POLLUTEv10 Example 3: Advection + Diffusion with Aquifer Mixing

This example builds directly on Example 2 by introducing advective transport and a permeable aquifer boundary. This scenario is much closer to real-world landfill hydrogeology, where both diffusion and groundwater flow control contaminant migration.

---

Overview of the Scenario

In this example, the system consists of:

• A 4 m thick aquitard (low permeability layer)
• A constant contaminant source at the top (landfill)
• A 3 m thick active aquifer zone (upper portion of a 20 m aquifer)
• Downward flow (advection) through the aquitard
• Mixing in the aquifer controlled by flow continuity

Key Enhancements from Example 2:

• ✅ Advection included (va ≠ 0)
• ✅ Aquifer explicitly represented as a boundary
• ✅ Flow continuity used to calculate dilution
• ❌ Still no sorption (Kd = 0)

---

Conceptual Model

The transport system includes:

1. Downward advection + diffusion through aquitard
2. Mass transfer into aquifer at 4 m depth
3. Dilution in flowing groundwater system

The aquifer is treated as a well-mixed receptor zone, not a full 3D domain.

---

Input Parameters

Property	Symbol	Value	Units
Darcy Velocity	va	0.1	m/a
Diffusion Coefficient	D	0.01	m²/a
Distribution Coefficient	Kd	0	cm³/g
Soil Porosity	n	0.4	–
Dry Density	ρd	1.5	g/cm³
Aquitard Thickness	H	4	m
Sub-layers	–	4	–
Source Concentration	c₀	1	g/L
Landfill Length	L	200	m
Landfill Width	W	300	m
Aquifer Thickness	h	3	m
Aquifer Porosity	nb	0.3	–
Base Outflow Velocity	vb	26.67	m/a

---

Governing Transport Equation

With both advection and diffusion:

$\frac{\partial C}{\partial t} + v_a \frac{\partial C}{\partial x} = D \frac{\partial^2 C}{\partial x^2}$∂t∂C​+va​∂x∂C​=D∂x2∂2C​

This equation shows:

• Advection term (va ∂C/∂x) → dominates transport
• Diffusion term (D ∂²C/∂x²) → smooths gradients

---

Flow Continuity Calculations

A key part of this example is determining the aquifer dilution using flow balance.

1. Inflow to Aquifer (Upgradient)

$$q_{in} = v_{in} \cdot h \cdot W = 20 \cdot 3 \cdot 300 = 18000 \, m^3/a$$

2. Flow from Landfill (Recharge)

$$q_a = v_a \cdot L \cdot W = 0.1 \cdot 200 \cdot 300 = 6000 \, m^3/a$$

3. Total Outflow

$$q_{out} = q_{in} + q_a = 18000 + 6000 = 24000 \, m^3/a$$

4. Base Outflow Velocity

$$v_b = \frac{q_{out}}{W \cdot h} = \frac{24000}{300 \cdot 3} = 26.67 \, m/a$$

---

Peak Concentration (Hand Calculation)

Because advection dominates, the peak aquifer concentration can be estimated:

$c_{max} = \frac{q_a \cdot c_0}{q_{out}}$

$$c_{max} = \frac{6000 \cdot 1}{24000} = 0.25 \, g/L$$

✔ Key Insight:

• The aquifer concentration is controlled by dilution, not diffusion
• This provides a quick validation check against model results

---

Graphical Output: Concentration vs Time

---

PDF Report

---

Key Results

• Peak aquifer concentration: 0.25 g/L
• Transport dominated by advection
• Dilution governed by flow continuity

---

Conclusions

• Advection significantly increases contaminant migration rate
• Aquifer dilution is critical in determining impact
• Simple hand calculations can approximate peak concentrations
• Model highlights importance of accurate hydrogeologic characterization

---

Engineering Warning

The parameter vb (base outflow velocity) must be carefully evaluated:

• Depends on:
  • Aquifer transmissivity
  • Hydraulic gradients
  • Landfill recharge
• In complex systems:
  • Numerical groundwater models may be required
  • Simple continuity assumptions may not be sufficient

---

Key Engineering Insights

• This example bridges the gap between:
  • Pure diffusion (Example 2)
  • Real-world transport systems
• Demonstrates:
  • Importance of flow systems
  • Sensitivity to Darcy velocity
  • Role of aquifer thickness in dilution

---

Applications

• Landfill impact assessments
• Groundwater risk evaluation
• Regulatory compliance modeling
• Hydrogeologic sensitivity analysis

---