Page 145 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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3. CHARACTERIZATION OF PETROLEUM FRACTIONS 125
0.915 (N), and 1.04 (A). Applying Eq. (3.40) for R i and VGC
(3.72). For cases that calculated x A is negative it should be
gives the following two relations. T1: IML 14:23 In these set of equations x A must be calculated from Eq.
set equal to zero and values of x P and x N must be normalized
(3.61) R i = 1.0482x P + 1.038x N + 1.081x A
in a way that x P + x N = 1. The same procedure should be
(3.62) VGC = 0.744x P + 0.915x N + 1.04x A applied to x P or x N if one of them calculated from the
A regression of 33 defined hydrocarbon mixtures changes above equations is negative. For 85 samples Eqs. (3.70) and
the numerical constants in the above equations by less than (3.72) give average deviation of 0.04 and 0.06 for x P and
2% as follows [29, 47]: x N , respectively. For 72 heavy fractions, Eqs. (3.72)–(3.74)
predict x P , x N , and x A with average deviations of 0.03, 0.04,
(3.63) R i = 1.0486x P + 1.022x N + 1.11x A and 0.02, respectively [36]. These deviations are within the
(3.64) VGC = 0.7426x P + 0.9x N + 1.112x A range of experimental uncertainty for the PNA composition.
Equations (3.70)–(3.74) are recommended to be used if
Simultaneous solution of Eqs. (3.60), (3.63), and (3.64) experimental data on viscosity are available. For cases that
gives the following equations for estimation of the PNA com- n 20 and d 20 are not available, they can be accurately estimated
position of fractions with M > 200. from the methods presented in Chapter 2.
(3.65) x P =−9.0 + 12.53R i − 4.228 VGC For fractions that kinematic viscosity is not available, Riazi
and Daubert [36] developed a series of correlations in terms of
(3.66) x N = 18.66 − 19.9R i + 2.973 VGC
other characterization parameters which are readily available
(3.67) x A =−8.66 + 7.37R i + 1.255 VGC or predictable. These parameters are SG, m, and CH and the
These equations can be applied to fractions with molecular predictive equations for PNA composition are as follows:
weights in the range of 200–600. As mentioned earlier, x P ,
x N , and x A calculated from the above relations may represent For fractions with M ≤ 200
volume, mole, or weight fractions. Equations (3.65)–(3.67) (3.75) x P = 2.57 − 2.877SG + 0.02876CH
cannot be applied to light fractions having kinematic viscosity
at 38 C of less than 38 SUS (∼3.6 cSt.). This is because VGC (3.76) x N = 0.52641 − 0.7494x P − 0.021811m
◦
cannot be determined as defined by Eqs. (2.15) and (2.16). For or
such fractions Riazi and Daubert [47] defined a parameter
similar to VGC called viscosity gravity function, VGF, by the (3.77) x P = 3.7387 − 4.0829SG + 0.014772m
following relations: (3.78) x N =−1.5027 + 2.10152SG − 0.02388m
(3.68) VGF =−1.816 + 3.484SG − 0.1156 ln ν 38(100) For fractions with M > 200
(3.69) VGF =−1.948 + 3.535SG − 0.1613 ln ν 99(210)
(3.79) x P = 1.9842 − 0.27722R i − 0.15643CH
2
where ν 38(100) and ν 99(210) are kinematic viscosity in mm /s (3.80) x N = 0.5977 − 0.761745R i + 0.068048CH
(cSt) at 38 and 99 C (100 and 210 F), respectively. For a
◦
◦
petroleum fraction, both Eqs. (3.68) and (3.69) give nearly the or
same value for VGF; however, if kinematic viscosity at 38 Cis (3.81) x P = 1.9382 + 0.074855m− 0.19966CH
◦
available Eq. (3.68) is preferable for calculation of VGF. These
equations have been derived based on the observation that at (3.82) x N =−0.4226 − 0.00777m+ 0.107625CH
a fixed temperature, plot of SG versus ln ν is a linear line for In all of these cases x A must be calculated from Eq. (3.72).
each homologous hydrocarbon group, but each group has Equations (3.75) and (3.76) have been evaluated with PNA
a specific slope. Further information on derivation of these
equations is provided by Riazi and Daubert [47]. Parameter composition of 85 fractions in the molecular weight range
VGF is basically defined for fractions with molecular weights of 78–214 and give average deviations of 0.05, 0.08, and
of less than 200. Based on the composition of 45 defined 0.07 for x P , x N , and x A , respectively. For the same data set
mixtures (synthetic) and with an approach similar to the Eqs. (3.77) and (3.78) give AAD of 0.05, 0.086, and 0.055 for
one used to develop Eqs. (3.65)–(3.67), three relationships in x P , x N , and x A , respectively. For 72 fractions with molecu-
terms of R i and VGF have been obtained to estimate the PNA lar weight range of 230–570, Eqs. (3.79)–(3.82) give nearly
composition (x P , x N , x A ) of light (M < 200) fractions [47]. the same AAD of 0.06, 0.06, and 0.02 for x P , x N , and x A ,
respectively. In cases that input parameters for the above
These equations were later modified with additional data for methods are not available Eqs. (3.77) and (3.78) in terms of
both light and heavy fractions and are given below [36].
SG and m are more suitable than other equations since re-
fractive index and molecular weight can be estimated more
For fractions with M ≤ 200
accurately than CH. Although Eqs. (3.77) and (3.78) have
(3.70) x P =−13.359 + 14.4591R i − 1.41344 VGF been derived from a data set on fractions with molecular
(3.71) x N = 23.9825 − 23.33304R i + 0.81517 VGF weights up to 200, they can be safely used up to molecu-
lar weight of 300 without serious errors. Most recently, Eqs.
(3.72) x A = 1 − (x P + x N ) (3.77) and (3.78) have been modified to expand the range
For fractions with M > 200 of application of these equations for heavier fractions, but
in general their accuracy is not significantly different from
(3.73) x P = 2.5737 + 1.0133R i − 3.573 VGC the equations presented here [45]. For example, for frac-
(3.74) x N = 2.464 − 3.6701R i + 1.96312 VGC tions with 70 < M < 250, Riazi and Roomi [45] modified Eqs.

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