POLLUTEv10 Example 7: Lateral Migration of a Radioactive Contaminant in Fractured Rock

This example demonstrates how POLLUTEv10 can be used to simulate the lateral migration of a radioactive contaminant in a fractured porous rock system. It focuses on transport along a single set of parallel fractures, incorporating advection, dispersion, matrix diffusion, and radioactive decay.

The scenario is particularly relevant for nuclear waste disposal assessments, deep geological repositories, and long-term contaminant fate modeling.

---

Conceptual Model Overview

The model assumes:

• A fractured rock domain extending effectively infinitely from the source
• Transport occurring primarily along fractures (fast pathways)
• Diffusion into the surrounding rock matrix (slow storage zone)
• A radioactive contaminant that undergoes decay over time

The analysis focuses on:

• First 50 m of transport distance
• Time period of 30 years

---

Key Modeling Assumptions

• Initial source concentration: co = 1 (normalized unit)
• The source is constant (no depletion) due to large supply
• Radioactive decay occurs continuously
• No sorption in fractures or matrix (Kf = Km = 0)
• Transport is governed by:
  • Advection
  • Dispersion
  • Matrix diffusion
  • First-order radioactive decay

---

Governing Radioactive Decay

The decay of the contaminant follows first-order kinetics:

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

Where:

• $C(t)$= concentration at time $t$t
• $C_0$ = initial concentration
• $\lambda$ = decay constant
• $t$ = time (years)

The decay constant is related to half-life:

$$\lambda = \frac{\ln(2)}{t_{1/2}} = \frac{0.693}{100} \approx 0.00693 \, \text{a}^{-1}$$

This means that over 30 years, only modest decay occurs, making transport processes dominant in plume evolution.

---

Input Parameters

Hydraulic and Transport Properties

Property	Symbol	Value	Units
Darcy Velocity	va	0.08	m/a
Dispersion in fractures	Df	6	m²/a
Matrix diffusion coefficient	Dm	0.0018	m²/a

---

Fracture Geometry

Property	Value
Fracture spacing (2H1)	0.05 m
Fracture aperture (2h1)	10 μm

These closely spaced fractures create highly efficient lateral pathways for contaminant migration.

---

Matrix Properties

Property	Value
Matrix porosity (nm)	0.05
Distribution coefficient (Km)	0 cm³/g
Dry density	2 g/cm³

With no sorption, the matrix acts purely as a diffusive sink, not a reactive barrier.

---

Domain and Simulation Setup

Property	Value
Fractured rock thickness (HT)	50 m
Number of sub-layers	5
Source concentration (co)	1
Half-life	100 years
Simulation time	30 years
Distance of interest	50 m

---

Special Feature: Maximum Sublayer Thickness

This example highlights a POLLUTEv10 special feature:

• Ability to define sublayers thicker than the default 5 units
• Allows efficient modeling of large domains (50 m) with fewer layers
• Maintains numerical stability while improving computational efficiency

This is especially useful in regional-scale fractured rock simulations.

---

Transport Processes Explained

1. Advective–Dispersive Flow in Fractures

• Advection drives the contaminant forward along fractures
• Dispersion spreads the plume longitudinally
• Results in rapid lateral migration over tens of meters

---

2. Matrix Diffusion

• Contaminants diffuse from fractures into the rock matrix
• Acts as a temporary storage mechanism
• Slows peak concentrations in fractures
• Leads to long-term back-diffusion

---

3. Radioactive Decay

• Reduces total contaminant mass over time
• Less significant over 30 years due to long half-life (100 years)
• Becomes more important in long-term (>100 year) simulations

---

Graphical Output: Depth vs Concentration

---

PDF Report

---

Engineering and Environmental Insights

• Fractured rock systems can enable fast contaminant migration, even with low matrix permeability
• Matrix diffusion is critical for realistic long-term predictions
• Radioactive decay alone is insufficient for short-term attenuation
• This type of modeling is essential for:
  • Nuclear waste repository design
  • Risk assessment of radioactive contaminants
  • Long-term groundwater protection strategies

---