Density Models

This guide documents the density correction models available in NeqSim for improving volumetric predictions.

Table of Contents

Overview

Density predictions from cubic equations of state (SRK, PR) often have systematic errors:

NeqSim provides volume translation and correlation-based methods to improve liquid density predictions.

Basic density access:

fluid.init(3);  // Initialize with derivatives
fluid.initPhysicalProperties();

double density = fluid.getPhase(1).getDensity("kg/m3");  // Liquid phase
double molarVolume = fluid.getPhase(1).getMolarVolume();  // m³/mol

Equation of State Density

Direct EoS Calculation

Cubic equations of state calculate compressibility factor $Z$:

\[PV = ZnRT\]

Molar volume is then: \(V_m = \frac{ZRT}{P}\)

Density: \(\rho = \frac{PM_w}{ZRT}\)

Issue with cubic EoS: At the critical point, $Z_c^{SRK} = 0.333$ and $Z_c^{PR} = 0.307$, while real hydrocarbons have $Z_c \approx 0.26$. This causes systematic liquid volume overprediction.

Volume Translation Methods

Peneloux Volume Shift

The Peneloux correction adds a constant shift to the EoS molar volume:

\[V_{corrected} = V_{EoS} - c\]

where $c$ is the volume shift parameter.

Class: Peneloux

Mixture shift: \(c_{mix} = \sum_i x_i c_i\)

Component shift correlation: \(c_i = 0.40768 \frac{RT_{c,i}}{P_{c,i}} \left( 0.29441 - Z_{RA,i} \right)\)

where $Z_{RA}$ is the Rackett compressibility factor (from COMP database).

Setting shift parameters:

// Enable Peneloux correction (default for SRK)
fluid.setDensityModel("Peneloux");

// Or set component-specific shifts
fluid.getPhase(0).getComponent("methane").setVolumeCorrectionConst(0.0);
fluid.getPhase(1).getComponent("n-heptane").setVolumeCorrectionConst(-0.0105);

Advantages:

Limitations:

Component-Specific Corrections

NeqSim stores volume correction constants in the COMP database. For heavy hydrocarbons or polar compounds, these may need tuning.

Accessing correction constants:

// Get current volume correction
double vc = fluid.getPhase(1).getComponent("n-decane").getVolumeCorrectionConst();

// Modify correction
fluid.getPhase(1).getComponent("n-decane").setVolumeCorrectionConst(-0.015);

Temperature-dependent shift (Jhaveri-Youngren): Some systems require temperature-dependent corrections:

\[c(T) = c_0 + c_1 (T - T_{ref})\]

This is implemented in specific component models.

Liquid Density Correlations

COSTALD

The COSTALD (COrreSponding STAtes Liquid Density) method is a generalized corresponding-states correlation for predicting liquid densities of pure compounds and mixtures. It is equivalent to the implementation in commercial simulators such as UniSim/HYSYS, Aspen Plus, and PRO/II.

Class: Costald (in neqsim.physicalproperties.methods.liquidphysicalproperties.density)

Method Overview

COSTALD has two parts:

  1. Saturated liquid volume — Hankinson and Thomson (1979)
  2. Compressed liquid correction — Aalto et al. (1996) modified Tait equation

The method automatically applies the compressed liquid correction when the system pressure exceeds the estimated saturation pressure.

Quick Start (Java)

// 1. Create fluid and run flash
SystemInterface fluid = new SystemSrkEos(293.15, 50.0);
fluid.addComponent("methane", 70.0);
fluid.addComponent("n-hexane", 20.0);
fluid.addComponent("water", 10.0);
fluid.setMixingRule("classic");
fluid.setMultiPhaseCheck(true);

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.TPflash();
fluid.initPhysicalProperties();

// 2. Switch liquid phases to COSTALD
fluid.setLiquidDensityModel("COSTALD");

// 3. Read density (applies to oil, liquid, and aqueous phases)
double oilDensity = fluid.getPhase("oil").getPhysicalProperties().getDensity();
double waterDensity = fluid.getPhase("aqueous").getPhysicalProperties().getDensity();

Quick Start (Python / Jupyter)

from neqsim import jneqsim

fluid = jneqsim.thermo.system.SystemSrkEos(293.15, 50.0)
fluid.addComponent("methane", 70.0)
fluid.addComponent("n-hexane", 20.0)
fluid.addComponent("water", 10.0)
fluid.setMixingRule("classic")
fluid.setMultiPhaseCheck(True)

ops = jneqsim.thermodynamicoperations.ThermodynamicOperations(fluid)
ops.TPflash()
fluid.initPhysicalProperties()

fluid.setLiquidDensityModel("COSTALD")

oil_density = fluid.getPhase("oil").getPhysicalProperties().getDensity()
water_density = fluid.getPhase("aqueous").getPhysicalProperties().getDensity()
print(f"Oil:   {oil_density:.1f} kg/m3")
print(f"Water: {water_density:.1f} kg/m3")

API Methods

Method Level Description
fluid.setLiquidDensityModel("COSTALD") System Applies COSTALD to all liquid/oil/aqueous phases at once
fluid.setLiquidDensityModel("Peneloux") System Switches back to the default Peneloux volume shift
phase.getPhysicalProperties().setDensityModel("Costald") Phase Applies COSTALD to a single phase
component.setCostaldCharacteristicVolume(v) Component Sets an explicit V* value (cm³/mol) for fine-tuning
component.getCostaldCharacteristicVolume() Component Returns the explicit V* if set, otherwise 0

Important: Call setLiquidDensityModel() after initPhysicalProperties(). Once set, the density model persists for subsequent calcDensity() calls until changed.

Saturated Liquid Volume (Hankinson-Thomson 1979)

The saturated liquid molar volume is:

\[V_s = V^* \cdot V_R^{(0)}(T_r) \cdot \left[1 - \omega \cdot V_R^{(\delta)}(T_r)\right]\]

where $T_r = T / T_{c,m}$ is the reduced temperature and $\omega$ is the acentric factor.

The dimensionless volume functions are:

\[V_R^{(0)} = 1 - 1.52816\,\tau^{1/3} + 1.43907\,\tau^{2/3} - 0.81446\,\tau + 0.190454\,\tau^{4/3}\] \[V_R^{(\delta)} = \frac{-0.296123 + 0.386914\,T_r - 0.0427258\,T_r^2 - 0.0480645\,T_r^3}{T_r - 1.00001}\]

where $\tau = 1 - T_r$.

Compressed Liquid Correction (Aalto et al. 1996)

When $P > P_{sat}$, a modified Tait correction shrinks the molar volume:

\[V = V_s^{sat} \cdot \frac{A + e^{(d - T_r)^B} \cdot (P_r - P_r^{sat})}{A + e \cdot (P_r - P_r^{sat})}\]

where:

\[A = a_0 + a_1 T_r + a_2 T_r^3 + a_3 T_r^6 + a_4 / T_r\] \[B = b_0 + b_1 \cdot \omega\]
Constant Value
$a_0$ -170.335
$a_1$ -28.578
$a_2$ 124.809
$a_3$ -55.5393
$a_4$ 130.01
$b_0$ 0.164813
$b_1$ -0.0914427
$c$ $e$ (Euler’s number)
$d$ 1.00588

The pseudocritical pressure is:

\[P_{c,m} = \frac{(0.291 - 0.080\,\omega_m) \cdot R \cdot T_{c,m}}{V^*_m}\]

The saturation pressure uses the Lee-Kesler correlation.

Mixing Rules

For mixtures, pseudocritical properties are calculated using the Hankinson-Thomson (1979) mixing rules (Poling, Table 4-12):

Characteristic volume (quadratic):

\[V^*_m = \frac{1}{4}\left[\sum_i x_i V^*_i + 3\left(\sum_i x_i {V^*_i}^{2/3}\right)\left(\sum_i x_i {V^*_i}^{1/3}\right)\right]\]

Acentric factor (linear):

\[\omega_m = \sum_i x_i \omega_i\]

Pseudocritical temperature:

\[T_{c,m} = \frac{\left[\sum_i x_i \sqrt{T_{c,i} \cdot V^*_i}\right]^2}{V^*_m}\]

These are the same mixing rules used in all major commercial simulators.

Characteristic Volume (V*) Estimation

The characteristic volume $V^$ is the most important parameter for COSTALD accuracy. It is not the same as the critical volume $V_c$ — for polar compounds such as water or glycols, $V^$ can be 10–20% lower than $V_c$.

NeqSim determines $V^*$ using a three-tier priority:

Priority Source When Used
1 Explicit V* (setCostaldCharacteristicVolume) User has literature or fitted V* value
2 Back-calculated from normal liquid density at 60 °F (288.71 K) Component has normalLiquidDensity > 0 and $T_r < 0.9$ at 288.71 K
3 Critical volume $V_c$ Fallback when no density data is available

The back-calculation (priority 2) solves:

\[V^* = \frac{M / \rho_{std}}{V_R^{(0)}(T_{r,std}) \cdot \left[1 - \omega \cdot V_R^{(\delta)}(T_{r,std})\right]}\]

where $\rho_{std}$ is the normal liquid density at 288.71 K from the component database. This is the same approach used by UniSim/HYSYS and PRO/II. It automatically handles:

Supported Compound Types

Compound Type V* Method Example Components Expected Accuracy
Light hydrocarbons ($T_c < 320$ K) Critical volume $V_c$ methane, ethane, propane 1–3%
Heavier hydrocarbons V* from density n-hexane, n-decane, nC16, nC20 1–2%
Polar / associating V* from density water, methanol, ethanol 3–5%
Glycols V* from density MEG, TEG, DEG 3–5%
TBP fractions V* from density C7, C10, C20 pseudo-components 2–5%
Plus fractions (C20+) V* from density Characterized heavy end 3–8%

Aqueous and Multi-Phase Systems

setLiquidDensityModel("COSTALD") applies to all liquid-type phases simultaneously: LIQUID, OIL, and AQUEOUS. This means a single call enables COSTALD for three-phase gas-oil-water systems.

// Gas-oil-water with MEG inhibitor
SystemInterface fluid = new SystemSrkEos(303.15, 80.0);
fluid.addComponent("methane", 70.0);
fluid.addComponent("n-hexane", 5.0);
fluid.addComponent("water", 10.0);
fluid.addComponent("MEG", 7.0);
fluid.setMixingRule("classic");
fluid.setMultiPhaseCheck(true);

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.TPflash();
fluid.initPhysicalProperties();

// Enable COSTALD for both oil and aqueous phases
fluid.setLiquidDensityModel("COSTALD");

if (fluid.hasPhaseType("oil")) {
    double oilRho = fluid.getPhase("oil").getPhysicalProperties().getDensity();
}
if (fluid.hasPhaseType("aqueous")) {
    double aqRho = fluid.getPhase("aqueous").getPhysicalProperties().getDensity();
}

Oil Characterization (TBP / Plus Fractions)

COSTALD works directly with the NeqSim TBP characterization. Each pseudo-component’s $V^*$ is automatically estimated from its specified density:

SystemInterface fluid = new SystemSrkEos(313.15, 100.0);
fluid.addComponent("methane", 50.0);
fluid.addComponent("ethane", 10.0);
fluid.addTBPfraction("C7", 5.0, 95.0 / 1000.0, 0.738);
fluid.addTBPfraction("C10", 4.0, 134.0 / 1000.0, 0.792);
fluid.addPlusFraction("C20", 3.0, 350.0 / 1000.0, 0.895);
fluid.getCharacterization().setTBPModel("PedersenSRK");
fluid.getCharacterization().setLumpingModel("PVTlumpingModel");
fluid.getCharacterization().characterisePlusFraction();
fluid.setMixingRule("classic");

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.TPflash();
fluid.initPhysicalProperties();

// COSTALD will use the density-based V* for each TBP fraction
fluid.setLiquidDensityModel("COSTALD");
double density = fluid.getPhase("oil").getPhysicalProperties().getDensity();

Tuning with Custom V*

If you have published V* values (from Hankinson-Thomson 1979 Table I, DIPPR, or the API Technical Data Book), you can set them explicitly for better accuracy:

// Set published V* for n-hexane (371.0 cm3/mol from H-T 1979)
fluid.getPhase("oil").getComponent("n-hexane").setCostaldCharacteristicVolume(371.0);

// Set V* for water (46.4 cm3/mol, significantly less than Vc = 56 cm3/mol)
fluid.getPhase("aqueous").getComponent("water").setCostaldCharacteristicVolume(46.4);

Explicit V* values override the density-based estimation. To revert to automatic estimation, set it back to 0:

fluid.getPhase("oil").getComponent("n-hexane").setCostaldCharacteristicVolume(0.0);

Switching Back to Default

// Switch back to Peneloux volume shift (default)
fluid.setLiquidDensityModel("Peneloux");

// Or set per-phase
fluid.getPhase("oil").getPhysicalProperties().setDensityModel("Peneloux volume shift");

Valid Range and Limitations

Parameter Valid Range Notes
Reduced temperature $T_r$ 0.25 – 0.95 Warns below 0.25; falls back to EOS above 1.0
Pressure Up to ~700 bar Compressed liquid correction from Aalto (1996)
Component types Hydrocarbons, polar, associating, pseudo-components Best for hydrocarbons; 3–5% for polar
Phases Liquid, oil, aqueous Does not apply to gas or solid phases

Limitations:

Comparison with Other Commercial Simulators

Feature NeqSim COSTALD NeqSim NASTALD UniSim/HYSYS Aspen Plus PRO/II
Saturated volume (H-T 1979) Yes Yes Yes Yes Yes
NBS polar correction (1982) No Yes Yes Yes Yes
Compressed liquid Aalto (1996) Aalto (1996) Thomson (1982) Thomson (1982) Thomson (1982)
V* from density back-calc Yes Yes Yes DIPPR database Yes
V* explicit override Yes Yes Yes Yes Yes
Polar compound support Via V* from density Via V* + polar term Via V* + polar Via DIPPR V* Via V* + polar
Aqueous phase support Yes Yes Yes Yes Yes
TBP fraction support Yes Yes Yes Yes Yes
Mixing rules Standard H-T Standard H-T Standard H-T Standard H-T Standard H-T

NeqSim uses the Aalto et al. (1996) modified Tait equation for compressed liquid correction rather than the Thomson et al. (1982) original Tait form used by most commercial simulators. The Aalto form works in reduced pressure units for better numerical behavior at high pressures.

The NASTALD variant adds the Thomson-Brobst-Hankinson (1982) polar correction term, which is the same approach used by UniSim/HYSYS, Aspen Plus, and PRO/II for polar compounds.

References

  1. Hankinson, R.W. and Thomson, G.H. (1979). “A New Correlation for Saturated Densities of Liquids and Their Mixtures.” AIChE J. 25, 653–663.
  2. Thomson, G.H., Brobst, K.R. and Hankinson, R.W. (1982). “An Improved Correlation for Densities of Compressed Liquids and Liquid Mixtures.” AIChE J. 28, 671–676.
  3. Aalto, M., Keskinen, K.I., Aittamaa, J. and Liukkonen, S. (1996). “An Improved Correlation for Compressed Liquid Densities of Hydrocarbons. Part 2. Mixtures.” Fluid Phase Equil. 114, 1–19.
  4. Poling, B.E., Prausnitz, J.M. and O’Connell, J.P. (2001). The Properties of Gases and Liquids, 5th ed. McGraw-Hill, Chapters 4.
  5. API Technical Data Book — Petroleum Refining, Chapter 6.

NASTALD (COSTALD with Polar Correction)

NASTALD extends the standard COSTALD method by adding the Thomson-Brobst-Hankinson (1982) polar correction term $V_R^{(p)}$. This improves accuracy for strongly polar and hydrogen-bonding compounds such as water, alcohols, and glycols.

Equation

The saturated volume for a polar substance becomes:

\[V_s = V^* \left[ V_R^{(0)} \left(1 - \omega_{SRK} \, V_R^{(\delta)}\right) + \omega_p \, V_R^{(p)} \right]\]

where $\omega_p$ is the substance-specific polar parameter and $V_R^{(p)}$ is the polar correction function:

\[V_R^{(p)} = \frac{e + f \, T_r + g \, T_r^2 + h \, T_r^3}{T_r - 1.00001}\]

with the universal constants:

Constant Value
$e$ -1.52816
$f$ 1.43907
$g$ -0.81446
$h$ 0.190454

For mixtures, the polar parameter is mixed via:

\[\omega_{p,mix} = \sum_i x_i \, \omega_{p,i}\]

Polar Parameters ($\omega_p$)

The following polar parameters are built into NeqSim:

Compound $\omega_p$ Source
Water 0.3478 Thomson et al. (1982)
Ammonia 0.2872 Thomson et al. (1982)
HF 0.3750 Thomson et al. (1982)
Methanol 0.1907 Thomson et al. (1982)
Ethanol 0.1471 Thomson et al. (1982)
1-propanol 0.1100 Thomson et al. (1982)
2-propanol 0.1050 Thomson et al. (1982)
1-butanol 0.0922 Thomson et al. (1982)
Acetic acid 0.1530 Thomson et al. (1982)
Acetone 0.0547 Thomson et al. (1982)
MEG 0.2213 Estimated
DEG 0.2000 Estimated
TEG 0.1800 Estimated

For compounds not in this table, $\omega_p = 0$ and NASTALD reduces to standard COSTALD.

Important Caveat: V* Back-Calculation

When V* is back-calculated from the component’s normalLiquidDensity (which is the default for most components), the polarity is already partially captured in the V* value. Adding the polar correction on top can lead to over-correction (typically 5-15% too high for alcohols and glycols).

The NASTALD polar correction is most beneficial when:

For most practical purposes, standard COSTALD with V* from density gives excellent results for polar compounds without needing the explicit polar term.

Usage

// Enable NASTALD (COSTALD with polar correction) for all liquid phases
fluid.setLiquidDensityModel("NASTALD");

// Run flash and get density
ops.TPflash();
fluid.initPhysicalProperties();
double rho = fluid.getPhase("aqueous").getDensity("kg/m3");

References

  1. Thomson, G.H., Brobst, K.R. and Hankinson, R.W. (1982). “An Improved Correlation for Densities of Compressed Liquids and Liquid Mixtures.” AIChE J. 28, 671–676.

Rackett Equation

The Spencer-Danner (1972) modified Rackett equation provides a simple corresponding-states method for saturated liquid density. It requires only critical properties and the Rackett compressibility factor $Z_{RA}$.

Pure Component Equation

\[V_s = \frac{R T_c}{P_c} \; Z_{RA}^{\left[1 + (1 - T_r)^{2/7}\right]}\]

where $T_r = T / T_c$ is the reduced temperature and $Z_{RA}$ is the Rackett compressibility factor (an empirically fitted parameter, not the true critical compressibility $Z_c$).

$Z_{RA}$ Selection Priority

  1. Database value — component.getRacketZ() from the NeqSim component database (fitted to experimental data)
  2. Yamada-Gunn estimate (1973) — If no database value is available:
\[Z_{RA} = 0.29056 - 0.08775 \, \omega\]

where $\omega$ is the acentric factor.

Mixture Rules (Li, 1971)

For mixtures, pseudo-critical properties are calculated via mole-fraction weighted mixing:

\[V_{c,mix} = \sum_i x_i V_{c,i}, \quad T_{c,mix} = \frac{\sum_i x_i V_{c,i} T_{c,i}}{V_{c,mix}}, \quad Z_{RA,mix} = \sum_i x_i Z_{RA,i}\] \[P_{c,mix} = \frac{Z_{RA,mix} \, R \, T_{c,mix}}{V_{c,mix}}\]

The mixture saturated volume is then:

\[V_{s,mix} = \frac{R \, T_{c,mix}}{P_{c,mix}} \; Z_{RA,mix}^{\left[1 + (1 - T_{r,mix})^{2/7}\right]}\]

Usage

// Enable Rackett density model for all liquid phases
fluid.setLiquidDensityModel("Rackett");

// Run flash and get density
ops.TPflash();
fluid.initPhysicalProperties();
double rho = fluid.getPhase("oil").getDensity("kg/m3");

// Access Z_RA for a component
double Zra = fluid.getPhase(1).getComponent("n-pentane").getRacketZ();

Strengths and Limitations

References

  1. Rackett, H.G. (1970). “Equation of State for Saturated Liquids.” J. Chem. Eng. Data 15, 514–517.
  2. Spencer, C.F. and Danner, R.P. (1972). “Improved Equation for Prediction of Saturated Liquid Density.” J. Chem. Eng. Data 17, 236–241.
  3. Li, C.C. (1971). “Critical Temperature Estimation for Simple Mixtures.” Can. J. Chem. Eng. 49, 709–710.
  4. Yamada, T. and Gunn, R.D. (1973). “Saturated Liquid Molar Volumes. The Rackett Equation.” J. Chem. Eng. Data 18, 234–236.

Usage Examples

Comparing Density Models

import neqsim.thermo.system.SystemSrkEos;
import neqsim.thermodynamicoperations.ThermodynamicOperations;

SystemInterface fluid = new SystemSrkEos(300.0, 50.0);
fluid.addComponent("methane", 0.1);
fluid.addComponent("n-pentane", 0.9);
fluid.setMixingRule("classic");

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.TPflash();
fluid.initPhysicalProperties();

// Default density (Peneloux volume shift)
double densityPeneloux = fluid.getPhase("oil").getPhysicalProperties().getDensity();
System.out.println("Peneloux: " + densityPeneloux + " kg/m3");

// Switch to COSTALD
fluid.setLiquidDensityModel("COSTALD");
double densityCostald = fluid.getPhase("oil").getPhysicalProperties().getDensity();
System.out.println("COSTALD:  " + densityCostald + " kg/m3");

// Switch to Rackett
fluid.setLiquidDensityModel("Rackett");
double densityRackett = fluid.getPhase("oil").getPhysicalProperties().getDensity();
System.out.println("Rackett:  " + densityRackett + " kg/m3");

// Switch back to Peneloux
fluid.setLiquidDensityModel("Peneloux");
double densityBack = fluid.getPhase("oil").getPhysicalProperties().getDensity();
System.out.println("Peneloux: " + densityBack + " kg/m3");

Comparing with NASTALD for Polar Systems

SystemInterface fluid = new SystemSrkEos(293.15, 1.01325);
fluid.addComponent("water", 0.8);
fluid.addComponent("methanol", 0.2);
fluid.setMixingRule("classic");

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.TPflash();
fluid.initPhysicalProperties();

// COSTALD (V* captures polarity via back-calculation)
fluid.setLiquidDensityModel("COSTALD");
double rhoCostald = fluid.getPhase("aqueous").getPhysicalProperties().getDensity();
System.out.println("COSTALD:  " + rhoCostald + " kg/m3");

// NASTALD (explicit polar correction)
fluid.setLiquidDensityModel("NASTALD");
double rhoNastald = fluid.getPhase("aqueous").getPhysicalProperties().getDensity();
System.out.println("NASTALD:  " + rhoNastald + " kg/m3");

Tuning Liquid Density

// Create fluid with known experimental density
SystemInterface fluid = new SystemSrkEos(293.15, 1.01325);
fluid.addComponent("n-hexane", 1.0);
fluid.setMixingRule("classic");

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.TPflash();
fluid.initPhysicalProperties();

double expDensity = 659.0;  // kg/m³ at 20°C
double calcDensity = fluid.getPhase(1).getDensity("kg/m3");
double error = (calcDensity - expDensity) / expDensity * 100;
System.out.println("Initial error: " + error + "%");

// Adjust volume correction to match experimental
double molarMass = fluid.getPhase(1).getMolarMass() * 1000;  // kg/kmol
double calcMolarVolume = molarMass / calcDensity;  // m³/kmol
double expMolarVolume = molarMass / expDensity;    // m³/kmol
double correction = (calcMolarVolume - expMolarVolume) / 1000;  // m³/mol

fluid.getPhase(1).getComponent("n-hexane").setVolumeCorrectionConst(correction);
fluid.initPhysicalProperties();

double newDensity = fluid.getPhase(1).getDensity("kg/m3");
System.out.println("Tuned density: " + newDensity + " kg/m³");

Density vs Temperature

SystemInterface fluid = new SystemSrkEos(300.0, 10.0);
fluid.addComponent("n-heptane", 1.0);
fluid.setMixingRule("classic");

double[] temps = {280, 300, 320, 340, 360, 380};

for (double T : temps) {
    fluid.setTemperature(T, "K");

    ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
    ops.TPflash();

    if (fluid.getPhase(1).getPhaseTypeName().equals("oil")) {
        fluid.initPhysicalProperties();
        double rho = fluid.getPhase(1).getDensity("kg/m3");
        System.out.println("T=" + T + " K: ρ=" + rho + " kg/m³");
    }
}

High-Pressure Density

// Compressed liquid density at high pressure
SystemInterface fluid = new SystemSrkEos(300.0, 500.0);  // 500 bar
fluid.addComponent("n-decane", 1.0);
fluid.setMixingRule("classic");

ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
ops.TPflash();
fluid.initPhysicalProperties();

double rho = fluid.getPhase(0).getDensity("kg/m3");
System.out.println("High-P density: " + rho + " kg/m³");

// For high-pressure liquids, Peneloux may be insufficient
// Consider using PC-SAFT or adjusting correction

Model Selection Guide

Situation Recommended Model Notes
General hydrocarbons Peneloux Default, good accuracy
Near saturation COSTALD Better for saturated liquids
Polar compounds (water, glycols) COSTALD V* from density handles polarity
Polar with database V* NASTALD Adds explicit polar correction term
Multi-phase (gas-oil-water) COSTALD Single call applies to oil + aqueous
Different model per phase Per-phase API e.g. COSTALD on oil, Peneloux on aqueous
TBP/plus fractions COSTALD V* from density input, no tuning needed
High pressure (> 200 bar) COSTALD Aalto compressed liquid correction
Quick simple estimate Rackett No high-pressure correction
Saturated hydrocarbons only Rackett Fast, 2–5% accuracy
Critical region GERG-2008 If available
Quick estimate EoS only 5–15% error typical

Expected Accuracy

Method Liquid Density Error Vapor Density Error
SRK (no correction) 5–15% 1–3%
SRK + Peneloux 1–3% 1–3%
PR (no correction) 3–10% 1–3%
PR + Peneloux 1–3% 1–3%
COSTALD (hydrocarbons) 1–2% N/A
COSTALD (polar/aqueous) 3–5% N/A
COSTALD (TBP fractions) 2–5% N/A
NASTALD (polar with database V*) 1–3% N/A
Rackett (hydrocarbons) 2–5% N/A
GERG-2008 0.1–0.5% 0.1–0.5%

API Reference

Setting Density Model

// Set COSTALD for all liquid phases (oil, liquid, aqueous)
fluid.setLiquidDensityModel("COSTALD");

// Set NASTALD (polar-corrected COSTALD) for all liquid phases
fluid.setLiquidDensityModel("NASTALD");

// Set Rackett equation for all liquid phases
fluid.setLiquidDensityModel("Rackett");

// Switch back to default Peneloux
fluid.setLiquidDensityModel("Peneloux");

// Set model for a specific phase type only
fluid.setLiquidDensityModel("COSTALD", "oil");      // Oil phase uses COSTALD
fluid.setLiquidDensityModel("Peneloux", "aqueous");  // Aqueous keeps Peneloux

// Valid phase type names: "oil", "aqueous", "liquid"

// Low-level: set per-phase directly
fluid.getPhase("oil").getPhysicalProperties().setDensityModel("Costald");
fluid.getPhase("aqueous").getPhysicalProperties().setDensityModel("Rackett");

Accepted Model Strings

setLiquidDensityModel(...) setDensityModel(...) Description
"COSTALD" "Costald" Standard COSTALD (Hankinson-Thomson)
"NASTALD" or "COSTALD-polar" "Costald polar" COSTALD with polar correction
"Rackett" "Rackett" Spencer-Danner modified Rackett
"Peneloux" "Peneloux volume shift" Default Peneloux volume translation

Accessing Density

// Mass density
double rhoMass = phase.getDensity("kg/m3");
double rhoMass2 = phase.getDensity("lb/ft3");

// Molar density
double rhoMolar = phase.getDensity("mol/m3");

// Molar volume
double Vm = phase.getMolarVolume();  // m³/mol

Density at Reference Conditions

// Calculate density at standard conditions without modifying the fluid
double rhoStd = fluid.getDensityAtReferenceConditions(15.0, "C", 1.01325, "bara");
// Returns density in kg/m3 at 15°C / 1.01325 bara

// API standard temperature (60°F)
double rhoAPI = fluid.getDensityAtReferenceConditions(15.56, "C", 1.01325, "bara");

// The original fluid state is NOT modified by this call

Volume Correction Parameters

// Get/set volume correction constant
double c = component.getVolumeCorrectionConst();
component.setVolumeCorrectionConst(newValue);

// Get Rackett parameter
double Zra = component.getRacketZ();

// Get/set COSTALD characteristic volume (V*)
double Vstar = component.getCostaldCharacteristicVolume();
component.setCostaldCharacteristicVolume(newValue);  // cm³/mol

References

  1. Peneloux, A., Rauzy, E., Freze, R. (1982). A Consistent Correction for Redlich-Kwong-Soave Volumes. Fluid Phase Equilib. 8, 7–23.
  2. Hankinson, R.W. and Thomson, G.H. (1979). A New Correlation for Saturated Densities of Liquids and Their Mixtures. AIChE J. 25, 653–663.
  3. Thomson, G.H., Brobst, K.R. and Hankinson, R.W. (1982). An Improved Correlation for Densities of Compressed Liquids and Liquid Mixtures. AIChE J. 28, 671–676.
  4. Aalto, M., Keskinen, K.I., Aittamaa, J. and Liukkonen, S. (1996). An Improved Correlation for Compressed Liquid Densities of Hydrocarbons. Part 2. Mixtures. Fluid Phase Equil. 114, 1–19.
  5. Rackett, H.G. (1970). Equation of State for Saturated Liquids. J. Chem. Eng. Data 15, 514–517.
  6. Spencer, C.F. and Danner, R.P. (1972). Improved Equation for Prediction of Saturated Liquid Density. J. Chem. Eng. Data 17, 236–241.
  7. Yamada, T. and Gunn, R.D. (1973). Saturated Liquid Molar Volumes. The Rackett Equation. J. Chem. Eng. Data 18, 234–236.
  8. Li, C.C. (1971). Critical Temperature Estimation for Simple Mixtures. Can. J. Chem. Eng. 49, 709–710.
  9. Jhaveri, B.S. and Youngren, G.K. (1988). Three-Parameter Modification of the Peng-Robinson Equation of State. SPE Reservoir Eng. 3, 1033–1040.
  10. Poling, B.E., Prausnitz, J.M. and O’Connell, J.P. (2001). The Properties of Gases and Liquids, 5th ed. McGraw-Hill.