🎓 Lesson 8
D5
Fundamentals of Energy Balances in Reactive Systems
Energy balances in reactive systems track how much energy goes into and comes out of a chemical reaction—like counting money in and out of a bank account for heat, work, and chemical change.
🎯 Learning Objectives
- ✓ Calculate the adiabatic flame temperature of explosive detonation products using standard enthalpies of formation
- ✓ Apply the generalized energy balance equation to design safe blasthole charging configurations with thermal constraints
- ✓ Analyze exothermic reaction heat release in ANFO vs. emulsion explosives to predict rock fracture efficiency
- ✓ Explain how heat losses to surrounding rock affect effective energy coupling in bench blasting
📖 Why This Matters
In mining blasting, over 95% of explosive energy is converted to heat—but only ~20–30% contributes to useful rock breakage. The rest dissipates as shock, gas expansion, ground vibration, and thermal loss. Without rigorous energy balancing, engineers risk undercharging (poor fragmentation), overcharging (excessive flyrock and cratering), or unsafe thermal buildup in confined boreholes. This lesson bridges reaction chemistry and field performance—turning textbook thermodynamics into actionable blast design.
📘 Core Principles
Energy balances in reactive systems begin with the general first-law expression: Q − W = ΔH + ΔKE + ΔPE. For typical blasting applications (steady-flow, negligible KE/PE changes), this reduces to Q = ΔHₛₜᵣₑₐₘ + Σnᵢ·hᵢ,ₒᵤₜ − Σnⱼ·hⱼ,ᵢₙ. Crucially, ΔH includes both sensible enthalpy changes (via Cp integrals) and chemical enthalpy changes (ΔH°ᵣₓₙ). Standard states (25°C, 1 atm) anchor tabulated ΔH°f values; non-standard conditions require temperature-dependent corrections using Kirchhoff’s law. In explosive systems, the reaction extent (ξ) governs stoichiometric conversion, and the ‘adiabatic flame temperature’ (Tₐd) represents the theoretical upper limit of product gas temperature—directly linked to pressure development and rock stress wave amplitude.
📐 Adiabatic Flame Temperature Estimation
The adiabatic flame temperature (Tₐd) estimates the maximum temperature reached by detonation gases assuming no heat loss. It is solved iteratively by equating total enthalpy of products at Tₐd to total enthalpy of reactants at reference temperature (usually 25°C), including ΔH°ᵣₓₙ. This is foundational for predicting gas pressure (via ideal gas law) and energy coupling efficiency.
💡 Worked Example
Problem: Estimate approximate Tₐd for stoichiometric ANFO (94% ammonium nitrate + 6% fuel oil) detonation: NH₄NO₃ + 0.15 C₁₀H₂₂ → products. Assume complete combustion to N₂, CO₂, H₂O(g), and residual O₂. Reactants at 25°C. Use average Cp,ₚᵣₒd ≈ 1.25 kJ/(mol·K) and ΔH°ᵣₓₙ = −3,850 kJ/kg ANFO.
1.
Step 1: Determine molar mass of ANFO mixture: 0.94×80.04 g/mol (NH₄NO₃) + 0.06×142.28 g/mol (C₁₀H₂₂) ≈ 83.7 g/mol.
2.
Step 2: Compute ΔH°ᵣₓₙ per mole ANFO: −3,850 kJ/kg × 0.0837 kg/mol ≈ −322 kJ/mol.
3.
Step 3: Apply energy balance: 0 = ΔH°ᵣₓₙ + ∫₂₉₈^Tₐd Σnᵢ·Cpᵢ dT ≈ −322,000 J/mol + (Σnᵢ·Cpᵢ)ₐᵥg·(Tₐd − 298). With Σnᵢ·Cpᵢ ≈ 12.5 kJ/K for 1 mol ANFO products, solve: Tₐd ≈ 298 + 322,000 / 12,500 ≈ 3,000 K.
4.
Step 4: Compare with empirical range: Field-measured peak gas temps for ANFO are 2,500–2,800 K due to incomplete reaction and heat loss—confirming model conservatism.
Answer:
The calculated Tₐd is ~3,000 K, which exceeds typical field-measured values (2,500–2,800 K) due to idealized assumptions—validating use as an upper-bound design parameter.
🏗️ Real-World Application
At BHP’s Olympic Dam open-pit copper mine (South Australia), energy balance modeling revealed that blastholes drilled through highly fractured, water-saturated dolomite showed 35% lower effective fragmentation energy than predicted. Post-blast calorimetry and infrared thermography confirmed >40% of explosive energy was absorbed as latent heat vaporizing pore water (≈2.26 MJ/kg) and sensible heating of wet rock (Cp ≈ 1.8 kJ/kg·K). Revised charging designs reduced powder factor by 12% while maintaining fragmentation—by explicitly incorporating moisture-dependent enthalpy sinks into the energy balance prior to blast design.
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