| name | thermal-energy-storage |
| description | Thermal energy storage (TES) — sensible heat storage (water tank, rock bed, aquifer ATES), latent heat storage (PCM: paraffin, salt hydrates, molten salts; Stefan problem melting), thermochemical storage (reversible reactions, energy density comparison), stratification, charging/discharging thermoclines, capacity sizing, cycle efficiency, ASHRAE 150, and grid-scale applications (CSP molten salt, ice storage, chilled water). |
Thermal Energy Storage (TES) — Complete Skill
TES Classification and Energy Density
Storage Mechanism Comparison
| Type | Mechanism | Energy Density [kWh/m³] | Temperature Range | Maturity |
|---|
| Sensible (water) | cp×ΔT | 20–80 | 0–95°C | Commercial |
| Sensible (rock/concrete) | cp×ΔT | 30–60 | 200–800°C | Commercial |
| Latent (PCM) | h_sf | 50–150 | Depends on PCM | Commercial |
| Molten salt | Sensible + partial latent | 50–80 | 290–565°C | Commercial (CSP) |
| Thermochemical | ΔH_rxn | 120–250 | High ΔT | Demo/R&D |
Sensible Heat Storage
Capacity Calculation
Stored energy:
Q_stored = m × cₚ × ΔT = ρ × V × cₚ × (T_hot − T_cold) [J or kWh; divide by 3.6×10⁶ for kWh]
Water tank (most common; district energy, buildings):
cₚ_water = 4,186 J/(kg·K); ρ = 997 kg/m³ (at 20°C)
Q = 4,186 × ρ × V × ΔT / 3.6×10⁶ = 1.162 × V[m³] × ΔT[K] [kWh]
Example: V = 500 m³; ΔT = 30°C → Q = 1.162 × 500 × 30 = 17,430 kWh = 17.4 MWh
Rock bed (high-temperature sensible):
Granite: cₚ = 790 J/(kg·K); ρ = 2,700 kg/m³ → energy density = 0.592 kWh/(m³·K)
Concrete: cₚ = 840 J/(kg·K); ρ = 2,200 kg/m³ → 0.514 kWh/(m³·K)
Application: Concentrated Solar Power (CSP) with solid media; heat transfer via air/steam/thermal oil
Stratification in Water Tanks
Thermal stratification: buoyancy-driven vertical temperature gradient; hot water rises; cold sinks
Thermocline: sharp temperature gradient between hot and cold zones
Richardson number: Ri = g×β×ΔT×L / (V²) >> 1 for stable stratification (β = 2.07×10⁻⁴ /K for water at 60°C)
Figure of merit (stratification efficiency):
η_str = (Q_actual drawn) / (Q_ideal from fully mixed tank)
Well-stratified: η_str ≈ 0.95–0.99; fully mixed: η_str = 1.0 (no penalty for mixing) — stratification gives higher charge extraction
Inlet stratification devices: slotted pipe diffusers; baffle plates; membrane stratifiers → minimize mixing during charge/discharge
Aquifer TES (ATES)
Underground aquifer stores hot or cold water seasonally:
Injection well (hot) ↔ Production well (cold)
Thermal recovery efficiency: η_ATES ≈ 0.7–0.85 (losses to ground)
Regulatory: groundwater quality protection; permits required; common in Netherlands, Sweden
Latent Heat Storage (PCM)
Phase Change Energy
Latent heat capacity:
Q_latent = m × h_sf [h_sf = specific enthalpy of fusion [kJ/kg]]
Total stored: Q_total = m × [cₚ_solid × (T_m − T_min) + h_sf + cₚ_liquid × (T_max − T_m)]
PCM Selection Criteria:
High h_sf (maximize energy density); T_m matching application; low subcooling; high k (conductivity); low cost; non-toxic; stable over cycles
Common PCM Properties:
| PCM | T_m [°C] | h_sf [kJ/kg] | ρ [kg/m³] | k [W/mK] | Application |
|---|
| Water/ice | 0 | 334 | 917 | 2.2 | Ice storage (cooling) |
| n-Hexadecane (paraffin) | 18 | 237 | 776 | 0.15 | Building thermal comfort |
| n-Octadecane (paraffin) | 28 | 244 | 777 | 0.15 | HVAC peak shifting |
| CaCl₂·6H₂O (salt hydrate) | 29 | 191 | 1,710 | 1.09 | Building; higher ρ |
| Na₂SO₄·10H₂O (Glauber's salt) | 32 | 254 | 1,460 | 0.54 | Building |
| Palmitic acid (fatty acid) | 63 | 212 | 850 | 0.22 | Solar heat |
| NaNO₃ (nitrate salt) | 307 | 172 | 2,260 | 0.5 | CSP |
| KNO₃ (nitrate salt) | 333 | 95 | 2,110 | 0.5 | CSP |
| NaCl | 801 | 481 | 2,160 | 7.0 | High-T industrial |
Stefan Problem — Melting Front
One-dimensional melting (slab geometry):
Heat conduction equation in liquid phase:
∂T/∂t = α_l × ∂²T/∂x² [α_l = k_l / (ρ×c_l)]
Stefan condition (energy balance at moving interface):
k_l × ∂T_l/∂x|{x=s} − k_s × ∂T_s/∂x|{x=s} = ρ × h_sf × ds/dt [s(t) = melt front position]
Exact solution (Neumann, semi-infinite slab):
s(t) = 2λ × √(α_l × t) [λ = root of: λ×exp(λ²)×erf(λ) = Ste/√π]
Stefan number: Ste = c_l × (T_wall − T_m) / h_sf [dimensionless driving force for melting]
Approximate (thin PCM, constant wall temperature):
s(t) ≈ √(2 × k_l × (T_wall − T_m) × t / (ρ × h_sf)) [simplified for Ste << 1]
Time to complete melting through thickness L:
t_melt = ρ × h_sf × L² / (2 × k_l × ΔT_wall)
Example:
L = 20 mm paraffin (h_sf = 244 kJ/kg; k_l = 0.15 W/mK; ρ = 777 kg/m³; T_m = 28°C)
T_wall = 50°C → ΔT = 22°C
t_melt = 777 × 244,000 × (0.02)² / (2 × 0.15 × 22) = 777 × 244,000 × 0.0004 / 6.6 = 11,470 s = 3.2 h
Poor conductivity limits charging rate → PCM must be combined with fins or metal foam
PCM Heat Transfer Enhancement
Low k problem: paraffin k ≈ 0.15 W/mK → slow charging; fins essential
Finned heat exchanger PCM:
Fin efficiency: η_fin = tanh(mL_fin) / (mL_fin) [m = √(h×P / (k_fin×A_c)); L_fin = fin half-height]
Total heat transfer: Q = h × (A_bare + η_fin × A_fin) × (T_HTF − T_m)
Metal foam/fiber: Al foam (k_foam ≈ 10–15 W/mK effective) → 10× reduction in melt time
Microencapsulation: PCM in polymer microcapsules (1–1,000 μm) → large surface area; slurries; k increases
Molten Salt TES (CSP Grid-Scale)
Two-Tank System
CSP two-tank molten salt:
Cold tank: 290°C; Hot tank: 565°C; ΔT = 275°C
Fluid: Solar Salt (60% NaNO₃ + 40% KNO₃); ρ = 1,830 kg/m³; cₚ = 1,530 J/(kg·K)
Energy density: ρ × cₚ × ΔT = 1,830 × 1,530 × 275 / 3.6×10⁶ = 213 kWh/m³
Storage sizing:
Q_stored = P_turbine × t_storage / η_steam [e.g., 100 MW × 6 h / 0.38 = 1,579 MWh_thermal]
V_hot = Q_stored / (ρ × cₚ × ΔT) = 1,579×10³×3,600 / (1,830 × 1,530 × 275) = 7,414 m³
Tank diameter D = 40 m; height H = 6 m typical for commercial CSP
Current CSP projects: Gemasolar (Spain) 15 h TES; Noor III (Morocco); Crescent Dunes (Nevada)
Single-Tank Thermocline
Single tank with hot/cold stratification:
Top = hot; bottom = cold; thermocline moves as charged/discharged
Filler material (quartzite rock + sand) reduces salt volume by 70%
Cost: ~60% of two-tank; but stratification degradation over cycles
Ice Storage (Cooling)
Ice-on-coil or ice slurry:
Charge at night (off-peak): refrigeration plant freezes water (0°C); Q_stored = m × 334 kJ/kg
Discharge during day (peak): melt ice for cooling load
Capacity:
Q_ice = 334 [kJ/kg] × m_ice; or Q_ice = V_ice × 334 × ρ_ice = V_ice × 334 × 917 / 3,600 = 85.2 kWh/m³
Tank sizing:
For 500 RT-h (refrigeration ton-hours = 500 × 3.517 kWh = 1,758.5 kWh):
V_ice = 1,758.5 / 85.2 = 20.6 m³ of ice
HVAC integration: chiller runs off-peak (lower electricity cost/emissions); building CWS loop uses melt water during peak
ASHRAE Standard 150: test method for TES performance (chilled water and ice)
Thermochemical TES
Principle: reversible endothermic/exothermic reaction stores chemical potential
Charge: heat input → endothermic reaction → products A + B stored separately
Discharge: combine A + B → exothermic → release heat
Example reactions:
| Reaction | T [°C] | ΔH [kJ/kg] | Energy density [kWh/kg] |
|---|
| CaO + H₂O ↔ Ca(OH)₂ | 450 | 1,860 | 0.517 |
| MgO + H₂O ↔ Mg(OH)₂ | 300 | 1,348 | 0.374 |
| CO₂ + CaO ↔ CaCO₃ | 850 | 1,779 | 0.494 |
| CH₄ + H₂O ↔ CO + 3H₂ | 600 | 6,050 | 1.680 |
Advantage: no heat loss during storage (products stored at ambient T); unlimited storage duration
Challenge: reaction kinetics; side reactions; degradation over cycles; complex reactor
Cycle Efficiency and Losses
Round-trip efficiency:
η_RTE = Q_out / Q_in [losses: heat loss during storage; degradation; heat exchanger losses]
Heat loss from insulated tank:
Q_loss = U × A × (T_storage − T_ambient) × t_storage [U = overall heat loss coefficient; A = surface area]
Well-insulated tank: U ≈ 0.5–2 W/(m²·K); Q_loss/Q_stored typically < 1%/day for large tanks
Chilled water: η_RTE ≈ 0.90–0.95 (pump energy; mixing losses)
Ice storage: η_RTE ≈ 0.85–0.92 (compressor penalty at lower T)
Molten salt CSP: η_RTE ≈ 0.99 (sensible only; minimal losses)
Standards and References
| Standard | Scope |
|---|
| ASHRAE Standard 150 | Test method for thermal energy storage equipment |
| IEA SHC Task 58 | Material and component development for compact heat storage |
| EPRI Report 3002002322 | Grid-scale TES assessment |
| NREL TES report | CSP thermal storage technology assessment |
| ISO 9488 | Solar energy vocabulary |
Output
Provide: application (building HVAC/CSP/industrial; charge/discharge profile; peak demand [kW]; storage duration [h]; temperature levels T_hot [°C] / T_cold [°C]), TES type selection (sensible/latent/thermochemical; basis: temperature, energy density, cost), capacity sizing (Q_required [kWh]; ρ, cₚ or h_sf for chosen medium; volume V [m³]; tank dimensions), PCM selection (if latent: T_m [°C]; h_sf [kJ/kg]; k [W/mK]; enhancement method: fins/foam; fin geometry calculation; melt/solidification time [h]), molten salt (if CSP: salt composition; ΔT [°C]; V_hot tank [m³]; tank diameter/height; energy density [kWh/m³]), charging analysis (charging rate Q̇_charge [kW]; HTF flow rate ṁ [kg/s]; inlet/outlet temperatures; LMTD [K]; heat exchanger area A [m²]), heat losses (U [W/m²K]; Q_loss [kWh/day]; insulation thickness δ [mm]; η_RTE [%]), economic estimate (cost of storage: $/kWh; payback period; utility peak demand savings [$/year]; ice storage: off-peak vs. on-peak rate differential), and applicable standard (ASHRAE 150; IEA Task 58; NREL/EPRI for CSP).
