Ind. Eng. Chem. Prod. Res. Dev. 1981, 20, 540-544
540 ._
k , = rate constant for the volatilization of lubricant, h-l = rate constant for increasing TAN, mg of KOH (g h)-l k x = rate constant for changing the parameter X,unit h-' k,, = rate constant for increasing TC, (mm h)-' k,, = rate constant for increasing T N , (mm h)-' Zk, = rate constant for bimolecular termination of peroxy radical, M-' s-' kinh = rate constant for inhibition with peroxy radical, M-' kA
-, E
125-
100-
E
075-
S-1 050.
0 25.
0 00
00
05
10
15
([lr~H]~-[lnH])
2.0
25
(wt%)
Figure 7. Linear relationship between ((InH],,- [InH])and TN: -, during induction period; - - -, after induction period.
it will be necessary to study how the values of k, and Ri are influenced by lubricant formulations or operating variables of engines.
Acknowledgment The authors are indebted to Dr. K. Yamazaki, Professor of Emeritus, University of Tokyo, for his valuable discussion and continual stimulation. The authors also express their appreciation to Mr. A. Matsunaga for his advice in the antioxidant analysis. Nomenclature A = TAN, mg of KOH g-' [InH] = concentration of antioxidant, M or w t % klst = overall first-order rate constant for antioxidant decay, h-' k,, = overall zero-order rate constant for antioxidant decay, M h-' or wt % h-' ka&J = rate constant for fresh oil addition, h-' k f = rate constant for the outward flow of lubricant from engine system, h-' k , = rate constant for the reflux of lubricant from pistoncylinder area into oil-sump, h-' k , = rate constant for oil sampling (averaged value on assuming continuous sampling), h-'
Ri = initiation rate or radical input rate from piston-cylinder area into oil sump, M s-' or wt % h-' tind = induction period for the oxidation of lubricant in oil sump, h [RON021 = concentration of nitrate, M or wt % [ROO.] = concentration of peroxy radical, M or wt % X = dummy variable for TAN or TC, unit TC = absorbance of carbonyl at 1705 cm-l, mm-' T N = absorbance of nitrate at 1630 cm-', mm-' Subscripts m = equilibrium conditions 0 = initial conditions tind = conditions at tind
Literature Cited Bardy, D. C.; Asseff, P. A. SA€ Pap. 1970, No. 700508. Boozer, C . E.; Hammond, G.S. J . Am. Chem. SOC. 1955, 77, 3233. Buchochenko,A. L.; Kaganskaya, K. Y., Neiman, M. B. Klnet. Katal. 1963, 2, 161. Burn, A. J. Adv. Chem. Ser. 1968, 75, 323. Denisov, E. T. Kinet. Katal. 1963, 4 , 508. Denisov, E. T.; Aleksandrov, A. L. Zh. Flz. Khlm. 1964, 38, 491. Guggenheim, E. A. Phil. Mag. 1926, 2, 538. Harie, 0. L.;Thomas, J. R. J . Am. Chem. SOC.1957, 79, 2973. Howard, J. A.; Ohkatsu, Y., Chenier, J. H. B., Ingold, K. U. Can. J . Chem. 1973, 51, 1543. Korcek, S.;Mahoney, L. R.,Johnson, M. D., Hoffman, S. SA€ Pap. 1978, No. 780955. Kreutz, K. L. Lubrlcation 1969, 55 (6), 53. Mahoney, L. R., Kwcek, S.,Hoffman, S.,Willermet, P. A. Ind. Eng. Chem. Prod. Res. Dev. 1978, 17, 250. Mahoney, L. R.; Otto, K. Korcek, S., Johnson, M. D. Ind. fng. Chem. Prod. Res. Dsv. 1980, 19, 11. Marquardt, D. W. J. SOC. Ind. Appl. Math. 1963, 1 1 , 431. Milllotis, G.; Boudoncie, B., Parc, G. Bull. SOC. Chlm. Fr. 1960a, 647. Milllotis, G.; Boudoncle, B., Parc, G. Bull. Soc.Chim. Fr. 1969b. 4462. Thomas, J. R.; Tolman, C. A. J . Am. Chem. SOC. 1962, 84, 2930.
Received for reuiew November 20, 1980 Revised Manuscript Received April 20, 1981 Accepted April 28, 1981
Kinetic Approach to Engine Oil. 3. Increase in Viscosity of Diesel Engine Oil Caused by Soot Contamination Seljiro Yasutoml, * Yoshihiro Maeda, and Tsutomu Maeda Lubricants 61 Petroleum Products Laboratory, Nippon Mining Co.,Ltd., 17-35, Niizo-minami 3-chome. Toda-shi, Saitama-ken 335, Japan
Used diesel engine oil is regarded as a suspension composed of Newtonian oil phase and the dispersed phase of soot particles. Most used oils can be treated as a Newtonian suspension in the range of the shear rate of usual measurements with a capillary viscometer. The increase in viscosity as a function of soot concentration can be described by a "modified Brinkman's equation" including an empirical parameter a which corrects the difference in the abilii to increase the viscosity between soot and inert spherical particles. A reference value of a is obtained from the data with wide varieties of lubricants used in fiiM service, while some peculiar condfions in a bench engine test induce a little discrepancy from the reference value.
Introduction Soot contamination is one of the most important causes of the increase in viscosity of diesel engine oils. The increase in viscosity is very dependent on the design of diesel 0196-4321/81/1220-0540$01.25/0
engine utilized. Parsons (1969), Smith and Chowings (19761, and Knight and Weiser (1976) have demonstrated that indirect-injection type induces a much greater rate for the soot contamination than the direct-injection type. @ 1981 American Chemical Society
Ind. Eng. Chem. Prod. Res.
In order to judge the degradation mode of diesel engine oil, it is necessary to investigate the viscosity increase due to the soot contamination under the conditions where the contribution of other degradation modes is negligible. Used diesel engine oil can be regarded as a suspension composed of Newtonian oil phase and the dispersed phase of soot particles. Einstein’s equation (1911) was derived from the Navier-Stokes equation in order to describe the rheological behavior of an ideal suspension containing inert spherical particles with no size distribution. Since this equation is not applicable to concentrated suspensions, many attempts have been made to extend the valid region of mathematical model toward higher concentrations. Brinkman’s equation is one of those derived from such attempts. Spearot (1974) has found that a relation similar to Brinkman’s equation describes the viscosity of thickened motor oil obtained from Seq. IIIC test as a function of the concentration of insolubles produced by its severe oxidation. The kinetic analysis in part 1 has shown that a simple exponential function holds for the increase in carbon residue or insolubles with time. This study deals with a kinetic analysis of the viscosity increase by using a modified model of Brinkman’s equation in conjunction with the results from part 1. Experimental Section Viscosity Measurement. Kinematic viscosity was measured with a capillary viscometer according to ASTM D-445. Since most of the data in this work had been obtained before the designation of the current metric system, viscosity was measured at 37.8 and 98.9 “C instead at 40.0 and 100.0 “C, respectively. Absolute viscosity is replaced by kinematic viscosity because of the small change in lubricant density after usage in diesel engines. Bench Engine Test. Details of bench engine test were previously described in part 1. The code number for tested oils is also the same as in part 1. Procedures for the Preparation of Fresh-Oil Suspension. Fresh-oil suspensions containing soot or carbon black were prepared. Soot was collected from the exhaust gas of the bench engine. Carbon black MCF-88 was obtained from Mitsubishi Chemical Industries Ltd. In order to disperse the particles homogeneously, a suspension in tetrahydrofuran was prepared by using a mortar with a pestle. The suspension was added into a fresh oil. Tetrahydrofuran was carefully stripped by nitrogen gas at a moderate temperature. The viscosity of the suspensions did not change after storage in the gravitational field for two weeks. Theoretical Consideration A dilute suspension containing inert spherical particles shows Newtonian behavior and its relative viscosity, qr, is represented by Einstein’s equation (1911), qr
=
7/90 =
1
+ 2-54
(1)
where the volume fraction of dispersion phase, 4, is described by the equation 4 = u2/(u1 + u2) (2) Let us consider that the viscosity of suspension increases from 7 to (7 + dq) by further adding a small portion of dispersion phase duP. The increased volume fraction, $’, is indicated by the equation $’ = duz/(ul + ~2 + du2) d ~ z / ( + ~ l~ 2 ) (3) On the other hand, differentiation of eq 2 gives the relation d $ / b = ui/(ui
+~
2
)
~
(4)
Dev., Vol. 20, No. 3, 1981 541
From eq 3 and 4, the next equation is obtained with respect to d$ d4J = [ui/(ui
+ uz)l[d~z/(ui+ 4 1 = (1 - $)$’ (5)
Equation 5 is transformed into eq 6
4’ = - 6) (6) Here, it is assumed that eq 1 is approximately valid for the addition of 4’ to a suspension which already contains 4. Substitution of eq 6 into eq 1 gives the following equations 7
-
+ d7 = 7[1 + 2.5d$/(l
- $)]
da/o = 2.5d$/(1 - 4)
(7) (8)
-
Integration of eq 8 under the boundary conditions of 7: 7o 9 and $: 0 $ gives the relation vr
= 9/70 = 1/(1- 4)2.5
(9)
Equation 9 is well known as Brinkman’s equation (1952). Equation 9 is transformed into next relation 7r44
=
(7/70)-o.4
= 1- 4
(10)
If soot particles can be regarded as inert spheres, eq 10 may hold for the viscosity of used diesel engine oils. However, soot shows the behavior of nonideal particles through volume effects by increasing effective volume due to solvation or through structural effects by the formation of aggregates due to the mutual interaction of particles. From the volume effects, soot particles may form “floc” by the solvation or the penetration of continuous oil phase into the porous structure of particles similar to kaolin in aqueous suspensions as indicated by Michaels and Bolger (1962). The volume fraction of the floc, $f, may be proportional to $ =4 (11) where a is a proportional constant. Substitution of $f into eq 10 instead of $ gives the relation $f
7r4,4 = (77/70)4,4 = 1 -
(u$
(12)
From the structural effects, the aggregate of soot in a used oil is subject to physical or mechanical disorder, and the oil acts as a pseudo-plastic fluid or, in an extreme case, as a Bingham fluid. Parsons (1969) has observed that an used oil containing 13.1 wt % insolubles indicates clear yield stress about 40 dyn/cm2 at room temperature. Some used oils containing a large amount of soot indicate some gelation tendency, while the following relation between yield stress, 7y,and $ has been found for various particles by Firth (1976). 7y
=
P$2
(13)
Here, the value of 7yfor a used oil at the soot concentration of 5 wt % ’ ,which is considered the upper limit for practical use, is estimated from the data of Parsons to be only 6 dyn/cm2 on assuming the same value of 0.Figure 1shows Newtonian behavior of two used oils at 0 “C by means of a Rotoviscometer. It has been recognized that the lower the temperature, the higher is the tendency for gelation. Since most commerical oils have sufficient ability of dispersion, their used oils may be treated as Newtonian suspensions in the range of shear rate by a capillary viscometer. Figure 2 shows linear relations between (C - C$/S,,) and the organic portion of coagulated n-heptane insolubles. The different line slope is observed probably because oil insolubles contains not only soot but other materials such
Ind. Eng. Chem. Prod. Res. Dev., Vol.
542
20, No. 3, 1981
(C-C,S~S,)
-
o
3C3
a
355
I&
3 37
100
a
v
r "
" Lo
w
10
0.01
1
0
3
2
(
10
100
Shear
Rate
1000
(sec-1)
5
4
6 wt %
c -C.S/s.I
I
9
8
7
10
Figure 4. Effect of added carbon black on increasing viscosity of fresh oil.
Figure 1. Viscosity of used diesel engine oil as a function of shear rate at 0 "C.
I
R
90
C
1
2
3 (
4
c - C.S/S.)
5
6
7
8
Wl%
Figure 5. Increase in viscosity of diesel engine oil in field service. PlantNo
!C-i.5/S0)
WI
1
I
0):
Figure 2. Relation between (C - C$/So) and organic portion of IBH.
__0 0
.
-
'
i.3
h
'*
0 92
090
'
I ~
05
c - COSlSD
a 094
*
Med um-Speed Trunkplbton Enqlne D
1 5
10
20
wt
Figure 6. Increase in viscosity of oil used in medium-speed diesel engine. 4 shows, the addition of carbon black into fresh oil also causes a viscosity increase, but soot particles indicate a greater increase than carbon black. The cy values are estimated to be 5.6 X and 1.5 X wt %-' for soot and carbon black, respectively. Plots of q, against (C - C$/So) for some oils used in field service by three engines including both direct and indirect injection types are summarized in Figure 5, where the value of cy is close to that in Figure 3. For the oils used in medium-speed diesel engine, (C- C$/So) does not always agree with soot concentration, because sulfated ash is no longer a good indicator for additive concentration on account of the removal of the inorganic component of additives through purification facilities. However, Figure 6 shows that the relationship in eq 14 is approximately maintained. Mutual agreement of the a values in Figures 3,5, and 6 suggesta the concept of a reference cy value for nonoxidized diesel engine oils. Vuk et al. (1976) has indicated that relevant properties such as diameter distribution and C/H ratio of both exhausted aggregates and constituent primary particles scarcely change over the range of exhausted gas temperature above 300 "C during the thirteen-mode operation. In addition, Braddock and Bradow (1975) found no remarkable difference in the particles exhausted from some
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 3, 1981 543
I
0.03
2
1
(
3
4
5
c - C.S/S.)
6
w 1%
1
0
Figure 7. Increase in viscosity of diesel engine oil during bench engine test.
3
2
w 1%
(C-C..S/S.)
Figure 10. Effect of ashless dispersant additive on the viscosity increase of diesel engine oil.
Sample 011 @11-15 0 Smoke 378‘c Smoke 989’C
0.9
0
\
0.8
\
Normal 3 7 B’C Normal 9 8 9’C
smoke Lwei Normal 0 9 Bosch Smoke 5 7 Bo&
I
0.0L 0
1
2
3
4
5
6
(C-C.S/S.)
7
8
9
w t%
Figure 8. Abnormal dependence of a value on temperature observed in smoke test.
0;
10
20
30
Test Duration
40
50
(hr)
Figure 11. Comparison between the increase of (C - C$3/So) and that of viscosity as a function of running duration.
I
0
1 1
2
3
Insol ubles
4
5
6
7
8
w t ”1.
Figure 9. Comparison of ZA with ZB for normal and smoke testa.
diesel passenger cars. These results may support the existence of the reference a value. On the other hand, used oil obtained from the bench engine test apparently indicates the linear relationship between (C - C$/So) and vr, but there are some differences in the a value for individual lubricants, as illustrated in Figure 7. This fact may be due to volatilization and oxidation in the piston-cylinder area as discussed in parts 1 and 2. In addition, large changes in a value were observed when the same test engine was operated under the conditions of higher smoke level by means of the partial blocking of intake port. As demonstrated in Figure 8, lower excess air in the smoke test reveals positive dependence of a value on temperature, while the oxidation of lubricant usually causes negative dependence. Comparison of I* and I B (Figure 9) suggests that these phenomena may be due to mutual interaction and size growth of the soot particles. Parsons (1969) has reported that ashless type dispersant additives prevent the viscosity increase by increasing the dispersion ability of the engine oil. However, as shown in Figure 10, such effects could not be observed insofar as the authors’ bench engine test was concerned. Therefore, the differences in viscosity increase in Figure 8 may mainly
be influenced by the relevant properties of the aggregate formed before distribution into lubricant. I t is expected that the combustion state reflects on the temperature dependence of the a value which may be available for the diagnosis of combustion state through oil analysis. The following relation has been confirmed in part 1. (C - CoS/So)= (C, - CoS,/So)[l - exp(-kl,,t)]
(15)
Substitution of eq 15 into eq 14 gives the final equation which can describe the viscosity increase as a function of running duration.
vr4.4 = (v/vO)P4 = 1 - a(C,
-
C$,/So)[l
- exp(-klStt)l (16)
An example of the comparison between the increase of (C - C$/So) and that of ( q / v o ) for Oil-2 is demonstrated in Figure 11, where solid curves represent their increases calculated from eq 15 and 16, respectively, and open symbols indicate the observed data. Kinetic parameters of (C, - C$3,/So) and kbt were determined to be 3.43 (wt 70) and 2.14 X (h-l), respectively, by Marquardt’s method (wt %-l) obtained from (1963). The value of a is 8.7 X the plot in Figure 7. Conclusion The increase in viscosity of diesel engine oil caused by soot contamination is described as a function of soot concentration by using the “modified Brinkman’s equation” containing an empirical parameter “a”. This
Ind. Eng. Chem. Prod. Res. Dev. 1981, 20, 544-546
544
model can also indicate the viscosity increase with time in conjunction with the first-order kinetic model proposed in part 1. In the near future, it will be necessary to elucidate the detailed factors influencing the value of “a”. Acknowledgment
The authors would like to express their appreciation to Dr. K. Yamazaki, Professor of Emeritus, University of Tokyo, for his valuable discussion and continual encouragement. Nomenclature
C = carbon residue concentration, wt % S = sulfated ash concentration, wt % ZA = concentration of insolubles according to procedure A, wt %
I B = concentration of coagulated insolubles according to procedure B, wt % IBH = concentration of coagulated n-heptane insolubles, wt % kist = overall first-order rate constant for lubricant transport, h-l WA = weight fraction of ash component in IBH ul, u2 = volume of dispersion medium and dispersion phase in suspension, respectively Greek Letters
a = proportional constant between r#J and r#Jf or between C#I and (C- C&7/So) in eq 12 and 14, respectively /3 = proportional constant between r#J2 and ry r#J = volume fraction of dispersion phase in suspension r#Jf = volume fraction of floc in suspension 9 = viscosity of used oil, CPor cSt q0 = viscosity of fresh oil, CPor cSt qr = T~
relative viscosity of used oil
= yield stress of Bingham fluid, dyn/cm2
Subscripts m = equilibrium conditions 0 = initial conditions L i t e r a t u r e Cited Braddock, J. N.; Bradow, R. L. SA€ Pap. 1075, No. 750682. Brinkman, H. C. J. Chem. phys. 1052, 20, 571. Einstein, A. Ann. Phys. (Leiprig) 1011, 3 4 , 951. Firth, B. A. J. ColloM Interface Sci. 1076, 57, 257. Knight, C. R.; Weiser, H. SA€ Pap. 1976, No. 760727. Marquardt, D. W. J. SOC.Ind. Appl. Math. 1063, 11, 431. Michaels, A. S.; Bolger, J. C. Ind. Eng. Chem. Fundam. 1062, 7, 24. Parsons, J. C. J. Inst. Pet. 1060, 55, 256. Smith, I. E.; Chowlngs, A. R. SAEPap. 1076, No. 760723. Spearot, J. A. Ind. Eng. Chem. Prod. Res. Dev. 1074, 13, 259. Vuk, C. T.; Jones, M. A,, Johnson, J. H. SAEPap. 1976, No. 760137.
Received for reuiew November 20, 1980 Revised Manuscript Received April 20, 1981 Accepted April 28, 1981
Thermal Decomposition during Vaporization of No. 2 Heating Oil Alexander Vranos United Technologies Research Center, Silver Lane, East Hartford, Connecticut 06 708
The thermal decomposition of surface vaporized no. 2 heating oil has been studied. The extent of decomposition of the fuel, as determined by measurement of n-alkanes and certain aromatics, was greatest at the lowest temperature and heating rate studied and was proportional to partial pressure of oxygen in the carrier gas and fuel. Alkane pyrolysis caused a net increase inthe concentratin of lighter alkanes with net loss of heavier alkanes. It was found that. the decrease in concentration of heavier alkanes was proportional to molecular weight. The aromatics pyrene and fluorene behaved in a manner similar to n-alkanes in that the concentration of the heavier molecule, pyrene, was reduced appreciably by vaporization while fluorene was unaffected. The results indicate that component volatility influences strongly the extent of decomposition during vaporization. Group-type liquid chromatographic analysis of aromatics supported this conclusion.
Introduction
Hydrocarbon fuel vaporization is an important process in a number of power plant applications. Vaporization may occur from free droplets or surfaces. In either case, the fuel may undergo decomposition, ultimately impacting power plant performance and emission levels. Despite its importance, the problem of fuel decomposition during vaporization has received relatively little attention. In previous papers (Vranos, 1980,1978,1977) the author has described the types of decomposition products, the influence of boiling mode, and possible mechanisms for the decomposition of vaporizing n-hexadecane. A single-component fuel was studied in order to aid the understanding of the decomposition mechanism. The work is continuing, and experiments are in progress to define the influence of dissolved oxygen level and environmental conditions on the decomposition of hexadecane. This paper is concerned with a preliminary description of the behavior of n-alkanes in no. 2 heating oil under surface vaporizing conditions. The results from this type of work would be useful, ulti-
mately, in any application where hydrocarbon fuel contacts and vaporizes from a hot surface. Experimental Section
Details of the apparatus have been presented in a previous paper (Vranos, 1978). Fuel (no. 2 heating oil) is vaporized from a heated surface into a carrier gas stream. In this experiment carrier gas and surface temperatures are equal. The carrier flow rate was 1275 cm/min (STP), and the carrier gas was either pure nitrogen or 2% oxygen in nitrogen. A steady flow of fuel was delivered to the surface through a 1.2-mm stainless steel hypodermic tube at a point approximately 0.6 cm above the surface. At a fuel flow rate of 0.75 cm3/min, steady vaporization occurred from a small puddle on the surface. The fuel was either air-saturated, oxygen-saturated, or deoxygenated prior to vaporization. The reactor effluent passed through a condenser and sample collection system. Normal alkanes, fluorene, and pyrene were measured before and after vaporization using a Hewlett-Packard Model 5830 gas chromatograph equipped with flame ion-
0196-4321/81/1220-0544$01.25/0@ 1981 American Chemical Society
