Understanding the Calculation of Liquid Ethylene Density

Liquid ethylene density calculation determines the mass per unit volume under specific conditions. This article explores formulas, tables, and real-world applications.

Discover detailed methods, variable explanations, and practical examples for accurate ethylene density computations. Essential for engineers and researchers alike.

• Calculate liquid ethylene density at -103°C and 1 atm pressure.
• Determine density variation of liquid ethylene between -110°C and -90°C.
• Find density of liquid ethylene at 5 MPa and -100°C using empirical formulas.
• Estimate liquid ethylene density for storage tank design at cryogenic conditions.

Comprehensive Tables of Liquid Ethylene Density Values

Accurate density values of liquid ethylene are critical for process design, safety, and storage. The following tables present density data across typical temperature and pressure ranges encountered in industrial applications.

These values are derived from standard references such as the NIST Chemistry WebBook and API Technical Data Sheets, ensuring reliability for engineering calculations.

Fundamental Formulas for Calculating Liquid Ethylene Density

Calculating the density of liquid ethylene requires understanding thermodynamic relationships and empirical correlations. Below are the primary formulas used in industry and research.

1. Basic Density Definition

Density (ρ) is defined as mass (m) per unit volume (V):

Where:

• ρ = density (kg/m³)
• m = mass (kg)
• V = volume (m³)

2. Temperature and Pressure Dependence

Density varies with temperature (T) and pressure (P). For liquids, the density can be approximated by:

Where:

• ρ(T,P) = density at temperature T and pressure P (kg/m³)
• ρ_ref = reference density at T_ref and P_ref (kg/m³)
• β = volumetric thermal expansion coefficient (1/°C)
• κ = isothermal compressibility (1/MPa)
• T = temperature (°C)
• P = pressure (MPa)
• T_ref = reference temperature (°C)
• P_ref = reference pressure (MPa)

Typical values for liquid ethylene:

• ρ_ref = 540 kg/m³ at T_ref = -100°C and P_ref = 0.1 MPa
• β ≈ 0.0012 1/°C
• κ ≈ 0.00015 1/MPa

3. Empirical Correlation Using Rackett Equation

The Rackett equation is widely used to estimate liquid density near the saturation point:

Where:

• ρ = liquid density (g/cm³)
• M = molar mass of ethylene (28.05 g/mol)
• V_c = critical molar volume (cm³/mol), approx. 94.0 cm³/mol for ethylene
• T_r = reduced temperature = T / T_c
• T = temperature in Kelvin (K)
• T_c = critical temperature of ethylene (282.34 K)

This formula provides a good approximation near the critical point and saturation conditions.

4. Peng-Robinson Equation of State (EOS) for Density Calculation

For more precise density calculations under varying conditions, the Peng-Robinson EOS is used:

Where:

• P = pressure (Pa)
• R = universal gas constant (8.314 J/mol·K)
• T = temperature (K)
• V_m = molar volume (m³/mol)
• a(T) = temperature-dependent attraction parameter
• b = co-volume parameter

Once V_m is solved from the cubic EOS, density is calculated as:

Where M is molar mass in kg/mol.

Parameters a and b are calculated from critical properties:

Where:

• T_c = critical temperature (K)
• P_c = critical pressure (Pa)

The temperature dependence of a(T) is given by:

Where c is an empirical constant related to acentric factor ω:

For ethylene, ω ≈ 0.086.

Real-World Applications and Detailed Examples

Example 1: Density Calculation at Cryogenic Storage Conditions

A storage tank contains liquid ethylene at -100°C and 0.1 MPa. Calculate the density using the thermal expansion and compressibility formula.

Given:

• T = -100°C
• P = 0.1 MPa
• ρ_ref = 540 kg/m³ at T_ref = -100°C, P_ref = 0.1 MPa
• β = 0.0012 1/°C
• κ = 0.00015 1/MPa

Since T = T_ref and P = P_ref, density is:

The density remains 540 kg/m³, confirming reference data.

Example 2: Density Estimation at Elevated Pressure and Temperature

Calculate the density of liquid ethylene at -90°C and 2 MPa using the thermal expansion and compressibility formula.

Given:

• T = -90°C
• P = 2 MPa
• ρ_ref = 540 kg/m³ at T_ref = -100°C, P_ref = 0.1 MPa
• β = 0.0012 1/°C
• κ = 0.00015 1/MPa

Calculate the denominator:

Calculate density:

The density decreases slightly due to temperature increase but is partially offset by pressure increase.

Example 3: Using Peng-Robinson EOS for Density at -100°C and 5 MPa

Calculate the molar volume and density of liquid ethylene at -100°C (173.15 K) and 5 MPa using Peng-Robinson EOS.

Given:

• T = 173.15 K
• P = 5,000,000 Pa
• M = 0.02805 kg/mol
• T_c = 282.34 K
• P_c = 5,040,000 Pa
• ω = 0.086
• R = 8.314 J/mol·K

Calculate parameters:

Calculate c:

Calculate α(T):

Calculate a(T):

Now solve the cubic Peng-Robinson EOS for molar volume V_m. This requires iterative or numerical methods (e.g., Newton-Raphson). For brevity, assume liquid root V_m ≈ 0.00004 m³/mol (typical for liquid ethylene).

Calculate density:

This value is higher than atmospheric pressure density due to compression at 5 MPa.

Additional Considerations in Liquid Ethylene Density Calculations

Several factors influence the accuracy and applicability of density calculations:

• Purity of Ethylene: Impurities alter density and phase behavior.
• Measurement Uncertainties: Temperature and pressure sensors must be precise.
• Phase Equilibria: Near saturation, vapor-liquid equilibrium affects density.
• Thermodynamic Models: Selection of EOS or empirical correlations depends on operating range.
• Safety Margins: Design calculations incorporate safety factors due to density variability.

For industrial applications, density data is often validated against experimental measurements and standards such as ASTM D1250 or API MPMS Chapter 11.

References and Further Reading

• NIST Chemistry WebBook – Authoritative source for thermophysical properties.
• American Petroleum Institute (API) – Standards for hydrocarbon properties.
• Peng-Robinson EOS Applications in Hydrocarbon Systems
• ASTM D1250 – Petroleum Measurement Tables