Overview

The TransientPipe class provides a 1D transient multiphase (gas-liquid) flow simulator for pipelines. It uses the drift-flux formulation combined with mechanistic flow regime detection to model complex phenomena like terrain-induced slugging, liquid accumulation at low points, and transient pressure wave propagation.

The model supports:

Key Features

Physical Models

Drift-Flux Model

The core model uses the Zuber-Findlay drift-flux formulation:

\[v_G = C_0 v_m + v_d\]

Where:

The distribution coefficient C₀ and drift velocity v_d depend on the flow regime:

Flow Regime C₀ Drift Velocity Correlation
Bubble 1.2 Harmathy (1960)
Slug 1.05-1.2 (Fr dependent) Bendiksen (1984)
Annular 1.0 Film drainage model
Stratified Calculated from momentum balance ~0

Three-Phase Flow Handling

When both oil and aqueous (water) liquid phases are present, the model calculates volume-weighted average liquid properties:

\[\begin{aligned} \rho_{L,\mathrm{avg}} &= \frac{V_{\mathrm{oil}}}{V_{\mathrm{total}}}\rho_{\mathrm{oil}} + \frac{V_{\mathrm{water}}}{V_{\mathrm{total}}}\rho_{\mathrm{water}}, \\ \mu_{L,\mathrm{avg}} &= \frac{V_{\mathrm{oil}}}{V_{\mathrm{total}}}\mu_{\mathrm{oil}} + \frac{V_{\mathrm{water}}}{V_{\mathrm{total}}}\mu_{\mathrm{water}}, \\ H_{L,\mathrm{avg}} &= \frac{V_{\mathrm{oil}}}{V_{\mathrm{total}}}H_{\mathrm{oil}} + \frac{V_{\mathrm{water}}}{V_{\mathrm{total}}}H_{\mathrm{water}}, \\ c_{L,\mathrm{avg}} &= \frac{V_{\mathrm{oil}}}{V_{\mathrm{total}}}c_{\mathrm{oil}} + \frac{V_{\mathrm{water}}}{V_{\mathrm{total}}}c_{\mathrm{water}}. \end{aligned}\]

Where:

This approach maintains the drift-flux framework while properly accounting for oil-water mixtures in the liquid phase. If only one liquid phase is present (oil OR water), that phase’s properties are used directly.

Flow Regime Detection

The model supports two methods for flow regime detection:

Mechanistic Approach (Default)

Uses mechanistic criteria to determine the local flow pattern:

  1. Single-Phase Check: If liquid holdup < 0.001 → Gas; if gas holdup < 0.001 → Liquid
  2. Taitel-Dukler (1976) for horizontal/near-horizontal pipes:
    • Stratified-Slug transition based on Kelvin-Helmholtz stability
    • Uses Lockhart-Martinelli parameter and Froude numbers
  3. Barnea (1987) for inclined pipes:
    • Unified model covering all inclinations
    • Bubble-slug transition at void fraction ≈ 0.25
    • Annular transition at high gas velocities

Minimum Slip Criterion

An alternative approach that selects the flow regime with the minimum slip ratio (closest to 1.0, i.e., homogeneous flow). This is based on the principle that the physical system naturally tends toward the flow pattern with minimum phase velocity difference.

FlowRegimeDetector detector = new FlowRegimeDetector();

// Enable minimum slip criterion
detector.setUseMinimumSlipCriterion(true);

// Or use the detection method enum
detector.setDetectionMethod(FlowRegimeDetector.DetectionMethod.MINIMUM_SLIP);

// Detect flow regime
FlowRegime regime = detector.detectFlowRegime(section);

The minimum slip criterion evaluates orientation-appropriate candidate regimes:

Numerical Method

The model solves the conservation equations using:

Conservative variables:

U = [ρ_G·α_G, ρ_L·α_L, ρ_m·u, ρ_m·e]

Quick Start

Basic Horizontal Pipeline

import org.apache.logging.log4j.LogManager;
import org.apache.logging.log4j.Logger;
import neqsim.process.equipment.pipeline.twophasepipe.LiquidAccumulationTracker;
import neqsim.process.equipment.pipeline.twophasepipe.TransientPipe;
import neqsim.process.equipment.stream.Stream;
import neqsim.thermo.system.SystemInterface;
import neqsim.thermo.system.SystemSrkEos;

// Define this as a class field in the enclosing example class.
private static final Logger logger =
    LogManager.getLogger("TransientPipeExample");

// Create two-phase fluid
SystemInterface fluid = new SystemSrkEos(300, 50); // 300 K, 50 bar
fluid.addComponent("methane", 0.8);
fluid.addComponent("n-pentane", 0.2);
fluid.setMixingRule("classic");
fluid.setMultiPhaseCheck(true);

// Create inlet stream
Stream inlet = new Stream("inlet", fluid);
inlet.setFlowRate(5, "kg/sec");
inlet.run();

// Create transient pipe
TransientPipe pipe = new TransientPipe("Pipeline", inlet);
pipe.setLength(1000);          // 1000 m
pipe.setDiameter(0.2);         // 200 mm
pipe.setRoughness(0.00005);    // 50 μm
pipe.setNumberOfSections(50);  // 50 cells
pipe.setMaxSimulationTime(60); // 60 seconds

// Run simulation
pipe.run();

// Get results
double[] pressures = pipe.getPressureProfile();
double[] holdups = pipe.getLiquidHoldupProfile();
double[] gasVel = pipe.getGasVelocityProfile();

Terrain Pipeline with Low Points

// Create pipe with terrain
TransientPipe pipe = new TransientPipe("TerrainPipe", inlet);
pipe.setLength(2000);
pipe.setDiameter(0.3);
pipe.setNumberOfSections(40);
pipe.setMaxSimulationTime(300);

// Define elevation profile with a low point
double[] elevations = new double[40];
for (int i = 0; i < 40; i++) {
    double x = i * 50.0; // Position along pipe
    if (x < 500) {
        elevations[i] = 0;
    } else if (x < 1000) {
        elevations[i] = -20 * (x - 500) / 500; // Downhill to -20m
    } else if (x < 1500) {
        elevations[i] = -20 + 20 * (x - 1000) / 500; // Uphill
    } else {
        elevations[i] = 0;
    }
}
pipe.setElevationProfile(elevations);

pipe.run();

// Check for liquid accumulation
LiquidAccumulationTracker accumulationTracker = pipe.getAccumulationTracker();
for (LiquidAccumulationTracker.AccumulationZone zone
        : accumulationTracker.getAccumulationZones()) {
    logger.info("Zone starts at: {} m", zone.startPosition);
    logger.info("Accumulated volume: {} m³", zone.liquidVolume);
}

Vertical Riser

TransientPipe riser = new TransientPipe("Riser", inlet);
riser.setLength(200);
riser.setDiameter(0.15);
riser.setNumberOfSections(40);

// Vertical profile
double[] elevations = new double[40];
for (int i = 0; i < 40; i++) {
    elevations[i] = i * 5; // 5m per section
}
riser.setElevationProfile(elevations);

riser.run();

// Significant pressure drop due to hydrostatic head
double[] P = riser.getPressureProfile();

Three-Phase Gas-Oil-Water Flow

// Create three-phase fluid
SystemInterface fluid = new SystemSrkEos(300, 50);
fluid.addComponent("methane", 0.40);
fluid.addComponent("propane", 0.10);
fluid.addComponent("n-heptane", 0.20);
fluid.addComponent("n-octane", 0.10);
fluid.addComponent("water", 0.20);
fluid.setMixingRule("classic");
fluid.setMultiPhaseCheck(true);

// Create stream and pipe
Stream inlet = new Stream("inlet", fluid);
inlet.setFlowRate(15, "kg/sec");
inlet.run();

TransientPipe pipe = new TransientPipe("ThreePhasePipe", inlet);
pipe.setLength(1000);
pipe.setDiameter(0.25);
pipe.setNumberOfSections(50);
pipe.run();

// The model automatically uses volume-weighted averaging for liquid properties
// when both oil and aqueous phases are present.
double[] pressure = pipe.getPressureProfile(); // Pa
double deltaPBar = (pressure[0] - pressure[pressure.length - 1]) / 1.0e5;
logger.info("Pipeline pressure drop: {} bar", deltaPBar);

Configuration Options

Geometry

Method Description Default
setLength(double) Total pipe length (m) -
setDiameter(double) Inner diameter (m) -
setRoughness(double) Wall roughness (m) 0.0001
setNumberOfSections(int) Discretization cells 50
setElevationProfile(double[]) Elevation at each node (m) null (horizontal)
setInclinationProfile(double[]) Inclination angles (rad) null

Simulation Control

Method Description Default
setMaxSimulationTime(double) Total simulation time (s) 3600
setCflNumber(double) CFL number (0.1-1.0) 0.5
setThermodynamicUpdateInterval(int) Flash update frequency 10
setUpdateThermodynamics(boolean) Enable/disable thermo updates true

Boundary Conditions

The default inlet boundary is CONSTANT_FLOW, and the default outlet boundary is CONSTANT_PRESSURE. The connected inlet stream supplies the mass flow during initialization and is re-read by each runTransient() call, so set the initial flow with inlet.setFlowRate(...) as shown in the quick start. Set a receiving pressure explicitly before the first run() or runTransient() call when the downstream pressure is known:

import java.util.UUID;
import neqsim.process.equipment.pipeline.twophasepipe.TransientPipe.BoundaryCondition;

pipe.setInletBoundaryCondition(BoundaryCondition.CONSTANT_FLOW);

pipe.setOutletBoundaryCondition(BoundaryCondition.CONSTANT_PRESSURE);
double specifiedOutletPressure = 30.0; // bara
pipe.setOutletPressure(specifiedOutletPressure);

// A zero-duration first call initializes the profiles without advancing time.
pipe.runTransient(0.0, UUID.randomUUID());
double[] initialPressure = pipe.getPressureProfile(); // Pa
double initializedOutletPressure =
    initialPressure[initialPressure.length - 1] / 1.0e5;
if (Math.abs(initializedOutletPressure - specifiedOutletPressure) > 1.0e-6) {
    throw new IllegalStateException("Outlet pressure boundary was not preserved");
}

setOutletPressure(double) accepts absolute pressure in bara. An explicit value is retained while the pipe is initialized and is imposed at the final computational section for a CONSTANT_PRESSURE outlet. If the setter is not called, initialization estimates the outlet pressure from inlet pressure, elevation, and friction and applies a lower bound of 1 bara. This estimate is an initial condition, not a substitute for a known receiving-system pressure.

Type Description
CONSTANT_PRESSURE Fixed pressure boundary
CONSTANT_FLOW Fixed mass flow rate
CONSTANT_VELOCITY Fixed velocity
CLOSED No-flow wall

Output Results

Profile Data

// Spatial profiles at end of simulation
double[] pressure = pipe.getPressureProfile();      // Pa
double[] temperature = pipe.getTemperatureProfile(); // K
double[] liquidHoldup = pipe.getLiquidHoldupProfile(); // fraction
double[] gasVelocity = pipe.getGasVelocityProfile();   // m/s
double[] liquidVelocity = pipe.getLiquidVelocityProfile(); // m/s

Time History

// Pressure history at all locations
double[][] pressureHistory = pipe.getPressureHistory();
// pressureHistory[time_index][position_index]

Slug Statistics

SlugTracker slugTracker = pipe.getSlugTracker();

int activeSlugCount = slugTracker.getSlugCount();
int totalGenerated = slugTracker.getTotalSlugsGenerated();
double avgLength = slugTracker.getAverageSlugLength();
double frequency = slugTracker.getSlugFrequency();

// Detailed statistics
String stats = slugTracker.getStatisticsString();
logger.info("{}", stats);

Note: Both TransientPipe (drift-flux) and TwoFluidPipe (two-fluid) use the same SlugTracker and LiquidAccumulationTracker components, but may predict different slug frequencies due to their underlying holdup models. See the Two-Fluid Model documentation for a detailed comparison.

Accumulation Zones

LiquidAccumulationTracker tracker = pipe.getAccumulationTracker();

for (LiquidAccumulationTracker.AccumulationZone zone
        : tracker.getAccumulationZones()) {
    logger.info("Zone start: {} m", zone.startPosition);
    logger.info("Zone end: {} m", zone.endPosition);
    logger.info("Accumulated volume: {} m³", zone.liquidVolume);
    logger.info("Maximum volume: {} m³", zone.maxVolume);
    logger.info("Is overflowing: {}", zone.isOverflowing);
}

Advanced Usage

Custom Flow Regime Detection

PipeSection[] sections = pipe.getSections();
FlowRegimeDetector detector = new FlowRegimeDetector();

for (PipeSection section : sections) {
    FlowRegime regime = detector.detectFlowRegime(section);
    logger.info("Position {}: {}", section.getPosition(), regime);
}

Drift-Flux Analysis

DriftFluxModel model = new DriftFluxModel();

for (PipeSection section : sections) {
    DriftFluxParameters params = model.calculateDriftFlux(section);
    
    logger.info("C0 = {}", params.C0);
    logger.info("Drift velocity = {} m/s", params.driftVelocity);
    logger.info("Void fraction = {}", params.voidFraction);
    logger.info("Slip ratio = {}", params.slipRatio);
}

Accessing Individual Sections

PipeSection[] sections = pipe.getSections();

for (int i = 0; i < sections.length; i++) {
    PipeSection s = sections[i];
    
    logger.info("Section {} (x={} m)", i, s.getPosition());
    logger.info("Pressure: {} bar", s.getPressure() / 1.0e5);
    logger.info("Temperature: {} K", s.getTemperature());
    logger.info("Liquid holdup: {}", s.getLiquidHoldup());
    logger.info("Gas velocity: {} m/s", s.getGasVelocity());
    logger.info("Liquid velocity: {} m/s", s.getLiquidVelocity());
    logger.info("Flow regime: {}", s.getFlowRegime());
    logger.info("Is low point: {}", s.isLowPoint());
}

Integration with ProcessSystem

import neqsim.process.processmodel.ProcessSystem;

ProcessSystem process = new ProcessSystem();

// Add inlet stream
Stream inlet = new Stream("inlet", fluid);
inlet.setFlowRate(10, "kg/sec");
process.add(inlet);

// Add transient pipe
TransientPipe pipeline = new TransientPipe("MainPipeline", inlet);
pipeline.setLength(5000);
pipeline.setDiameter(0.4);
pipeline.setNumberOfSections(100);
pipeline.setMaxSimulationTime(600);
process.add(pipeline);

// Add downstream equipment
Stream outlet = pipeline.getOutletStream();
// ... add separators, compressors, etc.

process.run();

Performance Considerations

Spatial Resolution

Time Step

Thermodynamic Updates

Flow Regime Definitions

Regime Description Typical Conditions
SINGLE_PHASE_GAS Gas only α_L < 0.001
SINGLE_PHASE_LIQUID Liquid only α_G < 0.001
BUBBLE Discrete bubbles in liquid Low gas velocity, vertical
SLUG Alternating liquid slugs and gas bubbles Moderate velocities
STRATIFIED_SMOOTH Separated phases, smooth interface Low velocities, horizontal
STRATIFIED_WAVY Separated phases, wavy interface Moderate velocities, horizontal
ANNULAR Liquid film on wall, gas core High gas velocity
CHURN Chaotic, oscillating flow High velocities, vertical

Troubleshooting

Simulation Instability

Symptoms: NaN values, oscillations, crashes

Solutions:

  1. Reduce CFL number: pipe.setCflNumber(0.3)
  2. Increase number of sections
  3. Check for unrealistic boundary conditions
  4. Verify fluid properties are physical

Slow Performance

Solutions:

  1. Reduce number of sections
  2. Increase thermodynamic update interval
  3. Use simpler equation of state
  4. Reduce simulation time

No Slugs Detected

Possible causes:

  1. Flow is single-phase (check inlet conditions)
  2. Pipe too short for slug development
  3. Velocities outside slug regime
  4. No terrain variation (add elevation profile)

References

  1. Taitel, Y. and Dukler, A.E. (1976). “A Model for Predicting Flow Regime Transitions in Horizontal and Near Horizontal Gas-Liquid Flow.” AIChE Journal, 22(1), 47-55.

  2. Barnea, D. (1987). “A Unified Model for Predicting Flow-Pattern Transitions for the Whole Range of Pipe Inclinations.” Int. J. Multiphase Flow, 13(1), 1-12.

  3. Bendiksen, K.H. (1984). “An Experimental Investigation of the Motion of Long Bubbles in Inclined Tubes.” Int. J. Multiphase Flow, 10(4), 467-483.

  4. Zuber, N. and Findlay, J.A. (1965). “Average Volumetric Concentration in Two-Phase Flow Systems.” J. Heat Transfer, 87(4), 453-468.

  5. Harmathy, T.Z. (1960). “Velocity of Large Drops and Bubbles in Media of Infinite or Restricted Extent.” AIChE Journal, 6(2), 281-288.

Comparison with Beggs and Brill Correlation

Overview

The TransientPipe model uses a different approach than empirical correlations like Beggs and Brill (1973). Understanding these differences helps in selecting the appropriate model for your application.

Model Comparison

Aspect TransientPipe Beggs and Brill
Approach Mechanistic drift-flux with AUSM+ scheme Empirical correlation from experiments
Basis Conservation equations + closure relations ~1500 experimental data points
Flow Regimes Taitel-Dukler, Barnea criteria Froude number based map
Transient Full transient capability Steady-state only
Terrain Section-by-section integration Overall correlation

Expected Differences

The models can differ materially because they use different conservation, holdup, slip, and flow-regime treatments. Do not use a fixed percentage as an acceptance tolerance: the difference depends on fluid, geometry, boundary conditions, discretization, and whether the transient solution has reached the intended comparison state. Compare like-for-like pressure, temperature, flow, and elevation boundaries and report the complete configuration with each benchmark result.

When to Use Each Model

Use TransientPipe when:

Use Beggs and Brill when:

Validation Approach

For critical applications, it is recommended to:

  1. Benchmark both models against field data or detailed CFD simulations
  2. Understand model assumptions - TransientPipe uses mechanistic closure relations that may need tuning for specific fluids
  3. Quantify uncertainty for the case - derive uncertainty from relevant measurements, parameter sensitivity, and model-form comparisons rather than a generic percentage
  4. Use multiple models - consensus from different approaches increases confidence

Comparison Test Examples

NeqSim includes comparison tests in TransientPipeVsBeggsAndBrillsComparisonTest.java:

// Example: Comparing models for horizontal multiphase flow
SystemInterface fluid = new SystemSrkEos(300.0, 50.0);
fluid.addComponent("methane", 0.8);
fluid.addComponent("n-pentane", 0.2);
fluid.setMixingRule("classic");
fluid.setMultiPhaseCheck(true);

// Setup Beggs and Brill
Stream bbStream = new Stream("BB_inlet", fluid);
bbStream.setFlowRate(2.0, "kg/sec");
bbStream.run();

PipeBeggsAndBrills bb = new PipeBeggsAndBrills("BeggsAndBrill", bbStream);
bb.setDiameter(0.2);
bb.setLength(500);
bb.setAngle(0);
bb.run();
double dpBeggsBrill = bb.getPressureDrop();

// Setup TransientPipe
Stream tpStream = new Stream("TP_inlet", fluid.clone());
tpStream.setFlowRate(2.0, "kg/sec");
tpStream.run();

TransientPipe tp = new TransientPipe("TransientPipe", tpStream);
tp.setLength(500);
tp.setDiameter(0.2);
tp.setNumberOfSections(25);
tp.setMaxSimulationTime(60);
tp.run();
double[] pressures = tp.getPressureProfile();
double dpTransient = (pressures[0] - pressures[pressures.length - 1]) / 1e5;

logger.info("Beggs & Brill: {} bar", dpBeggsBrill);
logger.info("TransientPipe: {} bar", dpTransient);

References for Model Comparison

  1. Beggs, H.D. and Brill, J.P. (1973). “A Study of Two-Phase Flow in Inclined Pipes.” Journal of Petroleum Technology, 25(5), 607-617.

  2. Ishii, M. and Hibiki, T. (2011). Thermo-Fluid Dynamics of Two-Phase Flow. 2nd ed. Springer.

See Also