🎓 Lesson 23
D5
Final Quiz: TES Sizing Mastery Assessment
TES sizing is figuring out how big a thermal energy storage system needs to be to store just enough heat or cold for an industrial process without wasting space or money.
🎯 Learning Objectives
- ✓ Calculate required TES capacity (kWh_th) from hourly thermal load profiles and desired autonomy duration
- ✓ Design a sensible TES tank geometry given storage medium properties, temperature differential, and site constraints
- ✓ Analyze the impact of stratification efficiency on effective usable capacity using dimensionless Richardson number criteria
- ✓ Explain trade-offs between high-temperature molten salt TES and low-temperature chilled water TES in terms of round-trip efficiency and O&M complexity
- ✓ Apply ASHRAE Guideline 36 and ISO 50001-compliant methods to validate TES sizing against energy performance baselines
📖 Why This Matters
In industrial decarbonization, TES is the silent enabler—shifting steam, hot oil, or chilled water demand away from peak fossil-fueled generation to off-peak renewables or waste heat recovery. A poorly sized TES can cause process interruptions, grid penalties, or $2M+ in overspending on insulated tanks or phase-change materials. This quiz tests your ability to translate real plant data into robust, standards-aligned designs—not just textbook answers.
📘 Core Principles
TES sizing rests on three pillars: (1) Load-driven capacity—derived from time-resolved thermal demand (kW_th) and required discharge duration (h); (2) Thermophysical fidelity—accounting for specific heat, density, phase change enthalpy, and losses across insulation, piping, and charge/discharge cycles; and (3) System integration effects—stratification quality, pump head requirements, thermal exchanger UA, and control logic latency. Advanced sizing also incorporates uncertainty quantification: ±15% load forecast error, ±5°C ambient swing, and 20-year degradation of PCM encapsulation integrity.
📐 Sensible TES Capacity Formula
This formula calculates the minimum required volume of a liquid-based sensible TES tank (e.g., water, thermal oil, or molten salt) based on energy demand, temperature lift, and material properties. It assumes ideal mixing and neglects stratification losses—so it serves as a baseline that must be increased by 10–25% for real-world performance.
Sensible TES Volume
V = Q / (ρ · cₚ · ΔT)Minimum geometric volume of a liquid-phase sensible TES system
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| V | Volume | m³ | Required tank internal volume |
| Q | Thermal energy requirement | J | Total energy to be stored (convert from kWh_th × 3.6×10⁶) |
| ρ | Density | kg/m³ | Mass density of storage fluid at mean temperature |
| cₚ | Specific heat capacity | J/kg·K | Constant-pressure specific heat of storage medium |
| ΔT | Effective temperature difference | K | Usable temperature span between charge and discharge states |
Typical Ranges:
Industrial hot water TES: 25 – 45 K
Molten salt (two-tank): 200 – 280 K
Chilled water TES: 5 – 10 K
💡 Worked Example
Problem: A food processing plant requires 4,200 kWh_th of 85°C hot water for 6 hours daily. The TES uses Therminol VP-1 (ρ = 860 kg/m³, cp = 2.1 kJ/kg·K) with ΔT = 40 K (105°C → 65°C). Calculate minimum tank volume.
1.
Step 1: Convert energy to joules: 4,200 kWh_th × 3.6×10⁶ J/kWh = 1.512×10¹⁰ J
2.
Step 2: Apply Q = m·cp·ΔT → m = Q / (cp·ΔT) = 1.512×10¹⁰ J / (2100 J/kg·K × 40 K) = 180,000 kg
3.
Step 3: Convert mass to volume: V = m / ρ = 180,000 kg / 860 kg/m³ = 209.3 m³
4.
Step 4: Apply 15% stratification & loss derating: V_design = 209.3 × 1.15 = 240.7 m³
Answer:
The design volume is 241 m³, which falls within the typical range of 200–350 m³ for mid-scale industrial hot oil TES systems.
🏗️ Real-World Application
At the Ørsted Avedøre Power Station (Denmark), a 30 MW_th latent TES using sodium nitrate–potassium nitrate eutectic (60/40 wt%) was sized to shift 8 hours of district heating demand from coal-fired peak to overnight wind-powered electric boilers. Engineers used dynamic TRNSYS simulation + field-measured heat loss coefficients (U = 0.18 W/m²·K) to downsize the initial 42,000 m³ sensible water tank proposal to a 12,800 m³ PCM-packed-bed system—reducing footprint by 69% and LCOH by €8.2/MWh_th.
🔧 Interactive Calculator
🔧 Open Thermal Energy Storage System Sizing for Industrial Applications Calculator📋 Case Connection
📋 Food Processing Steam Peak-Shaving with Bio-Based PCM
Steam demand spikes (up to 12 MW) during sterilization cycles exceeding boiler capacity
📋 Steel Reheating Furnace Waste Heat Recovery with Sensible Rock Bed TES
Flue gas at 650°C wasted during batch furnace idle periods; need to preheat charge air to 400°C
📋 Pharmaceutical Lyophilization Cold Storage Hybridization
Cryo-condenser load peaks (−55°C) during primary drying exceed chiller capacity; require sub-zero TES