Page 364 - Characterization and Properties of Petroleum Fractions - M.R. Riazi

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344 CHARACTERIZATION AND PROPERTIES OF PETROLEUM FRACTIONS
TABLE 8.7—Comparison of various methods of calculation of liquid thermal conductivity at 20 C (Example 8.3).
◦
b
a
API, Eq. (8.43)
Linear, Eq. (8.42) June 22, 2007 14:25 Eq. (8.52) RF, Eq. (8.44) RF, Eq. (8.46)
N C k exp K %Dev k %Dev k %Dev k %Dev k %Dev
5 0.114 0.114 0.4 0.113 −0.8 0.107 −6.6 0.107 −6.5 0.113 −0.6
6 0.121 0.121 0.2 0.119 −1.4 0.111 −8.4 0.112 −7.8 0.118 −2.4
7 0.1262 0.126 −0.1 0.124 −1.7 0.114 −9.7 0.116 −8.3 0.122 −3.3
8 0.1292 0.129 0.0 0.127 −1.5 0.116 −10.0 0.119 −7.6 0.126 −2.8
9 0.1316 0.132 0.0 0.130 −1.2 0.118 −10.2 0.123 −6.9 0.129 −2.2
10 0.133 0.133 0.0 0.132 −0.6 0.120 −9.9 0.125 −5.8 0.132 −1.1
Overall 0.1 1.2 9.1 7.1 2.1
a Linear refers to linear relation betweern k and T.
b RF referes to Riazi–Faghri methods.
where k 256 refers to the value of k at 256 K (0 F) and k 422 is liquid thermal conductivity of hydrocarbon systems:
◦
the value of k at 422 K (300 F). Using Eq. (8.41) and on the L i j k L
◦
m
basis of linear interpolation of thermal conductivity from the k = i j ij
above equations, the following relation was also derived for −1
the temperature range and molecular weight ranges specified (8.47) k = 2 1 L + 1 L where k ij = k ji and k ii = k i
L
ij
for Eq. (8.44): k i k j
x i V L

i
k = 10 −2 0.11594T b 0.7534 SG 0.5478 − 2.2989T b 0.2983 SG 0.0094 i = L
i x i V i
1.8T − 460 −2 0.2983 0.0094 in which k is the thermal conductivity of liquid mixture, V L

L
× + 2.2989 × 10 T b SG m i
300 is the liquid molar volume at a reference temperature (20 or
(8.46) 25 C), x i is mole fraction, and φ i is the volume fraction of
◦
component i in the mixture. Average error for this method
where T b and T are in kelvin and k is in W/m · K. Accuracy of is about 5% [5]. Li proposed a simpler mixing rule, which is
this equation for pure compounds with the specified ranges is recommended in the DIPPR manual [10] for nonhydrocarbon
about 3.8% [30] and it is recommended instead of Eq. (8.44). liquids:
−1/2

x wi
L
Example 8.3—Estimate values of thermal conductivity of (8.48) k = 2
m
L
liquid normal alkanes from C 5 to C 10 at 20 C and 1 atm, i k i
◦
using methods given in Eqs. (8.42)–(8.44) and (8.46). Com- where x wi is the weight fraction of i in the mixture. This
pare calculated values with experimental data as given in the equation gives an average deviation of about 4–6% [10]. The
literature [8, 10]. Jamieson method for a binary liquid mixture is suggested by
Poling et al. [18]:
Solution—Sample calculations are shown for n-C 5 and simi- (8.49) k = x w1 k + x w2 k − α 12 k − k L 1 − √ x w2 x w2
L
L
L
L

L
lar approach can be used to estimate values of k for other n- m 1 2 2 1
alkane compounds. From Table 2.1, for n-pentane T b = 36.1 C Parameter α 12 is an adjustable parameter that can be de-
◦
◦ termined from an experimental data on mixture thermal
(309.3 K), SG = 0.6317, T M =−129.7 C (143.45 K), and T c =
196.55 C (469.8 K). From reference [10], k 20 = 0.114 W/m · K.
◦
From Table 8.4, k = 0.1758 and k = 0.1079 W/m · K. 0.14
L
L
m
b
L Exp
Substituting in Eq. (8.42) k = 0.1758 + (0.1079 − 0.1758) ×
T
(298.15 − 143.45)/(309.3 − 143.45) = 0.1758 − 0.06334 = Method A
0.1145 W/m · K. This gives an error of + 0.43%. From 0.13 Method B
L
Eq. (8.43), n = 1.001 and C = 0.1811 and it gives k = 0.115, Method C
with 0.7% error. From Eq. (8.44), t = 0.68, A = 0.006524, Method D
L
B = 0.36787, C = 0.17677, and k = 0.107 (error of − 6.5%). Thermal Conductivity at 20_ o C, W/mK + 0.12 Method E
L
Equation (8.46) gives k = 0.1134, with error of − 0.57%.
Later in this section several other empirical correlations for
estimation of liquid thermal conductivity are presented. For 0.11
example, Eq. (8.52) is proposed for thermal conductivty of
coal liquids. This equation gives a value of 0.107 (−6.6%).
Summary of results are given in Table 8.7 and also shown 0.10
in Fig. 8.5. As expected, Eq. (8.44) because of its simplicity
and Eq. (8.52) proposed for coal liquids give the highest 2 4 6 8 10 12
Carbon Number
errors in estimation of thermal conductivity of liquid hydro-
carbons. FIG. 8.5—Estimation of liquid thermal con-
ductivity of n-alkanes at 20 C and atmospheric
◦
pressure (Example 8.3). Method A: Eq. (8.42);
For defined mixtures the following mixing rule proposed Method B: Eq. (8.43); Method C: Eq. (8.44);
by Li is recommended in the API-TDB [5] for calculation of Method D: Eq. (8.46); Method E: Eq. (8.52).
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