Tracers for Flow and Mass Transport Philip Bedient

Tracers for Flow and Mass Transport Philip Bedient Rice University 2004

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

Transport of Contaminants

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

Advection and Dispersion in a Soil Column Source Spill t = 0 Conc = 100 mg/L Longitudinal Dispersion t = t 1 n = Vv/Vt porosity Advection t = t 1 C t

Contaminant Transport in 1 -D Fx Fx + (d. Fx/dx) dx 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

Substituting in Fx for the x direction only yields Accumulation Dispersion Advection C = Concentration of Solute [M/L 3] D = Dispersion Coefficient [L 2/T] V = Velocity in x Direction [L/T]

2 -D Computed Plume Map Advection and Dispersion

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

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

Contaminant Transport Equation C = Concentration of Solute [M/L 3] DIJ = Dispersion Coefficient [L 2/T] B = Thickness of Aquifer [L] C’ = Concentration in Sink Well [M/L 3] W = Flow in Source or Sink [L 3/T] n = Porosity of Aquifer [unitless] VI = Velocity in ‘I’ Direction [L/T] x. I = x or y direction

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

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)

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.

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

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

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

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

Breakthrough Curves 2 dimensional Gaussian Plume

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

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

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

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

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 m. L/min was maintained Background water flow rate was 900 -1000 m. L/min

PLAN VIEW OF TANK Flow

Line A Shallow

Line B Intermediate

Line E Center

Line I Shallow

July 2004 New Tank prior to 95 E test (5. 5 ft to 9. 5 ft down tank)