Prediction of the viscosity of lubricating oil blends

Short Communications

Prediction

of the viscosity

of lubricating

J. M. Al-Besharah, C. J. Mumford*, Petroleum. Petrochemicals and Materials

S. A. Akashah, Division,

oil blends

and 0. Salman

Kuwait

institute for Scientific 24885, 13709 Safat, Kuwait *Department of Chemical Engineering and Applied Chemistry, Aston University, (Received 8 August 7988; revised 7 February 1989)

Research,

PO Box

Birmingham,

UK

This work presents a new method of predicting the kinematic viscosities of base oil blends. Three types of base oils and their blends were used to test the proposed method, together with the ASTM-D341 ’ and the REFUTAS’ index methods. With the proposed method, percentage deviations from the experimental values were significantly smaller than those when using the standard methods. Absolute average deviations of -,2.0% were obtained within the temperature range 20°C to 100°C. (Keywords:

oil;

viscosity;

models)

It is advantageous to be able to predict the physical properties of mixtures of petroleum products from the properties of the components. Preferably, minimal input data are fed into a model which can provide reliable and accurate predicted values. Viscosity is one of the most important flow properties of petroleum oils and their mixtures, and viscosity data are essential for solving transportation problems. The theory of the viscosity of mixtures based upon molecular interactions has been discussed by Eyring ef a1.3m5, who considered the flow of viscous molecules as a monomolecular or bimolecular chemical reaction, involving a molecule jumping from one equilibrium position to a neighbouring one. Therefore, for a certain molecule to move in a mixture of different molecules a potential energy barrier has to be overcome. This barrier is large for mixtures of different molecules, and smaller for molecules of similar nature. Gemant considered Eyring’s theory the most complete, but many modifications have recently been proposed. In practice, the viscosities of blends always bear non-linear or power relations to those of their components. Numerous empirical correlations have therefore been developed to predict the viscosities of mixtures of gases, non-polar liquids, pure hydrocarbons, and some petroleum products. Reid et ~1.’ defined the kinematic of two viscosity 0, of a mixture components A and B by

The API’” recommend the ASTM-D341 method for mixtures ofpetroleum liquids. The REFUTAS viscosity blending function’ is widely used to predict the kinematic viscosity of petroleum product blends. This method considers blending indices, provided in special tables, which are aggregated on a weight basis. The REFUTAS function I can be calculated from the equation,

where

and X is mole fraction of each component; M is molecular weight; I’ is kinematic viscosity, (cSt); and v,,~, t)BA are constants determined by least squares method. The ASTM-D341’ method is based on Wright’s method’,’ with the use of standard viscosity-temperature charts to predict the viscosities of blends of petroleum products. The following equation was proposed by Wright, log log Z=A-B

log T

(3)

where Z is (v+0.7+C-D+E-F+ GH); T is temperature in degrees Rankine; A, B are constants; C is exp. (- 1.148832.65868 v); D is exp. (-0.003813812.5645 v); E is exp. (5.4649137.6289 0); F is exp. (13.0458-74.6851 u); G is exp. (37.4619192.643 u); and H is exp. (80.4945400.468 u) The limits of applicability Z=(u+O.7) Z=(u+0,7+C) Z=(o+0.7+C-D)

are,

2 x 10’ to 2.00 (cSt) 2x 10’ to 1.65 (cSt)

2

’

2 x IO’ to 0.30 (cSt) Z=(u+0.7+C-DfE-FfG) 2 x 10’ to 0.24 (cSt) Z=(v+0.7+C-D+E-FfG-H) 2 x 10’ to 0.21 (cSt)

0016-2361;X9/060X0943$3.00 t 1989 Butterworth

& Co. IPublishers) Ltd.

(L’$_O.8)

(4)

The REFUTAS indices of the components, of known viscosities at the same temperature as the mixture, are first determined, and the index of the blend is then calculated, based on the weight fraction of each component.

Ih,&Mi; where, I,, is the blend REFUTAS index; y is the weight fraction of component i. The viscosity of the blend is hence computed from Equation (4) or read from a corresponding table. This method has been reported to be applicable to all blends of petroleum products but is less accurate for extreme blends such as gasoline and residues. The percentage deviations of the predicted viscosities from experimental values are of the order of2% for middle distillates. The API recommend the modified Kendal and Monroe equation” for the blending of pure hydrocarbons,

2 x 10’ to 0.90 (cSt) Z=(u+0.7+C-D+E)

3 Inv,=X,lnc,+3X,X,lnc,,

I = f(c) = 23.097 + 33.468 log log

L‘ mix=(i,

Xi,u:‘3]3

where 11mix is the viscosity of the mixture (cP); Xi is the mole fraction of component i; and pi is the viscosity of component i (cP).

FUEL,

1989,

Vol 68, June

809

Short Communications Khan et ~1.” developed two empirical double logarithm models to predict the viscosity of gas-free Athabasca bitumen. They proposed a non-linear viscosity model In In (~)={1.0+b,T+b,(b,7)2}ebrT (7) and a linear viscosity In In (p)=C,

model

In T+C,

(8)

where p is the viscosity in mPa s and T is the temperature in K. The two parameters for each model were determined by the least squares technique. The non-linear viscosity model yielded slightly better results, with an average deviation of 7.1% compared with 8.2% with the linear model. The temperature of these range for the applicability correlations is from 20°C to 130°C. Letsou and Stiel13 proposed a corresponding state approach that uses the acentric factor (0.1~). r/E= (r/e) + Oo(r/&)’

(9)

where (r/~)O=0.015174-O.O12135T, + 0.00751;2

(10)

Pedersen et a1.14 developed a new correlation based on the corresponding states principles to predict the viscosity of hydrocarbon mixtures ranging from dilute gases to heavy oils. The only input data needed are the critical constants and the molecular weight of each component. Good results have been obtained for viscosities of crude oils and satisfactory results for binary mixtures of pure hydrocarbons.

(11)

s= T”/6/M”2 P,213

(12)

T,, A4 and P, are the critical temperature, molecular weight, and critical pressure, respectively.

Blend number

Light base oil

Medium base oil

Heavy base oil

0.30 0.30 0.40 0.55 0.20 0.10 0.70 0.10

0.30 0.50 0.50 0.40 0.30 0.70 0.10 0.20

0.40 0.20 0.10 0.05 0.50 0.20 0.20 0.70

A NEW CORRELATION The viscosity of an ideal liquid mixture can be calculated by umix= cxiu,

(13)

For real mixtures such as lubricating oils, the viscosity of the mixture is not linearly related to those of its components. This is due to the interaction between the molecules of the components. Therefore an excess function must be included to account for the deviation from ideality. Recently a new correlation was developed by the present authorst5 to predict the kinematic viscosity of crude oil blends at constant pressure and temperature, using mixing rules and an excess viscosity function, as follows:

(vE)’ = 0.042552 -0.0767473 + 0.034OT;

Table 1 Fractional compositions of base oil blends

(In u),,,=CXilnvi+uE

I

(14)

where: Xi is weight fraction ofcomponent i; vi is kinematic viscosity of component i; t’m,r is kinematic viscosity of the mixture; and vE is excess viscosity

Table 2 Kinematic viscosities of the individual base oils and their b!ends at different temperatures Kinematic viscosity (cSt) 20°C Light base oil 68.43 Medium base oil 369.4 Heavy base oil 2011 Blend number 1 396.0 2 288.5 3 210.8 4 152.0 5 561.0 6 419.6 7 146.6 8 951.3

40°C

1OO’C

26.05 109.1 454.0

4.655 12.01 29.46

115.8 89.32 67.40 51.46 155.5 121.5 49.76 242.3

12.48 10.44 8.787 7.312 15.41 13.10 7.271 20.36

Table 3 The calculated kinematic viscosities of the base oil blends (2,3,4 and 5) using the 4-parameter correlation, ASTM-D341 method and REFUTAS index method

Blend number

Temperature (“C) 20 40 100

2

Exp. vis. (cSt)

4-parameter model __~. Calc. vis. % Dev.” @St)

ASTM-D341 Calc. vis. (cSt)

288.5 89.32 10.44

294.1 87.63 10.60

I .96 - 1.88 1.60

292.1 92.67 11.45

% Dev.”

I .24 3.75 9.70

REFUTAS index Calc. vis. (cSt)

% Dev.”

278.0 85.77 10.93

- 3.65 -3.97 4.73

3

20 40 100

210.8 67.40 8.787

215.7 65.84 8.950

2.32 -2.31 1.90

208.3 68.09 9.058

- 1.20 I .03 3.05

201.1 64.83 9.308

-4.62 -3.82 5.89

4

20 40 100

152.0 51.46 7.312

156.7 49.68 7.520

3.11 -3.47 2.90

157.0 55.17 8.202

3.30 7.20 12.20

154.5 49.29 7.907

1.65 -4.21 8.16

5

20 40 100

561.0 155.5 15.41

558.8 156.7 IS.17

-0.39 0.74 - I .60

563.5 154.6 15.05

0.45 -0.61 -2.30

530.1 146.7 14.35

-5.51 -5.68 -6.85

%AADb

20 40 100

1.95 2.1 2.0

1.55 3.15 6.81

3.86 4.42 6.42

%MAD

20 40 100

1.I5 - 1.73 1.2

0.95 2.84 5.66

- 3.03 -4.42 2.98

_ calculated value -experimental a % Deviauon = ~____experimental value b %AAD = absolute average deviation c%MAD = mean average deviation

810

FUEL, 19.89, Voi 68, June

value

, __

X LW

Short function.

shows promise for the prediction of the viscosities of blends of other petroleum products where the base oils are of relatively similar chemical composition.

The term c Xi In ui represents

the ideal behaviour Af the mixture, and cE is the excess viscosity function, which represents the non-ideal behaviour of the mixture. For ternary mixtures, the latter is represented as follows:

REFERENCES I

~,,,X,XJ,

RESULTS

2

(15)

where uij is the interaction parameter between components i and j. To apply Equation (15) to ternary mixtures of base oils, it is necessary to evaluate the interaction parameters (aij etc). The viscosities of four blends of the three components in different proportions are the same measured at temperature, and four simultaneous equations are then solved to calculate the interaction parameters. Once the parameters are known, the viscosity of any combination of the components at constant temperature and pressure can easily be determined. Since interactions of type aij and aijk between the molecules of the components are the main reason for non-ideal behaviour of the viscosity of the mixture, interactions of type aii between the molecules of the same component are neglected in this correlation. Very good predictions were obtained for the viscosities of crude oils; the deviation was in most cases less than 6%. The purpose of the present work was to apply this method to predict the kinematic viscosities of base oil blends, and to assess whether it is generally applicable to petroleum products. AND DISCUSSION

For production of lubricating oils, different types of base oils are generally blended to produce finished products of the requisite specifications. The viscosity or the viscosity index (VI) of the lubricating oil mixture is the most important criterion. A means of predicting the viscosity of the mixture accurately from data on the viscosities of the base oil components would therefore be useful. Three types of base oils {Spindle oil (light), base oil (medium), Bright stock (heavy)} were chosen to test the correlation. Eight blends of different composition by weight were prepared

Communications

-v

s

0

I

0

100 Observed

I

I

I

200

300

400

kinematic

viscosity

I 500

600 (cSt1

Figure 1 Kinematic viscosities of base oil blends 2,3,4 and 5 using the 4-parameter equation: 0,2o”C; l ,4O”C; n , 100°C

8 from the three individual base oils. The compositions of the blends are shown in Table 1. The ASTM D445/IP71i6 standard method was followed for all viscosity measurements. The viscometer used was of the suspended level type, immersed in a water or oil bath controlled to +O.OlC. The viscosity measurements did not deviate by >O.l% about the mean value. The kinematic viscosities of the components and blends at different temperatures are shown in Table2. Duplicate measurements did not differ by >0.3% from the mean values quoted. Blends 1,6,7 and 8 were used to calculate the interaction parameters aij and aijL. A comparison was made between the ASTM-D341 method, the REFUTAS index method, and the 4-parameter correlation. The percentage deviations of the calculated viscosities by each method from the measured values are shown in Tuble3. Blends 1, 6, 7 and 8 were not included in Table3 because they were used to calculate the interaction parameters. It is clear that the three methods are in excellent agreement. However, the new correlation gave the best results, with average absolute deviation ~2.0% over the temperature range from 20-100°C. The data obtained by this method are presented in Figure I. This correlation

9 10

11 12

13 14

15

16

ASTM-D341, The American

Society for Testing and Materials, Sunbury Report No. 3282, dated 15.7.47 and Report No. 3339, dated 6.10.47. British Petroleum Co., 1947 Ewell. R. H. and Eyring, H. J. Chem. Phrs. 1937, 5, 726 Frisch, D., Eyring, H., and Kincaid, J. F. J. App. PhJs. 1940, 11. 75 Powell, R. E., Roseveare, W. E. and Eyring, H. Ind. Eng. Chem. 1941,33,430 Gemant, A. J. App. Phrs. 1941, 12, 827 Reid, R. C., Prausnitz, J. M. and Sherwood. T. K. in ‘The Prouerties of gases and liquids’. 3rd Ed., M&rawHill Book Co., New York, USA, 1977, pp. 3-7. 73-88 and 457463 Wright, W. A. ‘Prediction of Oil Viscosity on Blending’, Am. Chem. Sot. Div. Petrol. Chem. Prepr., 19th meeting. 1946, pp. 71-82 Wright, W. A. J. qf Materials 1969, 4(l), 19 Technical Data Book-Petroleum Refining, American Petroleum Institute, Vol. II, Chapter 11, 3rd Ed., 1977, p. 29 Kendall, J. and Monroe, K. P. J. Am. Chem. Sot. 1917, 39(9), 1788 Khan, M.A., Mehrotra, A. K. and Svrcek, W. Y. J. of Canad. Per. Tech. 1984, p. 47-53. Letsou,A. and Stiel, L. I. AICHE J. 1973, 19,409 Pedersen, K. S., Fredenslund, A., Christensen, P. L. and Thomassen, P. Chem. Eng. Science 1984, 39(6), 1011 Al-Besharah, J. M., Akashah, S. A. and Salman, 0. Ind. Eng. Chem. Res. 1987, 26, 2445 ASTM-D445/IP71, The American Society for Testing and Materials, 1983

NOMENCLATURE aijk

M P, T, T,

WO V

rl p P i VE

interaction parameters moiecular weight critical pressure critical temperature reduced temperature Pitzer acentric factor kinematic viscosity = q/p dynamic viscosity absolute viscosity density Refutas index or blending excess viscosity function

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1989,

Vol68,

June

index

811