generalized kinematic viscosity-temperaturecorrelation for undefined petroleum fractions of ibp -...

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GENERALIZED KINEMATIC VISCOSITY-TEMPERATURECORRELATION FOR UNDEFINEDPETROLEUM FRACTIONS OF IBP – 95°C TO 455°C+

BOILING RANGESMohamed B. Amin a & Shafkat A. Beg aa Department of Chemical Engineering , King Fahd University of Petroleum and Minerals ,KFUPM Box 441, Dhahran, 31261, Saudi ArabiaPublished online: 23 Mar 2007.

To cite this article: Mohamed B. Amin & Shafkat A. Beg (1994) GENERALIZED KINEMATIC VISCOSITY-TEMPERATURECORRELATIONFOR UNDEFINED PETROLEUM FRACTIONS OF IBP – 95°C TO 455°C+ BOILING RANGES, Fuel Science and Technology International,12:1, 97-129

To link to this article: http://dx.doi.org/10.1080/08843759408916168

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FUEL SCIENCE AND TECHNOLOGY INT'L., 12(1), 97-129 (1994)

GENERALIZED KINEMATIC VISCOSITY-TEMPERATURE COl3.RELATION FOR UNDEFINED PETROLEUM

FRACTIONS OF IBP - 950C TO' 4550C+ BOILING RANGES

Mohamed B. Amin and Shafkat A. Beg, Department of Chemical Engineering

King Fahd University of Petroleum and Minerals KFUPM 13ox 441, Dhahran 31261, Saudi Arabia

(Keywords: Oil, kinematic viscosily-tempcralure, correlation)

A generalized kinematic viscosity-temperature correlation for undefined petroleum fractions of all boiling ranges including 455+oC fractions have been deve1o:ped to represent the data for a wide range of temperature from 30 to 2000C. The correlation is based on experimental kinematic viscosity data for twenty TBP fractions of Arab heavy, Arab medium, Arab light and Arab extra-light crude oils. The proposed correlation has been found to fit all th.e eperimental data consisting of 248 measurements of the kinematic viscosity with an overall average absolute deviation of 9.07% compared to 15.47% given by ASTM method.

Literature survey shows that whereas a large amount of work has been

done on various pure liquids and defined mixtures, very little information

has been published on the variation of kinematic viscosity of petroleum

fractions with temperature. Petroleum is an exceedingly complex mixture

Copyright @ 1994 by M.arce1 Dekker, Inc.

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98 AMlN AND BEG

and its physical and chemical characteristics, yields and properties of products

or fractions depend on the concentration of various types of hydrocarbons

and other minor constituents present. The analyses in terms of individual

components is virtually impossible which make the theoretical

developments of predictive procedure extremely difficult.

Watson el al. (1935) presented figures and the API Technical Data Book

(1978) replaced these figures with monographs to relate kinematic viscosity as

a function of temperature. At the present time i t is accepted as an industry

wide standard for predicting viscosities of light to moderately heavy oils.

Abolt et al. (1971) reduced the API monograph to equations with

reasonable accuracy but these were found to be subject to singularities.

Therefore, the correlation can not be extrapolated into the regions where no

experimental data are available.

Baltatu (1982) proposed the use of the modified corresponding-state

method reported by Ely and Hanley (1981) to predict the viscosity of

petroleum fractions. The input data required are the pseudo critical

parameters, the molecular weight and an acentric factor for each fraction of

interest. The acenlric factor, which is the key parameter in the proposed

correlation, bring considerable uncertainties concerning its estimation for

petroleum fractions. This is primarily a result of the compounded

inaccuracies introduced by the estimation of the intermediate correlating

parameters such as critical lemperature, critical pressure and the choice from

the several values of the boiling point. The alternative approach has been to

develop generalized correlations based on the experimental kinematic

viscosity data for a wide range of temperature. Amin and Maddox (1980) and

Beg, et al. (1988) carried out extensive research work on a correlative

procedure for predicting the viscosity of petroleum fractions. They used

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KtNEMATlC VtSCOSITY-TEMPERATURE CORRELATION 99

several modifications of Eyring's (1936) equation and one which best

correlated viscosity data was found to be in the following form:

q = A Exp ( B I T ) (1)

where q is the kinematic viscosity (c St), T, (K), the absolute temperature and

A and B are constants. Maddox (1980) and Beg, et al. (1988) and Amin

correlated the kinematic viscosity - temperature data by two separate

correlations applicable for temperature range of 95 OC to 455+ OC and 455+0C

frations of four Arabian commercial crude oils, respectively. These

correlations were found not only to predict the data obtained for four Arabian

crude oil fractions but were also found to predict the kinematic viscosities of

various fractions of large number of crude oils available in other parts of the

world. The predictions made by the proposed correlations were found to be

better compared to any correlation available in literature. The objective of the

present studies is to extend that work to develop unique correlation to

represent the data for petroleum fractions in the boiling range (95 OC to

455+ OC) of all four Arabian curde oils.

DEVELOPMENT OF KINEMATIC v l s c o s m - TEMPERATURE CORRELATION

A modified Eyring equation (1) has been considered for the

development of the generalized correlation. A logarithmic plot of the

kinematic viscosity TI against (11T) according to equation (1) gave a straight

line relationship which showed a general applicability of Eyring's equation to

the experimental data (Figures 1 to 4). The following scheme was, therefore,

employed for the desired analysis:

1. Prediction of constants A and B for each fraction of Arab heavy, Arab

medium, Arab light and Arab Berri crude fractions.

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AMlN AND BEG

/

o 9 5 Y - 205.C /

/

o 201.C - 260.C /

/ /

A 2 W C - 3LS'C

# 3L5.C - 455.C

- PROPOSED CORRELATION lE( I . I . )

-.-. A S l M CORRILATION

,

Figure 1 : Comparison of Experimental Kinematic Viscos i ty Data for Arab Heavy Crude Fractions w i t h Proposed Correlations Using Mole- cular Weight as one of the Characterizing Properties and ASM Correlarion.

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KINEMATIC VISCOSITY-TEMPERATURE CORRELATION 101

Figure 2 : Comparison of Experimental Kinematic Viscosity Data for Arab Medium Crude Fractions with Proposed Correlations Using Halecular Weight a s one of the Characterizing Properties and ASTM Correlation.

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AMlN AND BEG

9s.c - 205.C / /

o 2OS.C - 260.C /

A 260.C - 3L5.C . 3LS.C - L5S.C

- PROPOSED CORRELATIOH lEU 6 )

A S T H CORRELATION

Figure 3 : Comparison of Experimental Kinematic Viscosity Data f a r Arab Light Crude Fracxions wirh Proposed Correlat ions Using Molecular Weight a s one of the Characterizing Propert ies and ASTN Correlat ion.

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Figure 4 : Comparison of Experimental Kinematic Viscosity Data for Arab Berri Crude Fractions with Proposed Correlations Using mlecular Weight as one of the Characteriiina Properties and A S n l C~orrelation.

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104 AMIN AND BEG

2. Development of the most suitable correlations for constant A and B in terms

of following properties of TBP-fractions:

i) API gravity

ii) 50% true boiling point, Tb (K)

iii) Average boiling point (K)

.iv) Universal oil product characterization factor (UOPK)

V) Molecular weight

A complete program that performs a non-linear least square fitting of a

proposed function of given set of data was used to develop the necessary

correlations (Chandler, 1962). Table I shows the estimated values of the

constants A and B for each of the 20 fractions of the four crudes. The

variation in estimated values of B is in the range of 1000 to 6000 and the

values increase as the boiling point of the fraction increases. However, the

variation in the values of A is quite significant, i t ranges from 0.003 to 0.0005

showing a decreasing trend from low boiling to high boiling fraction of each

crude oil.

Such behavior would be expected as in Eyring's equation constant A is

inversely proportional to the molar volume of the liquid under

consideration. For high boiling fraction which correspond to high molecular

weight and therefore high molar volumes, the values of A decrease

progressively as TBP-range of a fraction increases for any crude. Further,

constant B in Eyring's equation is proportional to the boiling temperature of

liquid and as the boiling range of a fraction of any crude increases, B would

increase as well.

Table I1 shows the percentage absolute errors obtained using the

individual values of A and B to calculate the viscosities of each fraction. The

maximum absolute average error has been estimated as 8.58% for 345 OC -

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Table I. : Data for A and 6 of Modified Eyring's Equation for Saudi Arab Crude Oil Fractions.

Crude Oil TBP Fractions 0 C A B

Arab Heavy 95 - 205 .I330573478 1003.440 205 - 260 ,022175847 1348.300 260 - 345 ,013606436 1739.006 345 - 455 .004256005 2564656

455' .000054488 6026.134

Arab Medium 95 - 205 ,031791376 996.0330 205 - 260 022500927 1336.698

Arab Light 95 - 205 .035035133 951.1950 205 - 260 .022670120 1325.900 260 - 345 ,013078988 1747.507

Arab Rerri

455 OC fraction of the Arab light crude and minimum absolute average err01

of 0.06% has been obtained for 95 OC - 205 OC fraction of the Arab heavy crude.

In order to formulate a generalized kinematic viscosity-temperature

correlation, numerous attempts were made to relate constants A and B with

easily measurable and more representative properties of the crude fractions

such as API gravity, characterization factor, 50% true boiling point, averagt

boiling point and molecular weight.

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106 AMlN AND BEG

Tnblc 11. : Percent Absolute Average Errors of Proposed Correlation for Various Saudi Arabian Crude Oil Fractions Using Modified Eyring's Equation.

Cmde Oil Fractions O C % Absolute Average - Error

Arab Heavy

Arab Medium

Arab Berri

The parameter B was best correlated by the following expression for

twenty fractions of Arabian commercial crude oils.

B = Ci + Exp ( C z + C 3 T b ) + Cq (Mw/API) (2)

where, CI = 67.450, Cz = 5.329, C3 = 0.00329 and C4 = 44.264

The above equation fits the data for B with an average absolute error of 1.18%

and maximum absolute error of 5.08%.

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KINEMATIC VISCOSlm-TEMPERATURE CORRELATION 107

An extensive amount of work was carried out to develop a suitable

correlation for parameter A. The following form of correlation provided a

relatively better degree of f i t compared to other forms of correlation.

A = El + E2 Exp ( E j M w ) (3)

where. El = -1.954 x 10-3, Ez = 0.906 x 10-1 and E, = -7.773 10-3

The above equation fits the data for parameter A for the twenty fractions of

the four commercial crude oils with absolute average error of 7.641.

Substitution of constants A and B from equations (2) and (3) into modified

Eyring's equation ( 1 ) gives the following general kinematic viscosity-

temperature correlation:

q = [ -1.954 x 102 + 0.0906 exp ( -7.773 x 10-3 M ,I]

Exp [( (67.45 + exp (5.329 + 0.00329 Tb) + 44.263 ( M,/API) 1 / T] (4)

The validity of the proposed correlation can be checked by calculating

the viscosities for these fractions, and comparing them with the

corresponding experimental values. Table 111 lists the predicted values of the

kinematic viscosity, the corresponding experimental value and the error

involved in the prediction of each data point of the twenty fractions of the

four Arabian crudes. The average absolute error of the prediction of each

fraction is also listed. Table 111 also list the predictions made by the ASTM

method (1982) for each data point and the average absolute error for each

fraction. The analysis shows that the proposed correlation fits the

experimental data consisting of 248 viscosity measurements for the twenty

fractions of four Arabian crude oils with a wide boiling range (95 - 455+ OC)

with an overall absolute error of 9.07%.

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108 AMlN AND BEG

TableII1.: Comparison of Errors Using Proposed Correlation on Molecular Weight as one of the Characterizing and ASTM Correlation for Saudi Arabian Crude Oil Fractions.

Crude ARAB HEAVY

TBP RANGE P C ) (95 - 205) 50% TBP (0 K) 420.65 API 55.96 MOL. WT. 126.0 U.O.P.K. 12.07

Prooosed Correlation ASTM Method

T (O C) "exp "talc % Error ' k a k % Error

40.0 .75332 ,75719 .51 ,836 10.98 50.0 .68244 ,68662 .61 ,713 4.48 60.0 ,62160 ,62629 .75 ,610 -1.87 70.0 ,56836 ,57433 1.05 541 -4.81 80.0 ,52456 ,52927 .90 ,478 -8.88

- - - -

AVG. ARS. DEV. (%) .77

NOTE: A(ca1c) and B(ca1c) refer to constants of Eq. 4.4

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KINEMATIC VISCOSITY-TEMPERATURE CORRELATION

Table 111. (eantd.):

C ~ d e ARAB HEAVY

TBP RANGE P C ) (205 - 260) 50% TBP (0 K) 506.7 API MOL. WT U.O.P.K.

Proposed Correlation ASTM Method

T (O C) qexP ' k a k % Error ' k a ~ c % Errol

40.0 1.70350 1.50306 -11.77 1.925 12.74 50.0 1.45420 1.31617 -9.49 1.605 10.37 60.0 1.26750 1.16173 -8.34 1.420 12.03 70.0 1.11100 1.03290 -7.03 1.175 5.76 80.0 ,99356 ,92450 -6.95 1.033 3.97 90.0 ,89466 ,83254 -6.94 ,903 .93 100.0 ,80983 ,75394 4.90 ,811 .I4 110.0 ,74090 ,68631 -7.37 ,731 -1.34 120.0 ,67973 ,62775 -7.65 ,668 -1.73 130.0 ,62768 ,57672 -8.12 .608 -3.14 140.0 ,58097 .53202 -8.43 .557 4.13 1500 ,53697 ,49266 -8.25 ,520 -3.16 160.0 ,50238 ,45784 -8.87 ,487 -3.06 170.0 .47101 ,42688 -9.37 ,452 4.04 180.0 ,44127 ,39926 -9.52 ,431 -2.33

AVG. ABS. DEV. (%) 8.33 4.59

Akalc) = ,02058140 Bkalc) = 1343.687

(conrin

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AMlN AND BEG

Table Ill. iconld.1:

Crude ARAB HEAVY

TBP RANGE (0 C) (260 - 345) 50% TBP (0 K) 577.59 API 34.77 MOL. WT. 232.0 U.O.P.K. 11.90


T (O C) 'lexp %aIc % Error ncak 90 Error

40.0 3.75540 3.37972 -10.00 4.370 16.37 50.0 3.03650 2.84526 -6.30 3.565 17.40 60.0 2.50190 2.42019 -3.27 2.925 16.91 70.0 2.10280 2.07813 -1.17 2.502 18.99 80.0 1.81890 1.79989 -1.05 2.125 16.83 90.0 1.57200 1.57128 -.05 1.845 17.37 100.0 1.40450 1.38174 -1.62 1.681 19.68 110.0 1.25290 1.22324 -2.37 1.470 17.33 120.0 1.12670 1.08966 -3.29 1.324 17.51 130.0 1.00640 97624 -3.00 1.202 19.43 140.0 ,91813 ,87930 -4.23 1.102 20.03 150.0 ,841 70 79591 -5.44 1.024 21.66 160.0 ,77179 72375 -6.22 ,941 21.92 170.0 ,71228 ,66096 -7.20 ,872 22.42 180.0 ,63471 ,60604 -4.52 ,816 24.35

AVG. ABS. DEV. (I) 3.98 19.21

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Table 111. (contd.):

Crude ARAB HEAVY

TBP RANGE (0 C) (345 - 455) 5090 TBP (0 K) 677.59 API 25.42 MOL. WT. 331.0 U.O.P.K. 11.85

Prouosed Correlation ASTM Method

T (O C) "exp 'kale % Error 'kale % Error

40.0 19.13600 17.62633 -7.89 31.750 65.92 50.0 13.17300 13.68629 3.90 20.952 59.06 60.0 9.49810 10.78960 13.60 14.354 51.12 70.0 7.26990 8.62472 18.64 10.255 41.06 80.0 5.66360 6.98220 23.28 7.843 38.48 90.0 4.61250 5.71865 23.98 5.864 27.13 100.0 3.85310 4.73414 22.87 4.825 25.22 110.0 3.18520 3.95796 25.32 3.926 24.31 120.0 2.70260 3.33932 23.56 3.320 22.84 130.0 2.39330 2.84123 18.72 2.875 20.13 140.0 2.04270 2.43642 19.27 2.426 18.77 150.0 1.78250 2.10451 18.07 2.124 19.16 160.0 1.60330 1.83015 14.15 1.915 19.44 170.0 1.43750 1.60163 11.42 1.716 19.37 180.0 1.29310 1.40991 9.03 1.550 19.86 190.0 1.17860 1.24800 5.89 1.396 18.45 200.0 1.07820 1.11039 2.99 1.286 19.27

AVG. ABS. DEV. (%) 15.44 29.30

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A M l N A N D BEG

Table 111. lcantd.):

Crude ARAB HEAVY

TBP RANGE (0 C) (455+) 50% TBP (0 K) 825.93 API 7.64 MOL. WT. U.O.P.K.


% Error

-3.36 -2.05 -.51 6.52 6.12 4.79 5.34 -2.58 -7.25

% Error

n0.90 146.70 4.60

-41.80 -63.20 -72.80 -78.30 -83.00 -84.60

AVG. ABS. DEV. (%) 4.28 149.50

A(calc) = .00005509 Bkalc) = 6025.653

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Table 111. 1conld.L:

C ~ d e ARAB MEDIUM

TBP RANGE (0 C) (95 - 205) 50% TBP ( 0 K) 420.65 API 54.17 MOL. WT. 128.0 U.0.P.K. 11.96

P r o ~ o s e d Correlation ASTM Method

T (O C) "exp "calc % Error %alc % Error

40.0 .76559 ,75664 -1.17 ,862 12.59 50.0 ,69341 ,68578 -1.10 ,730 5.28 60.0 ,63179 ,62524 -1.04 ,635 2.28 70.0 ,57753 ,57312 -.76 ,560 -3.04 80.0 ,53494 ,52794 -1.31 ,492 -8.03

AVG. ABS. DEV. (%) 1.08 6.24

Akalc) = ,03154482 B(calc) = 995.026

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AMlN AND BEG

Table 111. lconld.):

C ~ d e ARAB MEDIUM

TBP RANGE (O C) (205 - 260) 50% TBP (0 K) 506.21 API 43.27 MOL. WT. U.O.P.K.

Pro~osed Correlation ASTM Method

T P C ) "exp "calc % Error 'lcalc % Error

40.0 1.65390 1.53804 -7.01 1.903 15.06 50.0 1.42360 1.34796 -5.31 1.575 10.63 60.0 1.23980 1.19076 -3.96 1.403 13.17 70.0 1.09280 1.05953 -3.04 1.152 5.41 80.0 ,98247 ,94901 -3.41 1.025 4.33 90.0 ,88085 ,85519 -2.91 ,891 1.15 100.0 ,79657 .77496 -2.71 ,793 -.45 110.0 ,72834 ,70588 -3.08 ,721 -1.01 120.0 ,67118 ,64602 -3.75 ,653 -2.71 130.0 ,61925 .59384 -4.10 .594 4.08 140.0 ,57328 ,54810 4.39 ,548 4.41 150.0 ,52882 .50780 -3.97 ,508 -3.94 160.0 ,49597 ,47213 -4.81 ,473 -4.63 170.0 46574 ,44042 -5.44 ,447 -4.02 180.0 ,43499 ,41209 -5.26 ,422 -2.99

AVG. ABS. DEV. (90) 4.21 4.59

A(calc) = ,02165730 B(calc) = 1334.934

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Crude A R A B MEDIUM



T (" C) qexp "calc % Error 'kalc % Error

40.0 3.46900 3.25057 -6.30 4.350 25.39 50.0 2.81700 2.74286 -2.63 3.470 23.18 60.0 2.34600 2.33816 -.33 2.090 23.70 70.0 1.99020 2.01181 1.09 2.460 23.60 80.0 1.79700 1.74581 -2.85 2.103 17.03 90.0 1.51540 1.52685 .76 1.840 21.42 100.0 1.21770 1.34499 10.45 1.630 22.11 110.0 1.20790 1.19265 -1.26 1.447 19.79 120.0 1.09490 1.06406 -2.82 1.285 17.36 130.0 ,96881 ,95472 -1.45 1.180 21.80 140.0 ,88619 ,86112 -2.83 1.074 21.19 150.0 A1322 ,78050 -4.02 ,991 21.86 160.0 ,75435 ,71064 -5.79 ,932 22.36 170.0 ,69444 ,64978 -6.43 :854 22.98 180.0 ,59072 ,59648 .98 ,794 2i.78

AVG. ABS. DEV. (90) 3.33 21.70

Akalc) = ,01344358 B(calc) = 1718.594

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AMlN A N D BEG


Crude ARAB MEDIUM

TBP RANGE (O C) (345 - 455) 50% TBP (O K) 672.87 API 25.67 MOL. WT. U.O.P.K.


T (O C) qexp ' k a k % Error 'Icalc ' % Error

40.0 17.32000 16.18210 -6.57 28.220 62.94 50.0 12.09600 12.61915 4.32 19.350 59.98 60.0 8.89520 9.98870 12.29 13.440 51.09 70.0 6.77650 8.01503 18.28 9.535 40.71 80.0 5.36200 6.51202 21.45 7.444 38.83 90.0 4.42490 5.35172 20.95 5.654 27.78 100.0 3.63360 4.44466 22.32 4.662 28.30 110.0 3.06190 3.72729 21.73 3.866 26.26 120.0 2.62940 3.15385 19.94 3.182 21.02 130.0 2.26290 2.69080 18.91 2.724 20.37 140.0 1.99170 2.31347 16.16 2.335 17.23 150.0 1.76780 2.00330 13.32 2.095 18.51 160.0 1.57960 1.74629 10.55 1.853 17.30 170.0 1.42010 1.53171 7.86 1.664 17.17 180.0 1.27910 1.35130 5.64 1.525 19.22 190.0 1.16490 1.19860 2.89 1.374 17.94

200.00 1.06550 1.06856 .29 1.264 18.62

AVG. ABS. DEV. (%) 13.15 29.60

A(ca1c) = ,00523431 B(ca1c) = 2516.607

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Table 111. (eontd.):

Cmde ARAB MEDIUM

TBP RANGE (0 C) (455+) 50% TBP (0 K) 795.37 API MOL. WT, U.O.P.K.


90 Error

16.64 20.50 38.31 29.87 29.19 25.66 24.62 18.56 11.60

% Error

373.50 56.30 -10.40 54.10 -68.80 -76.10 -79.50 -83.00 -85.10

AVG. ABS. DEV. (%) 23.88 98.50

A(calc) = .00021749 B(ca1c) = 5208.029

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AMlN AND BEG


Crude ARAB LIGHT



T (O C) ?exp "calc % Error ' k a ~ c % Error

40.0 ,72312 ,79133 9.43 ,800 10.63 50.0 ,67036 ,71805 7.11 ,740 10.39 60.0 ,61301 ,65538 6.91 ,690 12.56 70.0 ,56402 ,60136 6.62 ,630 11.70 80.0 ,51237 ,55450 8.22 ,602 17.49

AVG. ABS. DEV. (%) 7.66 12.55

A(ca1c) = ,03425256 B(ca1c) = 983.275

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KINEMATIC VISCOSITY-TEMPERATURE CORRELATTON

Table 111. (contd.1:

Crude ARAB LIGHT

TBP RANGE (0 C) (205 - 260) 50% TBP (0 K) 504.54 API MOL. WT. ~ -

U.O.P.K. 11.98


T (O C) "exp "cak % Error "talc % Error

40.0 1.60550 1.57439 -1.94 1.520 -5.33 50.0 1.38470 1.38207 -.I9 1.450 4.72 60.0 1.21000 1.22276 1.05 1.290 6.61 70.0 1.07090 1.08957 1.74 1.140 6.45 80.0 ,95657 ,97725 2.16 1.060 10.81 90.0 ,86112 .88178 2.40 ,950 10.32 100.0 ,77763 ,80003 2.88 360 10.59 110.0 ,71716 ,72955 1.73 ,800 11.55 120.0 ,66095 .66841 1.13 ,750 13.47 130.0 ,60837 ,61506 1.10 ,690 13.42 140.0 ,56232 ,56825 1.05 ,650 15.69 150.0 ,52300 ,52697 .76 .620 18.55 160.0 ,48701 ,49040 .70 ,575 18.07 170.0 ,45466 ,45784 .70 ,544 19.66 180.0 ,42645 ,42875 5 4 ,520 21.94

AVG. ABS. DEV. (%) 1.34 12.47

A(calc) = ,02336822 B(calc) = 1318.439

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I20 AMlN AND BEG

Table I l l . (contd.1:

Crude ARAB LIGHT

TBP RANGE C) (260 - 345) 50% TBP (0 K) 572.87 API MOL. WT. U.O.P.K. 11.92


T (O C) "exp ' k a k % Error %ale % Error

40.0 3.70140 3.33336 -9.94 3.200 -13.55 50.0 2.99110 2.81900 -5.75 2.600 -13.08 60.0 2.47480 2.40812 -2.69 2.150 -13.12 70.0 2.08980 2.07611 -.66 1.900 -9.08 80.0 1.79380 1.80497 .62 1.700 -5.23 90.0 1.56780 1.58138 3 7 1.490 4.96 100.0 1.37850 1.39535 1.22 1.300 -5.69 110.0 1.23690 1.23927 .19 1.280 3.48 120.0 1.11140 1.10731 -.37 1.195 7.52 130.0 1.00780 .99494 1.28 1.050 4.19 140.0 ,87147 ,89862 3.12 ,960 10.16 150.0 ,79743 ,81554 2.27 ,890 11.61 160.0 ,73253 ,74346 1.49 ,820 11.94 170.0 ,67737 ,68059 .48 ,790 16.63 180.0 ,62686 ,62547 -.22 ,720 14.86 190.0 ,58424 ,57692 -1.25 ,675 15.53 200.0 ,55079 ,53395 -.306 ,635 15.29

AVG. ABS. DEV. (%I 2.09 10.35

A(calc) = ,01481804 B(calc) = 1695.986

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Table 111. (conld.):

C ~ d e ARAB LIGHT

TBP RANGE (0 C) (345 - 455) 50' TBP (0 K) 677.32 API 24.78 MOL. WT. 332.0 U.O.P.K. 11.74


T (O C) qexp %ale % Error 'kalc % Error

40.0 19.07900 15.01249 -21.31 23.100 21.08 50.0 13.16400 11.71083 -1 1 .M 16.450 24.96 60.0 9.50840 9.27253 -2.48 11.920 25.36 70.0 7.20330 7.44248 3.32 6.400 -11.15 80.0 5.46820 6.04846 10.61 5.990 9.54 90.0 4.40300 4.97202 12.92 4.980 13.10 100.0 3.62110 4.13031 14.06 3.980 9.91 110.0 3.09320 3.46447 12.00 2.550 -17.56 120.0 2.64560 2.93207 10.83 2.300 -13.06 130.0 2.29430 2.50212 9.06 2.010 -12.39 140.0 2.04890 2.15166 5.02 1.700 -17.07 150.0 1.80640 1.86354 3.16 1.560 -13.64 160.0 1.66260 1.62474 -2.28 1.420 -14.59 170.0 1.51000 1.42534 -5.61 1.260 -16.56 180.0 1.36700 1.25766 -8.00 1.170 -14.41 190.0 1.21070 1.11572 -7.84 1.050 -13.27 200.0 1.12580 .99482 -11.63 1.005 -10.73

AVG. ABS. DEV. (I) 8.89 15.20

Atcalc) = ,00490676 B(calc) = 2513.349

(continua

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AMlN AND BEG

Table 111. (conld.):

Crude ARAB LIGHT

TBP RANGE (O C) (455+) 50% TBP ( O K ) 788.71 API 11.65 MOL. WT. U.O.P.K.

P r o ~ o s e d Correlation ASTM Method

T P C) "exp "talc 70 Error "calc % Error

100.0 138.98000 75.203383 -45.89 1700.000 1123.20 110.0 93.32900 54.38533 -41.73. 370.000 296.40 120.0 62.15300 39.98178 -35.67 110.000 77.00 130.0 44.03900 29.84498 -32.23 45.000 2.20 140.0 32.71700 22.59581 -30.94 21.000 -35.80 150.0 24.97300 17.33390 -30.59 13.000 -47.90 160.0 19.26800 13.46110 -30.14 7.000 -63.70 170.0 15.42300 10.57355 -31.44 4.700 -69.50 180.0 12.66300 8.39439 -33.71 3.300 -73.90 190.0 10.17000 6.73110 -33.81 2.500 -75.40 200.0 8.527000 5.44799 -36.1 1 1.900 -77.70

AVG. ABS. DEV. ('70) 34.75 176.61

Akalc) = .00030355 Bkalc) = 4364.607

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Table 111. (cantd.1:

Crude ARAB BERRl



T (O C) qexP "talc % Error qcalc % Error

40.0 ,74183 ,74843 .89 ,793 6.89 50.0 ,67488 .67857 .55 ,668 -1.02 60.0 ,61717 ,61886 .27 . ,573 -7.16 70.0 ,56166 ,56744 1.03 .510 -9.19 80.0 ,51552 ,52286 1.42 ,450 12.79

AVG. ABS. DEV. (%) .83 7.39

Akalc) = ,03154482 Bkalc) = 991.610

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AMlN AND BEG

Table 111. kontd.):

Crude ARAB BERRl

TBP RANGE (0 C) (205 - 260) 50% TBP (0 K) 505.37 API MOL. WT. U.O.P.K. 12.00

P ro~osed Correlation ASTM Method

T (O C) 'lexp 'lcalc % Error %ale % Error

40.0 1.62510 1.43538 -11.67 1.180 15.68 50.0 1.39820 1.25736 -10.07 1.552 10.99 60.0 1.21980 1.11021 -8.98 1.325 8.62 70.0 1.07600 ,98742 -8.23 1.104 2.61 80.0 ,96132 38406 -8.04 .961 -.03 90.0 ,86733 ,79636 -8.18 ,877 1.11 100.0 ,78076 .72138 -7.61 ,782 .I6 110.0 ,71758 ,65684 -.&6 ,702 -2.16 120.0 ,66006 ,60094 -8.96 ,642 -2.74 130.0 ,61065 ,55222 -9.57 .579 -5.18 140.0 ,56603 ,50954 -9.98 ,533 -5.04 150.0 ,52452 .47195 -10.02 ,497 -5.25 160.0 ,49133 ,43867 -10.72 ,468 -4.75 170.0 ,45463 ,40910 - 10.02 ,434 -4.54 180.0 ,42784 ,38269 -10.55 ,413 -3.47

AVG. ABS. DEV. (%) 9.40 4.88

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KINEMATIC VISCOSITY-TEMPERATURE CORRELATTON

Table 111. (rontd.1:

Crude A R A B BERRl



T (O C) %xp "calc 90 Error "talc % Error

40.0 3.48630 3.14562 -9.77 4.170 19.62 50.0 2.94740 2.65553 -9.90 3.190 8.23 60.0 2.44430 2.26471 -7.35 2.621 7.23 70.0 2.02910 1.94941 -3.93 2.145 5.71 80.0 1.75430 1.69231 -3.53 1.815 3.46 90.0 1.53230 1.48061 -3.37 1.563 2.00 10D.O 1.37360 1.30470 -5.02 1.352 -1.57 110.0 1.21690 1.15731 4.90 1.065 -12.48 120.0 1.09420 1.03285 -5.61 1.072 -2.03 130.0 1.00700 ,92699 -7.95 ,972 -3.48 140.0 ,89771 ,83635 -6.84 ,871 -2.98 150.0 ,83114 ,75825 -8.77 ,805 -3.15 160.0 ,75459 69056 -8.49 ,733 -2.86 170.0 ,69297 ,63157 -8.86 ,682 -1.58 180.0 ,61516 ,57990 -5.73 ,631 -1.97

AVG. ABS. DEV. (7%) 6.67 5.22

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AMlN AND BEG

Table 111. (conid.):

Crude ARAB BERRl

TBP RANGE P C ) (345 - 455) 50% TBP (0 K) 669.26 API 27.79 MOL. WT. 323.0 U.O.P.K. 11.98


T (O C) qexp 'kale % Error qcak 90 Error

40.0 15.45800 13.35911 -13.58 25.740 66.52 50.0 10.96600 10.49005 -4.34 17.525 59.81 60.0 8.12630 8.35759 2.85 12.540 54.31 70.0 6.18330 6.74741 9.12 9.155 48.06 80.0 4.97780 5.51388 1077 6.924 39.10 90.0 4.07110 4.55623 11.92 5.430 33.38 100.0 3.38870 3.80360 12.24 4.432 30.79 110.0 2.90060 3.20536 10.51 3.675 26.70 120.0 2.51470 2.72483 8.36 3.102 23.35 130.0 2.15970 2.33508 8.12 2.686 24.37 140.0 1.91090 2.01609 5.50 2.289 19.73 150.0 1.67760 1.75280 4.48 2.044 21.84 160.0 1.49260 1.53377 2.76 1.822 22.07 170.0 1.34360 1.35022 .49 1.632 20.47 180.0 1.22500 1.19535 -2.42 1.475 20.41 1900 1.11810 1.06382 -4.85 1.326 18.60 200.0 1.03080 ,95144 -7.70 1.226 18.93

AVG. ABS. DEV. (%I 7.06 32.32

A(ca1c) = .00540391 B(calc) = 2446.588

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Table 111. lcon~d.):

Crude ARAB BERRl

TBP RANGE (OC) (455+) 50% TBP (0 K) 765.37 API 16.09 MOL. WT. 440.0 U.O.P.K. 11.60


T 6' C) 'kxp ' k a k % Error ' h c % Error

120.0 23.85300 17.42726 -26.94 16.000 -32.90 130.0 18.41600 13.68131 -2571 1 0534 -43.00 140.0 1333300 10.8671 1 -18.49 7.100 -46.70 150.0 11.05500 8.72624 -21.07 4.800 -56.60 160.0 9.05590 7.07848 -21.84 3.500 -61.30 170.0 7.38260 5.79636 -21.49 2.700 -63.40 180.0 6.25000 4.78851 -23.38 2.070 -66.90 190.0 5.26880 3.98867 -24.30 1.700 -67.70 200.0 4.62670 3.34819 -27.63 1.400 -69.70

AVG. ABS. DEV. (%) 23.43 56.50

A(calc) = ,00100939 B(calc) = 3835.746

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AMlN AND BEG

CONCLUSIONS

A generalized kinematic viscosity-temperature correlation has been

developed for liquid petroleum fractions in the boiling temperature range of

95 to 455'OC fractions, based on a modified form of Eyring's equation. It'

requires the knowledge of three characterization properties i.e. API gravity,

50% boiling point and molecular weight for the prediction of the kinematic

viscosity. The correlation is based on experimental data for twenty fractions

of four Arabian commercial crudes over a wide range of temperature from

40 OC to 200 OC. The correlation gives an overall absolute average error of

9.0790 for 248 measurements as compared with the overall absolute average of

15.47% given by ASTM method.

ACKNOWLEDGEMENTS

The authors wish to thank King Abdul Aziz City for Science and

Technology for its financial support during the course of this research project

(Prolect AR3-024). The use of facilities at King Fahd University of Petroleum

and Minerals is also most gratefully acknowledged.

REFERENCES

Abbat, M.M., Kaufmann, T.G. and Domash, L., 1971, Can. J. Chem. Eng. 49,37.

Amin, M.B. and Maddox, R.N. 1980, Hydrocarbon Processing, 59, 131.

Annual Book of ASTM Standards, 1982, Parts 23-25, American Society for

Testing and Materials, Philadelphia.

API Technical Data Book - Petroleum Refining, 1978, American Petroleum

Institute, New York. Amin, M.B, and Beg, S.A., Fuel Sci. & Tech. Int. (In Press).

Baltatu, M.E., 1982, Ind. Eng. Chem. Process Des. Dev., 21, 192.

Beg, S.A., Amin, M.B. and Husain, I., 1988, The Chem. Eng. J. 381, 123.

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Chandler, J.P. 1962, Department of Computer Science, Oklahoma State

University, Stillwater, Oklahoma. Ely, F.]. and Hanky, H.]., 1981, Ind. Eng. Chem. Fundam., 20,323.

Eyring, J., 1936.1. Chem. Phys. 4,715.

Watson, K.M., Nelson, E.F. and Murphy, G.B., 1935, Ind. Eng. Chem., 27,1460.

RECEIVED: November 30, 1992 ACCEPTED: December 21. 1992

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generalized kinematic viscosity-temperaturecorrelation for undefined petroleum fractions of ibp -...

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