Acentric Factor

The acentric factor, is often a third parameter in corresponding states correlations. Figure 23-2 tabulates it for pure hydrocarbons. The acentric factor is a function of Pvp, Pc, and Tc. It is arbitrarily defined as

H= -log(Pvp/Pc)Tr=0.7-1.0 Eq 23-17This definition requires knowledge of the critical (pseudocritical) temperature, vapor pressure, and critical (pseudocritical)pressure. For a hydrocarbon mixture of known composition that contains similar components, a reasonably good estimate for the acentric factor is the molar average of the individual pure component acentric factors:

W= Yi*WiEq 23-18If the vapor pressure is not known, can be estimated38 for pure hydrocarbons or for fractions with boiling point ranges of50°F or less using:

EJEMPLO DEL FACTOR ACENTRICO:

A narrow-boiling petroleum fraction has a VABP of 418°F, an ASTM slope of 0.75 and an API gravity of 41°. Estimate its acentric factor. To use Eq 23-19 we need the average boiling point (MeABP); the pseudo-critical temperature (a function of MABP); and the pseudo-critical ressure (a function of Me- ABP).From Fig. 23-18, the correction to VABP for mean average is –3°F; the correction for MABP is –5°F. Note that for narrowboiling fractions, all boiling points approach the volumetric average. Then, MeABP = 415°F and MABP is 413°F.From Eq. 23-15, the pseudo-critical pressure is:T = 415 + 460 = 875 °RS for 41° API = 141.5/(131.5 + 41) = 0.871Ppc = 3.12281(109) (875)-2.3125(0.871)2.3201 = 356 psiaFrom Eq 23-16, the pseudo-critical temperature is:

ENTHALPY BEHAVIORThe change of enthalpy with temperature and pressure is complex. Predicting the enthalpy for a pure component or mixture is multi-step procedure that requires information that can only be obtained by experimental measurement. For pure components, use of a P-H diagram like those shown in Figs. 24-22 to 24-35 is recommended.The enthalpy behavior of mixtures can be predicted through thermodynamic correlations. Use of a good contemporary equation of state is ecommended for mixture enthalpy predictions. Fig. 24-2 shows graphically the change in enthalpy of three gas streams and two liquid streams as pressure is changed at constant temperature. Values for the plot were calculated by the Soave10 version of the Redlich-Kwong equationof state11. The curves in Fig. 24-2 are for no phase change and show typical behavior of gas phase enthalpy decreasing and liquid phase enthalpy increasing with increasing pressure. Enthalpies for mixtures of real gases and liquids can be predicted by hand calculation methods. The ones recommended for use are based on an extension of the principle of corresponding states and are shown graphically in Fig. 24-6 and 24-7.Ideal Gas State EnthalpiesEnthalpies for pure component gases are readily correlated as a power series of temperature for a wide range of components including all of those that occur in natural gas streams.Typical values for natural gas components are plotted in Figs. 24-3 and 24-4 for temperatures from -200 to 900°F. Enthalpies for gas mixtures can be obtained as the mole fraction average if molar enthalpies are used, or the weight fraction average if mass enthalpies are used.Many natural gas streams contain undefined, or pseudo, components. Ideal gas enthalpies for pseudo components are shown in Fig. 24-5. To use Fig. 24-5 the specific gravity, molecular weight and temperature (relative density, molecular mass and temperature) must be known. Fig. 24-5 is for paraffinic mixtures and should not be used for pseudo components derived form aromatic crude oils. The enthalpy datum chosen is zero enthalpy at zero absolute pressure and zero absolute temperature, the same datum as used in API Project 44.1 The choice of datum is arbitrary and a matter of convenience. Enthalpy differences, the values of interest, are not affected by the datum chosen. However, the same enthalpy datum should be used for all components in any one calculation.CHANGE OF ENTHALPY WITH PRESSUREFor purposes of correlation and calculation, the ideal and real gas behaviors are treated separately. The mixture ideal gas enthalpy at a specified temperature is calculated; the enthalpy change of the real gas mixture is calculated from a correlation prepared from experimental enthalpy easurements on a variety of mixtures. This relation can be expressed as:

La entalpía ideal a una temperatura dada, que se calcula a partir de una correlación elaborada a partir de mediciones experimentales de una variedad de mezclas de gas. Esta correlación puede ser expresada de la siguiente manera:

Donde:

la entalpía ideal esta dada a la temperatura deseada T y tiene unidades de BTU/mol.

el cambio de la entalpía con la presión, a partir de la diferencia entre la entalpía del gas ideal y la entalpía a la temperatura deseada.

es cero a la temperatura absoluta, de tal forma que la ecuación se puede describir como:

Los valores del cambio de la entalpía real de gas o líquido pueden ser obtenidos a partir del principio de estados

correspondientes. La correlación esta diseñada para temperaturas reducidas. La correlación se muestra en las Figuras 24-6 y 24-7 del

GPSA. La segunda carta es la correlación que muestra la desviación de un fluido real a partir del cambio de entalpía con la presión. El

valor de es calculada por:

Donde:

es el cambio de la entalpía de un fluido simple con la presión ( Fig. 24-6, GPSA)

es la desviación para un fluido simple (Fig 24-7 del GPSA)

change for a simplefluid from Fig. 24-7Figs. 24-6 and 24-7 can be used for gas and liquid mixtures.If the mixture is a gas, use the lower chart in each figure. Forliquids read the value from the isotherms at the top of thechart. The units of (H0 –H) will depend on the units of theuniversal gas constant, R, and Tc. For (H0 –H) in Btu/lb mole,R=1.986 Btu/(lb mole °R) and Tc is in °R.The reduced temperature and pressure are defined as Tr =T/Tc and Pr = P/Pc, where absolute temperature and pressuremust be used. Values for pure component critical temperature,pressure and acentric factor are in Section 23 Physical Properties.Section 23 also contains graphs relating ASTM distillationtemperature, molecular weight, specific gravity(relative density), critical temperature, and critical pressurefor undefined fractions. The fraction acentric factor can be estimatedfrom Eq 23-17.To use Figs. 24-6 and 24-7, the mixture composition must beknown. The mole fraction average (pseudo) critical temperatureand pressure are calculated using Kay’s Rule4 as illustrated

in Fig. 23-3 (TCm = yiTCi and PCm = yiPCi). The molefraction average mixture enthalpy is calculated from:Hm 0 yiHi

0 Eq 24-5The values of Hi

0 are obtained by multiplying the enthalpyvalue from Figs. 24-3 and 24-4 by the molecular weight of theindividual component.The mole fraction average acentric factor is calculated:m yi i Eq 24-6The information necessary to evaluate enthalpies for themixture from Figs. 24-3 to 24-7 is now known. Use of themethod will be clearer after study of the following illustrative

calculation.

Edmister (1958) proposed a correlation for estimating the acentric factor T of pure fluids and petroleum fractions. The equation, widely used in the petroleum industry, requires boiling point, critical temperature, andcritical pressure. The proposed expression is given by the following relationship:

where T acentric factorpc critical pressure, psiaTc critical temperature, °RTb normal boiling point, °RIf the acentric factor is available from another correlation, the Edmister equation can be rearranged to solve for any of the three other properties (providing the other two are known).

The acentric factor (w), first proposed by Pitzer (1955); is a measure of a fluid's deviation from the lave of corresponding states (see the section on compressibility factors). It is defined as:

where p, is the vapor pressure of the fluid at a temperature of 0.7T,, and p, is its critical pressure . As expected , w is equal to zero for noble gases like argon, and is close to zero for gases like methane.

El factor acéntrico definido por Pitzer (Pitzer, Lippman, Carl y Paterson, 1995) para componentes puros es:

log ' 110 −r P ; para Tr= 0.7 (36)donde:

P’r= Presión de vapor reducida, para una temperatura reducida Tr = 0.7 = Acéntricidad o no-esfericidad de la molécula; conforme aumenta el pesomolecular de los hidrocarburos, se incrementa. Los valores para Zc,a,b, sepuede observar que son los mismos que los de la ecuación original de Redlich-

Kwong (de Redlich-Kwong, 1949):