8.2 Subsurface Contaminant Transport & Hydrogeology

Understanding how fluids and contaminants move through the subsurface requires a solid grasp of fundamental soil properties, chemical partitioning mechanisms, and transport processes.

Fundamental Soil Properties

The physical matrix of the subsurface governs fluid storage and flow. Key parameters include:

• Porosity ($n$): The ratio of the volume of voids ($V_v$) to the total volume ($V_t$). It represents the maximum amount of fluid the soil can hold. $n = \frac{V_v}{V_t}$.
• Effective Porosity ($n_e$): The fraction of the total volume consisting of interconnected voids that contribute to fluid flow. In fine-grained soils like clays, $n_e$ can be significantly lower than $n$ due to dead-end pores and water bound tightly to soil particles.
• Void Ratio ($e$): The ratio of the volume of voids to the volume of solids ($V_s$). $e = \frac{V_v}{V_s}$. It is related to porosity by $n = \frac{e}{1+e}$.
• Bulk Density ($\rho_b$): The mass of dry soil divided by its total volume. It is typically expressed in g/cm³ or kg/L. $\rho_b = \rho_s(1 - n)$, where $\rho_s$ is the particle density (often assumed to be 2.65 g/cm³ for quartz soils).
• Fraction of Organic Carbon ($f_{oc}$): The mass fraction of organic carbon present in the soil. This is a critical parameter for predicting the sorption of organic contaminants.

Contaminant Partitioning

Chemicals entering the subsurface distribute themselves among the soil, water, and air phases based on their thermodynamic properties.

• Octanol-Water Partition Coefficient ($K_{ow}$): A laboratory-measured ratio describing a chemical's preference to partition into an organic phase (octanol) versus water. High $K_{ow}$ values indicate strong hydrophobicity (dislike of water).
• Organic Carbon Partition Coefficient ($K_{oc}$): Measures a chemical's tendency to sorb onto the organic carbon fraction of soil. It is frequently estimated from $K_{ow}$ using empirical correlations.
• Distribution Coefficient ($K_d$): The ratio of the contaminant concentration sorbed to the soil ($C_s$, in mg/kg) to the concentration dissolved in water ($C_w$, in mg/L). For organic chemicals, it is calculated as: $K_d = f_{oc} \times K_{oc}$.
• Henry's Law Constant ($H_c$): Governs the partitioning of a chemical between the aqueous phase and the vapor phase. A high $H_c$ means the chemical readily volatilizes from groundwater into soil gas.

Contaminant Transport Mechanisms

As contaminants migrate through an aquifer, their movement is governed by physical and chemical processes.

Advection

Advection is the transport of dissolved contaminants along with the bulk flow of groundwater. The average linear groundwater velocity (or seepage velocity), $v_x$, is calculated using a modified form of Darcy's Law:

$v_x = \frac{K}{n_e} \frac{dh}{dx}$

Where:

• $K$ = Hydraulic conductivity (length/time)
• $n_e$ = Effective porosity (dimensionless)
• $\frac{dh}{dx}$ = Hydraulic gradient (change in head over distance, dimensionless)

Mechanical Dispersion and Molecular Diffusion

• Mechanical Dispersion: As fluid moves through the tortuous pathways of the soil matrix, some fluid parcels travel faster than others, causing the contaminant plume to spread out longitudinally and transversely.
• Molecular Diffusion: The movement of molecules from areas of high concentration to low concentration due to random thermal motion, governed by Fick's Law. It is generally a slow process but becomes significant in low-permeability zones (like clays) where advective flow is negligible.

Retardation

When a contaminant sorbs to the soil matrix, its apparent velocity is slower than the groundwater velocity. This effect is quantified by the Retardation Factor ($R$):

$R = 1 + \frac{\rho_b K_d}{n_e}$

The retarded contaminant velocity ($v_c$) is simply the groundwater velocity divided by the retardation factor: $v_c = \frac{v_x}{R}$. An $R$ value of 1 indicates no sorption (the contaminant moves at the speed of groundwater). An $R$ value of 3 means the contaminant moves at one-third the speed of groundwater.

Biodegradation and Decay

Many organic contaminants, as well as radioactive isotopes, undergo decay over time. This is commonly modeled as a first-order kinetic process:

$C(t) = C_0 e^{-\lambda t}$

Where:

• $C(t)$ = Concentration at time $t$
• $C_0$ = Initial concentration
• $\lambda$ = First-order decay rate constant (time⁻¹)

The decay rate constant is related to the half-life ($t_{1/2}$) by the equation:

$t_{1/2} = \frac{\ln(2)}{\lambda} \approx \frac{0.693}{\lambda}$

Non-Aqueous Phase Liquids (NAPLs)

NAPLs are organic liquids that do not readily dissolve in water and exist as a separate phase in the subsurface.

• LNAPLs (Light Non-Aqueous Phase Liquids): Have a density less than water (e.g., gasoline, diesel fuel). When spilled, they percolate through the unsaturated zone and "float" on the water table. The water table fluctuation can smear the LNAPL vertically across the capillary fringe, creating a persistent source zone.
• DNAPLs (Dense Non-Aqueous Phase Liquids): Have a density greater than water (e.g., chlorinated solvents like PCE, TCE, TCA). DNAPLs sink through the water table, migrating downward until they encounter an impermeable confining layer (like a clay lens or bedrock). They can form pools on these layers or migrate along fractures in bedrock, making characterization and remediation exceptionally challenging.

Worked Calculation: Contaminant Transport

Problem: Groundwater flows through an aquifer with a hydraulic conductivity of 10 ft/day, a hydraulic gradient of 0.005 ft/ft, and an effective porosity of 0.25. A chemical spill introduces a contaminant with a distribution coefficient ($K_d$) of 2.0 L/kg. The soil bulk density ($\rho_b$) is 1.5 kg/L. Calculate the time it takes for the center of the contaminant mass to travel 100 feet.

Step 1: Calculate average linear groundwater velocity ($v_x$) $v_x = \frac{K}{n_e} \frac{dh}{dx} = \frac{10 \text{ ft/day}}{0.25} \times 0.005 = 0.2 \text{ ft/day}$

Step 2: Calculate the Retardation Factor ($R$) $R = 1 + \frac{\rho_b K_d}{n_e} = 1 + \frac{(1.5 \text{ kg/L})(2.0 \text{ L/kg})}{0.25} = 1 + \frac{3.0}{0.25} = 1 + 12 = 13$

Step 3: Calculate the retarded contaminant velocity ($v_c$) $v_c = \frac{v_x}{R} = \frac{0.2 \text{ ft/day}}{13} \approx 0.0154 \text{ ft/day}$

Step 4: Calculate the travel time $Time = \frac{\text{Distance}}{v_c} = \frac{100 \text{ ft}}{0.0154 \text{ ft/day}} \approx 6,493 \text{ days}$ (or about 17.8 years).