Pipe Wall Construction and Heat Transfer Modeling

This document describes the pipe wall construction and heat transfer modeling capabilities in NeqSim, including material properties, multi-layer walls, and surrounding environment modeling.

Overview
Pipe Materials
Material Layers
Pipe Wall Assembly
Surrounding Environment
Heat Transfer Calculations
API Reference
Examples

Overview

The pipe wall modeling system in NeqSim provides:

Material database with thermal properties
Multi-layer wall construction (pipe + insulation + coating)
Surrounding environment models (air, water, soil)
Heat transfer resistance calculations
Integration with transient flow simulation

Pipe Materials

Standard Materials

NeqSim includes pre-defined pipe materials with thermal properties:

Material	Thermal Conductivity (W/m·K)	Density (kg/m³)	Specific Heat (J/kg·K)
Carbon Steel	50.0	7850	490
Stainless Steel 316	16.3	8000	500
Duplex Steel	15.0	7800	500
Super Duplex	14.0	7800	500
Titanium	21.9	4500	523
Inconel 625	9.8	8440	410
Monel 400	21.8	8800	427
Copper	401.0	8960	385
HDPE	0.5	960	1800
PVC	0.19	1400	1000
GRP (Fiberglass)	0.3	1850	900

Creating Custom Materials

// Using standard material
PipeMaterial steel = PipeMaterial.CARBON_STEEL;

// Creating custom material
PipeMaterial custom = new PipeMaterial(
    "Custom Alloy",
    25.0,    // thermalConductivity (W/m·K)
    7500,    // density (kg/m³)
    480      // specificHeatCapacity (J/kg·K)
);

Material Properties

Thermal Conductivity ($k$): Ability to conduct heat (W/m·K)
Density ($\rho$): Material mass per unit volume (kg/m³)
Specific Heat Capacity ($C_p$): Energy to raise temperature by 1 K (J/kg·K)
Thermal Diffusivity: $\alpha = k / (\rho C_p)$ (m²/s)

Material Layers

A MaterialLayer combines a material with its thickness:

// Create insulation layer
MaterialLayer insulation = new MaterialLayer(
    "Polyurethane Foam",
    0.025,   // thermalConductivity (W/m·K)
    40,      // density (kg/m³)
    1500,    // specificHeatCapacity (J/kg·K)
    0.05     // thickness (m) = 50 mm
);

// Using pipe material
MaterialLayer pipeWall = new MaterialLayer(
    PipeMaterial.CARBON_STEEL,
    0.012    // thickness = 12 mm
);

Layer Properties

Property	Description	Units
`thickness`	Layer thickness	m
`thermalConductivity`	Heat conduction coefficient	W/(m·K)
`density`	Material density	kg/m³
`specificHeatCapacity`	Thermal capacity	J/(kg·K)

Pipe Wall Assembly

Multi-Layer Construction

The PipeWall class represents a complete pipe wall with multiple layers:

// Method 1: Create layer by layer
PipeWall wall = new PipeWall(0.15);  // inner radius = 150 mm

wall.addLayer(new MaterialLayer(PipeMaterial.CARBON_STEEL, 0.012));
wall.addLayer(new MaterialLayer("Insulation", 0.025, 40, 1500, 0.050));
wall.addLayer(new MaterialLayer("Coating", 0.3, 1200, 1400, 0.005));

// Method 2: Using PipeWallBuilder (fluent API)
PipeWall wall = new PipeWallBuilder()
    .innerRadius(0.15)
    .addPipeLayer(PipeMaterial.CARBON_STEEL, 0.012)
    .addInsulationLayer(0.025, 0.050)
    .addCoatingLayer(0.3, 0.005)
    .build();

Thermal Resistance

The total radial thermal resistance through a cylindrical wall:

\[R_{total} = \sum_{i=1}^{n} R_i = \sum_{i=1}^{n} \frac{\ln(r_{i+1}/r_i)}{2\pi k_i L}\]

Where:

$r_i$ = inner radius of layer $i$ (m)
$r_{i+1}$ = outer radius of layer $i$ (m)
$k_i$ = thermal conductivity of layer $i$ (W/m·K)
$L$ = pipe length (m)

Per unit length:

\[R'_{total} = \sum_{i=1}^{n} \frac{\ln(r_{i+1}/r_i)}{2\pi k_i} \quad \text{(m·K/W)}\]

Key Properties

double outerRadius = wall.getOuterRadius();           // m
double totalThickness = wall.getTotalWallThickness(); // m
double resistance = wall.getTotalResistancePerLength(); // m·K/W
double heatCapacity = wall.getThermalMass();          // J/(m·K)
int layerCount = wall.getLayerCount();

Surrounding Environment

Environment Types

The PipeSurroundingEnvironment class models the external conditions:

Environment	Description	Typical $h$ (W/m²·K)
Still Air	Natural convection	5-25
Moving Air	Forced convection	10-200
Seawater	Subsea pipelines	150-1000
Soil	Buried pipelines	1-10

Creating Environments

// Using factory methods
PipeSurroundingEnvironment air = 
    PipeSurroundingEnvironment.stillAir(25.0);  // 25°C

PipeSurroundingEnvironment seawater = 
    PipeSurroundingEnvironment.seawater(4.0);   // 4°C

PipeSurroundingEnvironment soil = 
    PipeSurroundingEnvironment.soil(15.0, 1.5); // 15°C, k=1.5 W/m·K

// Custom environment
PipeSurroundingEnvironment custom = 
    new PipeSurroundingEnvironment("Wind", 10.0, 50.0);
    // 10°C ambient, h = 50 W/m²·K

Convection Coefficients

Still Air (Natural Convection): $h \approx 5 + 5\sqrt{T_{surface} - T_{ambient}} \quad \text{W/(m²·K)}$

Seawater: $h \approx 150 + 70 \cdot v_{current}^{0.8} \quad \text{W/(m²·K)}$

Soil (Buried Pipe): $h_{equiv} = \frac{k_{soil}}{r_o \cdot \ln(2H/r_o)} \quad \text{W/(m²·K)}$

Where $H$ is burial depth and $r_o$ is outer radius.

Heat Transfer Calculations

Overall Heat Transfer Coefficient

The overall U-value combining all resistances:

\[\frac{1}{U A} = \frac{1}{h_i A_i} + \sum \frac{\ln(r_{o}/r_i)}{2\pi k L} + \frac{1}{h_o A_o}\]

Based on outer surface area:

\[U_o = \frac{1}{r_o \left(\frac{1}{h_i r_i} + \sum \frac{\ln(r_{i+1}/r_i)}{k_i} + \frac{1}{h_o}\right)}\]

Heat Transfer Rate

Heat flow per unit length:

\[q' = U_o \cdot 2\pi r_o \cdot (T_{fluid} - T_{ambient}) \quad \text{W/m}\]

Total heat flow:

\[Q = q' \cdot L = U_o \cdot A_o \cdot \Delta T \quad \text{W}\]

Temperature Profile

The fluid temperature along the pipe (steady-state):

\[T(x) = T_{ambient} + (T_{inlet} - T_{ambient}) \exp\left(-\frac{U_o \cdot \pi D_o}{\dot{m} C_p} x\right)\]

Wall Temperature Distribution

Temperature at interface between layers $j$ and $j+1$:

\[T_j = T_{fluid} - q' \cdot \left(\frac{1}{h_i \cdot 2\pi r_i} + \sum_{k=1}^{j} \frac{\ln(r_{k+1}/r_k)}{2\pi k_k}\right)\]

API Reference

PipeMaterial Enum

public enum PipeMaterial {
    CARBON_STEEL(50.0, 7850, 490),
    STAINLESS_316(16.3, 8000, 500),
    // ... more materials
    
    double getThermalConductivity();
    double getDensity();
    double getSpecificHeatCapacity();
    double getThermalDiffusivity();
}

MaterialLayer Class

public class MaterialLayer {
    // Constructors
    MaterialLayer(String name, double k, double rho, double cp, double t);
    MaterialLayer(PipeMaterial material, double thickness);
    
    // Properties
    double getThickness();
    double getThermalConductivity();
    double getDensity();
    double getSpecificHeatCapacity();
    
    // Calculations
    double getRadialResistance(double innerRadius);
    double getHeatCapacityPerLength(double innerRadius);
}

PipeWall Class

public class PipeWall {
    // Construction
    PipeWall(double innerRadius);
    void addLayer(MaterialLayer layer);
    
    // Properties
    double getInnerRadius();
    double getOuterRadius();
    double getTotalWallThickness();
    int getLayerCount();
    
    // Thermal calculations
    double getTotalResistancePerLength();
    double getUValuePerLength(double hInner, double hOuter);
    double getThermalMass();
}

PipeSurroundingEnvironment Class

public class PipeSurroundingEnvironment {
    // Factory methods
    static stillAir(double ambientTemp);
    static movingAir(double ambientTemp, double windSpeed);
    static seawater(double ambientTemp);
    static soil(double ambientTemp, double thermalConductivity);
    
    // Properties
    double getAmbientTemperature();
    double getConvectionCoefficient();
}

PipeWallBuilder Class

public class PipeWallBuilder {
    PipeWallBuilder innerRadius(double r);
    PipeWallBuilder innerDiameter(double d);
    PipeWallBuilder addLayer(MaterialLayer layer);
    PipeWallBuilder addPipeLayer(PipeMaterial material, double thickness);
    PipeWallBuilder addInsulationLayer(double k, double thickness);
    PipeWallBuilder addCoatingLayer(double k, double thickness);
    PipeWall build();
}

Examples

Example 1: Subsea Pipeline

// Create multi-layer subsea pipe wall
PipeWall subseaPipe = new PipeWallBuilder()
    .innerDiameter(0.254)  // 10" ID
    .addPipeLayer(PipeMaterial.DUPLEX_STEEL, 0.0127)
    .addInsulationLayer(0.15, 0.060)  // Syntactic foam
    .addCoatingLayer(0.22, 0.006)     // Polypropylene
    .build();

// Seawater environment at 4°C
PipeSurroundingEnvironment seawater = 
    PipeSurroundingEnvironment.seawater(4.0);

// Calculate overall U-value
double hInner = 500;   // W/m²·K (turbulent gas flow)
double hOuter = seawater.getConvectionCoefficient();
double U = subseaPipe.getUValuePerLength(hInner, hOuter);

System.out.printf("U-value: %.2f W/(m²·K)%n", U);

Example 2: Buried Gas Pipeline

// Create insulated buried pipeline
PipeWall buriedPipe = new PipeWallBuilder()
    .innerDiameter(0.508)  // 20" ID
    .addPipeLayer(PipeMaterial.CARBON_STEEL, 0.0127)
    .addCoatingLayer(0.22, 0.003)  // FBE coating
    .build();

// Soil at 12°C, buried 1.5m deep
PipeSurroundingEnvironment soil = 
    PipeSurroundingEnvironment.soil(12.0, 1.2);

// Print configuration
System.out.printf("Wall thickness: %.1f mm%n", 
    buriedPipe.getTotalWallThickness() * 1000);
System.out.printf("Total resistance: %.4f m·K/W%n", 
    buriedPipe.getTotalResistancePerLength());

Example 3: Temperature Profile Calculation

// Pipeline parameters
double length = 50000;     // 50 km
double mDot = 15.0;        // kg/s
double Cp = 2500;          // J/(kg·K) - gas
double Tinlet = 80;        // °C
double Tambient = 5;       // °C
double Uo = 2.5;           // W/(m²·K) - overall U-value
double Do = 0.32;          // m - outer diameter

// Calculate outlet temperature
double exponent = -Uo * Math.PI * Do * length / (mDot * Cp);
double Toutlet = Tambient + (Tinlet - Tambient) * Math.exp(exponent);

System.out.printf("Outlet temperature: %.1f °C%n", Toutlet);
System.out.printf("Heat loss: %.0f kW%n", mDot * Cp * (Tinlet - Toutlet) / 1000);

Example 4: Integration with Flow Simulation

// Create fluid
SystemInterface gas = new SystemSrkEos(323.15, 50e5);
gas.addComponent("methane", 0.9);
gas.addComponent("ethane", 0.07);
gas.addComponent("propane", 0.03);
gas.setMixingRule("classic");

// Create inlet stream
Stream inlet = new Stream("Inlet", gas);
inlet.setFlowRate(500000, "kg/hr");
inlet.run();

// Create pipeline with heat transfer
OnePhasePipeLine pipe = new OnePhasePipeLine("Export", inlet);
pipe.setNumberOfLegs(1);
pipe.setNumberOfNodesInLeg(100);
pipe.setPipeDiameters(new double[] {0.508, 0.508});
pipe.setLegPositions(new double[] {0.0, 50000.0});
pipe.setOuterTemperature(278.15);  // 5°C ambient

// Run steady-state
pipe.run();

// Get outlet conditions
System.out.printf("Outlet T: %.1f °C%n", 
    pipe.getOutStream().getTemperature("C"));
System.out.printf("Outlet P: %.1f bara%n", 
    pipe.getOutStream().getPressure("bara"));

References

Incropera, F.P. & DeWitt, D.P. (2011). Fundamentals of Heat and Mass Transfer. Wiley.
GPSA Engineering Data Book. Gas Processors Suppliers Association.
API 5L - Specification for Line Pipe.
DNVGL-ST-F101 - Submarine Pipeline Systems.

Pipe Wall Construction and Heat Transfer Modeling

Comprehensive Java library for thermodynamic, physical property, and process simulation. NeqSim provides tools for PVT analysis, phase equilibria, transport properties, and full process simulation.

Pipe Wall Construction and Heat Transfer Modeling

Table of Contents

Overview

Pipe Materials

Standard Materials

Creating Custom Materials

Material Properties

Material Layers

Layer Properties

Pipe Wall Assembly

Multi-Layer Construction

Thermal Resistance

Key Properties

Surrounding Environment

Environment Types

Creating Environments

Convection Coefficients

Heat Transfer Calculations

Overall Heat Transfer Coefficient

Heat Transfer Rate

Temperature Profile

Wall Temperature Distribution

API Reference

PipeMaterial Enum

MaterialLayer Class

PipeWall Class

PipeSurroundingEnvironment Class

PipeWallBuilder Class

Examples

Example 1: Subsea Pipeline

Example 2: Buried Gas Pipeline

Example 3: Temperature Profile Calculation

Example 4: Integration with Flow Simulation

References