Indian Journal of Chemical Technology Vol. 14, November 2007, pp. 642-645
An empirical correlation in predicting the viscosity of refined vegetable oils Anupama Gupta, S K Sharma & Amrit Pal Toor* Department of Chemical Engineering and Technology, Panjab University, Chandigarh, India Email:
[email protected] Received 10 July 2006; revised received 11 September 2007; accepted 20 September 2007 Accurate knowledge of transport properties of oil is essential for mass and heat flow. Viscosity is one of the important properties of an oil which needs to be determined as it influences the ease of handling, transport and nature of storage. The effect of temperature on viscosity of six refined vegetable oils viz. palm oil, rice bran oil, cottonseed oil, mustard oil, sunflower oil and soybean oil has been studied. An empirical correlation between reduced viscosity and reduced temperature has been derived for the determination of viscosities of refined vegetable oils showing Arrhenius behaviour above 20°C (293 K). This correlation predicts the viscosity of refined vegetable oils at temperatures more than 40-60°C above 20°C (293 K). Consistency tests for viscosity data using reduced parameters have been reported. The viscosities calculated using proposed empirical correlation agree well with the reported experimental values. Keywords: Refined vegetable oils, Temperature, Viscosity IPC Code (s): A23D, G01N
One of the important applications of refined cooking oils is that they can be used as raw materials for the production of bio diesel. More than 100 years ago, Rudolph Diesel tested vegetable oils as the fuel for his engine1. The biodiesel was characterized by determining its density, viscosity, higher heating value, cetane index, cloud and pour points2. Viscosity of oil affects its combustion efficiency. The effect of viscosity on the atomization process has also been described3. Although, viscosity is an important factor for biodiesel, methods for estimation of biodiesel viscosities are few compared to those for petroleum4-7. With the recent increases in petroleum prices and the uncertainties concerning petroleum availability, there is renewed interest in using vegetable oils in diesel engines8. There are more than 350 oil bearing crops identified among which only sunflower, safflower, soybean, cottonseed, rapeseed and peanut oils are considered as potential alternative fuels for diesel engines9,10.
Several studies have been carried out on viscosity of oils and fats. The effect of hydrogenation has been investigated on the density and viscosity of sunflower-seed oil11. Topallar and Bayrack12 have studied the effect of temperature on dynamic viscosity of acetone sunflower-seed oil mixtures. Modeling of the temperature effect on the dynamic viscosity of oils is important and has been investigated by some researchers13,14. Two parameters (Eqs 1 and 2), and three parameter equations (Eqs 3- 6) were used in these studies. ln µ = a + b ln T
… (1)
ln µ = a + b/T
… (2)
ln µ = a + b/(T + c)
… (3) 2
ln µ = a + b/T + c/T
… (4)
ln µ = a + b/T + cT
… (5)
ln µ = a + bT + cT2
… (6)
where a, b and c are constants and T is absolute temperature (K). The three parameter equations gave a better fit than the two parameter equations with a mean deviation of about 1% for canola oil with the former, compared with about 5% with the latter12. In a study on the viscosity of oils and fatty acids, it has been found that Eq. (5) was the best for correlating their viscosity data with temperature13. Other researchers used Eq. (4) for vegetable oils, including canola12. Lang et al.14 and Noureddini et al.15 found that the viscosity of canola and other vegetable oils was affected by temperature and proposed an equation to calculate viscosity in the temperature range from 4 to 100°C. Rapeseed oil exhibited a higher viscosity than canola oil, corn and soybean oils. This can be directly related to the contribution of saturated fatty acids15. The non edible oil from mahua (Madhuca indica) seeds has been tested as diesel fuel extruder. The kinematic viscosity of mahua oil can be reduced considerably with the increase in temperature to 80°C and by increasing the proportion of diesel in fuel blends. The viscosity values of fuel blends were higher than that of diesel at 40°C, which indicates the
NOTES
significant effect of temperature on viscosity of mahua and its blends16. The purpose of this study was to elucidate the effect of temperature on the kinematic viscosity of six refined vegetable oils and to develop an empirical correlation between reduced viscosity and reduced temperature showing Arrhenius behaviour. Experimental Procedure The commercially available refined vegetable oils namely palm oil, rice bran oil, cotton seed oil, mustard oil, sunflower oil and soybean oil are used in the present investigation. The reference temperature was 20°C (293 K). Viscosity was determined by using Red Wood Viscometer. Kinematic viscosity (in stokes) of liquid fuels is given by η/ρ = ν = At – B/t
… (7)
where t = time of flow of a fixed amount of oil (at fixed temperature) through the viscometer (in seconds), A and B are viscometer constants which depend upon the dimensions of the viscometer capillary through which oil flows. For red wood viscometer, t is the time of flow of 50 mL of oil and values of constants A and B for various values of t are given as: t 34-100 >100
A
B
0 .0026 0.00247
1.78 0.50
The accuracy of the Eq. (7) was checked by determining the viscosity of phenol at its melting point. The experimental values agreed with the literatures values within ±1.5%. Results and Discussion Figures 1 and 2 give a plot of log viscosity versus the reciprocal of absolute temperature for palm oil, rice bran oil, cottonseed oil, mustard oil, sunflower and soybean oil. These values at 40°C are quite comparable with the values given in the literature19,20. Figures 1 and 2 show that viscosity decreases with increase in temperature. The suitability of Eqs (1-6) in describing the temperature dependence of oil viscosity can be further studied by utilizing the viscosity data of these oils given in Table 1. Using experimental viscosity data for these six oils the constants were calculated using Eqs (1-6). Then these equations were used to calculate the values of the
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viscosities. The regression values were found from the experimental and calculated values of viscosities. According to experimental viscosity data the regression values for the oils with Eq. (2) varied from 0.998.99998. As this equation gave a good fit to the viscosity data, so Eq. (2) was further modified and the linear nature of the plot shows that viscous flow of these oils is an activated process in which energy distribution can be represented by Eq. (8) η = Z exp (Ev/ RT)
… (8)
The values of energy of activation values, Ev are reported in Table 2. The values show that the energy of activation is almost constant for all the oils studied here. Cohn and Turnbull21 suggested that the reduced temperature Tref/T could be a suitable criterion for depicting the behaviour of systems showing Arrhenius behaviour. However, their hypothesis was not tested experimentally. Figure 3 shows a plot of log viscosity
Fig. 1−Plot of log (η) versus 1/T, (♦) Palm oil, (■) Rice bran oil, (▲) Cotton seed oil
Fig. 2−Plot of log (η) versus 1/T, (♦) Mustard oil, (■) Sunflower oil, (▲) Soybean oil
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INDIAN J. CHEM. TECHNOL., NOVEMBER 2007
Table 1⎯Comparison of experimental and calculated values of viscosity Temp, K Viscosity Viscosity % Deviation experimental calculated (kg/m.s) using Eq. (9) (kg/m.s) (1) Palm oil (T, ref 293 K) 338 0.0215 0.0222 333 0.0253 0.0256 328 0.0293 0.0297 323 0.0341 0.0346 318 0.039 0.0406 313 0.0454 0.0477 308 0.0568 0.0565 303 0.0682 0.0672 298 0.0826 0.0804 (2) Mustard oil (T, ref 293 K) 338 0.01877 0.01843 328 0.0255 0.02469 323 0.0301 0.0288 318 0.0346 0.03368 313 0.0412 0.03964 308 0.0489 0.04689 303 0.0582 0.05579 298 0.0705 0.0668 (3) Cotton seed oil (T, ref 293 K) 338 0.0169 0.0177 333 0.0196656 0.0204 328 0.0223 0.02368 323 0.02591 0.0276 313 0.03599 0.038 303 0.05195 0.0535 298 0.06188 0.064 (4) Sunflower oil (T, ref 293 K) 338 0.0162 0.0165 333 0.020076 0.02 328 0.02235 0.0221 323 0.0255 0.0258 318 0.03055 0.0302 313 0.0356 0.0355 308 0.042 0.04205 303 0.0501 0.05 298 0.0615 0.0599 (5) Soybean oil (T, ref 293 K) 333 0.01883 0.01791 328 0.02014 0.02077 323 0.02285 0.0242 318 0.02701 0.0283 313 0.0351 0.0333 303 0.0466 0.0469 298 0.0573 0.0562 (6) Rice bran oil (T, ref 293 K) 338 0.01929 0.01929 333 0.0220 0.022 328 0.0254 0.0254 323 0.02977 0.02977 318 0.0342 0.0342 313 0.0396 0.0396 308 0.04715 0.04715 303 0.0565 0.0565 298 0.0701 0.0701
3.15 1.17 1.35 1.45 3.94 4.82 -0.53 -1.49 -2.74
Fig. 3−Effect of temperature on viscosity of different oils (♦) Palm oil, (■) Rice bran oil, (▲) cotton seed oil, (●)sunflower oil, (x) Mustard oil, (+) soybean oil
-1.84 -3.28 -4.51 -2.73 -3.94 -4.29 -4.23 -5.54 4.52 3.6 5.82 6.12 5.29 2.9 3.31 1.82 -0.38 -1.13 1.16 -1.16 -0.28 0.12 -0.2 -2.67 -5.14 3.033 5.57 4.56 -5.41 0.6 -1.96 -4.27 -3.29 -2.64 -3.22 -1.27 0.25 -0.32 -1.07 -4.78
Fig. 4−Plot of log (η /ηref) versus T/Tref
viscosity versus 1/T, the linear behaviour confirms the consistency of the experimental viscosity data. Greet and Magill22 suggested that reduced variable plot could be used for checking the consistency of viscosity data. In order to develop a generalized correlation between viscosity of the vegetable oils and temperature, reduced viscosity values log (η/ηref) have been plotted as a function of reduced temperature (Tref/T) in Fig. 4. A correlation between reduced parameters of viscosity (η/ηref) and temperature (Tref/T) for different oils can be expressed by the equation: log (η/ηref) = 4.8042(Tref/T) – 4.8092
… (9)
The correlation coefficient is 0.9902, which shows a high degree of accuracy. Table 1 shows the experimental and calculated values calculated using Eq. (9) for the oils selected in the present investigation. Figure 1 shows that a plot of log viscosity versus 1/T is linear in nature in the
NOTES
Table 2⎯Derived values of Ev Refined vegetable oil
Ev , kJ/mol
Palm oil Rice bran oil Cotton seed oil Mustard oil Sunflower oil Soybean oil
27.88 26.61 27.15 27.20 27.04 25.80
temperature range under investigation which confirms Arrhenius behaviour of these vegetable oils. This observation is further strengthened by the fact that the deviation between the experimental and theoretical values calculated using Eq. (9) is small as shown in Table 2. Conclusion A generalized correlation represented by Eq. (9) can predict the viscosity of an oil with reasonable accuracy in the temperature range 298-338 K. Nomenclature
A, B = Constants of instrument , Eq. (9) T = Temperature, K Tref = Reference temperature, K µ η ηref ν
References 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Greek
= = = =
Dynamic viscosity Viscosity, kg/m.s Viscosity at 293 K, kg/m.s Kinematic viscosity, mm2/s
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20 21 22
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