Wax Characterization and Modeling

Table of Contents

Overview

Package: neqsim.thermo.characterization, neqsim.thermo.component, neqsim.thermo.phase

Wax precipitation is a major flow assurance concern in oil and gas production, particularly in:

NeqSim provides four thermodynamic wax models, all integrated into the multiphase flash framework so that wax equilibrium is solved simultaneously with vapour-liquid and other solid equilibria.

Key Classes

Class Package Description
WaxCharacterise thermo.characterization Main wax characterization and parameter management
PhaseWax thermo.phase Wax phase with configurable thermodynamic model
ComponentWax thermo.component Pedersen model (default)
ComponentWonWax thermo.component Won model
ComponentWaxWilson thermo.component Wilson local-composition model
ComponentCoutinhoWax thermo.component Coutinho predictive UNIQUAC model
WaxFractionSim pvtsimulation.simulation Wax curve simulation and parameter fitting
WaxCurveCalculator pvtsimulation.flowassurance Wax curve with monotonicity enforcement
WaxFunction pvtsimulation.util.parameterfitting Levenberg-Marquardt fitting function

Wax Formation Theory

Solid-Liquid Equilibrium

The solid-liquid equilibrium for each wax-forming component $i$ is:

\[\ln\left(\frac{x_i^S \gamma_i^S}{x_i^L \gamma_i^L}\right) = \frac{\Delta H_{f,i}}{R T}\left(1 - \frac{T}{T_{f,i}}\right) - \frac{\Delta C_{p,i}^{SL}}{R}\left(\frac{T_{f,i}}{T} - 1 - \ln\frac{T_{f,i}}{T}\right) + \frac{\Delta V_i^{SL}(P - P_{ref})}{R T}\]

where:

Symbol Description
$x_i^S, x_i^L$ Mole fractions in solid and liquid
$\gamma_i^S, \gamma_i^L$ Activity coefficients in solid and liquid
$\Delta H_{f,i}$ Enthalpy of fusion at $T_{f,i}$
$T_{f,i}$ Fusion (triple point) temperature
$\Delta C_{p,i}^{SL}$ Heat capacity change upon fusion
$\Delta V_i^{SL}$ Volume change on fusion (Poynting correction)

The four models differ in how they calculate the activity coefficients $\gamma_i^S$ and $\gamma_i^L$, and how they correlate $\Delta H_f$, $T_f$, and $\Delta C_p$ with molecular weight and carbon number.

Key Temperatures

Temperature Description
WAT (Wax Appearance Temperature) Highest temperature where the first wax crystals appear
Pour Point Temperature below which the oil ceases to flow
Cloud Point Experimental equivalent of WAT (cross-polarized microscopy or DSC)

Pedersen Correlations for Wax Properties

The following correlations (Pedersen et al., 1991) relate wax thermodynamic properties to molecular weight (MW in g/mol):

\[T_f = 374.5 + 0.02617 \cdot MW - \frac{20172}{MW} \quad [\text{K}]\] \[\Delta H_f = \frac{0.1426}{0.238845} \cdot MW \cdot T_f \quad [\text{J/mol}]\] \[\Delta C_p^{SL} = (0.3033 \cdot MW - 4.635 \times 10^{-4} \cdot MW \cdot T) \times 4.184 \quad [\text{J/(mol·K)}]\]

Available Wax Models

1. Pedersen Model (Default)

Class: ComponentWax Key: "Pedersen"

The simplest model, based on Pedersen et al. (1991). Uses Clausius-Clapeyron with a heat capacity correction. Assumes ideal solid solution ($\gamma_i^S = 1$).

Strengths: Fast, robust, easy to tune, good for screening.

Limitations: No solid-phase non-ideality; may overpredict wax amounts at low temperatures.

Tunable parameters: A, B, C in the wax characterization (heat of fusion and triple point temperature correlations), plus heat of fusion and triple point multipliers.

2. Won Model

Class: ComponentWonWax Key: "Won"

Based on Won (1986, 1989). Uses a solubility parameter approach for the solid-phase activity coefficient, with molar volume and solubility parameter estimated from carbon number.

\[\ln \gamma_i^S = \frac{V_i}{RT}\left(\delta_i - \bar{\delta}\right)^2\]

where $V_i$ is the molar volume and $\delta_i$ is the solubility parameter of component $i$.

Strengths: Accounts for solid-phase non-ideality; better for multi-component waxes.

Limitations: Solubility parameters are empirical; less predictive for very heavy components.

3. Wilson Model

Class: ComponentWaxWilson Key: "Wilson"

Uses the Wilson local-composition equation for solid-phase activity coefficients, with binary interaction energies estimated from characteristic energy parameters. Includes full $\Delta C_p$ and sublimation enthalpy corrections.

\[\ln \gamma_i^S = 1 - \ln\left(\sum_j x_j \Lambda_{ji}\right) - \sum_k \frac{x_k \Lambda_{ik}}{\sum_j x_j \Lambda_{jk}}\]

Strengths: Better mixing rule than Won; accounts for local composition effects.

Limitations: More computationally expensive; binary parameters from correlations.

4. Coutinho Predictive UNIQUAC Model

Class: ComponentCoutinhoWax Key: "Coutinho"

A local-composition solid-solution model based on Coutinho (1998, 2001). Uses the UNIQUAC local-composition framework for solid-phase activity coefficients, with predictive interaction parameters derived from sublimation enthalpies.

\[\ln \gamma_i^S = \ln \gamma_i^{comb} + \ln \gamma_i^{res}\]

where the combinatorial part uses the Staverman-Guggenheim equation (size/shape corrections via UNIQUAC $r$ and $q$ parameters from Bondi group contributions), and the residual part uses interaction parameters $\lambda_{ij}$ estimated from:

\[\lambda_{ii} = -\frac{2}{Z}(\Delta H_{sub,i} - RT)\]

For self interactions, use $Z = 10$ (coordination number) and $\Delta H_{sub}$ as the sublimation enthalpy. For unlike molecules, the pair energy is the self energy of the shorter chain: $\lambda_{ij}=\lambda_{ji}=\lambda_{short,short}$.

Strengths: Accounts for molecular size and solid-solution non-ideality. The implemented correlations require validation against data for the fluid of interest.

Limitations: More sensitive to characterization quality; requires correct carbon number assignment for TBP fractions.

Model Selection API

Use setWaxModelType() on the fluid system before calling addSolidComplexPhase("wax"). Names are case-insensitive; unknown or null names raise IllegalArgumentException. Changing an already populated wax phase to a different model raises IllegalStateException and preserves the existing configuration. Selecting its current model again is allowed. The same rules apply to PhaseWax.setWaxComponentModel(). To compare models, construct one fresh fluid for each selection:

import neqsim.thermo.system.SystemSrkEos;

SystemSrkEos fluid = new SystemSrkEos(323.15, 50.0);
// ... add components ...
fluid.setMixingRule(2);

// Select wax model BEFORE adding solid phase
fluid.setWaxModelType("Coutinho");  // "Pedersen", "Won", "Wilson", or "Coutinho"
fluid.addSolidComplexPhase("wax");
fluid.setMultiphaseWaxCheck(true);
fluid.setMultiPhaseCheck(true);

Numerical behavior and limits

The alternative models use Morgan-Kobayashi (1994) vaporization enthalpies with the PERT2 coefficients. These correlations are evaluated only for wax-forming components and require 0 < T < Tc; methane and other excluded fluid components do not enter solid activity sums. Solid compositions are normalized over wax formers. Invalid correlation states or nonfinite/zero fugacity coefficients raise an exception instead of being passed into the phase-fraction calculation. Such an exception is not a prediction of zero wax.

All four models use the same liquid-reference, fusion, heat-capacity and pressure corrections. The pressure contribution is (Vs - Vl) * (P - 1 bara) / (R*T), with volumes in m³/mol and the pressure difference converted to Pa; the current solid-volume approximation is Vs = 0.9*Vl. Won’s solid cohesive energy includes both vaporization and fusion enthalpy. UNIQUAC uses relative interaction energies so that its pure-component activity coefficient is one, and its infinite-dilution coefficient is evaluated without dividing by a zero mole fraction.

The regression coverage for issue #3914 checks actual component classes, finite coefficients, pure-solid limits, pressure units and component inventories for the characterized methane/TBP/plus-fraction mixture at 261 and 275 K and 5 bara. It also cross-checks a Morgan-Kobayashi value against an independent implementation. These are numerical and thermodynamic consistency checks, not experimental qualification of each model’s WAT or wax amount. Use measured WAT and wax-fraction data to qualify or tune predictions for a specific oil.

Python (Jupyter)

from neqsim import jneqsim

fluid = jneqsim.thermo.system.SystemSrkEos(323.15, 50.0)
# ... add components ...
fluid.setMixingRule(2)

fluid.setWaxModelType("Coutinho")
fluid.addSolidComplexPhase("wax")
fluid.setMultiphaseWaxCheck(True)
fluid.setMultiPhaseCheck(True)

Getting Started

Step 1: Create a Waxy Fluid

SystemSrkEos fluid = new SystemSrkEos(323.15, 50.0);
fluid.addComponent("methane", 0.40);
fluid.addComponent("ethane", 0.10);
fluid.addComponent("propane", 0.08);
fluid.addComponent("n-butane", 0.05);
fluid.addComponent("n-pentane", 0.04);
fluid.addComponent("n-hexane", 0.03);
fluid.addTBPfraction("C7", 0.10, 95.0 / 1000, 0.72);
fluid.addTBPfraction("C10", 0.08, 135.0 / 1000, 0.78);
fluid.addTBPfraction("C15", 0.06, 210.0 / 1000, 0.82);
fluid.addTBPfraction("C20", 0.04, 280.0 / 1000, 0.85);
fluid.addTBPfraction("C30", 0.02, 420.0 / 1000, 0.88);

Step 2: Characterize Wax

fluid.setMixingRule(2);

// Characterize wax-forming fractions
fluid.getWaxModel().addTBPWax();

// Select model (optional, defaults to Pedersen)
fluid.setWaxModelType("Pedersen");

// Enable wax phase
fluid.addSolidComplexPhase("wax");
fluid.setMultiphaseWaxCheck(true);
fluid.setMultiPhaseCheck(true);
fluid.init(0);
fluid.init(1);

Step 3: Calculate WAT

import neqsim.thermodynamicoperations.ThermodynamicOperations;

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.calcWAT();
double watC = fluid.getTemperature() - 273.15;

calcWAT() now locates the numerical wax onset with independent, freshly initialized TP flashes at the current pressure. It brackets the transition through a wax mass fraction of 1e-8 of the whole fluid, then refines the temperature interval to 1e-4 K and repeats both endpoint flashes. The returned temperature is the warm endpoint (wax mass fraction at or below the threshold). The fluid retains that verified TP phase state; the operation does not append an artificial wax phase. Downstream wax amounts should be obtained with a new TPflash() at the operating temperature.

The initial temperature must lie within the numerical search bounds of 100-1000 K. The operation searches in 10 K increments from that guess and assumes a single wax appearance transition in the bracket. These bounds are solver guards, not a statement of physical model validity. Wax checks are enabled on the internal trials; the caller’s wax-check and fluid multiphase-check settings are preserved. Enable setMultiPhaseCheck(true) before calculation when an aqueous phase must be considered. Characterization and addSolidComplexPhase("wax") remain prerequisites.

Invalid inputs or missing wax formers/configuration raise IllegalArgumentException. Failure to find or reproduce a bracket, or a nonfinite/unbalanced TP trial, raises IllegalStateException with pressure, trial/bracket temperatures and the number of TP evaluations. Failure leaves the caller’s temperature, phase state and overall composition unchanged. Do not treat the initial temperature as a WAT after an exception.

This resolves the internal consistency failure in issue #3709: the characterized synthetic oil previously returned 54.4595 °C at 60 bara although fresh TP flashes already predicted wax at 64 °C. Regression tests compare direct WAT against a refined independent TP appearance bracket at 40, 60 and 80 bara, including different initial guesses, reordered/existing wax phases and added water. This checks consistency within the selected EOS, wax model and characterization; it is not experimental validation. Laboratory WAT and wax-fraction data are still needed for fluid-specific prediction, and equilibrium wax appearance does not by itself predict deposition rate or location.

Step 4: Wax Fraction vs Temperature

// Using WaxCurveCalculator (recommended)
import neqsim.pvtsimulation.flowassurance.WaxCurveCalculator;

WaxCurveCalculator calc = new WaxCurveCalculator(fluid);
calc.setPressure(50.0);
calc.setTemperatureRange(-10.0, 80.0, 2.0);
calc.calculate();

double wat = calc.getWaxAppearanceTemperatureC();
double[] temps = calc.getTemperaturesC();
double[] fractions = calc.getWaxWeightFractions();

Wax Curve Calculation

WaxCurveCalculator

The WaxCurveCalculator class provides the most robust way to generate wax precipitation curves. It scans from high to low temperature, performs a TP flash at each point, and applies monotonicity enforcement to remove non-physical artifacts.

WaxCurveCalculator calc = new WaxCurveCalculator(fluid);
calc.setPressure(100.0);
calc.setTemperatureRange(-10.0, 80.0, 1.0);
calc.setEnforceMonotonicity(true); // default
calc.calculate();

// Results
double watC = calc.getWaxAppearanceTemperatureC();
double[] temperaturesCurve = calc.getTemperaturesC();
double[] waxWtFractions = calc.getWaxWeightFractions();

// Multi-pressure evaluation
double[] pressures = {50.0, 100.0, 200.0};
Map<Double, Double> results = calc.calculateAtMultiplePressures(pressures, 10.0);

WaxFractionSim

The WaxFractionSim class is used for PVT-style wax fraction simulation and also supports parameter tuning via the Levenberg-Marquardt optimizer.

import neqsim.pvtsimulation.simulation.WaxFractionSim;

WaxFractionSim sim = new WaxFractionSim(fluid);
double[] temps = {293.15, 283.15, 273.15, 264.15, 263, 262, 261};
double[] pres  = {5, 5, 5, 5, 5, 5, 5};
sim.setTemperaturesAndPressures(temps, pres);
sim.runCalc();
double[] waxFrac = sim.getWaxFraction();

Fitting to Experimental Data

NeqSim includes a Levenberg-Marquardt optimizer for tuning wax model parameters to match experimental wax fraction data.

Tunable Parameters

Index Parameter Description Typical Range
0 A Wax characterization parameter A 0.8 - 1.3
1 B Wax characterization parameter B -0.01 to 0.01
2 C Wax characterization parameter C 0 to 0.001
3 HeatOfFusion multiplier Scales $\Delta H_f$ 0.8 - 1.2
4 TriplePointTemp multiplier Scales $T_f$ 0.98 - 1.02

Java Fitting Example

WaxFractionSim sim = new WaxFractionSim(fluid);
double[] temps = {293.15, 283.15, 273.15, 264.15, 263, 262, 261};
double[] pres  = {5, 5, 5, 5, 5, 5, 5};
sim.setTemperaturesAndPressures(temps, pres);

// Set experimental wax wt% data
double[][] expData = 4;
sim.setExperimentalData(expData);

// Configure optimizer (3 params = A, B, C; up to 5 with HoF and Tf)
sim.getOptimizer().setNumberOfTuningParameters(3);
sim.getOptimizer().setMaxNumberOfIterations(20);

// Run tuning
sim.runTuning();

// Recalculate with tuned parameters
sim.runCalc();
double[] fitted = sim.getWaxFraction();

Python (Jupyter) Fitting Example

from neqsim import jneqsim

WaxFractionSim = jneqsim.pvtsimulation.simulation.WaxFractionSim

sim = WaxFractionSim(fluid)
temps = [293.15, 283.15, 273.15, 264.15]
pres  = [5.0, 5.0, 5.0, 5.0]
sim.setTemperaturesAndPressures(temps, pres)

# Experimental wax wt% (must be 2D array)
exp_data = [[4.0, 7.0, 9.0, 10.0]]
sim.setExperimentalData(exp_data)

sim.getOptimizer().setNumberOfTuningParameters(3)
sim.getOptimizer().setMaxNumberOfIterations(20)
sim.runTuning()
sim.runCalc()

fitted = list(sim.getWaxFraction())

Flow Assurance Applications

Pipeline Wax Deposition Risk

// Check if operating below WAT
ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.calcWAT();
double wat = fluid.getTemperature() - 273.15;
double outletTemp = 15.0; // seabed temperature

if (outletTemp < wat) {
    double subcooling = wat - outletTemp;
    String risk = subcooling > 20 ? "HIGH" :
                  subcooling > 10 ? "MEDIUM" : "LOW";
    System.out.println("WAT: " + wat + " C, Subcooling: " + subcooling + " C, Risk: " + risk);
}

Multi-Pressure Pipeline Profile

WaxCurveCalculator calc = new WaxCurveCalculator(fluid);
double[] pressures = {50, 80, 100, 150, 200};
Map<Double, Double> waxAtPressures = calc.calculateAtMultiplePressures(pressures, 10.0);

Model Comparison and Selection Guide

Criterion Pedersen Won Wilson Coutinho
Speed Fast Fast Medium Medium
Parameters to tune 3-5 3-5 3-5 3-5
Solid non-ideality None Solubility param Wilson GE UNIQUAC GE
$\Delta C_p$ correction Yes Yes Yes Yes
Best for Screening, quick studies Multi-component waxes Moderate accuracy High accuracy, validation
Literature validation Pedersen 1991 Won 1986, 1989 - Coutinho 1998, 2001

Recommendations

  1. Screening and quick studies: Use Pedersen (default). Fast, robust, easy to tune.
  2. Engineering design (single oil): Use Pedersen or Won with parameter tuning to experimental data.
  3. Predictive work: Compare model sensitivity and obtain experimental validation before relying on absolute wax amounts.
  4. Multi-crude blending or new field: Validate the characterization and solid-solution model for the new compositions.

References

See Also