multiphase field-scale modeling: brine transport ann cook per per hatlevik jonathan levine brice...

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”