Heat Transfer in Pipelines

Overview

NeqSim’s PipeBeggsAndBrills class supports non-adiabatic operation with heat exchange to/from the surroundings. This is important for:

Heat Transfer Modes

1. Adiabatic (Default)

No heat exchange with surroundings:

pipe.setRunAdiabatic(true);  // Default

2. Constant Surface Temperature

Heat transfer with fixed ambient temperature:

pipe.setRunAdiabatic(false);
pipe.setRunConstantSurfaceTemperature(true);
pipe.setConstantSurfaceTemperature(277.15);  // 4°C (seawater)

3. Specified Heat Transfer Coefficient

pipe.setHeatTransferCoefficient(50.0);  // W/m²K

4. Estimated Heat Transfer

Uses internal correlations:

pipe.setHeatTransferCoefficientMethod("Estimated");

Heat Transfer Equations

Overall Heat Balance

The temperature change across a segment is calculated from:

\[\dot{Q} = U \cdot A \cdot \Delta T_{lm}\]

Where:

Log-Mean Temperature Difference

\[\Delta T_{lm} = \frac{(T_s - T_{out}) - (T_s - T_{in})}{\ln\left(\frac{T_s - T_{out}}{T_s - T_{in}}\right)}\]

Where:

Gnielinski Correlation

For internal convection in turbulent flow (3000 < Re < 5×10⁶):

\[Nu = \frac{(f/8)(Re - 1000)Pr}{1 + 12.7\sqrt{f/8}(Pr^{2/3} - 1)}\]

Where:

The internal heat transfer coefficient: \(h_{internal} = \frac{Nu \cdot k}{D}\)

Typical Heat Transfer Coefficients

Overall U-Values (Pipeline + Insulation)

Configuration U (W/m²K) Application
Bare steel in air 10-25 Onshore exposed
Bare steel in water 300-500 Uninsulated subsea
25mm insulation 3-5 Standard insulated
50mm insulation 1.5-3 Well insulated
75mm+ insulation <1.5 Heavily insulated
Pipe-in-pipe 0.5-2 High spec subsea

Internal Convection Coefficients

Fluid h_internal (W/m²K)
Gas (low P) 20-50
Gas (high P) 100-300
Light oil 100-300
Heavy oil 50-150
Water 1000-5000
Two-phase 200-1000

Usage Examples

Subsea Pipeline Cooling

SystemInterface gas = new SystemSrkEos(353.15, 100.0);  // 80°C wellhead
gas.addComponent("methane", 0.85);
gas.addComponent("ethane", 0.10);
gas.addComponent("propane", 0.05);
gas.setMixingRule(2);

Stream wellhead = new Stream("wellhead", gas);
wellhead.setFlowRate(100000, "kg/hr");
wellhead.run();

PipeBeggsAndBrills subsea = new PipeBeggsAndBrills("subsea", wellhead);
subsea.setLength(20000);           // 20 km
subsea.setDiameter(0.254);         // 10 inch
subsea.setElevation(-200);         // 200m water depth
subsea.setPipeWallRoughness(4.6e-5);
subsea.setNumberOfIncrements(40);

// Heat transfer to seawater
subsea.setRunAdiabatic(false);
subsea.setRunConstantSurfaceTemperature(true);
subsea.setConstantSurfaceTemperature(277.15);  // 4°C seabed
subsea.setHeatTransferCoefficient(5.0);        // Insulated

subsea.run();

double outletTemp = subsea.getOutletTemperature() - 273.15;
System.out.println("Arrival temperature: " + outletTemp + " °C");

Temperature Profile

// Get temperature along the pipeline
List<Double> tempProfile = subsea.getTemperatureProfile();
double segmentLength = 20000.0 / 40;

for (int i = 0; i < tempProfile.size(); i++) {
    double distance = i * segmentLength / 1000.0;  // km
    double tempC = tempProfile.get(i) - 273.15;
    System.out.println(distance + " km: " + tempC + " °C");
}

Hydrate and Wax Considerations

Hydrate Formation

Monitor temperature relative to hydrate equilibrium:

double hydroEqTemp = ...; // From hydrate flash
double margin = outletTemp - hydroEqTemp;
if (margin < 5.0) {
    System.out.println("WARNING: Close to hydrate region");
}

Wax Appearance

Check against wax appearance temperature (WAT):

double WAT = ...; // From wax analysis
if (outletTemp < WAT) {
    System.out.println("WARNING: Below WAT - wax may deposit");
}

Limitations

  1. Steady-state heat transfer: No thermal mass of pipe wall
  2. Constant ambient: No variation along pipe length
  3. Single U-value: Same coefficient for entire pipe
  4. No Joule-Thomson: Expansion cooling handled separately

Best Practices

1. Segment Sizing for Heat Transfer

Use more segments for accurate temperature profiles:

pipe.setNumberOfIncrements(50);  // For long, cooling pipelines

2. Validate Against Simple Cases

For long pipes with large temperature change, check: \(T_{out} \approx T_s + (T_{in} - T_s) \cdot e^{-UAL/(\dot{m}c_p)}\)

3. Consider Two-Phase Effects

Heat transfer coefficients are higher for two-phase flow due to turbulence.

See Also