POLLUTEv10 Example 11: Time-Varying Source Concentration with Diffusion (Chloride in Clay)

Modeling Transient Source Histories in Landfill Systems

POLLUTEv10 Example 11 focuses on a critical real-world scenario: time-varying source concentration combined with diffusion-only transport in a clay medium.

Unlike previous examples, this case highlights how changing contaminant inputs over time influence subsurface concentration profiles—even in the absence of groundwater flow.

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Problem Overview

This example simulates:

• A hypothetical landfill cell
• A conservative contaminant (chloride)
• No advection (Darcy velocity = 0)
• A time-dependent source concentration history
• A semi-infinite clay domain

Initial Conditions

• Clay pore water contains chloride at 120 mg/L
• Landfill cell is filled with water (6 m depth)
• No waste is present for the first 7 years

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Conceptual Model

The system evolves through several stages:

Stage 1: 0–7 Years (Pre-Waste Phase)

• Clean water in landfill cell
• Chloride diffuses from clay → into water
• Gradient driven by initial clay concentration (120 mg/L)

Stage 2: 7–10 Years (Waste Placement)

• Chloride concentration increases linearly to 2100 mg/L
• Gradient reverses direction

Stage 3: 10–13 Years (Peak Phase)

• Source concentration remains constant at 2100 mg/L

Stage 4: 13–15 Years (Decline Phase)

• Concentration decreases to 1180 mg/L

Stage 5: 15–19 Years (Stabilization)

• Concentration remains constant again

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Key Modeling Objective

The goal is to:

Predict chloride concentration distribution with depth at year 19

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Input Parameters

Property	Value	Units
Darcy Velocity (va)	0.0	m/a
Diffusion Coefficient (Dm)	0.00663	m²/a
Distribution Coefficient	0.0	cm³/g
Dispersivity	0.0	m
Soil Porosity (n)	0.37	–
Dry Density	1.6	g/cm³
Thickness of Interest (H)	1.5	m
Sub-layers	15	–
Source Concentration	Variable	mg/L
Leachate Height (Hr)	6.0	m

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Key Equation

Since there is no flow, transport is purely diffusive:

$D = D_m + \alpha \frac{v_a}{n}$

With:

• $v_a = 0$va​=0
• $\alpha = 0$α=0

➡️ Therefore:

• D = Dm
• Dispersion effects are negligible

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Time-Varying Source Representation

A key modeling technique in this example:

• The Reference Height of Leachate (Hr) is set very large during intervals
• This ensures the source concentration remains constant within each time step

This allows POLLUTEv10 to simulate:

• Stepwise or linear changes in concentration
• Complex source histories

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Transport Mechanisms

1. Diffusion Only

• Driven by concentration gradients
• No advective transport
• Symmetric spreading behavior

2. No Sorption

• Chloride is conservative
• Moves freely with no retardation

3. Infinite Domain Assumption

• Clay thickness is effectively infinite
• No boundary effects at depth

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Graphical Output: Concentration vs Time

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PDF Report

Key Insights

• Time-varying sources can significantly alter transport behavior
• Even without flow, diffusion redistributes contaminants over time
• Early conditions can influence long-term profiles
• Conservative species respond directly to boundary condition changes

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Importance of Sub-Layer Resolution

Accuracy depends on the number of sub-layers when using Variable Properties.

• Time-dependent inputs require fine discretization
• Recommended: ≥ 15 sub-layers
• Ensures accurate capture of transient gradients

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Practical Applications

This example is useful for:

• Landfill design and performance assessment
• Chloride migration studies
• Time-dependent contaminant modeling
• Calibration against monitoring data

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Important Disclaimer

This is a hypothetical example intended to demonstrate modeling techniques.

It is not a universal modeling approach for all landfill systems.

Proper application requires:

• Hydrogeologic expertise
• Site-specific parameter selection
• Engineering judgment

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Conclusion

POLLUTEv10 Example 11 demonstrates how time-varying source concentrations influence contaminant transport in diffusion-dominated systems.

Key takeaways:

• Diffusion alone can produce complex concentration profiles
• Source history plays a critical role in long-term outcomes
• Variable Properties enables realistic simulation of changing conditions

This example is essential for understanding transient contaminant behavior in low-permeability soils.

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