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**Subsurface Fate and Transport of Contaminants**

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**Contaminant Transport**

Describes mechanisms to move contaminants from source to receptor Important to calculate dose in risk analysis process

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**Solutes in saturated media can be transported by three mechanisms**

Diffusion Advection Dispersion

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Diffusion Diffusion - spreading of solute due to concentration gradient, minor at most GW velocity Diffusion controlled mass transport occurs if the concentration of a species is greater in one location than an adjacent location (concentration gradient) Fick’s second law used to calculate flux

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Advection Advection - transport with bulk flow of groundwater at average velocity of GW. Mass added to stream tubes remains in stream tubes, other processes move mass between stream tubes (diffusion, dispersion, Dominant transport mechanism

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Dispersion Mechanical Dispersion - mechanical mixing due to the velocity variations as groundwater moves through tortuous pathways Solute transport by advection and dispersion requires flow of groundwater to carry solutes along with liquid flow At most fluid flows advection and dispersion dominates over diffusion

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**Transformation Processes**

Sorption Radioactive decade Chemical transformation Volatilization Colloid transport Biotic

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**Contaminant Transport**

Advection Conc. Sorption, Dispersion Sorption, Dispersion And Degradation Time

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**Mathematics Change in mass storage with time =**

Mass inflow rate - mass outflow rate + mass production rate

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Mass Balance qx dz dy dx

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**Mass Balance - (1-Dimensional)**

Change in mass storage with time = Mass in/out due to advection, dispersion, diffusion and sources and sinks

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**Mass Balance (1-Dimensional)**

Divide by xyz and let x > 0 F = mass flux rate of contaminant due to advection, dispersion, and diffusion, mass area-1 time-1 r = source or sink term

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**Advective Groundwater Flow**

Q = vA

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Groundwater Flow

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**Source or sink terms R (mass/vol-time): Biotic Radioactive Decay**

Sorption

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**Solution Requires Definition of parameters**

Suitable numerical or analytical solution Boundary and initial conditions Analytical solution possible if 1-D, source or sink terms linear, boundary and initial conditions known

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**Solution to Mass Balance Including Advection and Dispersion Only**

C = the concentration at time t and distance x Co = original concentration L = distance t = time erfc = complimentary error function DL = dispersion coefficient vx = linear velocity

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**Solution to Mass Balance Including Diffusion Only**

C = the concentration at time t and distance x Co = original concentration x = distance t = time erfc = complimentary error function D* = effective diffusion coefficient

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**Example – Diffusion Process**

Assume Landfill A contains Na+1 = 10,000 mg/l and Ca+2 = 5,000 mg/l and assume Landfill B contains Fe+2 = 750 mg/l and Cr+3 = 600 mg/l. Landfill A has a 6 m clay liner under the waste and Landfill B has 3 m of clay under the waste. Assuming diffusion is the only process affecting solute transport, which of the four species will break through the clay layer in either of the landfills first? How long will that take?

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**Given Given: Effective diffusion coefficients D*: Species D* (m2/sec)**

Na+1 1.33E-09 Ca+2 7.05E-10 Fe2+ 7.19E-10 Cr3+ 5.94E-10

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Solution The erfc(z)* function has non-zero values only at z values less than 3. To solve this problem assume times and calculate at edge of clay layer for each case and keep changing the time until z has a value of 3. WHY? *Z=x/2((D*t)^0.5)

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**Assume Time is 5 years Z > 3 Species Clay layer (m) Conc (mg/l)**

D* (m2/sec) Z=x/2((D*t)^0.5) Na+1 6 10000 1.33E-09 Ca+2 5000 7.05E-10 Fe2+ 3 750 7.19E-10 Cr3+ 600 5.94E-10 Z > 3

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**Increase Time to 10 Years Z > 3 Species Clay layer (m)**

Concentration (mg/l) D* (m2/sec) Z=x/2((D*t)^0.5) Na+1 6 10000 1.33E-09 Ca+2 5000 7.05E-10 Fe2+ 3 750 7.19E-10 Cr3+ 600 5.94E-10 Z > 3

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**Increase Time to 12 Years Fe+2 will break through first Species**

Clay layer (m) Concentration (mg/l) D* (m2/sec) Z=x/2((D*t)^0.5) Na+1 6 10000 1.33E-09 Ca+2 5000 7.05E-10 Fe2+ 3 750 7.19E-10 Cr3+ 600 5.94E-10 Fe+2 will break through first

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**Decrease Time to 11 Years Fe+2 will break through ~ 11 years**

Species Clay layer (m) Concentration (mg/l) D* (m2/sec) Z=x/2((D*t)^0.5) Na+1 6 10000 1.33E-09 Ca+2 5000 7.05E-10 Fe2+ 3 750 7.19E-10 Cr3+ 600 5.94E-10 Fe+2 will break through ~ 11 years

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Last updated April 12, 2017 by Dr. Reinhart

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