Tracers for Flow and Mass Transport

1. Tracers for Flow and Mass Transport Philip Bedient Rice University 2004

2. 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

3. Transport of Contaminants

4. 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

5. 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

6. 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

7. 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]

8. 2-D Computed Plume Map Advection and Dispersion

9. Analytical 1-D, Soil Column • Developed by Ogata and Banks, 1961 • Continuous Source • C = Co at x = 0 t > 0 • C (x, ) = 0 for t > 0

10. Error Function - Tabulated Fcn Erf (0) = 0 Erf (3) = 1 Erfc (x) = 1 - Erf (x) Erf (–x) = – Erf (x) Erf x

11. 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

12. 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

13. 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)

14. 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.

15. 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

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

17. Domenico and Schwartz (1990) For planar source from -Y/2 to Y/2 and 0 to Z Y Flow x Z Geometry

18. Instantaneous Spill in 2-D Spill source C0released at x = y = 0, v = vx First order decay l and release area A 2-D Gaussian Plume moving at velocity V

19. Breakthrough Curves 2 dimensional Gaussian Plume

20. Tracer Tests • Aids in the estimation of average hydraulic conductivity between sampling locations • Involves the introduction of a non-reactivechemical species of knownconcentration • Average seepage velocities can be calculated from resulting curves of concentration vs. time using Darcy’s Law

21. 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

22. Hour 14 Hour 43 Hour 85 Hour 8 Hour 30 Hour 55 Hour 79

23. Outlet 13 11 9 10 14 12 1 4 5 2 3 6 7 8 24 21 23 22 25 26 28 27 17 15 19 20 16 18 Inlet Bromide Tracer Front - ECRS Black Arrows @ t= 40 hrs Red Arrows @ t= 85 hrs

24. 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

25. PLAN VIEW OF TANK Flow

26. Line A Shallow

27. Line B Intermediate

28. Line E Center

29. Line I Shallow

30. July 2004 New Tank prior to 95E test (5.5 ft to 9.5 ft down tank)