modeling proppant transport in fractures using ansys · modeling proppant transport in fractures...
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© 2011 ANSYS, Inc. September 8, 20111
Modeling Proppant Transport in Fractures Using ANSYS
Dr. D. Dakshinamoorthy and Dr. Y. DaiANSYS Inc
© 2011 ANSYS, Inc. September 8, 20112
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
© 2011 ANSYS, Inc. September 8, 20113
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.
© 2011 ANSYS, Inc. September 8, 20114
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
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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.
© 2011 ANSYS, Inc. September 8, 20116
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)
© 2011 ANSYS, Inc. September 8, 20117
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
© 2011 ANSYS, Inc. September 8, 20118
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.
© 2011 ANSYS, Inc. September 8, 20119
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.
© 2011 ANSYS, Inc. September 8, 201110
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
© 2011 ANSYS, Inc. September 8, 201111
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
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DEM
DEM modeling of Proppant Transport
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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
© 2011 ANSYS, Inc. September 8, 201114
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
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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)
© 2011 ANSYS, Inc. September 8, 201116
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
© 2011 ANSYS, Inc. September 8, 201117
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
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Proppant Transport: Solution Domain
Typical Fracture is Considered
300 ft
40 ft
Fracture Width = 0.5 cm
© 2011 ANSYS, Inc. September 8, 201119
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
© 2011 ANSYS, Inc. September 8, 201120
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
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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
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Typical Results: Contours of Velocity
Frac‐Fluid VelocityVelocity Decreases Due to Leak off
Settled Bed after t‐secs
© 2011 ANSYS, Inc. September 8, 201123
Typical Results: Contours of Velocity
Proppant Velocity
Settled Bed after t‐secs
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.
© 2011 ANSYS, Inc. September 8, 201124
Typical Results: Contours of Pressure
Pressure drop across the fracture can be calculated during the settling process
Settled Bed after t‐secs
© 2011 ANSYS, Inc. September 8, 201125
Typical Results: Contours of Volume Fraction of Proppant
Settled Proppant Bed after t‐secs
Bed Height
Proppant Volume Fraction
Extent of proppant placement
© 2011 ANSYS, Inc. September 8, 201126
300 µm Vs 500 µm Settling
300 µm– Proppant 500 µm ‐ Proppant
Settling of Two Different Proppant Sizes
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© 2011 ANSYS, Inc. September 8, 201127
Snapshots of 300 µm and 500 µm500 µm300 µm
time
© 2011 ANSYS, Inc. September 8, 201128
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
© 2011 ANSYS, Inc. September 8, 201129
Proppant Transport: Wash Out Process
300 µm– Proppant 100 µm ‐ Proppant
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© 2011 ANSYS, Inc. September 8, 201130
Proppant Transport: Wash Out ProcessThis image cannot currently be displayed.
© 2011 ANSYS, Inc. September 8, 201131
Proppant Transport: Wash Out Process
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
© 2011 ANSYS, Inc. September 8, 201132
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
© 2011 ANSYS, Inc. September 8, 201133
Questions or Comments !!!!!
Thank you Very Much