🎓 Lesson 1
D1
What Makes a System Thermodynamically Open or Closed?
A thermodynamic system is 'open' if it lets both energy and matter flow in and out, and 'closed' if only energy can cross its boundary—but no matter enters or leaves.
🎯 Learning Objectives
- ✓ Explain the physical distinction between open and closed systems using real mining process examples
- ✓ Analyze a blasthole charging operation to classify it as open or closed based on mass and energy exchange
- ✓ Apply the first law of thermodynamics to both open and closed systems in steady-state and transient blasting scenarios
- ✓ Design a simplified energy balance for a vented detonation chamber (open) versus an isolated explosive cartridge test (closed)
📖 Why This Matters
In mining blasting, whether you’re modeling detonation energy release, predicting gas venting from a blast, or simulating heat transfer in rock fragmentation, misclassifying the system boundary leads to incorrect energy balances—and unsafe or inefficient designs. For example, treating a vented borehole as closed ignores critical mass loss of hot gases, overestimating peak pressure by up to 40%. Getting this right is foundational for accurate process simulation in software like ANSYS Autodyn or MATLAB-based blast models.
📘 Core Principles
All thermodynamic analysis begins with defining the system boundary. A closed system (e.g., a sealed explosive cartridge during initiation) contains constant mass—its boundary is impermeable to matter but permeable to energy (heat, work). An open system (e.g., a blasthole during detonation) has a control surface through which explosive gases, fragmented rock, and air flow—requiring mass flow rate terms in energy and entropy balances. The choice dictates which form of the first law applies: for closed systems, ΔU = Q − W; for open systems, the general control-volume form includes enthalpy fluxes (ṁh), kinetic/potential energy, and accumulation terms (∂/∂t ∫ρe dV). Real-world blasting processes are almost always open—except in highly constrained lab-scale tests.
📐 First Law for Open vs. Closed Systems
The first law expresses energy conservation. Its form changes based on system type. For closed systems, internal energy change dominates. For open systems under steady flow, enthalpy transport becomes critical—especially when high-velocity gas ejection carries significant flow work.
💡 Worked Example
Problem: A 150-mm-diameter blasthole is charged with 8 kg of ANFO and detonated. During peak gas expansion (0–20 ms), 1.2 kg of gaseous products vent upward at 1800 m/s, carrying specific enthalpy h = 3.2 MJ/kg. Heat loss to rock is estimated at 1.8 MJ; no shaft work is done. Assume negligible ΔKE/ΔPE for solid rock. What is the net energy change of the control volume (the blasthole region)?
1.
Step 1: Identify system type — open (mass exits), unsteady (transient detonation phase)
2.
Step 2: Apply general first law: dE_cv/dt = Q̇ − Ẇ + Σṁ_in h_in − Σṁ_out h_out + Σṁ_in(e_k,in + e_p,in) − Σṁ_out(e_k,out + e_p,out)
3.
Step 3: Simplify: Q = −1.8 MJ (loss), Ẇ = 0, ṁ_in = 0, ṁ_out = 1.2 kg, h_out = 3.2 MJ/kg, e_k,out = (1/2)v² = 0.5 × (1800)² = 1.62 MJ/kg → total outflow enthalpy + KE = 3.2 + 1.62 = 4.82 MJ/kg ⇒ total outflow energy = 1.2 × 4.82 = 5.784 MJ
4.
Step 4: Accumulation = Q − outflow = −1.8 − 5.784 = −7.584 MJ
Answer:
The control volume loses 7.58 MJ of energy—primarily via high-velocity gas ejection. This confirms why ignoring mass flow (i.e., assuming closed system) would underestimate energy loss by >5 MJ, leading to overprediction of in-hole pressure.
🏗️ Real-World Application
At the Bingham Canyon Mine (Rio Tinto), blast design engineers model the initial detonation phase (0–50 ms) as an open system to calibrate coupled thermo-mechanical simulations in LS-DYNA. They define the control volume around the borehole collar and explicitly track mass flux of CO₂, N₂, and H₂O vapor measured via high-speed schlieren imaging and piezoelectric pressure sensors. In contrast, laboratory sensitivity testing of emulsion explosives in hermetically sealed bomb calorimeters uses a closed-system assumption—valid because containment prevents mass loss, enabling precise ΔU measurement per ASTM E709.
🔧 Interactive Calculator
🔧 Open Thermodynamics & Process Simulation Calculator📋 Case Connection
📋 Bioethanol Distillation Energy Integration at Brazilian Sugarcane Mill
Steam demand exceeded boiler capacity during peak season; column flooding observed