3C. Gas Compressibility and Density by Several Methods Back to Main

This page is used to determine the density of gas using several equations of state methods. Any equation correlating P, V and T is called an equation of state.

Equation (3.1)

Because of simplicity, Equation (3.1) is often corrected by a compressibility factor z.

Equation (3.11)

It is then rewritten in the form

Equation (3.12)

Where: P = Pressure of the gas

MW = Molecular Weight

z = Compressibility Factor

R = Proportionality Constant or Universal Gas Constant

T = Temperature of the gas

n = number of moles of gas of volume V at P and T

To calculate the gas compressibility and density, the method of calculation must be decided. Choose Katz correlation and Kay's rule using gas composition, Katz correlation using natural gas relative density, Katz correlation with a correction for sour gases, or SRK equation of state by clicking on and shading the circle provided for that selection.

A. Katz correlation and Kay’s rule using gas composition.

This is the simplest method for calculating z. The values of and for use with Katz Compressibility Factor Chart (Figure 3.2) may be found from Kay’s Rule. This rule states that

Equation (3.13) And

Where: = is the mole fraction of each component in the mixture

And = the critical values of each component found from Physical Constants Table. (A link would be here to take you directly to the table)

Dividing the actual, absolute temperature and pressure by the corresponding critical values gives the necessary reduced Values.

Equation (3.6) And

B. Katz correlation and natural gas relative density.

Often density calculations are required when very little information is available. Approximate Pseudo – Critical Properties of Natural Gas Chart (Figure 3.4) can be used to estimate pseudocritical temperature and pressure if no analysis is available. This is a very approximate correlation.

C. Katz correlation with a correction for sour gases.

The more dissimilar the molecules, the less accurate the prediction becomes. Sour fluids containing sulfur compounds and/or carbon dioxide are a disorderly lot. It depends on the application, but the reliability of this approach is seldom better than ± 10% and has a high likelihood of being in the 15 – 20% range. The moral – don’t fret about this just recognize it and make the system flexible enough to handle the uncertainty.

The Katz rule may be extended to gases containing and also referred to as sour gases. Wichert and Aziz proposed the approach. The approach utilizes an adjustment of and which is found from Kay’s combination rule, and which was used to prepare the Katz chart. It uses a correction parameter, e found from Correction Factor Chart for Sour Gases (Fig 3.3). This Correction parameter is used to adjust the pseudocritical found from Kay’s Rule. The adjusted values then used to fund the reduced pressure and the temperature for use with Katz Compressibility Factor Chart (Figure 3.2). The equations for making the adjustments follow.

Equation (3.14)

METRIC:

Equation (3.15)

ENGLISH:

Where: and = adjusted critical values for use in Katz Compressibility Factor Chart (Figure 3.2)

And = pseudocriticals from Kay’s Rule

e = correction factor from Correction Factor Chart for Sour Gases (Figure 3.3)

B = mol fraction in the gas

D. SRK Equation of State (Soave Modification to the RK equation)

A number of modifications to these equations of states have been published and are used in the oil and gas industry. The purpose of the modifications is to improve the validity of the model. The SRK is used primarily for computer solutions.

Once the method of calculation has been chosen the Temperature, Pressure, Mole %, and with choice B. the Relative density of the gas must be entered into their entry spaces. To do so use the mouse to click the curser in the entry spaces and input the data. Once this has been done, select Run to execute the solution.

The component table is a list of the possible compounds along with their symbols to be used with this program. In the far right column titled Mole % use the mouse to choose the available cell and enter the mole Mole % of each component in the mixture. Use the Up and Down arrow keys to move from cell to cell. The total for the Mole % should be 100.00.

Temperature is the temperature of the Liquid in SI units, Celsius and Kelvin or in English units, Fahrenheit and Rankine.

° C = 0.556 (° F - 32), K = ° C + 273, ° F = (1.8)(° C) + 32, ° R = ° F + 460

Pressure is the force exerted per unit area of the liquid. For engineering purposes absolute pressure is used.

To convert unit values of data, please refer to “Set Auto Convert and Unit Conversion” in the main page.

The list of definitions that follow are to define the answers.

Compressibility Factor () is a measure of the deviation of the actual relation from the ideal-gas equation state (PV = nRT).

Average Molecular Weight:

Where: MW = Molecular Weight

= is the mole fraction of each component in the mixture

The relative density of gas is the molecular weight of the gas divided by the molecular weight of air

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