Advancing the Next Generation of RockFluid Imaging and Stimulation Technologies

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Studies to Advance the Next Generation of
Rock-Fluid Imaging and Stimulation Technologies
Department of Hydraulic and Ocean Engineering
National Cheng Kung University
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Research Team Wei-Cheng Lo NCKU
Garrison Sposito UCB LBNL Ernest
Majer LBNL Peter Roberts - LANL
Collaborators Steven Pride LBNL
Kurt Nihei LBNL James Berryman -
LBNL Funding DOE - NGOTP, LDRD
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Outline of the Presentation

• Motivation
• Porous Medium with One Fluid
• Governing Equations Biot Equation
• Porous Medium with Two Fluids
• Governing Equations
• Numerical Simulation Free Vibration Problem

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Motivation

• Acoustic wave phenomena in fluid-containing
  porous media have received considerable attention
  in recent years, not only because of their
  practical importance in reservoir engineering,
  but also because of an increasing scientific
  awareness of poroelastic behavior in groundwater
  aquifers.

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Field Observations
Fluctuations of water level in a 52-m deep well
induced by seismic waves excited by passing
trains and an earthquake.
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Stimulation Observed from Earthquakes and
Artifical Sources (Lost Hills)
Group of 26 Wells to the Northeast that responded
both to the earthquake events of Sept-Oct 1999
and to ISS
Group of 5 Wells to the Southeast that did not
respond either to the earthquake events or to ISS
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Motivation

• Acoustic wave phenomena in fluid-containing
  porous media have received considerable attention
  in recent years, not only because of their
  practical importance in reservoir engineering,
  but also because of an increasing scientific
  awareness of poroelastic behavior in groundwater
  aquifers.

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Roberts et al., Environ. Engin. Sci.
18(2)67-79 (2001)
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Trichloroethene Removalby Stress Pulsing
20-40 mesh packed sand
Stimulation time 360s Pore
pressure gradient 3 kPa/m Free-phase TCE
observed Permeability 1.1x10-10 m2
(111 d) Roberts et al., Environ. Engin. Sci.
18(2)67-79 (2001)
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Applications

• Stress wave energy has demonstrated potential
  for enhancing hydrocarbon recovery from
  subsurface environments
• Using seismic wave tomography, oil - bearing
  formations and NAPL (nonaqueous phase liquid) -
  contaminated sites can be located.
• In biomechanics, ultrasonic waves are used to
  evaluate properties of soft tissues and
  cancellous bones

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Problems to be Addressed

• Enhancement of NAPL removal from groundwater and
  oil production from reservoirs
• Science-based methods needed to increase the
  efficiency of oil recovery and contaminant
  extraction
• Seismic stimulation has promise but not full
  validation
• Identify physical mechanisms
• Optimize stimulation techniques

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Statement of Problem

• Porous medium containing two immiscible fluids
  (oil and water or air and water)
• Solid porous, isotropic, homogeneous, and
  elastic
• Fluids compressible and viscous

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Methodology
Multiphase fluid flow in porous media continuum
mechanics of mixtures
Coupled
Elastic wave propagation linear stress-strain
relations
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Mass Balance Equations
Storage
Outflow
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Momentum Balance Equations
Gravity
Interphase Exchange
Inertia
Stress
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Constraints on Constitutive Relationships

• Local action
• Objectivity
• Symmetry
• Entropy inequality
• Linearity

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Simplifying Assumptions

• Fluid phases are macroscopically inviscid
• Temperature is constant
• The drag tensors A and R are diagonal with the
  same principal axes
• Cross-coupling caused by viscous drag is
  neglected

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Constitutive Relationships
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Mass Balance Equations with Constitutive
Relationships and Simplifying Assumptions
no change!
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Momentum Balance Equations with Constitutive
Relationships and Simplifying Assumptions
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Linear Stress-Strain Relations in Unsaturated
Porous Media

• Mass balance equations applied to each phase
• Constitutive relation between capillary pressure
  and fluid saturation
• Closure relation for porosity change (a linear
  combination of the dilatations of the solid and
  two fluid phases)

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Linear Stress-Strain Relations in Unsaturated
Porous Media
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Elastic Coefficients
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Porous Medium with Two Fluids
Governing Equations Lo et al., 2005
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Porous Medium with One Fluid (Dilatational
Motions)
Governing Equations (Biot, 1956)
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Viscous and Inertial Coupling Parameters
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Dispersion Relations
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Dispersion Relations for the Free Vibration
Problem
Input elasticity and hydraulic data
Viscous and inertial coupling parameters Water
retention curve Hydraulic conductivity function
Select vibrational frequency
Three roots for wave number
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Dilatational Wave Propagationin Unconsolidated
Fine Sandy Loam Containing either Water and Oil
or Water and Air

• Three body waves exist in partially-saturated
  porous media.
• P1, P2, and P3 designate these waves in order of
  decreasing speed.
• The P3 wave is related to capillary pressure
  between the two interstitial fluids.

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Dilatational Wave Propagationin Unconsolidated
Fine Sandy Loam Phase Velocity (P1 Wave)
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Dilatational Wave Propagationin Unconsolidated
Fine Sandy Loam Attenuation Coefficient (P1
Wave)
air-water system
oil-water system
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Physical Mechanism

• First term is proportional to the square of the
  difference in material densities of the two pore
  fluids, multiplied by the product of their
  relative mobilities.
• A second term in the model expression is
  inversely proportional to the square of an
  average kinematic shear viscosity weighted by
  relative permeability.
• The first term should be large for an air-water
  mixture, but small for an oil-water mixture,
  whereas the reverse should be true for the second
  term.

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Physical Mechanism
air-water system
oil-water system
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Dilatational Wave Propagationin Unconsolidated
Fine Sandy Loam Phase Velocity (P2 Wave)
air-water system
oil-water system
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Dilatational Wave Propagationin Unconsolidated
Fine Sandy Loam Attenuation Coefficient (P2
Wave)
air-water system
oil-water system
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Physical Mechanism

• Effective dynamic shear viscosity parameter for a
  two-fluid system defined in terms of relative
  mobilities

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Physical Mechanism
air-water system
oil-water system
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Dilatational Wave Propagationin Unconsolidated
Fine Sandy Loam Attenuation Coefficient (P2
Wave)
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Dilatational Wave Propagationin Unconsolidated
Fine Sandy Loam Phase Velocity (P3 Wave)
air-water system
oil-water system
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Dilatational Wave Propagationin Unconsolidated
Fine Sandy Loam Attenuation Coefficient (P3
Wave)
air-water system
oil-water system
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Dilatational Wave Propagationin Unconsolidated
Fine Sandy Loam Attenuation Coefficient (P3
Wave)
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Insights from Numerical Results

• The P1 wave is a sound wave, whereas the P2 and
  P3 waves are related to dissipative behavior.
• Waves of higher frequency have higher
  attenuation.
• The P3 wave has the highest attenuation
  coefficient and the lowest phase velocity.
• The P1 and P2 waves in a two-fluid system are
  analogous to the fast and slow compressional
  waves in Biot theory.

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Insights from Numerical Results

• Phase speed of the propagating (P1) wave is equal
  to a characteristic wave speed for in-phase
  solid-fluid motions, defined as the square root
  of the ratio of the effective bulk modulus to the
  effective density of the fluid-filled porous
  medium.

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Insights from Numerical Results

• Attenuation of the P1 wave was strongly affected
  by the nature of the pore fluids.
• In the air-water mixture attenuation is
  associated with differences in material density
  and relative mobility between the pore fluids,
  whereas in the oil-water mixture an effective
  kinematic shear viscosity parameter governs
  attenuation.

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Insights from Numerical Results

• Attenuation of the P2 and P3 waves is related to
  an effective dynamic shear viscosity parameter,
  equal to the inverse sum of relative mobilities
  for the two fluids, and so will be dominated by
  the fluid which has the larger value of relative
  mobility.

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Insights from Numerical Results

• The P2 and P3 waves were also found to have the
  same constant quality factor.
• Comparison of our numerical results with previous
  research in sandstones showed that the P2 and P3
  waves are controlled by the properties of the
  nonwetting pore fluid and the state of
  consolidation of the porous medium.

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Porous Medium with One Fluid (Dilatational
Motions)
Governing Equations (Biot, 1956)
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Decoupling (frequency domain)
Eigenvalue
Eigenvector
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Decoupling (time domain)
Lo et al., 2006
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Future Works

• Boundary value problem
• Experimental verification
• - Laboratory
• - Field