Review of fracturing modeling technology

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Review of fracturing modeling technology
2009 SPE Hydraulic Fracturing Technology
Conference

• A .(Tony) Settari
• University of Calgary
• TAURUS Reservoir Solutions Ltd.
• ASettari_at_taurusrs.com
• January 19, 2009

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Overview

• Evolution of the fracture modeling
• Some current developments
• Outlook in the future

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Historical evolution of fracturing modeling
main milestones

• Analytical models of the 1960s and 70s
• Decoupled 2-D numerical models of geometryprop
  transport 1970s
• Pseudo-3D and planar 3-D decoupled models
  1980s
• Interest in acid frac modeling in 1980s and 90s
• Modeling of high leak-off processes
  (waterflooding) in 1990s
• Coupled modeling including geomechanical aspects
  and production modeling 2000 - present

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Analytical models of the 1960s and 1970s

• Main features
• Analytical 2-D geometry equations, linear
  elasticity
• Analytical, 1-D, single phase leak-off, constant
  reservoir properties
• Confining stress constant (in time and space)
• 1-D single phase reservoir flow only

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Carters propagation model (1957)

• Analytical solution for frac length Lf f(t)
• Constant reservoir and fracture height
• Fracture of constant width W, volume V2 WHfLf
• Constant injection rate i
• Leak-off velocity law u C/?( t t0)

For small x Lf C1 ? t For large x Lf C2 ?
?t
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2-D numerical models of 1970s

• Fracturing design models centered around fracture
  geometry, based on hard rock (LEFM) fracture
  mechanics
• Use linear elasticity for frac geometry
  calculation
• Analytical, 1-D, single phase leak-off, constant
  res. properties
• Confining stress constant (in time) or simple
  analytical estimates of stress changes (back
  stress)
• each fracture is an independent event
• Still decoupled from reservoir behavior
• Only 2-D frac geometry prediction
• Productivity evaluation - independent step (no
  feedback)

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KGD
PKN
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3-D frac design models of 1980s

• Leap in realism of fracture geometry
• Pseudo 3-D models
• Equilibrium height models Nolte and Smith
  (Amoco), Palmer,
• Dynamic height model Settari and Cleary (HFS,
  1984, 1986)
• Planar 3-D geometry models
• Terra Tek
• MIT (Cleary), U of Texas Austin, ..
• Lumped 3-D (Keck and Cleary)
• FracPro, Mayers (MFRAC)
• More realistic geometry and proppant transport,
  but most not coupled with reservoir flow (at
  least initially)
• No geomechanical effects
• poro- and thermoelastic stresses analytical
  except some 3-D models
• No stress effects on reservoir perm and
  compressibility

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Examples of 3-D design model types
Dynamic grid, decoupled from reservoir
Fixed grid (GOFHER)
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Research models

• Non-planar 2-D and 3-D models
• Models to look at basic physics or special
  geometries
• Lack practical features to be useful for everyday
  design

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Proppant and acid transport modeling

• They are analogous but acid transport is more
  complex and has more interactions with other
  parts of the model
• Development parallels the evolution of the frac
  geometry models from 1-D to 3-D
• Work needs to continue not all current
  knowledge about the physics is included in the
  current proppant models
• The low apparent frac conductivities observed (in
  particular in tight gas) are due to a combination
  of effects

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Types of acid transport models
1-D Cf(x)
2-D Cf(x,z)
Lumped in y
Lumped in y
x
x
y
uniform in z
y
z
z
3-D Cf(x,y,z)
2-D Cf(x,y)
x
y
uniform in z
y
z
z
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High leak-off fracture models in the 1990s

• Applications waterflood fracturing, PWRI
• Strong poroelastic/thermal effects, large
  leak-off
• Models without coupling with reservoir and/or
  geomechanics can be fixed to some extent but
  ultimately are not suitable
• Some special models coupled with reservoir
  developed (Clifford, Shell )
• Additional physics Formation plugging

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Current effort Towards fully coupled modeling

• Convergence of applications and needs
• Waterflood and PWRI fracturing (complex leak-off
  tied to reservoir)
• Explaining large volumes injected into disposal
  wells
• Increasing evidence of stress effects on
  permeability and porosity in waterfracs etc.
• Fracturing in unconsolidated and naturally
  fractured media (oil sands, shale, CBM)
• Requires geomechanical approach reservoirs are
  geomaterials

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Fracturing in geomaterials
a) primary SPF, no formation failure
(classical fracture mechanics)
b) SPF and secondary fracturing (hard rock,
fractured media)
c) Conceptual model of fracturing In coal
(SPFstimulated volume)
d) Fracturing In unconsolidated media
(SPFdilated/sheared volume)
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Fully coupled fracture modeling

• Fully coupled formulation shopping list
• Fully coupled fracture geometry and reservoir
  (leak-off)
• Reservoir properties dependent on effective
  stress and failure
• Fully coupled stress/fracture modeling
• Fracture geometry represented in the stress model
• Tip/other fracture mechanics effects included
• Flow transmissibility coupled to fracture width
• Other geomechanical effects
• Permeability plugging in PWRI
• Drilling cuttings transport
• Some recent models
• Ji and Settari (2007) (part of GEOSIM)
• Dean and Schmidt (2008)
• Zhai and Sharma (2007), etc.

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Pseudo 3-D or 3-D uncoupled fracture models
Injection only (no production modeling)
Linear elasticity for fracture geometry, no
stress solution around the frac
1-D single phase reservoir model
Propagation controlled by frac mech fracture
flow
Water blockage and cleanup approximated by
leakoff coeff
Proppant transport
Dynamic frac width Wf and volume
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Fully coupled model fracture mechanics,
reservoir simulation, heat transport and
full-field geomechanics
Injection/production
Stress-strain model
Propagation controlled by frac mech stressflow
Multiphase reservoir model
Wf causes stress displ.
Dynamic fracture during pumping
Water blockage and cleanup
Conductive fracture during production/PBU
Dynamic frac width Wf and volume
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What about production modeling of fractured wells?

• With coupled modeling, separate models no longer
  needed integrated within the same tool
• We can handle any complexity used in reservoir
  simulation frac design and reservoir
  engineering will be on the same footing!
• Recent advances in geomechanics of fractured
  media can be employed to model creation or
  re-opening and closure of fracture systems during
  the job and production

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Model for fractured/jointed media geomech
model dual porosity/perm flow model
Tensor K
Fracture properties
Fracture grid
Transfer function
Matrix properties
Desorption mass transfer
Matrix grid

• Solid model equivalent continuum (joint sets)
• DYNAMIC Elastic properties

Dynamic tensor permeability for fracture system,
nonlinear porosity (storage capacity)
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Is it always necessary to use the most complex
model?

• Example Partially coupled model
• Simplified fracture mechanics
• Surprisingly successful and computationally
  efficient
• Examples
• PWRI/CRI disposal well (15 year prediction)
• Tight gas waterfracs (comprehensive history match)

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Example 1 PWRI/CRI fracture propagation in a
layered formation

• Injection schedule included water handling, waste
  water and CRI from development drilling over long
  period of time (15 years)
• Complex fracture propagation results

volume
time
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The snapshot shows predicted dynamic fracture
shape at one time in response to Produced Water
and Cuttings Reinjection schedule (fracture is
the magenta colour area)
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Example 2 Tight gas well in Wyoming (SPE 119394)
Cleanup
Fracing sequences
Reserves Spacing Frac optimization
Production, PLTs, ..
Buildup
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Shear fracturing N2 stimulation of CBM

• Highly driven by geomechanics
• Illustrates that the hydraulic fracture can be
  small compared to the stimulated volume

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N2 fracturing in a thin coal seam
Horiz frac, const perm
Vert frac, const perm
Vert frac, permf(stress)
No frac, permf(stress), kx4 ky
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Challenges for the future

• To keep the commercial software up to date with
  the research
• To make the developing coupled modeling
  technology available to practicing engineers for
  integrated analysis of fractured well
• Potential benefits
• Combine fracturing design/evaluation with
  reservoir engineering and reserve forecasting
• Integrate frac modeling with interpretation of
  fracture mapping
• Use much more of the available data to constrain
  the models and therefore make them more reliable
• Advances needed
• Order of magnitude speed increase (3-D modeling
  )
• Resolve some old numerical issues
• Make models applicable to wider range of
  situations

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Thank youDiscussion