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

Knowledge Center

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

POLLUTEv10 simulation of chloride diffusion in clay with time varying landfill source concentration

Written by

GAEA Technologies

in

,
Share the knowledge

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.

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

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

Key Modeling Objective

The goal is to:

Predict chloride concentration distribution with depth at year 19

Input Parameters

PropertyValueUnits
Darcy Velocity (va)0.0m/a
Diffusion Coefficient (Dm)0.00663m²/a
Distribution Coefficient0.0cm³/g
Dispersivity0.0m
Soil Porosity (n)0.37–
Dry Density1.6g/cm³
Thickness of Interest (H)1.5m
Sub-layers15–
Source ConcentrationVariablemg/L
Leachate Height (Hr)6.0m

Key Equation

Since there is no flow, transport is purely diffusive:

D=Dm+αvanD = D_m + \alpha \frac{v_a}{n}

With:

  • va=0v_a = 0va​=0
  • α=0\alpha = 0α=0

➡️ Therefore:

  • D = Dm
  • Dispersion effects are negligible

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

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

Graphical Output: Concentration vs Time

PDF Report

Loader Loading…
EAD Logo Taking too long?

Reload Reload document
| Open Open in new tab

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

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

Practical Applications

This example is useful for:

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

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

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.

1 / ?