Page 83 - Characterization and Properties of Petroleum Fractions

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2. CHARACTERIZATION AND PROPERTIES OF PURE HYDROCARBONS 63
2.5.2.2 Hall–Yarborough Method
This method for estimation of critical volume follows the gen- factor, ω: 1.1088
eral form of Eq. (2.39) in terms of M and SG and is given as (2.104) Z c = ω + 3.883
[75]:
Usually for light hydrocarbons Eq. (2.103) is more accurate
(2.100) V c = 1.56 M 1.15 SG −0.7935 than is Eq. (2.104), while for heavy compounds it is the op-
posite; however, no comprehensive evaluation has been made
Predictive methods in terms of M and SG are usually useful
for heavy fractions where distillation data may not be avail- on the accuracy of these correlations.
Based on the methods presented in this chapter, the most
able.
appropriate method to estimate Z c is first to estimate T c , P c ,
2.5.2.3 API Method and V c through methods given in Sections 2.5.1 and 2.5.2 and
then to calculate Z c through its definition given in Eq. (2.8).
In the most recent API-TDB [2], the Reidel method is rec- However, for consistency in estimating T c , P c , and V c , one
ommended to be used for the critical volume of pure hydro- method should be chosen for calculation of all these three
carbons given in terms of T c , P c , and the acentric factor as parameters. Figure 2.8 shows prediction of Z c from various
follows:
correlations for n-alkanes from C 5 to C 36 and comparing with
RT c data reported by API-TDB [2].
(2.101) V c =
P c [3.72 + 0.26(α R − 7.00)]
in which Ris the gas constant and α R is the Riedel factor given Example 2.7—The critical properties and acentric factor of
in terms of acentric factor, ω. n-hexatriacontane (C 36 H 74 ) are given as follows [20]: T b =
770.2K,SG = 0.8172, M = 506.98, T c = 874.0K, P c = 6.8 bar,
(2.102) α R = 5.811 + 4.919ω V c = 2090 cm /mol, Z c = 0.196, and ω = 1.52596. Calculate
3
M, T c , P c , V c , and Z c from the following methods and for each
In Eq. (2.101), the unit of V c mainly depends on the units of
T c , P c , and R used as the input parameters. Values of R in property calculate the percentage relative deviation (%D) be-
tween estimated value and other actual value.
--`,```,`,``````,`,````,```,,-`-`,,`,,`,`,,`---
different unit systems are given in Section 1.7.24. To have V c
3
in the unit of cm /mol, T c must be in kelvin and if P c is in a. Riazi–Daubert method: Eq. (2.38)
bar, then the value of R must be 83.14. The API method for b. API methods
calculation of critical volume of mixtures is based on a mixing c. Riazi–Daubert extended method: Eq. (2.46a)
rule and properties of pure compounds, as will be discussed d. Riazi–Sahhaf method for homologous groups, Eq. (2.42),
in Chapter 5. Twu’s method for estimation of critical volume P c from Eq. (2.43)
is given in Section 2.5.1. e. Lee–Kesler methods
f. Cavett method (only T c and P c ), Z c from Eq. (2.104)
2.5.3 Prediction of Critical Compressibility Factor g. Twu method
h. Winn method (M, T c ,P c ) and Hall–Yarborough for V c
Critical compressibility factor, Z c , is defined by Eq. (2.8) and i. Tabulate %D for various properties and methods.
is a dimensionless parameter. Values of Z c given in Table 2.1
show that this parameter is a characteristic of each com- Solution—(a) Riazi–Daubert method by Eq. (2.38) for M, T c ,
pound, which varies from 0.2 to 0.3 for hydrocarbons in the P c , and V c are given by Eqs. (2.50), (2.63), (2.64), and (2.98).
range of C 1 –C 20 . Generally it decreases with increasing car- (b) The API methods for prediction of M, T c , P c , V c , and
bon number within a homologous hydrocarbon group. Z c is Z c are expressed by Eqs. (2.51), (2.65), (2.66), (2.101), and
in fact value of compressibility factor, Z, at the critical point (2.104), respectively. (c) The extended Riazi–Daubert method
and therefore it can be estimated from an EOS. As it will be
expressed by Eq. (2.46a) for hydrocarbons heavier than C 20
seen in Chapter 5, two-parameter EOS such as van der Waals and constants for the critical properties are given in Table 9.
or Peng–Robinson give a single value of Z c for all compounds For T c , P c , and V c this method is presented by Eqs. (2.67),
and for this reason they are not accurate at the critical re- (2.68), and (2.99), respectively. The relation for molecular
gion. Three-parameter EOS or generalized correlations gen- weight is the same as the API method, Eq. (2.51). (d) Riazi–
erally give more accurate values for Z c . On this basis some Sahhaf method is given by Eq. (42) in which the constants
researchers correlated Z c to the acentric factor. An example for n-alkanes given in Table 2.6 should be used. In using this
of such correlations is given by Lee–Kesler [27]: method, if the given value is boiling point, Eq. (2.49) should be
used to calculate M from T b . Then the predicted M will be used
(2.103) Z c = 0.2905 − 0.085ω
to estimate other properties. In this method P c is calculated
Other references give various versions of Eq. (2.103) with from Eq. (2.43). For parts a, b, c, g, and h, Z c is calculated from
slight differences in the numerical constants [6]. Another ver- its definition by Eq. (2.8). (e) Lee–Kesler method for M, T c ,
sion of this equation is given in Chapter 5. However, such P c , and Z c are given in Eqs. (2.54), (2.69), (2.70), and (2.103),
equations are only approximate and no single parameter is respectively. V c should be back calculated through Eq. (2.8)
capable of predicting Z c as its nature is different from that of using T c , P c , and Z c . (f) Similarly for the Cavett method, T c and
acentric factor. P c are calculated from Eqs. (2.71) and (2.72), while V c is back
Another method to estimate Z c is to combine Eqs. (2.101) calculated from Eq. (2.8) with Z c calculated from Eq. (2.104).
and (2.102) and using the definition of Z c through Eq. (2.8) (g) The Twu methods are expressed by Eqs. (2.73)–(2.92) for
to develop the following relation for Z c in terms of acentric M, T c , P c , and V c . Z c is calculated from Eq. (2.8). (h) The Winn

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