Compressibility Z factor

Density is the most commonly measured property of a gas, and is obtained experimentally by measuring the specific gravity of the gas (density of the gas relative to air = 1). As pressure increases, so does gas density, but the relationship is non-linear since the dimensionless gas compressibility (z-factor) also varies with pressure. The gas density (pg) can be calculated at any pressure and temperature using the real gas law ... 

Many petroleum engineering and process design calculations dealing with natural gases require knowledge of deviation factors or compressibility Z factors. Experimental data from pressure-volume-temperature (P-V-T) measurements are seldom available. The Z-factors are available in charts [27] or tables as a function of pseudo-reduced temperatures T and pressures P. However, use of these charts is often time consuming and involves complex calculations. 

Fig. 5-13. Compressibility (Z) factors of gases and vapors. Courtesy Hougen and Watson, Chem. Process Principles, vol. 1, John Wiley 6c Sons, Inc., New York.)...

The above equation is valid at low pressures where the assumptions hold. However, at typical reservoir temperatures and pressures, the assumptions are no longer valid, and the behaviour of hydrocarbon reservoir gases deviate from the ideal gas law. In practice, it is convenient to represent the behaviour of these real gases by introducing a correction factor known as the gas deviation factor, (also called the dimensionless compressibility factor, or z-factor) into the ideal gas law ... 

Below 7 MPa, the dominant variable for the compressibility factor in the PVT equation is the molecular weight of the gas. At this pressure level, the addition of ethane or propane increases the molecular weight of the gas more rapidly than the z factor decreases. Thus there is an advantage to removing ethane, propane, etc. from the gas. 

The van der Waals equation is not a particularly accurate tool for prediction of compressibility Z, but it is the first theory to illuminate the nature of the attractive and repulsive forces that lead to departure from the perfect gas law. There are many more accurate equations of state that use more parameters, including the Benedict-Webb-Rubin equation, the Redlich-Kwong equation, and the Peng-Robinson equation. The compressibility factor can also be expanded into the virial form... 

Compressibility factor is also known as gas deviation factor, supercompressibility, or z-factor. Sometimes the reciprocal of compressibility factor is called supercompressibility. 

The Law of Corresponding States says that all pure gases have the same z-factor at the same values of reduced pressure and reduced temperature. Figure 3-5 gives a test of this theory for compressibility data of methane, propane, n-pentane, and n-hexane.4 Some of the deviation between lines at constant reduced temperatures may be due to experimental error and some due to inexactness of the theory. 

The accuracy of the compressibility equation bf state is not any better than the accuracy of the values of the z-factors used in the calculations. The accuracy of Figures 3-7 and 3-8 was tested with data from 634 natural gas samples of known composition.8 Experimentally determined z-factors of these gases were compared with z-factors obtained from the charts using Kay s rules for calculating the pseudocritical properties and Figure 3-10 for properties of heptanes plus. 

Measured z-factors for the same natural gases were compared with compressibility factors calculated with Figures 3-11,3-7, and 3-8. The average absolute error was less than 2% throughout the range of specific gravities from 0.57 to 1.68. 

This coefficient normally is referred to simply as compressibility or gas compressibility. You must understand that the term compressibility is used to designate the coefficient of isothermal compressibility whereas, the term compressibility factor refers to z-factor, the coefficient in the compressibility equation of state. Although both are related to the effect of pressure on the volume of a gas, the two are distinctly not equivalent. 

The compressibility equation is the most commonly used equation of state in the petroleum industry. We will combine this equation with the equation which defines the coefficient of isothermal compressibility. Since z-factor changes as pressure changes, it must be considered to be a variable. 

Pseudoreduced compressibility is a function of z-factor and pseudore-duced pressure. Thus, a graph relating z-factor to pseudoreduced pressure, Figure 3-7, Figure 3-8, or Figure 3-9, can be used with Equation 6-14 to calculate values of Cpr. 

Compressibility factor at standard conditions may be calculated using z-factors tabulated in Appendix A, where... 

The use of compressibility factors to correct for the non-perfect behavior of gases is well suited for en eering calculations which usually require the computation of the volmne occupied by a gas at a given temperature and pressure. However, it is sometimes necessary to calculate the pressure exerted by a non-perfect gas at a given volume and temperature or the temperature of a non-perfect gas at a given pressure and volume. Calculations of this type using a Z factor can best be illustrated by examples. 

Determination of the Z Factor. The data obtained in the determination of r and may also be used to evaluate the compressibility factor Z (and consequently v) as a function of pressure at reservoir tem-peratui-e. Since the volume of the gas phase is known both under reservoir conditions and standard conditions the value of Z may be computed using the equation... 

Fluid Molecular weight, (gm/mol) Density of Liquid (gm/mol) Temp, of liquid ( K) Dipole moment (debyes) Critical Temp. Factor, (Tytc) C>K/ C) Critical Pressure (F e) (bar) (atm) (psi) Critical Volume, (cmVmol) Critical Compress. (Z)c ... 

Computer programs [28,29] for calculating the Z factors have been developed solely as a function of temperature and pressure of the gas. Furthermore, numerical methods and mathematical representations of the charts have been used to estimate the Z factors. Takacs [30] reviewed the various methods of estimating the Z-factors. Here, use is made of a modified form of the method developed by Awoseyin [31 ]. This method gives a compressibility factor to within 5% for natural hydrocarbon gases with specific gravities between 0.5 and 0.8 and for pressures up to 5000 psia. The Z factor can be expressed as ... 

Alternatively if compressibility factor charts are available, these Z factors may be used to compute the fugacity of pure component i by use of the following equation which is readily obtained by commencing with Eqs. (14-12) and (14-26)... 

For a high-pressure and/or high-temperature system, the compressibility factor z factor) should be introduced, which is obtained from the knowledge of the critical temperature and critical pressure of the system (the reader is advised to refer to a thermodynamics book for example. Ref. 1). 

For nonideal gases, the z factor (compressibility factor) is introduced. It is a function of the critical temperature and pressure. 

Here we assume that the real gas factor or compressibility (Z) of the sorptive gas in the adsorption equilibrium state considered. 

This method utilizes essentially the concept developed by Fitzer in 1955. According to the principle of three-parameter corresponding states, the compressibility factor z, for a fluid of acentric factor w, is obtained by interpolating between the compressibilities Zj and Z2 for the two fluids having acentric factors w, and (p -... 

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