Ind. Eng. Chem. Prod.
530
Res. Dev. 1981, 20,530-536
Bormann. S.;Brossas. J.; Franta, E.; Gramain, Ph.; Kirch, M.; Lehn, J. M. Tetrahedron 1975, 31, 2791. Bourgoin, M.; Wong, K. H.; Hui, J. Y.; Smid, J. J. Am. Chem. Soc. 1975, 97. 3462. - -Bradshaw, J. S.; Stott, P. E. Tetrahedron 1980, 36, 461. Chrlstensen. J. J.; Lamb, J. D.; Izatt, S. R.; Starr, S. E.; Weed, G. C.; Astin, M. S.,Stitt, B. D.; Izatt, R. M. J. Am. Chem. SOC. 1978, 100, 3219. Izatt, R. M. Science 1971, 174, 459. Christensen, J. J.; Hili, J. 0.; Cinquini, M.; Colonna, S.; Molinarl, H.; Montanari, F.; Tundo, P. J. Chem. SOC. Chem. Commun. 1976, 394. Dietrich, B.; Lehn, J. M.; Sauvage. J. P. Tetrahedron 1973, 29, 1647. Dletrich, B.; Lehn. J. M.; Sauvage, J. P. Tetrahedron Lett. 1989, 2889. Dotsevi, G. Yao-Sogah; Cram, D. J. J. Am. Chem. SOC. 1978, 98, 3038. Dotsevi, G.Yao-Sogah; Cram, D. J. J. Am. Chem. SOC. 1979, 101, 3035. Felgenbaum, N. M.; Michal, R. M. J. folym. Sci. A1 1971, 9 , 817. Graf, E.; Lehn, J. M. J. Am. C h m . SOC. 1976, 98, 6403. Gramain, Ph.; Frere, Y. Macromolecules 1979a, 12, 1038. Gramain. Ph.; Frere, Y. N o w . J. Chim. 1979b, 3 , 59. Gramain, Ph.; Frere, Y. Polymer 1980, 21, 921. Gramain, Ph.; Kleiber, M.; Frere, Y., Polymer 1980, 21, 915. Herceg. M.; Weiss, R. Acta Ctystalbgr. 1973a, 29, 542. Herceg, M.; Weiss. R. Chim. Miner. 1973b, 10, 509. Hermann, K. G.; Schlefer, H. P. Angew. Chem. 1980, 19, 406. Izatt, R. M.; Lamb, J. D.; Christensen, J. J.; Haymore, B. L. J. Am. Chem. SOC.1977, 99, 8344. Izatt, R. M.; Lamb, J. D.; Chrlstensen, J. J. J. Am. Chem. SOC. 1979, 99, 8344. Jepson, B. E.; Dewitt, R. J. Inorg. Nucl. Chem. 1976, 38, 1175. Karger, B. L. “Modern Practice of Llquid Chromatography”, Kirkland, J. J., Ed.; Wiley: New York, 1971. Kimura, K.; Maeda, T.; Shono, T. Talanta 1979, 26, 945; folym. Bull. 1979, 1 , 403. King, R. 8.; Heckley. R. P. J. Am. Chem. SOC. 1974, 96, 3118. Kobuke, Y.; Janji, K.; Hozlguchi, K.; Asada, M.; Nakayama, Y.; Furukuwa, J. J. Am. Chem. SOC. 1976, 98, 7414. Kopdow, S.;HogenIsch, T. E.; Smid, J. Macromolecules 1971, 4, 359. Kuistad, S.;Malmsten, L. A. Thesis, University of Lund (Sweden), 1979. Kutchukov, P.; Rkhard, A.; Quivoron, C. €ur. folym. J. 1980, 16, 753. Lacoste, J.; Schue,F.; Bywater, S.; Kaempf, B. Polym. Lett. 1978, 14, 201. Lehn, J. M.; Montavon, F. Helv. Chim. Acta 1978, 61, 67.
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Lehn, J. M.; Montavon. F. Helv. Chim. Acta 1976, 59, 1566. Lehn, J. M. “Structure and Bonding”; Sprlnger-Verlag: Berlin, 1973; pp 16. 71. McLaughlin, S. G. A.; Szabon, G.; Ciani, S.;Eisenman, G. J. Me”. Bbl. 1972, 9 , 3. Metz, 8.; Weiss, R. Inwg. Chem. 1974, 13, 2094. Moore, S. S.;Tarnowki, T. L.: Newcomb, N.; Cram, D. J. J. Am. Chem. SOC. 1977, 99, 6398. Moras, D.; Weiss, R. Acta Crystallogr. 1973, 829, 1059. Muller, W. H. Naturwlssenschsflen 1970. 57. 248. Mulier, W. H.;Muller, W. A. Natunvtssenscheflen 1974, 81, 455. Pearson, R. G. “Hard and Soft Ackk and Bases”, Pearson, R. G., Ed.; Wiley: New York, 1973. Pedersen, C. J. J. Am. Chem. Soc. 1987, 89, 2495, 7017. Pedersen, C. J.; Frensdorff, H. K. Angew. Chem. Int. Ed. Engl. 1972, 1 1 , 16.
Reusch, C. F.; Cussler, E. L. AICHE J. 1973, 79, 736. Schmidtchen, F. P. Angew. Chem. Int. Ed. Engl. 1977, 16, 720. Shchori, E.; Jagur-Olodzinski. J. J. Appl. folym. Sci. 1976, 20, 773. Simon, J. Thesis ULP Strasbourg, France, 1976. Souchay, P.; Lefebvre, J. “Equilibres et r6activlt0s des complexes en solution”, Masson Ed.; Paris, 1969; p 9. Sousa, L. R.; Hoffman, D. H.; Kaplan, L.; Cram, D. J. J. Am. Chem. Soc. 1974, 96, 7100. Tadeka, ’f.; Osho, K.; Segawa, Y. C h m . Lett. 1979, 601. Timko, J.; Helgeson, R.; Cram, D. J. Am. Chem. Soc. 1976, 100, 2828. Varma, A. J.; Magewicz, T.; Smid, J. J. Polym. Sci. folym. Chem. Ed. 1979. 17, 1573. Vcgtle, F. Symposium on Macrocycllc Ligends, Basel, Swkerland, 1980. Warshawsky, A.; Kallr R.; Dlshe, A.; Berkovk. H.; Patchornlk. A. J. Am. Chem. SOC. 1979, 101, 4249. Weber, E.; V-, F. “Kontakte”, Merck, E., Ed.; Darmstadt, Germany, 1977; p 36. Wong, K. H.; Yagi, K.; Smid, J. J. Me”. Bbl. 1974, 18, 379. Yabi, K.; Ruig, J. A.; Sanchez, M. L. Makromol. Chem. Rap. Commun. 1980, 1 , 263.
Received for review February 17, 1981 Accepted April 20,1981
Kinetic Approach to Engine Oil. 1. Analysis of Lubricant Transport and Degradation in Engine System Seljlro Yasutomi, Yoshlhlro Maeda, and Tsutomu Maeda Lubricants & Petroleum Products Laboratory, Nippon Mining Co., Lfd., 17-35, Niizo-minami 3-chom8, Toda-shi, Saltama-ken 335, Japan
A kinetic analysis of lubricant transport and degradation within a lightduty diesel engine was carried out by using a flow reactor model involving two mixing chambers. For high-speed diesel engines, volatile loss is one of the most important mechanisms in the oil consumption process. A new model including the volatile loss has been developed and its valiii has been confirmed experimentally by followingthe increase in sulfated ash which consists of first-order and zero-order terms derived from the lubricant transport and the addition of fresh oil, respectively. This model can also explain the changes in a series of properties such as total acid number, carbon residue, oil insolubles, and total base number using similar first-order rate constants to that for sulfated ash.
Introduction A great number of studies on engine oil have covered many subjects, for example, development of new lubricants, establishment of test procedures, oil analyses, lubrication monitoring, and so on. Though advanced works on each subject using laboratory methods deal with highly specialized problems, the generalized relations between the mutual results obtained from laboratory methods and actual engine tests have not been clarified. On the other hand, oil classification systems, such as the API grading system, have been developed in order to convert many parameters related with engine oil performance into a one-dimensional indication, and have been widely used to select suitable oil grades or to indicate the overall performance of a lubricant. However, the char-
acteristic parameters of an engine system which allow the quantitative expression of engine oil behavior have not been elucidated. For the above-mentioned reasons, it is desirable to extract intrinsic parameters for the engine system from accumulated data in order to establish a systematic data bank. Since the performance of an engine oil is completely determined by the dynamic process of the whole system consisting of engine and lubricant, dynamic analysis should be, if possible, desirable for describing the system. As the first step, lubricant transport and degradation in an engine system will be analyzed. Some kinetic analyses of engine oil have already been made, for example, with respect to contamination of soot generated in an indirect-injection diesel engine by Smith and Chowings
0196-4321/81/1220-0530$01.25/00 1981 American Chemical Society
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 3, 1981 531
Table I. Basic Details and Operating Conditions of Test Engine basic details number of cylinders, arrangement bore and stroke, mm piston displacement, L type of combustion chamber volume of swirl chamber, cm3 diameter of swirl chamber port, cm compression ratio rated power, (PS-rpm) break mean effective pressure, kgf / cmz a
Fresh O i l
operating conditions
4L
speed, rpm
4000
83 X 100 2.16
power, PS
60
fuel consumption rate, mm3 (st * Cy1)swirl lub. oil temp, chamber “C
36
27: 2 8 b
lub. oil charge, kg
5.5
0.759; 0.859
coolant temp, “C
inlet: 75 outlet: 80
21.6,O 20.EJb 47-3200
air inlet temp,
25
120
OC fuel temp,
25
“C 8.41,“
For “old type”.
7.10b
sulfur in fuel, %
Oil-Sump
Piston-CylindorArea
Figure 1. A flow reactor model of internal combustion engine.
0.4
For “current type”.
(1976). However, their model does not take account the volatile loss of lubricant which may be one of the most important factors in the oil consumption process, especially for high-speed diesel engines due to their higher thermal loading and smaller oil-sump capacity. This paper will describe an advanced model including the volatile loss, the validity of the model, and its application to the changes in various properties of engine oil. Experimental Section Bench Engine Test. A light-duty naturally aspirated indirect-injection diesel engine was employed. There are two types of the engine termed “old type” and “current type”. They only differ from one another in the volume and the shape of swirl chamber which result in changing the compression ratio. Basic details of the test engine and operating conditions are summarized in Table I. The reasons for selecting this type of engine are as follows. (1) Fuel dilution is so small it can be neglected. (2) Soot contamination rate is much greater than that for direct injection type as shown by Parsons (1969), Smith and Chowings (19761, and Knight and Weiser (1976). Thus, drastic changes in lubricant properties can be expected. Materials. Twenty commercial and specially formulated engine oils with performances similar to those corresponding to API service grades CC or CD were used. Data Analysis. Data analyses were made according to the equation X = X, - (X,- Xo)exp(-klStt) (1) In the case where the value of X, is not zero, but a certain limiting value, the classical method for determining kist, X,, and Xoby logarithmic conversion does not provide sufficient reliability. Therefore, the method developed by Marquardt (1963) was applied for the direct determination of the three parameters. Modeling of Engine The changes in the composition of engine oil are affected by the rate of oil consumption as has been widely recognized. This fact clearly indicates that the engine should
be regarded as a “flow reactor” instead as a “closed reactor”. A flow reactor model consisting of two mixing chambers is schematicallyillustrated in Figure 1. In order to analyze the lubricant transport and degradation in the engine system, some assumptions are made as follows. (1) Operating variables of the engine are maintained constant over the duration of the engine test. (2) Mechanisms involved in the oil consumption process are composed of: (a) outward flow of lubricant from the engine system; (b) volatile loss; (c) sampling. (3) Fresh oil is supplied continuously to keep the charge of engine oil fixed. Let us consider an ideal tracer contained in engine oil, which can never cause any physical or chemical changes and can never be mixed into engine oil from any sources except added fresh oil. The change in the ideal tracer concentration, T, can be described by the mass balance equation containing first-order and zero-order rate constants, kl, and ,k dT/dt = -kl,tT + k,,,, (2) where
(3) = kf + ks k,,, = kaddTO = (kf + k, + kv)To (4) and kfis the rate constant for the outward flow of lubricant from engine system, kv is the rate constant for the volatilization of lubricant, k, is the rate constant for oil sampling, and kadd is the rate constant for fresh oil addition. Integration of eq 2 gives eq 5. T = T , - (T, - To)exp(-klntt) t5 ) where T- = kaddTO/klst (6) hat
From eq 6, kadd can dso be represented by the equation (7) ksdd = klstT- / TO The value of kadd can be calculated from those of kbt, T,, and Towhich are determined by the analysis according to eq 5. The mass rate of oil addition, Rdd, can be obtained from the equation by knowing the quantity of engine oil charged, Q. Radd = kaddQ (8) If the above model is consistent, calculated Radd from eq 8 should agree with observed values. Analysis of Lubricant Transport Lubricant transport in an engine was analyzed by following the increase in sulfated ash. For fresh oils, sulfated ash measured by ASTM D-876 indicates total concentration of the metals contained in some additives, while, for used oils, this indicates not only the metals derived from
532
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 3, 1981
Table 11. Analytical Results of Sulfated Ash
s-:
so: wt %
oil no. 1
1.45
2 -
1.45 ~.
3 4 5 6 7
1.12 1.24 1.76 1.55 1.48 1.46 1.68 1.66 1.24 1.83 1.26 1.54 1.23 2.01 2.07 2.50 1.55 1.57
~
8 9 10 11 12 13 14 15 16 17 18 19 20
wt
z
2.08 1.97 2.15 2.21 2.74 2.10 1.94 2.09 2.75 2.79 1.81 2.72 1.77 2.11 1.85 3.34 2.86 4.50 2.03 2.09
~
( Radd)cpd,c
kid, 10-’h-’
1.74 2.14 1.60 1.83 1.60 1.78 2.79 2.08 2.48 1.94 1.64 1.50 1.83 2.00 1.81 1.28 1.58 1.57 1.77 1.69
1.82‘“ 2.35 1.46 1.72 1.56 1.58 2.69 2.37 2.37 2.00 2.04 1.57 1.74 1.81 1.53 1.40 1.58 1.59 1.66 1.74
g h144 175 154 169 134 118 194 185 214 185 164 128 134 137 127 128 120 157 120 127
( Radd)qbsd, g h-
139 162 164 165 126 130 200 166 222 180 134 123 142 151 145 119 120 155 128 124
Determined from eq 9 by using observed value of kdd a Determined from eq 5’ according to Marquardt’s method. where Q = 5500 g. according to Marquardt’s method. Calculated from the relation Radd = Qk,,S,/S,,
7
240 -
*‘O
220 $200-
180 L?
2U 160 2 140.
1.4L U
011 - 1
o.oo
10 Test
20
30
Duration
40
120 -
50 (hr)
Figure 2. Typical behavior of the increase in sulfated ash.
the additives but worn metals gradually accumulated in lubricants. However, the influence of the worn metals can usually be neglected because iron concentrations in used oils are at most 100 ppm, namely 0.03% as iron sulfate. Moreover, sulfated ash is not affected by the conversion of overbased component into its sulfate salt due to the neutralization with combustion products. Therefore, sulfated ash can be assumed as a similar component to the ideal tracer. Typical changes in sulfated ash, S, in Figure 2 indicate the first-order reaction curve as expected from eq 5. Equations 5’ and 7‘ may approximately be valid as the substitutes for eq 5 and 7, respectively. S = S, - (S, - So) exp(-klstt) (5’) kadd = klstS-/SO (7’) As shown in Figure 3 and Table 11, Raddcalculated from eq 7’ and 8 are in good agreement with observed values. When the values of kist, k,, and kadd are known, those of kf and k, are easily determined. In addition, the following relation can be obtained from eq 5‘ and 7‘ S/so = kadd/klat - (kadd/kist - 1) e d - k l s t t ) (9)
100
Ind. Eng. Chem. Prod. Res. Dev., Vol. 20, No. 3, 1981 533
0' 0.0
0.2
0.4
0.6
0.8
1.0 exp(-klsyt 1
Figure 4. Linear increase in TAN as a function of exp(-kl,t) without oxidation in oil sump.
ind.
-ia 7 $ 9
Fa 7
6
n+l
f(t) = A = 5 4
z 3 a I2
1
c
time
observed as shown in Figure 5, where a break point exists at exp(-klstthd).For the non-steady-state oxidation, direct analysis by the integral form becomes more difficult because the actual rate of oxidation gradually increases with time. It is convenient to make analysis according to the differential form df(t)/dt = dF(t)/dt - k,,$(t) (13) where f(t) and F(t) are the polynomial supporting functions describing apparent and actual increase in TAN, respectively. The function of f(t) can be determined from the observed change of TAN by means of the least-squares treatment.
11
0
t
Figure 6. Schematic figure of the comparison between actual and apparent increase in TAN during non-steady-stateoxidation.
0.2
0.4
0.6
0.8
1.0
exp(-klst.t 1 Figure 5. Linear increase in TAN as a function of exp(-klstt)with oxidation in oil sump.
On the other hand, oxidation in the oil sump occasionally occurs on account of the high lubricant temperature of 120 O C . The oxidation mode in the oil sump can be classified into two types: (1) steady-state oxidation and (2) non-steady-state oxidation. In the steady-state oxidation, actual oxidation rate is constant so that the same procedure described above may be applicable. (13) A = A m - ( A m - At,) exp(-klEt(t - thd)) In the present study, the steady-state oxidation was only
XU#-'
i=l
(14)
Numerical integration of eq 13 may give F(t) by correcting the influence of the lubricant transport as schematically illustrated in Figure 6. This treatment may apply to other non-steady-state changes of lubricant composition in the engine system. (B) Carbon Residue. The increase of carbon residue in diesel engine oils occurs primarily due to the accumulation or the condensation of lubricant additives, soot, and oxidized polymeric matter. During the induction period, it seems reasonable to assume stationary rates for increasing these materials. As Figure 7 shows, carbon residue concentration, C, also follows the similar equations dC/dt = -kl& + (kaddCO + kc) (15) C = C, - (C, - Co) exp(-kl,,t) (16) where c m = (kaddCO + kC)/klst and kc is the rate constant for increasing carbon residue. Equation 2 may be valid for sulfated ash, namely dS/dt = -k,tS + kaddSO (17) therefore kadd = (dS/dt + kistS)/So (18) Substitution of eq 18 into eq 15 gives the equation d(C - C$/S,)/dt = -kl,t(C - CoS/So) + kc (19)
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Ind. Eng. Chem. Prod. Res. Dev., Vol. 20,No. 3, 1981
r
g~ 8 76-
50,
I
E $ 4 -
a
5
2
3-
21 -
0 0.0 0.2 0.4
0.6
0.8
1.0 exp(- ktsrt
Figure 7. Linear increase in carbon residue as a function of exp(-klstt) without oxidation in oil sump.
0.0 0.2 0.4
0.6
0.8
1.0
exP(-klst t 1 Figure 9. Linear increase in coagulated n-heptane insolubles as a function of exp(-kl,,t).
’ 1 6.9.11.18
5,
01 0.0 0.2 0.4
0.6 0.8
1.0
exp(-kl,tt 1 Figure 8. Linear increase in carbon residue as a function of exp(-k&) with oxidation in oil sump.
A new parameter (C - C,,5’/So) is convenient for estimating the net concentration of soot in used oils. This will be discussed precisely in part 3 of this series. As Figure 8 indicates, the lubricant oxidation in the oil sump causes the increase of carbon resudue in proportion to that of TAN except for Oil-17. Therefore, the same analytical process as that for TAN may be applicable. C = C, - (C, - C,,,) exp(-k,,,(t - tind)) (20)
(C)Insolubles. Two procedures for measuring oil insolubles in used oils (ASTM D-893) have widely been used. The one is “Procedure A” to measure the portion of larger particles in insolubles, and the other is “Procedure B” using a coagulant to catch all insoluble particles. Since the former insolubles is affected by some physical factors such as particle diameter, density or viscosity of dispersant oil, it is less meaningful to make the kinetic analysis. In
0
0.0 0.2 0.4
0.6
0.8
1.0
exp(-klst’t
1
Figure 10. Linear increase in coagulated benzene insolubles as a function of exp(-klatt).
contrast, the latter insolubles includes almost all particles. During the induction period, concentration of the coagulated insolubles, I, may also follow the equations dZ/dt = -kiJ + kI (21) I = Z,(1 - exp(-k,,,t)) (22) where I- = k~/kl,t (22) and kI is the rate constant for increasing coagulated insolubles. As Figures 9 and 10 show, both plots of n-heptane and benzene insolubles against exp(-klstt) reveal the validity of eq 20 and 21. (In the authors’ laboratory, n-
Ind. Eng. Chem. prod. Res. Dev.. Vol. 20, No. 3, 1981 535
4 5 6 7
8 9 10
D
11
E
3 12 - 13 .14 15 16 17
0.0
0.2
0.4
0.6
0.8
1.0
exp(-kl,yt) Figure 11. Linear change in TBN 88 a function of exp(-k,&).
heptane has been used instead of n-pentane.) In the oxidation in the oil sump, the insolubles for Oil-5 also increase according to the equation (23) I = I, - (1--It,) exp(-k& - tind)) (D) T B N (Total Base Number). There are two procedures to measure TBN of lubricants designated by ASTM. The one is the hydrochrolic acid titration method (ASTM D-664) and the other is the perchrolic acid titration method (ASTM D-2896). It is difficult to conclude which values of TBN indicate the lubricant ability concerning the detergency and/or the corrosion protection, Apart from the interrelations between TBN and the lubricant performance, TBN by hydrochrolic acid is influenced hy (1)titration rate, (2) type of overbased additives, and (3) determination of end point, while TBN by perchrolic acid indicates good agreement with the stoichiometric value (Abhott and Bowman 1966). Therefore, the kinetic analysis has been made for the change of the latter TBN. As Figure 11shows, eq 24 and 25 hold for changing the TBN, B, but there is negative or positive slope depending on the sign of the term (kddBO- kB). dB/dt = -kl,tB (kaddBO- kB) (24) B = B, - (B- - Bo) exp(-kl,t) (25) where B- = (kaddBo - ks)/kist and k8 is the rate constant for decreasing TBN. (E)Comparison of Rate Constants for Lubricant Degradation. The values of kA,kB,kc, and k,, for the individual oils tested are summarized and dispyayed in Figure 12, where shaded bars represent the equal value of rate constant irrespective of oxidation in the oil sump. During the induction period, k A has a characteristic value for each engine oil. However, the values of kc can be classified into two groups according to the type of the test engine. This fact suggests that most of the increase in carbon residue is due to soot contamination and thereby
+
18 19 20
-
0
4
8
1 2 0
lO-b&hi’
12
6
18
10-2mgKOMg+r)~1
During Induction Period Alter Induction Period b r i n g and After Ird&ion Period
Figure 12. Comparison of zero-order rate constant for various properties of engine oil: 1, kc; 2, k,; 3, k,; 4, k,.
k, can almost he regarded as a characteristic parameter of the diesel engine used. In addition, the values of the rate constant for increasing coagulated n-heptane insolubles, k,,, are in general agreement with those of kc. This may be ascribable to the same contributions of the soot contaminant to the insoluhles. After the induction period, kA,kc, and k, have larger values than those in the induction period. %owever, k8 may not he affected by the oxidation. The amount of sulfur reacted with overbased component to the total sulfur in fuel is about 0.4%, which is about three times as large as that for marine engine oils used in some fishing boats (Kusama, (1973). Conclusion This paper represents a kinetic analysis of lubricant transport and degradation within a light-duty diesel engine. This analysis will indicate the characteristics of the system consisting of engine and lubricant, when the data for a number of cases are accumulated and are compared with each other. Moreover, it can give reasonable criteria for the oil drain interval in conjunction with the limiting values for lubricant properties. In the near future, dominant factors influencing various rate constants should be elucidated from both mechanical and chemical points of view. 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.
530
Ind. Eng. Chem. Prod. Res. Dev. 1981, 20, 536-540
Nomenclature A = TAN, mg of KOH g-’ B = TBN, mg of KOH g-’ C = carbon residue concentration, wt % Z = insolubles concentration, wt ‘70 I,, = concentration of coagulated n-heptane insolubles, wt % = concentration of coagulated benzene insolubles, wt % kl, = overall first-order rate constant for lubricant transport,
ZBB
h-l k,,,, = overall zero-order rate constant for increasing ideal tracer, wt % h-’ kadd = rate constant for fresh oil addition, h-’ kf = rate constant for the outward flow of lubricant from engine system, h-’ k, = rate constant for oil sampling (averaged value on assuming continuous sampling), h-’ k, = rate constant for the volatilization of lubricant, h-’ kA = rate constant for increasing TAN, mg of KOH.(g h)-’ kB = rate constant for decreasing TBN, mg of KOH4g h1-l kc = rate constant for increasing carbon residue, wt % h-’ kI = rate constant for increasing insolubles, wt % h-’ k,,, k, = rate constant for increasing ZBH and ZBB, respectively, wt % h-l
Q = quantity of engine oil charged, g Radd = mass rate for fresh oil addition, g h-l S = sulfated ash concentration, wt % T = ideal tracer concentration, wt % tind = induction period for the oxidation of lubricant in oil sump, h X = dummy variable for the parameter of engine oil, unit Subscripts m = equilibrium conditions 0 = initial conditions tind = conditions at tind Literature Cited A b b o t A. D.; Bowman. L. 0. J. Jpn. Pet. Inst. 1966, 9 , 184. Knight, C. R.; Welser, H. SA€ Pap. 1976. No. 760721. Kusama, K.; J. Marine Eng. Soc. Jpn. 1973, 8 , 868. Mahoney, L. R.; Otto, K., Korcek, S., Johnson, M. D. Ind. Ens. Chem. prod. Res.-L?ev. 1980, 19, 11. Marquardt, D. W.; J . SOC. I d . Appl. Math. 1963, 1 1 , 431. Parsons, J. C.; J . Inst. Pet. 1969, 55, 256. SmRh, I. B.; Chowings, A. R. SAEPap. 1976, No. 760723.
Received for review November 20, 1980 Revised Manuscript Received April 20, 1981 Accepted April 28, 1981
Kinetic Approach to Engine Oil. 2. Antioxidant Decay of Lubricant in Engine System Seijiro Yasutomi, Yoshlhlro Maeda, and Tsutomu Maeda Lubricants & Petroleum Products Laboratory, Nippon Mining Co.,Ltd., 17-35, Nh-minami 3-chome, Toda-shi, Saitama-ken 335, Japan
Antioxidant decay of lubricants within a lightduty diesel engine was studied by using specially formulated oils containing p ,p’-dioctyldiphenylamine. The decay curve of the antioxidant fotlows the same function consisting of first-order and zero-order terms as that for the changes in other typical properties of lubricants. However, its first-order rate constant is much greater than that derived from lubricant transport. This descrepancy may be attributed to the possibility that the antioxidant is completely consumed in the piston-cylinder area and that there is no reflux back to the oil sump. The analysis of the zero-order term suggests that the oxidation mode of engine oil in the oil sump is “initiated oxidation” caused by radical species produced in the piston-cylinder area.
Introduction Oxidation stability is one of the most important requirements of engine oil in order to maintain proper functions of a lubricant for a long period. Oxidation of engine oil has been studied by means of laboratory methods as well as authorized engine tests. Most of the laboratory methods employ heterogeneous metal catalysts in order to accelerate the degenerated oxidation at high temperatures. However, dominant mechanisms of the oxidation within an engine system have not yet been clarified quantitatively. The kinetic analysis described in part 1has emphasized that the characteristics of an engine as a flow reactor are of great importance concerning the degradation of lubricant. Bardy and Asseff (1970) also indicated that the oxidation of engine oil is greatly influenced by the amount of charged oil and the rate of fresh oil addition. On the other hand, Mahoney et al. (1978) and Korcek et al. (1978) have reported a series of interesting results based upon their original methodology using an initiator to yield the 0196-4321/81/ 1220-0536$0i.25/0
information on “total antioxidant capacity”. This new parameter, which indicates the radical scavenging capacity of engine oil, will provide more useful information in conjunction with the evidence of “initiated oxidation” caused by radical species within an engine system. This study deals with a kinetic analysis of the antioxidant decay in a light-duty diesel engine in order to investigate the initiation mechanism for the oxidation in an oil sump. It is well known that Zn-dialkyldithiophosphate (ZDDP), which has been widely used for typical engine oils, acts not only as a peroxide decomposer but as a radical scavenger (Burn, 1968; Howard et al., 1973). The inhibition behavior of ZDDP has many reaction stages which make the analysis much more difficult. On the contrary, diphenylamine has been studied by many workers (Boozer and Hammond, 1955; Thomas and Tolman, 1962; Buchochenko et al., 1961), and the material is not sublimed dissimilar from some phenolic antioxidants. Therefore, simply formulated oils containing an antioxidant analogous to diphenylamine were utilized. 0 1981 American Chemical Society
