes

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Snapshots of 300 µm and 500 µm500 µm300 µm

time


Can Euler‐Granular model capture wash‐out process?

Sliding or Slipping – Bed load transport can be captured by Euler‐Granular Model A small fraction of the bed is patched with proppant and the bed load transport is studied Two proppant sizes are investigated

Proppant Transport: Wash Out Process



300 µm– Proppant 100 µm ‐ Proppant

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Proppant Transport: Wash Out ProcessThis image cannot currently be displayed.



Euler‐Granular model is capturing the effect of wash out process

300 µm – Proppant mound didn’t wash out The mound created a re‐circulating zone

upstream and allowed settling in this zone The mound also grew over a period of time 100 µm – Proppant mound did wash out. The mound started loosing proppant and the

height decreased This is not due to saltation or suspended bed

transport – only due to bed load transport


The results clearly shows the value of using Euler‐Granular model to capture the settling and wash‐out process

Euler‐Granular model does capture the effect of hindered settling, leak‐off and retardation on the proppant transport in fractures

Euler‐Granular model can clearly be used for studying the bed load transport process

Results Discussion


Questions or Comments !!!!!

Thank you Very Much

Modeling Proppant Transport in Fractures Using ANSYS · Modeling Proppant Transport in Fractures...

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