🎓 Lesson 10
D5
From Batch to Flow: Setting Up MIN3P for Waste Rock Heap Simulations
MIN3P is a computer program that simulates how water, chemicals, and reactions move together through waste rock piles over time.
🎯 Learning Objectives
- ✓ Configure MIN3P input files for a 2D unsaturated waste rock heap using site-specific hydrogeologic and geochemical parameters
- ✓ Analyze simulated pH, sulfate, and Fe(II)/Fe(III) profiles to diagnose ARD generation potential and timing
- ✓ Design a sensitivity test protocol to quantify the impact of oxygen diffusion rate and pyrite oxidation kinetics on heap effluent quality
- ✓ Explain the conceptual differences between batch (well-mixed) and flow-through (advective–diffusive) reactive transport modes in heap leaching contexts
📖 Why This Matters
Waste rock heaps can generate acid rock drainage (ARD) for decades—costing millions in treatment and closure liabilities. Traditional batch leach tests (e.g., ASTM D5744) misrepresent field-scale oxygen transport and water flow dynamics. Transitioning from batch to flow modeling with MIN3P lets engineers forecast ARD onset, optimize cover design, and meet regulatory timelines—turning reactive transport from a black box into a predictive engineering tool.
📘 Core Principles
Reactive transport in waste rock heaps couples three physical processes: (1) variably saturated water flow (governed by Richards’ equation), (2) solute advection–dispersion–diffusion (governed by the advection–dispersion equation), and (3) multi-step geochemical reactions—including pyrite oxidation, ferrihydrite precipitation, and pH-dependent mineral equilibria. MIN3P implements these via operator splitting: first solving flow, then transport, then chemistry at each time step. Crucially, it treats oxygen as a dissolved species subject to both advective delivery and diffusive supply from the atmosphere—a key distinction from batch systems where O₂ is assumed unlimited or absent.
📐 Oxygen Diffusion-Limited Oxidation Rate
This empirical rate law links observed pyrite oxidation to oxygen availability in unsaturated zones—critical for initializing MIN3P kinetic parameters. It accounts for gas-phase diffusion resistance, which dominates oxidation rates below ~5% volumetric water content.
💡 Worked Example
Problem: Given: effective O₂ diffusion coefficient in pore air = 1.8 × 10⁻⁵ m²/s; porosity = 0.35; volumetric water content = 0.12; pyrite surface area = 2.4 m²/kg; O₂ concentration gradient = 0.008 mol/m⁴; temperature = 15°C.
1.
Step 1: Compute gas-phase tortuosity factor τ_g using Millington–Quirk relation: τ_g = (θ_v / θ_s)² = (0.12 / 0.35)² ≈ 0.117
2.
Step 2: Calculate effective diffusion coefficient: D_eff = D_O₂ × (θ_v / τ_g) = 1.8e−5 × (0.12 / 0.117) ≈ 1.85e−5 m²/s
3.
Step 3: Apply Fick’s first law: J_O₂ = −D_eff × dC/dx = 1.85e−5 × 0.008 = 1.48e−7 mol/(m²·s)
4.
Step 4: Convert to pyrite oxidation rate using stoichiometry (1 mol O₂ oxidizes 0.25 mol FeS₂): R_pyrite = J_O₂ × 0.25 × M_FeS₂ × SA = 1.48e−7 × 0.25 × 119.98 g/mol × 2.4 m²/kg ≈ 2.66 × 10⁻⁶ kg/(kg·s) = 0.23 kg/(tonne·day)
Answer:
The calculated oxidation rate is 0.23 kg/(tonne·day), which falls within the typical range of 0.1–0.5 kg/(tonne·day) for moderately reactive sulfidic waste under aerobic unsaturated conditions.
🏗️ Real-World Application
At the Mount Polley tailings storage facility (British Columbia), MIN3P was used to simulate 30-year ARD evolution in the waste rock embankment after the 2014 breach. Model inputs included field-measured hydraulic conductivity (10⁻⁷ to 10⁻⁵ m/s), measured pyrite content (1.8 wt%), laboratory-derived oxidation kinetics (k = 1.2 × 10⁻¹⁰ mol/(m²·s)), and atmospheric boundary conditions. The simulation predicted peak sulfate release at year 12—validated by pore water monitoring wells—and guided placement of an oxygen-limiting clay–peat cover, reducing predicted long-term acidity by 78%.
✏️ Model Setup Exercise
Using the provided MIN3P template and data package (rock density = 2.4 g/cm³, porosity = 0.32, van Genuchten α = 0.008 1/m, n = 1.8, initial pyrite = 2.1 wt%, initial pH = 6.8), students must: (1) edit the *FLOW.INP file to define a 2D 20-m-high heap with 1-m grid spacing and no-flow lateral boundaries; (2) modify *CHEM.INP to include pyrite, ferrihydrite, and gypsum with kinetic rate laws; (3) set the time step to 30 days and total simulation time to 10 years; (4) run MIN3P and extract pH and SO₄²⁻ concentration vs. depth at t = 5 years.
🔧 Interactive Calculator
🔧 Open Mine Waste Characterization & Geochemical Modeling Calculator📋 Case Connection
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