Interfacial Properties

This guide documents the interfacial property calculations available in NeqSim, including surface tension and related phenomena.

Overview
Surface Tension Models
Model Selection by Interface Type
Usage Examples
Adsorption Calculations
Mathematical Background

Overview

Interfacial tension (IFT) describes the energy required to create a unit area of interface between two phases. It is critical for:

Capillary pressure calculations
Droplet/bubble formation
Mass transfer at interfaces
Enhanced oil recovery studies
Separator design

Units:

Default output: N/m (Newtons per meter)
Alternative: mN/m (milliNewtons per meter = dyne/cm)

Basic usage:

fluid.initPhysicalProperties();
double sigma = fluid.getInterphaseProperties().getSurfaceTension(0, 1);  // N/m

Surface Tension Models

Parachor (Macleod-Sugden)

The Parachor method is an empirical correlation relating surface tension to density difference and component parachors.

Class: ParachorSurfaceTension

Equation: $\sigma^{1/4} = \sum_i P_i \left( \frac{\rho_L x_i}{M_{mix,L}} - \frac{\rho_V y_i}{M_{mix,V}} \right)$

where:

$P_i$ is the parachor of component $i$ (from COMP database)
$\rho$ is molar density (mol/m³)
$x_i, y_i$ are liquid and vapor mole fractions
$M_{mix}$ is mixture molar mass

Parachor values:

Stored in COMP database as PARACHOR column
For CPA models, use PARACHOR_CPA

Applicable interfaces: Gas-liquid, Gas-aqueous

Best for:

Hydrocarbon systems
Quick estimates
When parachor values are available

Usage:

fluid.getInterphaseProperties().setInterfacialTensionModel("gas", "oil", "Parachor");

Gradient Theory (GT)

The Gradient Theory is a rigorous thermodynamic approach based on density functional theory.

Classes:

GTSurfaceTension - Full gradient theory (most rigorous)
GTSurfaceTensionSimple - Simplified version
GTSurfaceTensionODE - ODE-based solver

Physical basis:

Near an interface, the Helmholtz energy depends on density gradients:

\[A = \int_{-\infty}^{\infty} \left[ a_0(\boldsymbol{n}) + \frac{1}{2}\sum_i\sum_j c_{ij} \frac{dn_i}{dz}\frac{dn_j}{dz} \right] dz\]

where:

$a_0$ is the homogeneous fluid Helmholtz energy
$c_{ij}$ are the influence parameters
$n_i$ is the number density of component $i$
$z$ is the spatial coordinate

Surface tension calculation: $\sigma = \int_{-\infty}^{\infty} \sum_i\sum_j c_{ij} \frac{dn_i}{dz}\frac{dn_j}{dz} dz$

Influence parameter correlation: $c_i = (A_i t_i + B_i) a_i b_i^{2/3}$

where:

$t_i = 1 - T/T_{c,i}$
$a_i, b_i$ are EoS parameters
$A_i, B_i$ are component-specific constants

Applicable interfaces: All phase pairs

Best for:

High accuracy requirements
Near-critical conditions
When EoS is well-calibrated

Usage:

// Full gradient theory
fluid.getInterphaseProperties().setInterfacialTensionModel("gas", "oil", "Full Gradient Theory");

// Simplified version (faster)
fluid.getInterphaseProperties().setInterfacialTensionModel("gas", "oil", "Simple Gradient Theory");

Linear Gradient Theory (LGT)

A linearized approximation of gradient theory that is computationally efficient.

Class: LGTSurfaceTension

Approximation: Assumes linear density profile between bulk phases:

\[n_i(z) = n_i^L + \frac{n_i^V - n_i^L}{L} z\]

This allows analytical integration:

\[\sigma = \sum_i\sum_j c_{ij} \frac{(n_i^V - n_i^L)(n_j^V - n_j^L)}{L}\]

where $L$ is optimized to minimize Helmholtz energy.

Applicable interfaces: Gas-liquid

Best for:

Balance of accuracy and speed
Parametric studies
When full GT is too slow

Usage:

fluid.getInterphaseProperties().setInterfacialTensionModel("gas", "oil", "Linear Gradient Theory");

Firozabadi-Ramley

A correlation specifically designed for liquid-liquid interfaces (oil-water).

Class: FirozabadiRamleyInterfaceTension

Equation: $\sigma_{ow} = \sigma_o + \sigma_w - 2\sqrt{\sigma_o \sigma_w} \phi$

where:

$\sigma_o, \sigma_w$ are oil and water surface tensions
$\phi$ is an interaction parameter

Applicable interfaces: Oil-water (liquid-liquid)

Best for:

Oil-water systems
When aqueous phase is present
Three-phase systems

Usage:

fluid.getInterphaseProperties().setInterfacialTensionModel("oil", "aqueous", "Firozabadi Ramley");

Model Selection by Interface Type

NeqSim automatically selects models based on phase types, but you can override:

Using Model Numbers

// Set interfacial tension model set by number
fluid.getInterphaseProperties().setInterfacialTensionModel(0);  // Default set

Number	Gas-Oil	Gas-Aqueous	Oil-Aqueous
0	Parachor	Parachor	Firozabadi-Ramley
1	Full GT	Simple GT	Simple GT
2	LGT	LGT	LGT
3	Parachor	Parachor	Firozabadi-Ramley
4	Simple GT	Parachor	LGT
5	Parachor	Parachor	Firozabadi-Ramley

Using Named Models

// Set specific models per interface
fluid.getInterphaseProperties().setInterfacialTensionModel("gas", "oil", "Full Gradient Theory");
fluid.getInterphaseProperties().setInterfacialTensionModel("gas", "aqueous", "Parachor");
fluid.getInterphaseProperties().setInterfacialTensionModel("oil", "aqueous", "Firozabadi Ramley");

Available model names:

"Parachor" or "Weinaug-Katz"
"Full Gradient Theory"
"Simple Gradient Theory"
"Linear Gradient Theory"
"Firozabadi Ramley"

Usage Examples

Basic Surface Tension

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

// Create and flash fluid
SystemInterface fluid = new SystemSrkEos(300.0, 50.0);
fluid.addComponent("methane", 0.8);
fluid.addComponent("n-decane", 0.2);
fluid.setMixingRule("classic");
fluid.setMultiPhaseCheck(true);

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

// Initialize physical properties
fluid.initPhysicalProperties();

// Get surface tension between phase 0 and 1
double sigma = fluid.getInterphaseProperties().getSurfaceTension(0, 1);
System.out.println("Surface tension: " + sigma * 1000 + " mN/m");

Comparing Surface Tension Models

String[] models = {"Parachor", "Full Gradient Theory", "Linear Gradient Theory"};

SystemInterface baseFluid = createTwoPhaseFluid();
ThermodynamicOperations ops = new ThermodynamicOperations(baseFluid);
ops.TPflash();
baseFluid.initPhysicalProperties();

for (String model : models) {
    SystemInterface fluid = baseFluid.clone();
    fluid.getInterphaseProperties().setInterfacialTensionModel("gas", "oil", model);
    fluid.initPhysicalProperties();
    
    double sigma = fluid.getInterphaseProperties().getSurfaceTension(0, 1) * 1000;
    System.out.println(model + ": " + sigma + " mN/m");
}

Surface Tension vs Pressure (Approaching Critical)

SystemInterface fluid = new SystemSrkEos(350.0, 10.0);
fluid.addComponent("methane", 0.5);
fluid.addComponent("n-pentane", 0.5);
fluid.setMixingRule("classic");
fluid.setMultiPhaseCheck(true);

double[] pressures = {10, 30, 50, 70, 90, 100, 110};

for (double P : pressures) {
    fluid.setPressure(P, "bar");
    
    ThermodynamicOperations ops = new ThermodynamicOperations(fluid);
    ops.TPflash();
    
    if (fluid.getNumberOfPhases() >= 2) {
        fluid.initPhysicalProperties();
        double sigma = fluid.getInterphaseProperties().getSurfaceTension(0, 1) * 1000;
        System.out.println("P=" + P + " bar: σ=" + sigma + " mN/m");
    } else {
        System.out.println("P=" + P + " bar: Single phase");
    }
}
// Surface tension approaches zero at critical point

Three-Phase System

SystemInterface fluid = new SystemSrkCPAstatoil(300.0, 30.0);
fluid.addComponent("methane", 0.6);
fluid.addComponent("n-heptane", 0.3);
fluid.addComponent("water", 0.1);
fluid.setMixingRule(10);
fluid.setMultiPhaseCheck(true);

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

// Get all interfacial tensions
int nPhases = fluid.getNumberOfPhases();
for (int i = 0; i < nPhases; i++) {
    for (int j = i + 1; j < nPhases; j++) {
        double sigma = fluid.getInterphaseProperties().getSurfaceTension(i, j);
        System.out.println("Phase " + i + " - Phase " + j + ": " + 
            sigma * 1000 + " mN/m");
    }
}

Adsorption Calculations

NeqSim also supports adsorption calculations at solid surfaces.

Setup

// Initialize adsorption
fluid.getInterphaseProperties().initAdsorption();

// Set adsorbent material
fluid.getInterphaseProperties().setSolidAdsorbentMaterial("ite");

// Calculate adsorption
fluid.getInterphaseProperties().calcAdsorption();

Access Results

AdsorptionInterface ads = fluid.getInterphaseProperties().getAdsorptionCalc("gas");
// Access adsorption quantities per component

Mathematical Background

Thermodynamic Definition

Surface tension is defined as:

\[\sigma = \left( \frac{\partial G}{\partial A} \right)_{T,P,n}\]

where $G$ is Gibbs energy and $A$ is interfacial area.

Young-Laplace Equation

The pressure difference across a curved interface:

\[\Delta P = \sigma \left( \frac{1}{R_1} + \frac{1}{R_2} \right)\]

where $R_1, R_2$ are the principal radii of curvature.

Temperature Dependence

Surface tension typically decreases with temperature:

\[\sigma = \sigma_0 \left( 1 - T/T_c \right)^n\]

where $n \approx 1.26$ (Guggenheim exponent).

At the critical point: $\sigma \rightarrow 0$.

Pressure Dependence

Surface tension generally decreases with increasing pressure because:

Density difference decreases
Phases become more similar as pressure increases

Near the critical point, $\sigma \propto (\rho_L - \rho_V)^{3.9}$.

Typical Values

Interface	Temperature	Typical IFT
Methane-Water	25°C, 100 bar	50-70 mN/m
Crude Oil-Gas	Reservoir	5-30 mN/m
Crude Oil-Water	25°C	20-30 mN/m
n-Hexane-Air	25°C	18 mN/m
Water-Air	25°C	72 mN/m
Near critical	-	0-1 mN/m

References

Macleod, D.B. (1923). On a Relation between Surface Tension and Density. Trans. Faraday Soc.
Sugden, S. (1924). The Variation of Surface Tension with Temperature and Some Related Functions. J. Chem. Soc.
Cahn, J.W., Hilliard, J.E. (1958). Free Energy of a Nonuniform System. J. Chem. Phys.
Miqueu, C., et al. (2004). Modelling of the Surface Tension of Pure Components with the Gradient Theory. Fluid Phase Equilib.
Firozabadi, A., Ramey, H.J. (1988). Surface Tension of Water-Hydrocarbon Systems at Reservoir Conditions. JCPT.

Interfacial Properties

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

Interfacial Properties

Table of Contents

Overview

Surface Tension Models

Parachor (Macleod-Sugden)

Gradient Theory (GT)

Linear Gradient Theory (LGT)

Firozabadi-Ramley

Model Selection by Interface Type

Using Model Numbers

Using Named Models

Usage Examples

Basic Surface Tension

Comparing Surface Tension Models

Surface Tension vs Pressure (Approaching Critical)

Three-Phase System

Adsorption Calculations

Setup

Access Results

Mathematical Background

Thermodynamic Definition

Young-Laplace Equation

Temperature Dependence

Pressure Dependence

Typical Values

References