Fugacity Coefficient Tool Calculator

Calculator Inputs

Use x₁ = 1 for a pure-component estimate.

Component 1 Name

Component 2 Name

Phase Root

Pressure (bar)

Temperature (K)

Component 1 Mole Fraction

Component 1 Critical Temperature (K)

Component 1 Critical Pressure (bar)

Component 1 Acentric Factor

Component 2 Critical Temperature (K)

Component 2 Critical Pressure (bar)

Component 2 Acentric Factor

Binary Interaction Parameter k_ij

Example Data Table

Case	P (bar)	T (K)	x₁	Component 1	Component 2	k_ij	Phase
Methane rich gas	50	300	0.80	Methane: T_c 190.56, P_c 45.99, ω 0.011	Ethane: T_c 305.32, P_c 48.72, ω 0.099	0.013	Vapor
CO₂ and nitrogen	80	320	0.60	CO₂: T_c 304.13, P_c 73.77, ω 0.225	Nitrogen: T_c 126.20, P_c 33.98, ω 0.037	-0.020	Vapor
Liquid-like propane	15	280	1.00	Propane: T_c 369.83, P_c 42.48, ω 0.152	Not used for pure estimate	0.000	Liquid

Formula Used

This tool uses the Peng-Robinson equation of state with classical quadratic mixing rules for a pure fluid or a simple binary system.

P = RT / (V - b) - a / (V(V + b) + b(V - b))

κ = 0.37464 + 1.54226ω - 0.26992ω²

α = [1 + κ(1 - √(T / T_c))]²

a_i = 0.45724 R²T_c²α / P_c, b_i = 0.07780 RT_c / P_c

a_mix = ΣΣ z_iz_j√(a_ia_j)(1 - k_ij), b_mix = Σ z_ib_i

A = a_mixP / (R²T²), B = b_mixP / (RT)

ln φ_i = (b_i/b_mix)(Z - 1) - ln(Z - B) - [A/(2√2B)] × [(2Σz_ja_ij/a_mix) - (b_i/b_mix)] × ln[(Z + (1 + √2)B)/(Z + (1 - √2)B)]

The tool solves the cubic EOS for real compressibility roots and then applies the chosen phase root to evaluate fugacity coefficients and component fugacities.

How to Use This Calculator

Enter pressure and temperature in bar and kelvin.
Provide names and critical properties for both components.
Set component 1 mole fraction between 0 and 1.
Use x₁ = 1 for a pure fluid estimate.
Enter the binary interaction parameter if mixture data exists.
Select vapor root for gas phases and liquid root for condensed phases.
Submit the form to view Z, roots, fugacity coefficients, and fugacity values.
Use the export buttons to save the output as CSV or PDF.

Frequently Asked Questions

1. What does the fugacity coefficient represent?

It measures deviation from ideal-gas behavior. A value near one suggests mild nonideality, while larger departures indicate stronger intermolecular effects at the selected pressure, temperature, and composition.

2. Which thermodynamic model does this tool use?

The calculator uses the Peng-Robinson equation of state. It is widely used for hydrocarbon systems, gases, phase-equilibrium studies, and engineering estimates involving nonideal fluids.

3. When should I choose the vapor root?

Choose the vapor root for gas-like states and superheated conditions. In multiphase regions, the largest valid compressibility root usually represents the vapor phase solution.

4. When should I choose the liquid root?

Choose the liquid root when the state is compressed or saturated on the liquid side. The smallest valid compressibility root generally represents the denser phase.

5. Why can the coefficient be smaller or larger than one?

Values below one often reflect net attractive effects. Values above one can appear when repulsive or excluded-volume effects dominate under dense or high-pressure conditions.

6. What units should I use?

Enter pressure in bar, temperature in kelvin, and critical pressure in bar. The reported fugacity values are also returned in bar for consistency.

7. Can this tool handle mixtures?

Yes. It supports a simple binary mixture using one mole fraction and one binary interaction parameter. Set component 1 mole fraction to one for a pure estimate.

8. Can I rely on this for final design decisions?

Use it for screening, education, and preliminary engineering checks. Final design work should also consider validated property packages, laboratory data, and process-specific phase-equilibrium models.