Heat Transfer

Pipeline Temperature Drop

Calculate temperature drop in pipelines using overall heat transfer coefficient, insulation properties, burial depth, and ambient conditions for flow assurance, hydrate prevention, and thermal design per GPSA standards.

Launch Calculator Heat transfer coefficient

Typical U-value

0.1-1.0 Btu/hr·ft²·°F

Bare pipe: 1-2. Insulated: 0.1-0.3. Buried uninsulated: 0.3-0.6 Btu/hr·ft²·°F.

Temp drop rate

1-5°F per mile

Typical above-ground gas pipeline: 1-3°F/mile. Buried: 0.5-1.5°F/mile depending on insulation.

Critical length

Hydrate formation

Calculate maximum distance before temp drops below hydrate point: critical for flow assurance.

Contents

Quick start

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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
Cross-section of insulated buried pipe showing five thermal resistance layers from fluid core to soil with temperature profile dropping through each layer and R_total equation
Thermal resistances in series: Internal film (R₁), pipe wall (R₂), insulation (R₃), coating (R₄), and soil/air (R₅) determine overall heat loss.

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
Graph showing exponential temperature decay along pipeline for insulated and uninsulated cases, with characteristic length L_c marked where temperature drop reaches 37% of initial difference
Temperature decay: Insulation extends effective transport distance approximately 3× by reducing heat loss rate; L_c indicates 37% ΔT remaining.

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. Joule-Thomson Cooling at Pressure Reduction

Unlike gradual heat loss along a pipeline, Joule-Thomson (J-T) cooling occurs instantaneously at pressure reduction points—control valves, regulators, chokes, and orifice plates. This isenthalpic expansion causes significant temperature drops that can trigger hydrate formation.

The Joule-Thomson Effect

When gas expands through a throttling device with no heat exchange (isenthalpic process), temperature changes due to intermolecular forces. For most gases at typical pipeline conditions, expansion causes cooling.

Temperature drop across valve: ΔT = μ_JT × ΔP Where: μ_JT = Joule-Thomson coefficient (°F/psi) ΔP = Pressure drop (psi) Rule of thumb (natural gas): ΔT ≈ 6-7°F per 100 psi pressure drop

Rigorous J-T Coefficient Calculation

The calculator uses peer-reviewed correlations for accurate J-T coefficient estimation based on reduced temperature and pressure.

Property Correlation Reference
Pseudo-critical temperature T_pc = 169.2 + 349.5×SG - 74.0×SG² Sutton (1985)
Pseudo-critical pressure P_pc = 756.8 - 131.0×SG - 3.6×SG² Sutton (1985)
J-T coefficient function f(Pr,Tr) = 2.343×Tr^(-2.04) - 0.071×Pr + 0.0568 ACS Omega (2021)
Full J-T coefficient equation: μ_JT = (T_pc / P_pc) × f(Pr, Tr) / Cp × 0.058 Where: Pr = P / P_pc (reduced pressure) Tr = T / T_pc (reduced temperature, °R) Cp = Specific heat capacity (BTU/lb·°F) T in Rankine, P in psia 0.058 = calibration factor to match measured data

Step-Wise Integration

For large pressure drops (>150 psi), the J-T coefficient varies significantly. The calculator uses step-wise integration:

  • Divide total ΔP into 50 psi increments
  • Recalculate μ_JT at each step using updated T and P
  • Sum temperature drops: ΔT_total = Σ(μ_JT,i × ΔP_step)

This approach improves accuracy for large pressure drops from regulators or choke valves.

Hydrate Temperature Prediction

Hydrates form when gas temperature drops below the hydrate equilibrium temperature. The calculator averages two industry correlations:

Correlation Equation Valid Range
Katz (1945) T_hyd = -54.5 + 13.1×ln(P) + 40×γ 0.6 < SG < 0.9
Towler-Mokhatab (2005) T_hyd = 13.47×ln(P) + 34.27×ln(γ) - 1.675×ln(P)×ln(γ) - 20.35 Modern refinement
Safety margin: The calculator compares downstream temperature to hydrate temperature. A margin <10°F triggers warnings; negative margin indicates high hydrate risk requiring mitigation (line heater, methanol injection, or dehydration).

Example: Pressure Regulation Station

Given: Natural gas (SG=0.65), P1=800 psia, T1=80°F, P2=250 psia

Step 1: Pseudo-critical properties
T_pc = 169.2 + 349.5(0.65) - 74.0(0.65)² = 365°R
P_pc = 756.8 - 131.0(0.65) - 3.6(0.65)² = 670 psia

Step 2: J-T coefficient (at inlet)
Tr = 540°R / 365°R = 1.48
Pr = 800 / 670 = 1.19
Cp = 0.48 BTU/lb·°F
f(Pr,Tr) = 2.343(1.48)^(-2.04) - 0.071(1.19) + 0.0568 = 1.03
μ_JT = (365/670) × 1.03 / 0.48 × 0.058 = 0.068°F/psi

Step 3: Temperature drop (step-wise)
ΔP = 550 psi (11 steps of 50 psi)
ΔT_total ≈ 42°F (varies through integration)
T_downstream = 80 - 42 = 38°F

Step 4: Hydrate check
T_hydrate @ 250 psia ≈ 44°F (Katz + Towler avg)
Margin = 38 - 44 = -6°F (HYDRATE RISK!)

Pure Component J-T Coefficients

For pure gases and non-hydrocarbon components, the calculator uses published J-T coefficients from GPSA and Katz. The rigorous correlation above is used only for natural gas mixtures (SG 0.55–0.85).

Gas μ_JT (°F/psi) Notes
Methane (C₁) 0.072 Primary NG component
Ethane (C₂) 0.105 Higher MW = larger effect
Propane (C₃) 0.095 Moderate J-T effect
Nitrogen (N₂) 0.015 Low J-T effect
Carbon Dioxide (CO₂) 0.028 Acid gas component
Air 0.025 Reference gas
Hydrogen (H₂) -0.005 Heats on expansion (inverts)
Hydrogen note: H₂ has a negative J-T coefficient at typical temperatures—it heats upon expansion rather than cooling. This is important for hydrogen pipeline and fuel cell applications.

6. 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" insulated buried gas pipeline, 50 miles, inlet 120°F, ground temp 55°F, flow 100 MMSCFD, U = 0.10 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) / (0.10 × π × 1)
L_c = 320,000 ft = 61 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) = 3.7 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, Sections 13, 17, 20
  • Holman, J.P. – Heat Transfer
  • API RP 14E – Offshore Production Platform Piping Systems
  • ASME B31.4 / B31.8 – Pipeline Transportation Systems
  • Sutton, R.P. (1985) – "Compressibility Factors for High-Molecular-Weight Reservoir Gases", SPE 14265
  • ACS Omega (2021) – "Joule-Thomson Coefficient Correlation for Natural Gas"
  • Katz, D.L. (1945) – "Prediction of Conditions for Hydrate Formation in Natural Gases"
  • Towler, B.F. & Mokhatab, S. (2005) – "Quickly Estimate Hydrate Formation Conditions in Natural Gases"

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