Tracers for Flow and Mass Transport

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Tracers for Flow and Mass Transport

• Philip Bedient
• Rice University
• 2004

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Transport of Contaminants

• Transport theory tries to explain the rate and
  extent of migration of chemicals from known
  source areas
• Source concentrations and histories must be
  estimated and are often not well known
• Velocity fields are usually complex and can
  change in both space and time
• Dispersion causes plumes to spread out in x and y
• Some plumes have buoyancy effects as well

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Transport of Contaminants
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What Drives Mass Transport Advection and
Dispersion

• Advection is movement of a mass of fluid at the
  average seepage velocity, called plug flow
• Hydrodynamic dispersion is caused by velocity
  variations within each pore channel and from one
  channel to another
• Dispersion is an irreversible phenomenon by which
  a miscible liquid (the tracer) that is introduced
  to a flow system spreads gradually to occupy an
  increasing portion of the flow region

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Advection and Dispersionin a Soil Column
Source Spill t 0 Conc 100 mg/L
Longitudinal Dispersion t t1
n Vv/Vt porosity
Advection t t1
C
t
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Contaminant Transport in 1-D
Fx (dFx/dx) dx
Fx
y
z
Fx total mass per area transported in x
direction
Fy total mass per area transported in y
direction
Fz total mass per area transported in z
direction
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Substituting in Fx for the x direction only yields
Accumulation Dispersion Advection
C Concentration of Solute M/L3 D
Dispersion Coefficient L2/T V Velocity in x
Direction L/T
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2-D Computed Plume Map Advection and Dispersion
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Analytical 1-D, Soil Column

• Developed by Ogata and Banks, 1961
• Continuous Source
• C Co at x 0 t gt 0
• C (x, ) 0 for t gt 0

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Error Function - Tabulated Fcn
Erf (0) 0 Erf (3) 1 Erfc (x) 1 - Erf
(x) Erf (x) Erf (x)
x Erf(x) Erfc(x)
0 0 1
.25 .276 .724
.50 .52 .48
1.0 .843 .157
2.0 .995 .005
Erf
x
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Contaminant Transport Equation
C Concentration of Solute M/L3 DIJ
Dispersion Coefficient L2/T B Thickness of
Aquifer L C Concentration in Sink Well
M/L3 W Flow in Source or Sink L3/T n
Porosity of Aquifer unitless VI Velocity in
I Direction L/T xI x or y direction
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Analytical Solutions of Equations

• Closed form solution, C C ( x, y, z, t)
• Easy to calculate, can often be done on a
  spreadsheet
• Limited to simple geometries in 1-D, 2-D, or 3-D
• Limited to simple sources such as continuous or
  instantaneous or simple combinations
• Requires aquifer to be homogeneous and isotropic
• Error functions (Erf) or exponentials (Exp) are
  usually involved

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Numerical Solution of Equations

• Numerically -- C is approximated at each point
  of a computational domain (may be a regular grid
  or irregular)
• Solution is very general
• May require intensive computational effort to get
  the desired resolution
• Subject to numerical difficulties such as
  convergence problems and numerical dispersion
• Generally, flow and transport are solved in
  separate independent steps (except in
  density-dependent or multi-phase flow situations)

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Domenico and Schwartz (1990)

• Solutions for several geometries (listed in
  Bedient et al. 1999, Section 6.8).
• Generally a vertical plane, constant
  concentration source. Source concentration can
  decay.
• Uses 1-D velocity (x) and 3-D dispersion (x,y,z)
• Spreadsheets exist for solutions.
• Dispersion axvx, where ax is the dispersivity
  (L)
• BIOSCREEN (1996) is handy tool that can be
  downloaded.

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BIOSCREEN Features

• Answers how far will a plume migrate?
• Answers How long will the plume persist?
• A decaying vertical planar source
• Biological reactions occur until the electron
  acceptors in GW are consumed
• First order decay, instantaneous reaction, or no
  decay
• Output is a plume centerline or 3-D graphs
• Mass balances are provided

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Domenico and Schwartz (1990)
y
Plume at time t
Vertical Source
x
z
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Domenico and Schwartz (1990)

• For planar source from -Y/2 to Y/2 and 0 to Z

Y
Flow x
Z
Geometry
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Instantaneous Spill in 2-D

• Spill source C0 released at x y 0, v vx
• First order decay l and release area A

2-D Gaussian Plume moving at velocity V
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Breakthrough Curves
2 dimensional Gaussian Plume
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Tracer Tests

• Aids in the estimation of average hydraulic
  conductivity between sampling locations
• Involves the introduction of a non-reactivechemic
  al species of knownconcentration
• Average seepage velocities can be calculated
  from resulting curves of concentration vs. time
  using Darcys Law

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What can be used as a tracer?

• An ideal tracer should
• 1. Be susceptible to quantitative determination
• 2. Be absent from the natural water
• 3. Not react chemically or be absorbed
• 4. Be safe in drinking water
• 5. Be inexpensive and available
• Examples
• Bromide, Chloride, Sulfates
• Radioisotopes
• Water-soluble dyes

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Hour 14
Hour 43
Hour 85
Hour 8
Hour 30
Hour 55
Hour 79
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Bromide Tracer Front - ECRS
Black Arrows _at_ t 40 hrs
Red Arrows _at_ t 85 hrs
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New Experimental Tank

• 5000 mg/L Bromide tracer in advance of ethanol
  test
• Pumped into 6 wells for 7 hour injection period
• Pumping rate of 360 mL/min was maintained
• Background water flow rate was 900-1000 mL/min

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PLAN VIEW OF TANK
Flow
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Line A Shallow
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Line B Intermediate
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Line E Center
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Line I Shallow
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July 2004 New Tank prior to 95E test (5.5 ft to
9.5 ft down tank)