Page 67 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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2. CHARACTERIZATION AND PROPERTIES OF PURE HYDROCARBONS 47
parameter and SG represents the size parameter. Therefore,
in Eq. (2.31) one can replace parameters A and B by T b and parameters and transport properties are discussed in Chap-
ters 5, 6, and 8. It is shown by various investigators that the
SG. However, it should be noted that T b is not the same as ratio of T b /T c is a characteristic of each substance, which is
parameter A and SG is not the same as parameter B, but it related to either T c or T b [36, 43]. This ratio will be used to
is their combination that can be replaced. There are many correlate properties of pure hydrocarbons in Section 2.3.3.
other parameters that may represent A and B in Eq. (2.31). Equation (2.31) can be written once for T c in terms of V and I
For example, if Eq. (2.25) is applied at a reference state of T 0 and once for parameter T b /T c . Upon elimination of parameter
and P 0 , it can be written as V between these two relations, a correlation can be obtained
to estimate T c from T b and I. Similarly through elimination
of T c between the two relations, a correlation can be derived
(2.32) V T 0 ,P 0 = f 3 (A, B, T 0 , P 0 )
to estimate V in terms of T b and I [42].
is the molar volume of the fluid at the reference It should be noted that although both density and refrac-
where V T 0 ,P 0
state. The most convenient reference conditions are tempera- tive index are functions of temperature, both theory and ex-
ture of 20 C and pressure of 1 atm. By rearranging Eq. (2.32) periment have shown that the molar refraction (R m = VI )is
◦
one can easily see that one of the parameters A or B can be nearly independent of temperature, especially over a narrow
molar volume at 20 C and pressure of 1 atm [28, 36, 42]. range of temperature [38]. Since V at the reference tempera-
◦
To find another characterization parameter we may con- ture of 20 C and pressure of 1 atm is one of the characteriza-
◦
sider that for nonpolar compounds the only attractive force tion parameters, I at 20 C and 1 atm must be the other char-
◦
is the London dispersion force and it is characterized by fac- acterization parameter. We chose the reference state of 20 C
◦
tor polarizability, α, defined as [38, 39] and pressure of 1 atm because of availability of data. Simi-
larly, any reference temperature, e.g. 25 C, at which data are
◦
3 M n − 1
2
(2.33) α = × × 2 available can be used for this purpose. Liquid density and re-
fractive index of hydrocarbons at 20 C and 1 atm are indicated
4π N A ρ n + 2 ◦
where by d 20 and n 20 , respectively, where for simplicity the subscript
N A = Avogadro’s number 20 is dropped in most cases. Further discussion on refractive
M = molecular weight index and its methods of estimation are given elsewhere [35].
ρ = absolute density From this analysis it is clear that parameter I can be used
n = refractive index as one of the parameters A or B in Eq. (2.31) to represent the
In fact, polarizability is proportional to molar refraction, R m , size parameter, while T b may be used to represent the energy
defined as parameter. Other characterization parameters are discussed
M n − 1
2 in Section 2.3.2. In terms of boiling point and specific gravity,
(2.34) R m = × Eq. (2.31) can be generalized as following:
2
ρ n + 2
b
(2.38) θ = aT SG c
b
M
(2.35) V = where T b is the normal boiling point in absolute de-
ρ
grees (kelvin or rankine) and SG is the specific gravity at
60 F(15.5 C). Parameter θ is a characteristic property such as
◦
◦
2
n − 1
(2.36) I = molecular weight, M, critical temperature, T c , critical pres-
2
n + 2 sure, P c , critical molar volume, V c , liquid density at 20 C,
◦
in which V is the molar volume and I is a characterization d 20 , liquid molar volume at 20 C and 1 atm, V 20 , or refrac-
◦
parameter that was first used by Huang to correlate hydrocar- tive index parameter, I,at20 C. It should be noted that
◦
bon properties in this way [10, 42]. By combining Eqs. (2.34)– θ must be a temperature-independent property. As mentioned
(2.36) we get before, I at 20 C and 1 atm is considered as a character-
◦
istic parameter and not a temperature-dependent property.
R m actual molar volume of molecules
(2.37) I = = Based on reported data in the 1977 edition of API-TDB, con-
V apparent molar volume of molecules
stants a, b, and c were determined for different properties
R m , the molar refraction, represents the actual molar volume and have been reported by Riazi and Daubert [28]. The con-
of molecules, V represents the apparent molar volume and stants were obtained through linear regression of the loga-
their ratio, and parameter I represents the fraction of total rithmic form of Eq. (2.38). Equation (2.38) in its numerical
volume occupied by molecules. R m has the unit of molar vol- form is presented in Sections 2.4–2.6 for basic characteri-
ume and I is a dimensionless parameter. R m /M is the specific zation parameters. In other chapters, the form of Eq. (2.38)
refraction and has the same unit as specific volume. Parame- will be used to estimate the heat of vaporization and trans-
ter I is proportional to the volume occupied by the molecules port properties as well as interconversion of various distil-
and it is close to unity for gases (I g = 0), while for liquids it lation curves. The form of Eq. (2.38) for T c is the same as
∼
is greater than zero but less than 1 (0 < I liq < 1). Parameter the form Nokay [44] and Spencer and Daubert [45] used to
I can represent molecular size, but the molar volume, V,isa correlate the critical temperature of some hydrocarbon com-
parameter that characterizes the energy associated with the pounds. Equation (2.38) or its modified versions (Eq. 2.42),
molecules. In fact as the molecular energy increases so does especially for the critical properties and molecular weight,
the molar volume. Therefore, both V and I can be used as two have been in use by industry for many years [2, 8, 34, 46–56].
independent parameters to characterize hydrocarbon proper- Further application of this equation will be discussed in
ties. Further use of molar refraction and its relation with EOS Section 2.9.
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