Ind. Eng.
Chem. Prod. Res. Dev., Vol.
18, No. 4, 1979
371
A Mathematical Model Relating Viscosity to Penetration Applicable to a Wide Range of Asphalts A. M. Abushlhada' and Y. AI-Farkh Petroleum and Petrochemicals Department, Kuwait Institute for Scientific Research. Kuwait
A mathematical model has been prepared for bitumens relating viscosity measured at 120 OC to penetration measured at 25 "C. This enables the viscosity of a bitumen sample to be calculated from its penetration, a property which may be determined both rapidly and easily. Over 90 observations were used in the development of the model. The model gave differences between calculated and observed values of viscosity of less than 10%.
Introduction The temperature susceptibility of paving-type asphalt cements is of great importance to civil engineers. Viscosity is the major property which can give an insight into the asphalt temperature susceptibility. The less susceptible asphalts will have higher viscosities at a given temperature and these higher viscosities result in less creep at the given temperature (Merrington, 1949). Because of the considerable value to road construction of this information which can be derived from viscosity data, several methods have been adopted in the past to measure the viscosities of asphalts. These viscosities cover a wide range extended from the order of a few centipoises a t high temperature to 1O'O P or greater at low temperatures. The method chosen depends upon the purpose for which the measurement is required upon the hardness of the asphalt binder to be tested. This large variation in methods and techniques for measuring viscosities has encouraged several authors to develop theories and to carry out experimental programs to relate viscosity with some other more easily measurable properties such as penetration. The authors ( H b t e a d and Welborn, 1971; Pwinauskm, 1967; Welborn et al., 1966) have reported the use of the following linear relationship between the log of viscosity a t 60 "C and the log of penetration at 25 "C log (P/Pi) = M log ( V / Vi) (') where P = penetration at 25 "C, dmm, V = viscosity at 60 "C, P corresponding to P, P1 = penetration at 25 "C at another level, Vl = viscosity at 60 "C, P corresponding to P1,and M = slope of the log-log plot = A log V I A log P. This model was tested using 84 different series of asphalt cements, and close agreement was found between the calculated values and those obtained by experiments. Saal(1933) proposed an interesting relationship between viscosity and penetration, postulating that both the viscosity and the penetration should be determined at the same temperature. The initial formula was 9.1 x 109 V = p1.93
agreement with the theoretically deduced formula 4
where V and P have the same definition as that stated in eq 1. However, this was the subject to revision (Saal et al., 1946); see eq 3 1.58 X 1O'O (3) = p2.16
V / P = 0.0216t (5) where V = viscosity in poises, P = density in g/cm3, and t = Saybolt Furol viscosity in seconds. Table I shows the results obtained for the bitumen samples including penetration at 25 "C and viscosities at 120
Equations 2 and 3 hold only for purely viscous asphalts (Newtonian$. S a d (1933) has found that eq 3 has a close 00 19-78901791127 8-037 1$07 .0010
a1
+ 0.5b12 = PT V
(4)
where a = constant denoting the resistance to penetration of the penetration needle, 1 = the depth of penetration in centimeters, b = constant for needle resistance calculated to be 2.10 for the needle standardized by ASTM, T = duration of load in seconds, P = penetration, and V = viscosity. Rhodes and Volkman (1937) and Traxler and Moffat (1938) were able to use eq 3 to calculate the viscosity of several types of asphalt cements after making a correction for the conical shape of the needle. Tons and Chritz (1975) have extensively studied the possible relationships between viscosity and penetration for 43 Michigan asphalts. They proposed two equations. With the first equation all 43 samples were used, while in the second they excluded three samples which were highly shear susceptible. In the present work, a new mathematical model is presented. In this model the viscositv at 120 "C is related to penetration at 25 "C. A total of 96 observations were used to establish the model by using a polynomial regression technique, Results and Discussion Several methods and instruments were adopted for viscosity measurements to cover a wide range of asphalts. The Saybolt Furol viscometer is commonly used-in the United States, the Redwood instrument in Great Britain, and the Engler instrument on the continent of Europe. Asphalts being tested with these instruments have to be homogeneous liquids. The temperatures commonly used range from 100 to 150 "C. In the present work where the Saybolt Furol viscometer has been used to measure viscosity, the direct measured results are flow times in seconds; however, these can be converted to absolute viscosity values (poises) by the use of conversion factors developed for the particular instrument. Thus the time of efflux in seconds can be converted to poises using the following formula
"C. The values of viscosity listed in column 4 of Table I are the values calculated from the adopted model. This model was developed using 90 observations of different grades of asphalt. The asphalts were prepared under cer0 1979 American Chemical Society
372
Ind. Eng. Chem. Prod. Res. Dev., Vol. 18, No. 4, 1979
Table I. Values of Penetration and Viscosity for KISR Bitumen viscosity penetration 150 127 72 46 129 97 75 166 117 93 70 200 155 59 40 210 199 151 135 98 77 130 90 125 29 124 89 96 73 54 43 155 95 71 64 28 81 63 160 132 210 190 111 60 190
exptl 237 252 439 648 258 334 383 210 282 359 430 204 211 506 716 192 204 220 246 343 378 234 353 266 905 237 362 3 08 410 564 718 216 289 382 422 429 397 505 216 23 2 199 216 253 481 222
calcd 222.35 249.17 410.60 635.89 246.31 310.32 394.42 211.46 265.45 322.11 422.23 204.93 218.29 500.78 719.09 204.43 204.85 221.48 238.29 307.55 384.42 244.88 331.79 252.19 917.01 253.73 335.20 313.15 405.04 546.39 675.58 218.29 316.06 416.33 461.75 438.41 366.10 469.07 214.83 242.18 204.43 205.30 276.92 492.48 205.30
viscosity % diff
penetration
exptl
calcd
% diff
6 1 6 1 4 7 2 0.6 5 10 1 0.4 3 1 0.4 6 0.4 0.6 3 10 1 4 6 5 1 7 7 1 1 3 5 1 9 8 9 1 7 7 0.5 4 2 4 9 2 7
105 86 119 92 72 188 50 200 150 127 105 135 127 115 108 103 73 185 185 190 150 90 65 95 75 60 220 180 197 200 193 180 115 215 204 131 108 95 220 198 62 83 40 30 240
304 330 249 295 390 210 613 209 227 258 311 216 262 264 278 326 396 206 216 200 211 311 438 324 383 461 194 206 230 202 205 211 288 225 229 243 308 313 202 203 4 28 398 715 902 181
289.94 345.98 261.96 325.25 410.60 205.30 588.37 204.93 222.35 294.17 289.94 238.29 249.17 269.13 283.20 294.69 405.04 205.79 205.79 205.30 222.35 331.79 454.64 316.06 394.42 492.48 202.15 206.62 204.86 204.93 205.01 206.62 269.13 203.65 204.85 243.50 283.20 316.06 202.15 204.94 455.23 368.45 716.60 908.81 183.71
4 4 5 10 5 2 4 1 2 3 6 10 4 1 1 9 2 0.09 5 2 5 6 3 2 2 6 4 0.3 10 1 0 2 6 9 10 0.2 8 0.9 0.09 0.9 6.3 7.5 0.0 0.0 1
Table 11. F Values and Correlation Coefficients for Different Orders of the Model
F values
correl coeff
power of X
196 511 882 881 763 649
0.7902 0.9473 0.9788 0.9841 0.9854 0.9858
1 2 3 4 5 6
p3D
B!€
m -!€
-m
tain conditions described in our earlier publication (Abushihada and Al-Farkh, 1979). All of the 90 experimental results were utilized in a nonlinear polynomial regression program to produce models with terms in the order of 1 to 6. The values of the appropriate correlation coefficient and the F values for the six models are shown in Table 11. It is clear that the F value reaches a maximum for the model including X terms of order 3; i.e., the higher and lower orders models display lower F values. Values of the correlation coefficient show a continuous increase with an increase in the order of terms of X. Thus, the optimum model relating viscosity to penetration was found to have the order of X3.The model is shown below in the form of eq 6 V = 1325 - 19.544P 0.1149P2- 2.251 X 10-4p (6)
+
653
M . f
e!€
,
2
".; 8 3%
.
M .
im
.
m . 1!€
.
,a! !€
Pentrrf>m 10
m
yl
lo
!€
M
70
m
03
,m
>lo
,m
1 y I ,lo
!!€
162 1-0
LM 103
:m
?lo
-2"
?yl
Figure 1. Standard curve for viscosity vs. penetration.
where V and P are the viscosity and penetration, respectively. In column 5 of Table I it can be seen that the percentage differences between the experimental viscosities and those calculated from the model do not differ by more than 10%. The particular relationship between viscosity and penetration which has appeared in the form of eq 6 is shown graphically in Figure 1 for the data shown in Table I.
Ind. Eng. Chem. Prod. Res. Dev., Vol. 18, No. 4, 1979
The main advantage of the present model (eq 6) over the other models depicted in the literature is its applicability to a wide range of road asphalts having penetrations in the range of 28 to 240. Most of the asphalts and asphaltic cements required for road construction, waterproofing, dampproofing, and sealing lie within this range. These applications cover more than 90% of asphalt usage worldwide, thus demonstrating the importance of the model presented here. Acknowledgment The authors acknowledge the cooperation of the Kuwait Institute for Scientific Research for providing all of the facilities for this work to be executed. Thanks are due to
373
Mr. Marron for reading the manuscript. Literature Cited Abushihada, A,, AI-Farkh, Y., Ind. Eng. Chem. Prod. Res. Dev., 18, 230 (1979). Halstead, W., Welborn, J., Highw. Res. Rec., 350 (1971). Merrlngton, A,. "Viscosity", Edward Arnold and Co., London, 1949. Puzlnauskas, V., Proc. Assoc. Asphalt Paving Technol., 38, 489 (1987). Rhodes, E., Volkman, E., J . Appl. Phys., 8 , 492 (1937). Saal, R., Baas, P., Heukelom, W., J . Chem. Phys., 43, 23 (1946). Saal, R., Proc. WorU. Petrol. Congr., London, 2 , 515 (1933). Tons, E.,Chritz, P., Proc. Assoc. Asphalt Paving Technol., 44, 387 (1975). Traxler. R., Moffatt, T., Ind. Eng. Chem., Anal. Ed., 10, 188 (1938). Welborn, J., Oglio, E., Zenewitz, J., Proc. Assoc. Asphalt Paving Technol., 35, 19 (1966).
Received for review June 4, 1979 Accepted August 16, 1979
A New Process for the Production of Trimethylhydroquinone Y. Ichikawa,' Y. Yamanaka, N. Suruki, T. Naruchl, 0. Kobayashi, and H. Tsuruta Products Development Institute, Teijin Lid., 2- 1 Hinode-cho, Iwakuni-shi, Yamaguchi-ken 740, Japan
A newly developed synthetic procedure for trimethylhydroquinone (IV), a feedstock for the synthesis of vitamin E, is reported. All conventional methods produce IV via 2,3,6-trimethylbenzoquinone and have disadvantages in their multisteps or the use of expensive raw materials. To overcome these defects, a process for IV with fewer steps using phenol (I) was developed. The first step is a gas-phase methylation of I with methanol. The second
6 I
MeOH
_c
H3C@CH3
o2
4
H3CQ
I I
_c
OH
H3C CH3
H3
H
3
C
e
C
H
3
H3C
III
OH
IV
I1 step is a liquid-phase oxidation of I1 with inolecular oxygen at high pressure in basic solution. This step is newly developed by these investigators. The last step is a high-temperature thermal rearrangement of I11 in basic solution. Technical data and know-how necessary for the construction of a commercial plant resulting from long-term operation of a test plant have been obtained.
Vitamin E (a-tocopherol) has the structure shown in Figure 1. It has been widely used as a nutrient and an antioxidant in the field of foodstuffs and animal husbandry as well as medicine. The demand of vitamin E in the U.S. and Europe was about 1930 tons/year in 1973. It is especially increasing in the U.S. (Figure 2). Natural vitamin E has been restricted in availability, so synthetic vitamin E will be increasingly used in the future. I t has been produced by the condensation ring closure of trimethylhydroquinone (TMHQ) with isophytol or phytol. We report on the newly developed synthetic procedure for TMHQ, which is one of the raw materials used for vitamin E. Many synthetic processes of TMHQ have been known. The typical example of these is shown in Figures 3 and 4, where the introduced substituents X, Y, and Y' are not required for TMHQ itself. The process becomes not only multistaged and confused but also it is not favorable from the viewpoint of pollution owing to the production of byproducts.
* Address correspondence to this author at the Research and Development Division, Teijin L a . , 1-1,2-chome, Uchisaiwai-cho, Chiyoda-ku, Tokyo 100, Japan.
Table I. Example of Methylation Product substance
content
remarks
2,4,6-trimethylphenol phenol o-cresol 2,4- and 2,6-xylenol anisole aromatic hydrocarbons m-methylated derivative
main trace minor minor minor trace trace
product recycle recycle recycle recycle
As we have described, all conventional methods produce TMHQ via 2,3,6-trimethylbenzoquinonein the same way and obtain it by the reduction of the quinone compound. Our method can produce TMHQ without using a quinone reduction process. In Figure 4 the raw material, 2,3,6-trimethylphenol, can be obtained as a byproduct of cresol production, but it is expensive and its supply is affected by the production of cresol. We have investigated many procedures of TMHQ synthesis with fewer steps using a cheap starting material which is commercially available. We now have developed a new synthetic method €or TMHQ shown in this report. Our method consists of three steps and phenol is used as one of the raw materials (Figure 5).
0019-7890/79/1218-0373$01.00/00 1979 American Chemical Society
