Temperature Drop
Engineering fundamentals for pipeline heat transfer
1. Heat Transfer Fundamentals
Fluid temperature changes along a pipeline due to heat exchange with surroundings. For hot fluids, temperature drops; for cold fluids (below ambient), temperature rises toward equilibrium.
Heat Transfer Mechanisms
- Convection (internal): Fluid to pipe wall—depends on flow regime and fluid properties
- Conduction: Through pipe wall, insulation, and soil (if buried)
- Convection (external): Pipe surface to air (above-ground) or conduction to soil
- Radiation: Usually minor for pipelines at moderate temperatures
🔄 Heat Transfer Resistances
Cross-section of insulated pipe showing thermal resistance layers: (1) Internal film (h_i), (2) Pipe wall (k_steel), (3) Insulation layer (k_ins), (4) External coating, (5) Soil or air (h_o or k_soil). Show temperature profile dropping through each layer from T_fluid to T_ambient. Label each resistance R₁ through R₅. Include radii r₁, r₂, r₃ for each interface.
Key Parameters
| Parameter |
Symbol |
Units |
| Overall heat transfer coefficient |
U |
BTU/hr·ft²·°F |
| Thermal conductivity |
k |
BTU/hr·ft·°F |
| Convection coefficient |
h |
BTU/hr·ft²·°F |
| Mass flow rate |
ṁ |
lb/hr |
| Specific heat |
Cp |
BTU/lb·°F |
2. Overall Heat Transfer Coefficient
The overall U-value combines all thermal resistances in series from fluid to surroundings.
General Equation
Overall U (based on outside area):
1/U_o = (r_o/r_i)/h_i + r_o×ln(r_o/r_i)/k_pipe + r_o×ln(r_ins/r_o)/k_ins + 1/h_o
Where:
U_o = Overall coefficient (BTU/hr·ft²·°F)
r_i = Inside radius (ft)
r_o = Outside radius of pipe (ft)
r_ins = Outside radius of insulation (ft)
h_i = Internal convection coefficient
h_o = External convection coefficient
k = Thermal conductivity
Thermal Conductivity Values
| Material |
k (BTU/hr·ft·°F) |
| Carbon steel |
26–30 |
| Stainless steel |
8–10 |
| Calcium silicate insulation |
0.032–0.045 |
| Mineral wool |
0.023–0.030 |
| Polyurethane foam |
0.012–0.018 |
| Dry soil |
0.15–0.25 |
| Wet soil |
0.6–1.0 |
| Saturated soil |
1.0–1.5 |
Convection Coefficients
Internal (turbulent flow, Dittus-Boelter):
h_i = 0.023 × (k/D) × Re^0.8 × Pr^0.3
External (natural convection, horizontal pipe):
h_o ≈ 1.0–2.0 BTU/hr·ft²·°F (still air)
h_o ≈ 3–10 BTU/hr·ft²·°F (light wind)
Typical pipeline U-values:
Bare pipe in still air: 1.5–2.5 BTU/hr·ft²·°F
Insulated pipe: 0.1–0.5 BTU/hr·ft²·°F
Buried pipe: 0.3–1.0 BTU/hr·ft²·°F
3. Temperature Profile Equations
Temperature varies exponentially along the pipeline, approaching ambient asymptotically.
Steady-State Temperature Profile
Temperature at distance L:
T(L) = T_amb + (T_inlet - T_amb) × exp(-U×π×D×L / (ṁ×Cp))
Or using decay constant:
T(L) = T_amb + (T_inlet - T_amb) × exp(-L/L_c)
Where:
L_c = ṁ×Cp / (U×π×D) = characteristic length (ft)
At L = L_c, temperature difference drops to 37% of inlet difference.
Heat Loss Rate
Total heat loss:
Q = ṁ × Cp × (T_inlet - T_outlet)
Heat loss per unit length:
q = U × π × D × (T_fluid - T_amb) [BTU/hr·ft]
Log mean temperature difference:
LMTD = (ΔT_inlet - ΔT_outlet) / ln(ΔT_inlet/ΔT_outlet)
Q_total = U × A × LMTD
📈 Temperature Profile Along Pipeline
Graph with Distance (miles) on X-axis, Temperature (°F) on Y-axis. Show exponential decay curve from T_inlet approaching T_ambient asymptotically. Mark characteristic length L_c where ΔT drops to 37%. Show second curve for insulated pipeline (slower decay). Include horizontal dashed line for ambient temperature. Label key temperatures and distances.
4. Buried Pipeline Calculations
For buried pipelines, soil thermal resistance replaces external convection. Burial depth significantly affects heat transfer.
Soil Thermal Resistance
Soil resistance (per unit length):
R_soil = ln(2H/D + √((2H/D)² - 1)) / (2π × k_soil)
Simplified for H >> D:
R_soil ≈ ln(4H/D) / (2π × k_soil)
Where:
H = Depth to pipe centerline (ft)
D = Pipe outside diameter (ft)
k_soil = Soil thermal conductivity (BTU/hr·ft·°F)
Buried Pipeline U-Value
Overall U for buried insulated pipe:
1/(U×D) = 1/(h_i×D_i) + ln(D_o/D_i)/(2k_pipe) + ln(D_ins/D_o)/(2k_ins) + R_soil
U = 1 / (D × Σ Resistances)
Ground Temperature
| Depth (ft) |
Temperature Variation |
| Surface |
Follows air temperature |
| 3–4 |
±15°F seasonal swing |
| 6–8 |
±5°F seasonal swing |
| > 15 |
Nearly constant (≈ annual mean air temp) |
Soil moisture: Wet soil conducts heat 3–5× better than dry soil. Design should consider worst-case (wet) conditions for cooling applications and best-case (dry) for heating/maintaining temperature.
5. Applications
Why Temperature Matters
- Hydrate formation: Low temperatures in wet gas cause hydrate plugs
- Wax deposition: Crude oil below WAT (wax appearance temp) deposits paraffin
- Viscosity increase: Heavy oil becomes difficult to pump when cold
- Two-phase flow: Condensation changes flow regime and pressure drop
- Thermal stress: Temperature changes cause pipe expansion/contraction
Example Calculation
Given: 12" buried gas pipeline, 50 miles, inlet 120°F, ground temp 55°F, flow 100 MMSCFD, U = 0.5 BTU/hr·ft²·°F
Step 1: Mass flow rate
ṁ = 100×10⁶ × 0.044 lb/scf / 24 hr = 183,000 lb/hr
Step 2: Characteristic length
Cp = 0.55 BTU/lb·°F, D = 1 ft
L_c = (183,000 × 0.55) / (0.5 × π × 1)
L_c = 64,000 ft = 12.1 miles
Step 3: Outlet temperature
L = 50 miles = 264,000 ft
T_out = 55 + (120-55) × exp(-264,000/320,000)
T_out = 55 + 65 × 0.44 = 55 + 29 = 84°F
Step 4: Heat loss
Q = 183,000 × 0.55 × (120-84) = 3.6 MM BTU/hr
Temperature Maintenance Options
| Method |
Application |
| Insulation |
Reduce heat loss, slow cooling rate |
| Electric heat tracing |
Maintain minimum temp, prevent freezing |
| Steam tracing |
Process plants, short runs |
| Hot oil/water circulation |
Subsea flowlines, heavy oil |
| Direct electrical heating (DEH) |
Subsea pipelines |
References
- GPSA Engineering Data Book, Section 17
- Holman, J.P. – Heat Transfer
- API RP 14E – Offshore Production Platform Piping Systems
- ASME B31.4 / B31.8 – Pipeline Transportation Systems