Liquid Ethylene Density Calculator

Introduction

The Liquid Ethylene Density Calculator is a specialized tool designed to accurately determine the density of liquid ethylene based on temperature and pressure inputs. Ethylene (C₂H₄) is one of the most important organic compounds in the petrochemical industry, serving as a fundamental building block for numerous products including plastics, antifreeze, and synthetic fibers. Understanding the density of liquid ethylene is crucial for engineering applications, process design, storage considerations, and transportation logistics in industries ranging from petrochemical manufacturing to refrigeration systems.

This calculator employs precise thermodynamic models to estimate liquid ethylene density across a range of temperatures (104K to 282K) and pressures (1 to 100 bar), providing engineers, scientists, and industry professionals with reliable data for their applications. The density of liquid ethylene varies significantly with temperature and pressure, making accurate calculations essential for proper system design and operation.

How Liquid Ethylene Density is Calculated

The Mathematical Model

The density of liquid ethylene is calculated using a modified DIPPR (Design Institute for Physical Properties) correlation with pressure correction. This approach provides accurate density estimates across the liquid phase region of ethylene.

The base equation for calculating liquid ethylene density at reference pressure is:

$\rho = A \cdot (1 - \frac{T}{T_c})^n - B \cdot T$

Where:

• $\rho$ = Density of liquid ethylene (kg/m³)
• $A$ = Base density coefficient (700 for ethylene)
• $T$ = Temperature (K)
• $T_c$ = Critical temperature of ethylene (283.18K)
• $n$ = Exponent (0.29683 for ethylene)
• $B$ = Temperature coefficient (0.8 for ethylene)

To account for pressure effects, a pressure correction term is applied:

$\rho_P = \rho \cdot (1 + \kappa \cdot (P - P_{ref}))$

Where:

• $\rho_P$ = Density at pressure P (kg/m³)
• $\rho$ = Density at reference pressure (kg/m³)
• $\kappa$ = Isothermal compressibility (approximately 0.00125 MPa⁻¹ for liquid ethylene)
• $P$ = Pressure (MPa)
• $P_{ref}$ = Reference pressure (0.1 MPa or 1 bar)

Valid Ranges and Limitations

This calculation model is valid within specific ranges:

• Temperature: 104K to 282K (covering the liquid phase of ethylene)
• Pressure: 1 to 100 bar

Outside these ranges, ethylene may exist in gaseous or supercritical states, requiring different calculation methods. The critical point of ethylene is at approximately 283.18K and 50.4 bar, beyond which ethylene exists as a supercritical fluid.

Step-by-Step Guide to Using the Calculator

Input Parameters

1. Temperature Entry:

   • Enter the temperature value in Kelvin (K)
   • Valid range: 104K to 282K
   • If you have temperature in Celsius (°C), convert using: K = °C + 273.15
   • If you have temperature in Fahrenheit (°F), convert using: K = (°F - 32) × 5/9 + 273.15

2. Pressure Entry:

   • Enter the pressure value in bar
   • Valid range: 1 to 100 bar
   • If you have pressure in other units:
     • From psi: bar = psi × 0.0689476
     • From kPa: bar = kPa × 0.01
     • From MPa: bar = MPa × 10

Interpreting Results

After entering valid temperature and pressure values, the calculator will automatically display:

1. Liquid Ethylene Density: The calculated density value in kg/m³
2. Visualization: A graph showing density variation with temperature at the selected pressure

The results can be copied to clipboard using the provided button for use in reports, simulations, or other calculations.

Temperature (K) 100 150 200 250 300

Density (kg/m³) 200 300 400 500 600 700 800

10 bar 50 bar 100 bar Pressure 10 bar 50 bar 100 bar

Example Calculations

Here are some example calculations to demonstrate how the density varies with temperature and pressure:

Temperature (K)	Pressure (bar)	Density (kg/m³)
150	10	567.89
200	10	478.65
250	10	372.41
200	50	487.22
200	100	498.01

As shown in the table, liquid ethylene density decreases with increasing temperature (at constant pressure) and increases with increasing pressure (at constant temperature).

Implementation in Various Programming Languages

Here are code implementations of the liquid ethylene density calculation in several programming languages:

1def calculate_ethylene_density(temperature_k, pressure_bar):
2    """
3    Calculate the density of liquid ethylene based on temperature and pressure.
4    
5    Args:
6        temperature_k (float): Temperature in Kelvin (valid range: 104K to 282K)
7        pressure_bar (float): Pressure in bar (valid range: 1 to 100 bar)
8        
9    Returns:
10        float: Density of liquid ethylene in kg/m³
11    """
12    # Constants for ethylene
13    A = 700
14    Tc = 283.18  # Critical temperature in K
15    n = 0.29683
16    B = 0.8
17    kappa = 0.00125  # Isothermal compressibility in MPa⁻¹
18    P_ref = 0.1  # Reference pressure in MPa (1 bar)
19    
20    # Convert pressure from bar to MPa
21    pressure_mpa = pressure_bar / 10
22    
23    # Calculate density at reference pressure
24    rho_ref = A * (1 - temperature_k/Tc)**n - B * temperature_k
25    
26    # Apply pressure correction
27    rho = rho_ref * (1 + kappa * (pressure_mpa - P_ref))
28    
29    return rho
30
31# Example usage
32temp = 200  # K
33pressure = 50  # bar
34density = calculate_ethylene_density(temp, pressure)
35print(f"Liquid ethylene density at {temp}K and {pressure} bar: {density:.2f} kg/m³")
36

1/**
2 * Calculate the density of liquid ethylene based on temperature and pressure.
3 * 
4 * @param {number} temperatureK - Temperature in Kelvin (valid range: 104K to 282K)
5 * @param {number} pressureBar - Pressure in bar (valid range: 1 to 100 bar)
6 * @returns {number} Density of liquid ethylene in kg/m³
7 */
8function calculateEthyleneDensity(temperatureK, pressureBar) {
9    // Constants for ethylene
10    const A = 700;
11    const Tc = 283.18;  // Critical temperature in K
12    const n = 0.29683;
13    const B = 0.8;
14    const kappa = 0.00125;  // Isothermal compressibility in MPa⁻¹
15    const P_ref = 0.1;  // Reference pressure in MPa (1 bar)
16    
17    // Convert pressure from bar to MPa
18    const pressureMPa = pressureBar / 10;
19    
20    // Calculate density at reference pressure
21    const rhoRef = A * Math.pow(1 - temperatureK/Tc, n) - B * temperatureK;
22    
23    // Apply pressure correction
24    const rho = rhoRef * (1 + kappa * (pressureMPa - P_ref));
25    
26    return rho;
27}
28
29// Example usage
30const temp = 200;  // K
31const pressure = 50;  // bar
32const density = calculateEthyleneDensity(temp, pressure);
33console.log(`Liquid ethylene density at ${temp}K and ${pressure} bar: ${density.toFixed(2)} kg/m³`);
34

1' Excel VBA Function for Liquid Ethylene Density Calculation
2Function EthyleneDensity(TemperatureK As Double, PressureBar As Double) As Double
3    ' Constants for ethylene
4    Dim A As Double: A = 700
5    Dim Tc As Double: Tc = 283.18 ' Critical temperature in K
6    Dim n As Double: n = 0.29683
7    Dim B As Double: B = 0.8
8    Dim kappa As Double: kappa = 0.00125 ' Isothermal compressibility in MPa⁻¹
9    Dim P_ref As Double: P_ref = 0.1 ' Reference pressure in MPa (1 bar)
10    
11    ' Convert pressure from bar to MPa
12    Dim PressureMPa As Double: PressureMPa = PressureBar / 10
13    
14    ' Calculate density at reference pressure
15    Dim rho_ref As Double: rho_ref = A * (1 - TemperatureK / Tc) ^ n - B * TemperatureK
16    
17    ' Apply pressure correction
18    EthyleneDensity = rho_ref * (1 + kappa * (PressureMPa - P_ref))
19End Function
20
21' Usage in Excel cell:
22' =EthyleneDensity(200, 50)
23

1function density = ethyleneDensity(temperatureK, pressureBar)
2    % Calculate the density of liquid ethylene based on temperature and pressure
3    %
4    % Inputs:
5    %   temperatureK - Temperature in Kelvin (valid range: 104K to 282K)
6    %   pressureBar - Pressure in bar (valid range: 1 to 100 bar)
7    %
8    % Output:
9    %   density - Density of liquid ethylene in kg/m³
10    
11    % Constants for ethylene
12    A = 700;
13    Tc = 283.18;  % Critical temperature in K
14    n = 0.29683;
15    B = 0.8;
16    kappa = 0.00125;  % Isothermal compressibility in MPa⁻¹
17    P_ref = 0.1;  % Reference pressure in MPa (1 bar)
18    
19    % Convert pressure from bar to MPa
20    pressureMPa = pressureBar / 10;
21    
22    % Calculate density at reference pressure
23    rho_ref = A * (1 - temperatureK/Tc)^n - B * temperatureK;
24    
25    % Apply pressure correction
26    density = rho_ref * (1 + kappa * (pressureMPa - P_ref));
27end
28
29% Example usage
30temp = 200;  % K
31pressure = 50;  % bar
32density = ethyleneDensity(temp, pressure);
33fprintf('Liquid ethylene density at %gK and %g bar: %.2f kg/m³\n', temp, pressure, density);
34

1#include <iostream>
2#include <cmath>
3
4/**
5 * Calculate the density of liquid ethylene based on temperature and pressure.
6 * 
7 * @param temperatureK Temperature in Kelvin (valid range: 104K to 282K)
8 * @param pressureBar Pressure in bar (valid range: 1 to 100 bar)
9 * @return Density of liquid ethylene in kg/m³
10 */
11double calculateEthyleneDensity(double temperatureK, double pressureBar) {
12    // Constants for ethylene
13    const double A = 700.0;
14    const double Tc = 283.18;  // Critical temperature in K
15    const double n = 0.29683;
16    const double B = 0.8;
17    const double kappa = 0.00125;  // Isothermal compressibility in MPa⁻¹
18    const double P_ref = 0.1;  // Reference pressure in MPa (1 bar)
19    
20    // Convert pressure from bar to MPa
21    double pressureMPa = pressureBar / 10.0;
22    
23    // Calculate density at reference pressure
24    double rho_ref = A * pow(1.0 - temperatureK/Tc, n) - B * temperatureK;
25    
26    // Apply pressure correction
27    double rho = rho_ref * (1.0 + kappa * (pressureMPa - P_ref));
28    
29    return rho;
30}
31
32int main() {
33    double temp = 200.0;  // K
34    double pressure = 50.0;  // bar
35    double density = calculateEthyleneDensity(temp, pressure);
36    
37    std::cout << "Liquid ethylene density at " << temp << "K and " 
38              << pressure << " bar: " << density << " kg/m³" << std::endl;
39    
40    return 0;
41}
42

1public class EthyleneDensityCalculator {
2    /**
3     * Calculate the density of liquid ethylene based on temperature and pressure.
4     * 
5     * @param temperatureK Temperature in Kelvin (valid range: 104K to 282K)
6     * @param pressureBar Pressure in bar (valid range: 1 to 100 bar)
7     * @return Density of liquid ethylene in kg/m³
8     */
9    public static double calculateEthyleneDensity(double temperatureK, double pressureBar) {
10        // Constants for ethylene
11        final double A = 700.0;
12        final double Tc = 283.18;  // Critical temperature in K
13        final double n = 0.29683;
14        final double B = 0.8;
15        final double kappa = 0.00125;  // Isothermal compressibility in MPa⁻¹
16        final double P_ref = 0.1;  // Reference pressure in MPa (1 bar)
17        
18        // Convert pressure from bar to MPa
19        double pressureMPa = pressureBar / 10.0;
20        
21        // Calculate density at reference pressure
22        double rhoRef = A * Math.pow(1.0 - temperatureK/Tc, n) - B * temperatureK;
23        
24        // Apply pressure correction
25        double rho = rhoRef * (1.0 + kappa * (pressureMPa - P_ref));
26        
27        return rho;
28    }
29    
30    public static void main(String[] args) {
31        double temp = 200.0;  // K
32        double pressure = 50.0;  // bar
33        double density = calculateEthyleneDensity(temp, pressure);
34        
35        System.out.printf("Liquid ethylene density at %.1fK and %.1f bar: %.2f kg/m³%n", 
36                          temp, pressure, density);
37    }
38}
39

Use Cases and Applications

Industrial Applications

1. Petrochemical Processing:

   • Accurate density values are essential for designing distillation columns, reactors, and separation equipment for ethylene production and processing.
   • Flow calculations in pipelines and process equipment require precise density data.

2. Cryogenic Storage and Transportation:

   • Ethylene is often stored and transported as a cryogenic liquid. Density calculations help determine storage tank capacities and loading limits.
   • Thermal expansion considerations during warming require accurate density-temperature relationships.

3. Polyethylene Manufacturing:

   • As the primary feedstock for polyethylene production, ethylene properties including density affect reaction kinetics and product quality.
   • Mass balance calculations in production facilities rely on accurate density values.

4. Refrigeration Systems:

   • Ethylene is used as a refrigerant in some industrial cooling systems, where density affects system performance and efficiency.
   • Charge calculations for refrigeration systems require accurate density data.

5. Quality Control:

   • Density measurements can serve as quality indicators for ethylene purity in production and storage.

Research Applications

1. Thermodynamic Studies:

   • Researchers studying phase behavior and equation of state models use density data to validate theoretical models.
   • Accurate density measurements help in developing improved correlations for liquid properties.

2. Material Development:

   • Development of new polymers and materials based on ethylene requires understanding of the monomer's physical properties.

3. Process Simulation:

   • Chemical process simulators require accurate density models for ethylene to predict system behavior.

Engineering Design

1. Equipment Sizing:

   • Pumps, valves, and piping systems handling liquid ethylene must be designed based on accurate fluid properties including density.
   • Pressure drop calculations in process equipment depend on fluid density.

2. Safety Systems:

   • Relief valve sizing and safety system design require accurate density values across operating ranges.
   • Leak detection systems may use density measurements as part of their monitoring approach.

Alternatives to Calculation

While this calculator provides a convenient way to estimate liquid ethylene density, there are alternative approaches:

1. Experimental Measurement:

   • Direct measurement using densitometers or pycnometers provides the most accurate results but requires specialized equipment.
   • Laboratory analysis is typically used for high-precision requirements or research purposes.

2. Equation of State Models:

   • More complex equations of state such as Peng-Robinson, Soave-Redlich-Kwong, or SAFT can provide density estimates with potentially higher accuracy, especially near critical conditions.
   • These models typically require specialized software and more computational resources.

3. NIST REFPROP Database:

   • The NIST Reference Fluid Thermodynamic and Transport Properties Database (REFPROP) provides high-accuracy property data but requires a license.

4. Published Data Tables:

   • Reference handbooks and published data tables provide density values at discrete temperature and pressure points.
   • Interpolation between table values may be required for specific conditions.

Historical Development of Ethylene Density Calculations

Early Studies of Ethylene Properties

The study of ethylene's physical properties dates back to the early 19th century when Michael Faraday first liquefied ethylene in 1834 using a combination of low temperature and high pressure. However, systematic studies of liquid ethylene density began in the early 20th century as industrial applications for ethylene expanded.

Development of Correlations

In the 1940s and 1950s, as the petrochemical industry grew rapidly, more precise measurements of ethylene properties became necessary. Early correlations for liquid density were typically simple polynomial functions of temperature, with limited accuracy and range.

The 1960s saw the development of more sophisticated models based on the principle of corresponding states, which allowed properties to be estimated based on critical parameters. These models improved accuracy but still had limitations, especially at high pressures.

Modern Approaches

The Design Institute for Physical Properties (DIPPR) began developing standardized correlations for chemical properties in the 1980s. Their correlations for liquid ethylene density represented a significant improvement in accuracy and reliability.

In recent decades, advances in computational methods have enabled the development of more complex equations of state that can accurately predict ethylene properties across wide ranges of temperature and pressure. Modern molecular simulation techniques also allow for prediction of properties from first principles.

Experimental Techniques

Measurement techniques for liquid density have also evolved significantly. Early methods relied on simple displacement techniques, while modern methods include:

• Vibrating tube densitometers
• Magnetic suspension balances
• Pycnometers with temperature control
• Hydrostatic weighing methods

These advanced techniques have provided the high-quality experimental data needed to develop and validate the correlations used in this calculator.

Frequently Asked Questions

What is liquid ethylene?

Liquid ethylene is the liquid state of ethylene (C₂H₄), a colorless, flammable gas at room temperature and atmospheric pressure. Ethylene must be cooled below its boiling point of -103.7°C (169.45K) at atmospheric pressure to exist as a liquid. In this state, it's commonly used in industrial processes, particularly as a feedstock for polyethylene production.

Why is ethylene density important?

Ethylene density is crucial for designing storage tanks, transportation systems, and process equipment. Accurate density values enable proper sizing of equipment, ensure safety in handling, and allow precise calculation of mass flow rates, heat transfer, and other process parameters. Density also affects the economics of storage and transportation, as it determines how much ethylene can be contained in a given volume.

How does temperature affect liquid ethylene density?

Temperature has a significant impact on liquid ethylene density. As temperature increases, the density decreases due to thermal expansion of the liquid. Near the critical temperature (283.18K), the density changes more dramatically with small temperature variations. This relationship is particularly important in cryogenic applications where temperature control is essential.

How does pressure affect liquid ethylene density?

Pressure has a moderate effect on liquid ethylene density. Higher pressures result in slightly higher densities due to compression of the liquid. The effect is less pronounced than temperature effects but becomes more significant at pressures above 50 bar. The relationship between pressure and density is approximately linear within the normal operating range.

What happens to ethylene density near the critical point?

Near the critical point (approximately 283.18K and 50.4 bar), ethylene's density becomes highly sensitive to small changes in temperature and pressure. The distinction between liquid and gas phases disappears at the critical point, and the density approaches the critical density of about 214 kg/m³. The calculator may not provide accurate results very close to the critical point due to the complex behavior in this region.

Can this calculator be used for gaseous ethylene?

No, this calculator is specifically designed for liquid ethylene within the temperature range of 104K to 282K and pressure range of 1 to 100 bar. Gaseous ethylene density calculations require different equations of state, such as the ideal gas law with compressibility corrections or more complex models like Peng-Robinson or Soave-Redlich-Kwong.

How accurate is this calculator?

The calculator provides density estimates with an accuracy of approximately ±2% within the specified temperature and pressure ranges. Accuracy may decrease near the boundaries of the valid ranges, particularly near the critical point. For applications requiring higher precision, laboratory measurements or more complex thermodynamic models may be necessary.

What units does the calculator use?

The calculator uses the following units:

• Temperature: Kelvin (K)
• Pressure: bar
• Density: kilograms per cubic meter (kg/m³)

Can I convert the density to other units?

Yes, you can convert the density to other common units using these conversion factors:

• To g/cm³: Divide by 1000
• To lb/ft³: Multiply by 0.06243
• To lb/gal (US): Multiply by 0.008345

Where can I find more detailed ethylene property data?

For more comprehensive ethylene property data, consult resources such as:

• NIST REFPROP database
• Perry's Chemical Engineers' Handbook
• Yaws' Handbook of Thermodynamic Properties
• AIChE DIPPR Project 801 database
• Journal publications in fluid phase equilibria and thermophysical properties

References

1. Younglove, B.A. (1982). "Thermophysical Properties of Fluids. I. Argon, Ethylene, Parahydrogen, Nitrogen, Nitrogen Trifluoride, and Oxygen." Journal of Physical and Chemical Reference Data, 11(Supplement 1), 1-11.

2. Jahangiri, M., Jacobsen, R.T., Stewart, R.B., & McCarty, R.D. (1986). "Thermodynamic properties of ethylene from the freezing line to 450 K at pressures to 260 MPa." Journal of Physical and Chemical Reference Data, 15(2), 593-734.

3. Design Institute for Physical Properties. (2005). DIPPR Project 801 - Full Version. Design Institute for Physical Property Research/AIChE.

4. Span, R., & Wagner, W. (1996). "A new equation of state for carbon dioxide covering the fluid region from the triple‐point temperature to 1100 K at pressures up to 800 MPa." Journal of Physical and Chemical Reference Data, 25(6), 1509-1596.

5. Lemmon, E.W., McLinden, M.O., & Friend, D.G. (2018). "Thermophysical Properties of Fluid Systems" in NIST Chemistry WebBook, NIST Standard Reference Database Number 69. National Institute of Standards and Technology, Gaithersburg MD, 20899.

6. Poling, B.E., Prausnitz, J.M., & O'Connell, J.P. (2001). The Properties of Gases and Liquids (5th ed.). McGraw-Hill.

7. American Institute of Chemical Engineers. (2019). DIPPR 801 Database: Data Compilation of Pure Compound Properties. AIChE.

8. Setzmann, U., & Wagner, W. (1991). "A new equation of state and tables of thermodynamic properties for methane covering the range from the melting line to 625 K at pressures up to 1000 MPa." Journal of Physical and Chemical Reference Data, 20(6), 1061-1155.

Try Our Calculator Now

Our Liquid Ethylene Density Calculator provides instant, accurate density values based on your specific temperature and pressure requirements. Simply enter your parameters within the valid ranges, and the calculator will automatically determine the liquid ethylene density for your application.

Whether you're designing process equipment, planning storage facilities, or conducting research, this tool offers a quick and reliable way to obtain the density information you need. The included visualization helps you understand how density changes with temperature at your selected pressure point.

For any questions or feedback about this calculator, please contact our support team.