Role of Gas compressibility Z in oil and gas industries with a solved problem

A gas reservoir has the following gas composition: the initial reservoir and temperature are 3000 psia and 180 deg F, respectively

. Component yi

CO2 0.02

N2 0.01

Cl 0.85

C2 0.04

C3 0.03

i - C4 0.03

n - C4 0.02

Calculate the gas compressibility factor under initial reservoir conditions.

General

Oil and gas compressibility plays an important role in reservoir simulation, material balance calculations, design of high-pressure surface equipment and the interpretation of well test analysis, specifically for systems below the bubble point pressure. Accurate information on the oil fluid compressibility above and below bubble point pressure is very important for reservoir evaluation.

What is compressibility

At low pressures and relatively high temperatures, the volume of most gases is so large that the volume of the molecules themselves may be neglected. Also, the distance between molecules is so great that the presence of even fairly strong attractive or repulsive forces is not sufficient to affect the behaviour in the gas state. However, as the pressure is increased, the total volume occupied by the gas becomes small enough that the volume of the molecules themselves is appreciable and must be considered. Also, under these conditions, the distance between the molecules is decreased to the point at which the attractive or repulsive forces between the molecules become important. This behaviour negates the assumptions required for ideal gas behaviour, and serious errors are observed when comparing experimental volumes to those calculated with the ideal gas law. Consequently, a real gas law was formulated (in terms of a correction to the ideal gas law) by use of a proportionality term.

The volume of a real gas is usually less than what the volume of an ideal gas would be at the same temperature and pressure; hence, a real gas is said to be compressible. The ratio of the real volume to the ideal volume, which is a measure of the amount that the gas deviates from perfect behaviour, is called the compressibility factor.

 It is also called the gas deviation factor and given the symbol z. The gas deviation factor is by definition the ratio of the volume actually occupied by a gas at a given pressure and temperature to the volume it would occupy if it behaved ideally, or:

 -------- [1]

Note that the numerator and denominator of Eq. 1 refer to the same mass. (This equation for the z factor is also used for liquids.) Thus, the real gas equation of state is written:

 ---------------- [2].

The gas deviation factor, z, is close to 1 at low pressures and high temperatures, which means that the gas behaves as an ideal gas at these conditions. At standard or atmospheric conditions, the gas z factor is always approximately 1. As the pressure increases, the z factor first decreases to a minimum, which is approximately 0.27 for the critical temperature and critical pressure. For temperatures of 1.5 times the critical temperature, the minimum z factor is approximately 0.77, and for temperatures of twice the critical temperature, the minimum z factor is 0.937. At high pressures, the z factor increases above 1, where the gas is no longer compressible. At these conditions, the specific volume of the gas is becoming so small, and the distance between molecules is much smaller so that the density is more strongly affected by the volume occupied by the individual molecules. Hence, the z factor continues to increase

Why compressibility of gases is important?

The natural gas compressibility factor is a measure of the amount of the gas deviates from perfect gas behaviour. it is directly related to the density of a gas stream, hence its flow rate and isothermal compressibility. In the gas industry, it is an important tool for computing reservoir fluid properties either directly or indirectly. Accurate estimation of compressibility factor (z) is very essential, most especially when it comes to quick estimation of initial gas in place. It is also an important factor to rely on when dealing with gas metering, where the volume flow of gas obtained from the orifice meter depends on the accuracy of the z-factor. Natural gas compressibility factor (z) is also a key factor in the gas industry for natural gas production and transportation. Compressibility factors can characterize the formation and behaviour of hydrates.

Compressibility Factor (z) vs hydrate

In the petroleum industry, one of the topmost obstruction confronted inflow is the formation of gas hydrate in pipelines, which are the root cause of the logjam of the oil and gas production, transportation and processing. Thermodynamically, the formation of gas hydrate is very dependent on the changes of pressure and temperature, the amount of pressure and temperature given to the system, the amount of the gas moles absorbed by the water molecules. Compressibility factor can predict the behaviour of a hydrate as said above.

Z value plays important role in characterizing a hydrate

Compressibility Factor (Z) vs Temp for CH4 hydrate

Compressibility Factor (Z) vs Temp for CO2 hydrate

Two typical hydrates looking completely different with different properties

Compressibility Factor (Z) vs Temp for CH4 hydrate                   

There are two images. The top one describes the relationship of the compressibility factor of CH4 on temperature. From the image, it is indicated that the value of Z increased when hydrate formation started, y-axis while Z values depressed x-axis in the dissociation of hydrates. The values of Z for CH4 alleged in between 0.85 to 0.91 which included in the CH4 boundary region.

Compressibility Factor (Z) vs Temp for CO2 hydrate

The second image, compressibility Factor (Z) vs Temp for CO2 hydrate shows Compressibility factor Z increased when hydrate formation started while Z values were depleted in the dissociation of CO2 hydrate as well. However, the Z values for CO2 ranges between 0.73-0.79 which were lower than CH4 compressibility values due to lesser pressure requirement for CO2 hydrates.

Compressibility factor for mixtures or unknown pure compounds

The gas deviation factor, z, is close to 1 at low pressures and high temperatures, which means that the gas behaves as an ideal gas at these conditions. At standard or atmospheric conditions, the gas z factor is always approximately 1. As the pressure increases, the z factor first decreases to a minimum, which is approximately 0.27 for the critical temperature and critical pressure. For temperatures of 1.5 times the critical temperature, the minimum z factor is approximately 0.77, and for temperatures of twice the critical temperature, the minimum z factor is 0.937. At high pressures, the z factor increases above 1, where the gas is no longer compressible. At these conditions, the specific volume of the gas is becoming so small, and the distance between molecules is much smaller, so that the density is more strongly affected by the volume occupied by the individual molecules. Hence, the z factor continues to increase above unity as the pressure increases.

If the gas deviation factor is not measured, it may be estimated from correlations. The correlations depend on the pseudoreduced temperature and pressure, which in turn depend on the pseudocritical temperature and pseudocritical pressure. The pseudocritical temperature and pseudocritical pressure normally can be defined most simply as the molal average critical temperature and pressure of the mixture components. Thus,

        [3]    

where:

ppc = pseudocritical pressure of the gas mixture

Tpc = pseudocritical temperature of the gas mixture

pci = critical pressure of component i in the gas mixture

Tci =critical temperature of component i in the gas mixture

yi =mole fraction of component i in the gas mixture.

These relations are known as Kay’s rule.

The pseudocritical temperature and pressure are not the actual critical temperature and pressure of the mixture but represent the values that must be used for the purpose of comparing corresponding states of different gases on the z-factor chart (image below). It has been found to approximate the convergence of the lines of constant volume on a pressure/temperature diagram.

Pseudo-reduced pressure, Ppr = p/pc

 -Pseudo-reduced temperature, Tpr = T / Tpc

Where:

p = system pressure, psia

ppr = pseudo-reduced pressure, dimensionless

T = system temperature, °R

Tpr = pseudo-reduced temperature, dimensionless

ppc, Tpc = pseudo critical pressure and temperature,

Problem

A gas reservoir has the following gas composition: the initial reservoir pressure and temperature are 3000 psia and 180 F, respectively.

Component yi

CO2 0.02

N2 0.01

Cl 0.85

C2 0.04

C3 0.03

i - C4 0.03

n - C4 0.02

Calculate the gas compressibility factor under initial reservoir conditions.

Solution

Step 1.

Determine the pseudo-critical pressure and temperature from Equation [3]

where:

ppc = pseudocritical pressure of the gas mixture

Tpc = pseudocritical temperature of the gas mixture

pci = critical pressure of component i in the gas mixture

Tci =critical temperature of component i in the gas mixture

yi =mole fraction of component i in the gas mixture.

ppc = 666.18

Tpc = 383,38

Step 2.

Calculate the pseudo-reduced pressure and temperature by applying Equations Ppr = p/pc and Tpr = T / Tpc

Ppr = 3000/666.38 =4.5

Tpr = 640/383.38 = 1.67 [ °R = °F + 459.67, 180 deg F = 640 R]

Step 3.

Determine the z-factor from above graph

Z = 0.85

Credit: Google