TwoFluidPipe Model Documentation

Overview

The NeqSim TwoFluidPipe model implements a transient two-fluid multiphase flow solver for pipeline and riser simulations. It solves separate conservation equations for gas and liquid phases, enabling accurate prediction of:

This document provides comprehensive documentation of the model’s capabilities, governing equations, and usage.

Conservation Equations

Mass Conservation

Separate mass conservation equations for gas and liquid phases:

Equation Mathematical Form Description
Gas mass ∂(αG ρG)/∂t + ∂(αG ρG vG)/∂x = ΓG Gas phase continuity with mass transfer
Liquid mass ∂(αL ρL)/∂t + ∂(αL ρL vL)/∂x = -ΓG Liquid phase continuity with mass transfer
Mass transfer ΓG Flash-based calculation Evaporation/condensation with optional kinetic limits

Where:

Momentum Conservation

Separate momentum equations for each phase:

Component Implementation
Gas momentum Full 1D momentum with wall shear, interfacial shear, pressure gradient
Liquid momentum Full 1D momentum with wall shear, interfacial shear, pressure gradient
Wall friction Pipe roughness-based (Colebrook/Blasius correlations)
Interfacial friction Flow-regime dependent correlations

Energy Conservation

| Feature | Description | |———|————-| | Mixture energy equation | Full energy balance including kinetic and potential terms | | Joule-Thomson effect | Enabled by default for accurate temperature prediction | | Multi-layer heat transfer | RadialThermalLayer and MultilayerThermalCalculator classes |

Flow Regime Detection

The flow regime detector uses Taitel-Dukler transitions:

Regime Detection Criteria Status
STRATIFIED_SMOOTH Low gas velocity, stable interface ✅
STRATIFIED_WAVY Kelvin-Helmholtz instability criterion ✅
SLUG Liquid bridging criterion ✅
ANNULAR Weber number > 30 ✅
CHURN Transition between slug and annular ✅
BUBBLE High liquid fraction, low gas velocity ✅

Holdup Correlations

Minimum Holdup Configuration

The model enforces a minimum liquid holdup to prevent unrealistically low values in gas-dominant systems. By default, an adaptive minimum is used that scales with the no-slip holdup, making it suitable for both lean gas and rich condensate systems.

Configuration Methods

Method Default Description
setUseAdaptiveMinimumOnly(boolean) true Use correlation-based minimum only
setMinimumLiquidHoldup(double) 0.001 Absolute floor (when adaptive-only = false)
setMinimumSlipFactor(double) 2.0 Multiplier for no-slip holdup
setEnforceMinimumSlip(boolean) true Enable/disable minimum constraint

Lean Gas Systems

For lean wet gas (< 1% liquid loading), use adaptive-only mode:

pipe.setUseAdaptiveMinimumOnly(true);  // Default
pipe.setMinimumSlipFactor(2.0);
// Minimum holdup = lambdaL × 2.0 = 0.6% for 0.3% liquid loading

Rich Condensate Systems

For rich gas condensate (> 5% liquid loading), either mode works:

// Option 1: Adaptive (recommended)
pipe.setUseAdaptiveMinimumOnly(true);

// Option 2: Fixed floor (OLGA-style)
pipe.setUseAdaptiveMinimumOnly(false);
pipe.setMinimumLiquidHoldup(0.01);  // 1% floor

Minimum Holdup Correlations

The adaptive minimum uses Beggs-Brill type correlations:

Flow Regime Correlation Exponents
Stratified αL = 0.98 × λL^0.4846 / Fr^0.0868 Segregated flow
Slug/Churn αL = 0.845 × λL^0.5351 / Fr^0.0173 Intermittent flow
Annular Film model + 1.065 × λL^0.5824 / Fr^0.0609 Distributed flow

Where λL = no-slip liquid holdup, Fr = Froude number = v²/(g×D)

Stratified Flow Holdup

The calculateStratifiedHoldupMomentumBalance() method calculates liquid holdup from momentum balance:

Holdup = f(τwG, τwL, τi, ∂P/∂x, geometry)

Implementation features:

Velocity-Dependent Slip Model

The model captures liquid accumulation at low velocities using Froude number correlation:

// Slip ratio as function of mixture Froude number
double baseSlip = 3.0;
double maxSlip = 25.0;
double exponent = 0.85;
double slip = baseSlip + (maxSlip - baseSlip) * Math.exp(-exponent * Frm);
Parameter Value Physical Meaning
baseSlip 3.0 Minimum slip at high velocity
maxSlip 25.0 Maximum slip at near-zero velocity
exponent 0.85 Velocity sensitivity factor

Terrain Tracking

Terrain Effects Model

The applyTerrainAccumulation() method implements terrain-induced multiphase flow effects:

1. Low Point Liquid Accumulation

Uses Froude number criterion (Fr < 0.5 indicates accumulation):

double Fr_liquid = vL / Math.sqrt(g * diameter * (rhoL - rhoG) / rhoL);
if (Fr_liquid < 0.5) {
    // Calculate accumulated volume based on velocity deficit
}

2. Riser Base Severe Slugging

Detects severe slugging potential using Pots criterion:

double pi_ss = (inletPressure - outletPressure) / (rhoL * g * riserHeight);
if (pi_ss > 1.0) {
    // Severe slugging potential flagged
}

3. Uphill Liquid Fallback

Uses Turner droplet model for critical gas velocity:

double vG_critical = 3.0 * Math.pow(sigma * g * (rhoL - rhoG) / (rhoG * rhoG), 0.25);
if (vG < vG_critical) {
    // Liquid fallback occurs
}

4. Downhill Drainage

double drainageRate = Math.sqrt(2 * g * dz * holdup);

Multi-Layer Thermal Model

New Classes

  1. RadialThermalLayer - Represents a single thermal layer with material properties
  2. MultilayerThermalCalculator - Calculates U-value and transient heat transfer

Supported Layer Materials

| Material | k [W/(m·K)] | ρ [kg/m³] | Cp [J/(kg·K)] | |———-|————-|———–|—————| | Carbon Steel | 50.0 | 7850 | 480 | | FBE Coating | 0.3 | 1400 | 1000 | | PU Foam | 0.035 | 80 | 1500 | | Syntactic Foam | 0.15 | 650 | 1100 | | Aerogel | 0.015 | 150 | 1000 | | Concrete | 1.4 | 2400 | 880 |

Usage Example

TwoFluidPipe pipe = new TwoFluidPipe("subsea-export", inletStream);
pipe.setLength(20000.0); // 20 km
pipe.setDiameter(0.254); // 10 inch
pipe.setWallThickness(0.015);
pipe.setSurfaceTemperature(4.0, "C"); // Cold seabed

// Configure with 50mm PU foam + 40mm concrete
pipe.configureSubseaThermalModel(0.050, 0.040, 
    RadialThermalLayer.MaterialType.PU_FOAM);

// Set hydrate formation temperature
pipe.setHydrateFormationTemperature(20.0, "C");

// Calculate cooldown time
double cooldownHours = pipe.calculateHydrateCooldownTime();
System.out.printf("Cooldown to hydrate: %.1f hours%n", cooldownHours);

// Run simulation
pipe.run();

// Get thermal summary
System.out.println(pipe.getThermalSummary());

Thermal Calculations

Model Capabilities Summary

Category Feature Method/Correlation
Conservation Equations    
Gas mass Full continuity equation Flash-based mass transfer
Liquid mass Full continuity equation Flash-based mass transfer
Gas momentum 1D momentum balance Wall and interfacial shear
Liquid momentum 1D momentum balance Wall and interfacial shear
Mixture energy Full energy balance Optional J-T effect
Closure Models    
Stratified holdup Momentum balance Taitel-Dukler geometry
Annular holdup Film model Ishii-Mishima entrainment
Slug holdup Empirical correlation Dukler correlation
Interfacial friction Flow-regime specific Multiple correlations
Terrain Effects    
Low point accumulation Froude criterion Fr < 0.5 triggers accumulation
Riser base slugging Pots criterion πSS > 1.0 indicates severe slugging
Uphill fallback Turner model Critical gas velocity check
Thermal Model    
Multi-layer heat transfer Series resistance RadialThermalLayer class
Cooldown calculation Lumped capacitance MultilayerThermalCalculator
Hydrate/wax risk Temperature tracking Section-by-section monitoring
Numerical Methods    
Time stepping CFL-based Fixed step with sub-cycling
Spatial discretization Finite volume Upwind scheme

Validation Status

Implemented Tests

Integration Tests (TwoFluidPipeIntegrationTest)

Validation Tests (TwoFluidPipeValidationTest)

Beggs-Brill Correlation Comparison:

Pipeline Scenario Validation:

Terrain-Induced Slugging Patterns:

Test Coverage Summary

| Test Category | Tests | Status | |————–|——-|——–| | Integration Tests | 24 | ✅ All passing | | Validation Tests | 13 | ✅ All passing | | Total | 37 | ✅ All passing |

References

  1. Bendiksen, K.H., Maines, D., Moe, R., & Nuland, S. (1991). “The Dynamic Two-Fluid Model OLGA: Theory and Application.” SPE Production Engineering, 6(02), 171-180.

  2. Taitel, Y., & 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.

  3. Pots, B.F.M., Bromilow, I.G., & Konijn, M.J.W.F. (1987). “Severe Slug Flow in Offshore Flowline/Riser Systems.” SPE Production Engineering, 2(04), 319-324.

  4. Turner, R.G., Hubbard, M.G., & Dukler, A.E. (1969). “Analysis and Prediction of Minimum Flow Rate for the Continuous Removal of Liquids from Gas Wells.” Journal of Petroleum Technology, 21(11), 1475-1482.

  5. Bai, Y., & Bai, Q. (2010). “Subsea Pipelines and Risers.” Elsevier. Chapter on Thermal Design.

  6. Beggs, H.D. & Brill, J.P. (1973). “A Study of Two-Phase Flow in Inclined Pipes.” Journal of Petroleum Technology, SPE-4007-PA.