🎓 Lesson 22
D5
Case Review: District Heating Seasonal TES — Long-Term Stratification Integrity
Seasonal thermal energy storage (TES) for district heating keeps summer heat in large insulated tanks or underground aquifers so it can be used to warm buildings during winter.
🎯 Learning Objectives
- ✓ Analyze stratification stability using Richardson number and thermal inertia metrics
- ✓ Design minimum insulation thickness and liner specifications to meet ≤3% annual heat loss targets
- ✓ Calculate required storage volume for a given district heating load profile and supply temperature drop
- ✓ Explain how groundwater flow, sediment heterogeneity, and tank geometry impact long-term stratification integrity
- ✓ Apply EN 15316-4-6 and VDI 2078 guidelines to evaluate seasonal TES system performance
📖 Why This Matters
In cold-climate cities like Helsinki, Stockholm, or Edmonton, up to 60% of annual building energy demand is for space heating—but peak demand occurs in winter while abundant low-cost heat (e.g., solar thermal, industrial waste heat) is available in summer. Seasonal TES bridges this temporal mismatch. However, if stratification collapses over months—due to mixing, conduction, or infiltration—the stored heat becomes unusable or inefficient. This lesson focuses on *long-term stratification integrity*: the engineering discipline ensuring that hot and cold layers remain distinct for 6–12 months, directly determining whether a multi-million-euro TES investment delivers decarbonization value—or fails silently.
📘 Core Principles
Stratification integrity hinges on three interdependent phenomena: (1) *Thermal buoyancy*, governed by density differences between warm and cold water (via the equation of state for water); (2) *Suppression of turbulent mixing*, quantified by the bulk Richardson number (Ri_b), where Ri_b > 0.25 indicates stable stratification; and (3) *Long-term thermal confinement*, requiring minimization of conductive/convective losses across boundaries (tank walls, soil interface, or aquifer caprock). Over time, small perturbations—groundwater seepage, thermal creep through insulation, or pump-induced recirculation—accumulate. Therefore, design must address not just initial stratification, but its *evolution* under real-world boundary conditions over ≥10 years. Key metrics include stratification ratio (ΔT_actual / ΔT_theoretical), exergy retention, and normalized heat loss per m³·K·year.
📐 Bulk Richardson Number for Stratification Stability
The bulk Richardson number (Ri_b) predicts whether natural convection will erode stratification. Ri_b > 0.25 indicates stable, persistent layering; values < 0.1 signal imminent mixing. It integrates temperature gradient, velocity shear, and fluid properties—and is the primary dimensionless criterion used in EN 15316-4-6 Annex B for TES validation.
Bulk Richardson Number (Ri_b)
Ri_b = (g/ρ₀)(dρ/dz) / (du/dz)²Dimensionless number predicting stability of thermal stratification against shear-induced mixing.
Variables:
| Symbol | Name | Unit | Description |
|---|---|---|---|
| g | Gravitational acceleration | m/s² | Standard acceleration due to gravity |
| ρ₀ | Reference fluid density | kg/m³ | Average density of the stratified fluid column |
| dρ/dz | Vertical density gradient | kg/m⁴ | Rate of change of density with depth |
| du/dz | Vertical velocity shear | s⁻¹ | Rate of change of horizontal velocity with depth |
Typical Ranges:
Stable stratification (design target): > 0.25
Marginal stability (requires monitoring): 0.1 – 0.25
Unstable (mixing expected): < 0.1
💡 Worked Example
Problem: A 30-m-diameter, 35-m-deep cylindrical water tank stores heat at 85°C (top 5 m) and 15°C (bottom 30 m). During maintenance pumping, average vertical velocity shear is measured at 0.002 s⁻¹. Water density at 85°C = 968 kg/m³; at 15°C = 999 kg/m³. Gravity = 9.81 m/s². Calculate Ri_b and assess stratification stability.
1.
Step 1: Compute mean density gradient: dρ/dz ≈ (999 − 968) kg/m³ / 35 m = 0.886 kg/m⁴
2.
Step 2: Compute g/ρ₀ ≈ 9.81 / 983.5 ≈ 0.0100 s⁻² (using ρ₀ = average density = 983.5 kg/m³)
3.
Step 3: Apply Ri_b = (g/ρ₀)(dρ/dz) / (du/dz)² = (0.0100)(0.886) / (0.002)² = 0.00886 / 0.000004 = 2215
4.
Step 4: Compare to threshold: Ri_b = 2215 ≫ 0.25 → highly stable stratification under these shear conditions
Answer:
The result is Ri_b = 2215, which far exceeds the stability threshold of 0.25—indicating robust stratification resistance to shear-induced mixing under current operational conditions.
🏗️ Real-World Application
The Drake Landing Solar Community (Okotoks, Alberta, Canada) implemented a borehole thermal energy storage (BTES) system with 144 vertical 35-m-deep boreholes in glacial till. Over 10 years of operation (2007–2017), stratification integrity was maintained via: (1) controlled injection/extraction rates limiting velocity shear (Ri_b > 1200), (2) grouting with low-conductivity bentonite clay to suppress lateral conduction, and (3) real-time temperature profiling using fiber-optic DTS sensors. Annual heat loss averaged 2.3%, meeting ASHRAE Guideline 34-2022 targets. Post-monitoring revealed that minor stratification erosion occurred only near borehole tops—prompting redesign of inlet diffusers in Phase II to improve laminar inflow.
🔧 Interactive Calculator
🔧 Open Thermal Energy Storage System Sizing for Industrial Applications Calculator📋 Case Connection
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📋 District Heating Network Seasonal TES with Stratified Water Tank
Summer solar thermal surplus (90°C) must be stored for winter space heating (60°C return), requiring 6-month retention