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
Introduction to DNAPLs
• Types• Sources• Behavior
PCE, TCE, DCE, VC, CT, CF, DCM,
TCA
gh
an
anc )(
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
Brine Treatment Technology
• How does it work?– Mobilization of the NAPL
• Increase Gravimetric Forces• Decrease Capillary Trapping Forces
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
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
Brine Treatment Technology
• How does it work?
No Flow Boundary
No Flow Boundary
Brine Treatment Technology
• How does it work?
Pump in Pump in Brine LayerBrine Layer
Brine Treatment Technology
• How does it work?
Lower Lower Water TableWater Table
Brine Treatment Technology
• Gravimetric Forces
Removal Removal of of DNAPLDNAPL
Brine Treatment Technology
• How does it work?
Brine Treatment Technology
• How does it work?
Removal Removal of of DNAPLDNAPL
Brine Treatment Technology
• How does it work?
Brine Treatment Technology
• How does it work?
Remove Remove BrineBrine <1% Original
DNAPL Mass
Brine Treatment Technology
• How does it work?
<1% Original = MeetDNAPL Mass Standards
Brine Treatment Technology
• Why is it novel?– $$ Cheaper $$– Higher rates of removal than current
technologies
Pump and Treat Natural Attenuation
Possible Instabilities in the System
• Physical– Density (changes and/or differences)– Excessive Surfactant Concentration bypass– Pore Clogging
• Model– Fingering – Gravity - Rayleigh
Rayleigh-Taylor Instability
• Initial density stratified domain
• Unstable system (small perturbations)
• Occur in model and physical system
Brine
Ground
Water
Rayleigh Number
• Dimensionless Number
• Ratio
dispersiondiffusion
ngravitatiobuoyancy
Ra
Modified Rayleigh Number
T
c
D
HURa
Lamb
Lamb
VD
VPe
0
*
1250*1
*
Pe
RaRa
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
Conservation Equations
• Species Balance Equation
• Species-Summed Flow Equation
SUTRA Transport
Math Magic
SUTRA Fluid FlowSpecies Summed
Flow Equation
Darcy’s Law
Math Magic
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
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
Simulations Ran
1. Brine slumping model
2. Fully saturated fresh water system with brine injection
3. Unsaturated brine injection
4. Multiple well configurations
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
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.
Evaluate Instabilities
Extraction Well
Injection Wells
Fingering
waterbrine qq
Fingering due to viscous instability
waterbrine
dl
dhkq
SUTRA MODELINGBCs
SUTRA MODELINGInitial Injection
SUTRA MODELINGBrine Injection
Transport and Flow EquationsAKA “The Magic”