multiphase field-scale modeling: brine transport ann cook per per hatlevik jonathan levine brice...
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Multiphase Field-scale Multiphase Field-scale Modeling: Brine TransportModeling: Brine Transport
Ann CookAnn CookPerPer Hatlevik
Jonathan LevineBrice LooseBrice Loose
Keegan Roberts Keegan Roberts Amber Sallerson Amber Sallerson
Katy SchulteKaty SchulteMartina VlckovaMartina Vlckova
Thomas WillinghamThomas Willingham
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Introduction to DNAPLs
• Types• Sources• Behavior
PCE, TCE, DCE, VC, CT, CF, DCM,
TCA
gh
an
anc )(
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Introduction to DNAPLs
• Long lived • Difficult to remove• Health Hazards
– Liver problems– Increased risk of cancer– Nervous system, or circulatory problems1
Density of Water (rw)
Density of DNAPL (rn)
~1 g/mL ~1.45-1.62 g/mL
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Brine Treatment Technology
• How does it work?– Mobilization of the NAPL
• Increase Gravimetric Forces• Decrease Capillary Trapping Forces
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glr an
an )(
Brine Treatment Technology
• sn-a = NAPL-aqueous interfacial tension• r = effective pore size• rn = NAPL density• ra = aqueous phase density• g = gravitational acceleration• l = characteristic length of NAPL
pool in vertical direction
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Brine Treatment Technology
• How does it work?– Closed system on 5 sides
Area of Remediation Sheet-piles
Plan ViewImpermeable Layer (e.g., clay)
Profile View
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Brine Treatment Technology
• How does it work?
No Flow Boundary
No Flow Boundary
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Brine Treatment Technology
• How does it work?
Pump in Pump in Brine LayerBrine Layer
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Brine Treatment Technology
• How does it work?
Lower Lower Water TableWater Table
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Brine Treatment Technology
• Gravimetric Forces
Removal Removal of of DNAPLDNAPL
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Brine Treatment Technology
• How does it work?
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Brine Treatment Technology
• How does it work?
Removal Removal of of DNAPLDNAPL
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Brine Treatment Technology
• How does it work?
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Brine Treatment Technology
• How does it work?
Remove Remove BrineBrine <1% Original
DNAPL Mass
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Brine Treatment Technology
• How does it work?
<1% Original = MeetDNAPL Mass Standards
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Brine Treatment Technology
• Why is it novel?– $$ Cheaper $$– Higher rates of removal than current
technologies
Pump and Treat Natural Attenuation
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Possible Instabilities in the System
• Physical– Density (changes and/or differences)– Excessive Surfactant Concentration bypass– Pore Clogging
• Model– Fingering – Gravity - Rayleigh
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Rayleigh-Taylor Instability
• Initial density stratified domain
• Unstable system (small perturbations)
• Occur in model and physical system
Brine
Ground
Water
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Rayleigh Number
• Dimensionless Number
• Ratio
dispersiondiffusion
ngravitatiobuoyancy
Ra
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Modified Rayleigh Number
T
c
D
HURa
Lamb
Lamb
VD
VPe
0
*
1250*1
*
Pe
RaRa
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SUTRA
• Code written by USGS• Simulates single phase fluid flow and
transport in the subsurface• Uses a combination of finite-element
and finite difference methods to solve a series of equations
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Conservation Equations
• Species Balance Equation
• Species-Summed Flow Equation
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SUTRA Transport
Math Magic
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SUTRA Fluid FlowSpecies Summed
Flow Equation
Darcy’s Law
Math Magic
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Requirements for SUTRA
DL < 4aL
Pe < 2
• DL = local distance between sides of an element measured in the direction parallel to local flow
• aL = longitudinal dispersivity
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SUTRA Goal
• To model a freshwater system where we inject brine– 3D model– Relatively small in the y-direction
• Visualize system instabilities
• Removal of brine from system
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Simulations Ran
1. Brine slumping model
2. Fully saturated fresh water system with brine injection
3. Unsaturated brine injection
4. Multiple well configurations
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Example Problem: Slumping brine interface
which admits an analytic solution in the case that the vertical scale is much less that the horizontal (H << R), and a constant hydraulic conductivity (Kc)
High frequency spatial hydraulic conductivity
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Homogenization permits approximation of K(x,z,t) as a constantthat captures the variability
Homogenized equations compare well with the accepted numerical solution. High frequency variations are absent.
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Evaluate Instabilities
Extraction Well
Injection Wells
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Fingering
waterbrine qq
Fingering due to viscous instability
waterbrine
dl
dhkq
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SUTRA MODELINGBCs
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SUTRA MODELINGInitial Injection
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SUTRA MODELINGBrine Injection
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Transport and Flow EquationsAKA “The Magic”