a chemical kinetics model to predict diesel engine performance

A chemical kinetics model to predict diesel engine performance.

Part II. Bench-test procedures

Stephen M. Hsua and Chun-I Chenb

aNational Institute of Standards and Technology, Gaithersburg, MDbUniversity of Maryland, College Park, MD

Received 10 March 2002; accepted 19 May 2002

Bench tests have been used to screen lubricants and additives for industrial fluids in machinery applications for a long time. As the

cost of engine testing increases dramatically, the need for simple laboratory bench tests increases. Bench tests simulate a particular

aspect of the engine operation such as oxidation or wear, but the engine operation blends both mechanical, chemical, and combustion

processes together and allows these parameters to interact freely. There are many bench tests providing a measure of oxidation

stability under simulated conditions. For a given application, while the generic aspects of the lubricant degradation mechanism may

be similar, environmental factors such as oxygen availability, the presence of specific metals (catalytic effects), and residence times of

the oil at high-temperature regions may be specific to that application. Universal bench-test procedures that can predict oxidation

stability therefore are not feasible. As described in part I of this paper, a computer simulation program has been developed combining

a chemical kinetic model and a finite-difference program to simulate the engine operating conditions to predict lubricant performance

in a diesel engine. This paper describes the bench-test procedures used to determine the kinetic constants used in the kinetic model to

describe the lubricant degradation processes. The bench tests are specifically designed for the determination of kinetic constants in

general for a particular reaction path but take into account the particular environmental factors intrinsic in the Caterpillar 1K engine

dynamometer test.

KEY WORDS: bench tests, chemical kinetic model, simulation, diesel engine, lubricant performance

1. Introduction

There are many bench tests in use today [1–11].Bench tests are used to screen lubricants, formulations,and/or additives before more expensive tests are used.Most bench tests are designed to simulate a specificaspect in a particular application, such as wear, oxida-tion stability, sludge and deposit formation. Userexperience dictates the usefulness of these bench tests.Very few correlations of bench-test results and enginetest results or field experience are available in the lit-erature. This lack of correlation stems from the fact thatmost machinery is complex and its operation involvesnot only wear but also oxidation, corrosion, evapora-tion, and decomposition of the lubricant. Since mostbench tests can only simulate a single aspect of thecomplex interaction, the correlation if it exists, does notalways work. There are always exceptions to the rules.

When several bench tests are used to evaluate thesame lubricant and each bench test simulates a partic-ular aspect of the machinery operation, the issuebecomes how to interpret the combined test results. Oneapproach is to treat each bench test as a fail/pass. So if alubricant passes three out of four tests, it fails. Thisapproach has limited success but the conclusion is oftennot borne out by actual engine test experience. Theestablishment of the pass/fail criterion is also difficult. Inan engine, oxidation, wear, volatility, degradation, cor-

rosion, etc. all interact with each other. A bad corrosionproblem may accelerate the wear and oxidation toinduce early failure.

Another approach is to correlate the actual machin-ery test results with the results from several bench testsby assuming a simple linear functional relationship.Attempts in doing this usually encounter the difficulty ofdetermining the proper functional relationship amongthe various bench-test results.

While the pursuit of a single ‘‘black box test’’ to pre-dict actual engine performance continues, this paperdescribes a new way to look at the bench tests as a way tomeasure fundamental reaction kinetic constants useful ina step-wise computer simulation which incorporates thenecessary interaction patterns of various chemical andmechanical parameters. This approach, though difficult,provides a rational basis to link different aspects of theoxidation/degradation processes together to predict thelubricant performance in an engine. This new way oflooking at combining various bench tests proves to beuseful in predicting lubricant performance in a dieselengine, as described in part I of this paper.

2. Bench-test design and selection

In an engine, lubricant interacts with the materials,combustion products, engine blow-by, and air under a

Tribology Letters, Vol. 14, No. 2, February 2003 (# 2003 ) 91

1023-8883/03/0200-0091/0 # 2003 Plenum Publishing Corporation

variety of temperatures, pressures, and loading condi-tions. The engine operation can be represented by threereactors in series: the oil sump (reactor 3); the piston topring groove zone (reactor 2); and the piston cylinder-liner interface (reactor 1). Simplified first-order kineticequations have been developed to describe the lubricantdegradation processes as shown in figure 1(13). If thereaction rates can be determined independently in a setof controlled laboratory bench tests which take intoaccount the key chemistries, metal-surface catalysis, andengine-operating environment, then this set of kineticequations can be solved using a numerical technique as afunction of time to simulate the engine operation.

The key reactions occurring in an engine are: evap-oration, thermal degradation, oxidation, oxidative vola-tility, polymerization, anddeposit formation.Evaporativeloss can come from several sources: vaporization due tohigh vapor pressure at high temperatures; thermaldecomposition of the oil into smaller molecules hencelower boiling points (higher vapor pressure); oxidation ofmolecules producing small molecules and fragments.

The reaction model shown in figure 1 serves as thebasis for the development of specific bench-test proce-dures. The lubricant (RH) evaporates at a rate of k4 andreacts with oxygen at a rate of k1 to form the primaryoxidation products (Q). The oxidized products also

evaporate and further oxidize to form high-molecular-weight products (P) which eventually form deposits (D).The extent of reactions is determined by the relativemagnitudes of the rate constants (k’s).

Given this kinetic model, we need to select bench-testprocedures that can provide a reasonable measure of therate constants expected in a diesel engine environment.Since the engine operates over a range of temperaturesand pressures depending on the loading sequence anddriving conditions, it is necessary to correlate the bench-test results as a function of temperature. This isaccomplished by using an Arrhenius equation todescribe the change of the reaction constant as a func-tion of temperature.

For evaporation under engine-operating conditions,thermal gravimetric analysis under oxygen atmosphereson steel pans was selected [4]. This test gives a more openevaporation under oxidative conditions. The tests wereconducted in a constant temperature mode at three ormore temperatures appropriate for the range of tem-peratures encountered in the 1K engine test. These tem-peratures typically range from 160 to 250 �C. Themaximum slope of the weight-loss curve is taken as theconstant at that temperature. These rate constants werethen correlated with an Arrhenius equation over thetemperature range. So in the computer simulation,evaporation rates were available to the simulation pro-gram over the temperature range. The particular tem-peratures selected for a particular lubricant for thethermal gravimetric analysis are not important.Depending on the volatility of the lubricant, adjustmentscan be made so that the evaporation rate constants aremeasured across the volatility range of the lubricant.

For oxidation stability, the oxidation induction timesas measured by pressurized Differential ScanningCalorimetry was selected [9] based on the small volumeof lubricant required, short test time, and minimumoxygen diffusion resistance. The test condition also has agood correlation with diesel performance [9]. These testswere conducted over a temperature range, typically from180 to 260 �C. The test conditions are: 0.8mg samplesize, isothermal temperature, steel pan with steel cover,one hole, 15 psi oxygen pressure at 30ml/min. The use ofsteel pans is important because it takes into account thesteel catalytic effect without oxygen diffusion limita-tions.

For high-molecular-weight products and deposit rateconstants, a modified micro-oxidation test was selected[12,13]. A detailed test procedure and equipment havebeen described elsewhere [13]. Briefly, the test consists oflow carbon steel pellets (1.91 cm diameter) with the topsurface machined into a depression with a 15 � edgeangle which counteracts the surface tension of thelubricant and provides relatively uniform thin lubricantfilm. Forty micro-liters of lubricant was injected and thepellet was placed into a glass tube. The glass tube wasplaced in a constant-temperature aluminum bath. AFigure 1. Simplified chemical reaction model and the rate equations.

92 S.M. Hsu, C.-I. Chen/Chemical kinetics model to predict engine performance. Part II. Bench-test procedures

constant flow of dry air at 20ml/min was passed overthe surface of the fluid and then out of the system.Again, a range of temperatures was necessary to providethe kinetic constants required by the simulation pro-gram. The temperature range selected for the Caterpillar1K test was from 220 to 270 �C. Each test was conductedin two sequences. One in argon to assess the evaporativeloss of the lubricant so that the temperature can beadjusted as well as to establish a baseline for the depositweight. Then the test was run in air at the same tem-perature. The test was conducted in 10, 20, and 30 minduration. At the end of each test, the steel pellet wasrinsed in hexane and then rinsed with 10ml of tetra-hydrofuran (THF). The extracted THF fraction wasthen analyzed in a gel permeation chromatography unitfor molecular-weight analysis. For deposit tests, the testduration was adjusted to 20, 30, and 40 minutes andafter the hexane rinse, the deposit was weighed on ananalytical balance as described in [12].

In this manner, the rate constants (k’s) can beobtained from independent bench tests designed tomeasure individual reaction rate constants. The follow-ing sections describe in detail how each rate constant isdetermined from the bench-test results.

3. Determination of k1

Oxidation induction times as measured by the DSCtest under oxygen atmosphere are used to determine theprimary oxidation reaction rate constant k1 (RH react-ing to primary oxidation products, Q). Cold-rolled steelpans with a special design [9] are used to simulate themetal-catalyzed reaction rates in the engine. But nospecific environmental conditions are included in the testsuch as fuel, engine blow-by, sulfuric acid effects.

The oxidation rate constant needs to be determinedas a function of multiple temperatures so that the rateconstant can be expressed as an Arrhenius equation interms of an activation energy (�E) and a pre-exponen-tial constant (A). Isothermal DSC tests at three or moretemperatures were used to determine the activationenergy. Figure 2 shows the data on CT5113 oil at fourtemperatures, i.e., 200, 225, 250, and 260 �C. Afterobtaining the induction time, a ln (induction time)versus 1/temperature plot can be constructed, as shownin figure 3. The slope from the plot can be used todetermine the activation energy. Results from theregression indicate that the activation energies for bothoils are about the same. The activation energy for theinitiation step of the oxidation process of CT 5126 isabout 135 kJ/mol (32 kcal/mol) and is about 160 kJ/mol(38 kcal/mol) for CT 5113. Naidu [13] reported a valueof 75 kJ/mol (20 kcal/mol) for the primary oxidationstep of TMPTM. Lockwood [14] reported a value of94 kJ/mol (22 kcal/mol) for the primary oxidation stepof TMPTH. These values are only about one-half to

two-thirds of the numbers obtained in this study.However, Barnes [15] reported a value of 150 kJ/mol(36 kcal/mol) for the initiation step of pentaerythritoloxidation. Since the oils used in this study are advancedformulations designed for ultrahigh temperatureoperation, the activation energy results are reasonableand within the range of expected values.

The pre-exponential constant A is determined byrunning a ramping temperature DSC test. In this testcondition, the temperature is increased continuously at10 �C per minute. The exact rate of temperature rampingis not significant and sometimes the ramping rate needsto be adjusted for a particular lubricant. This is shownin figure 4. The resulting heat flow versus temperaturecurve indicates the oxidation rate from temperature 1 totemperature 2. The lubricant basically is oxidized com-pletely over this temperature range. The conversion ofun-oxidized lubricant to 100% oxidized lubricant can beobtained by dividing a particular point on the heat-flow

Figure 2. DSC results of oil CT5113 at different temperatures.

S.M. Hsu, C.-I. Chen/Chemical kinetics model to predict engine performance. Part II. Bench-test procedures 93

curve by the total area of the curve, i.e., fractionalconversion. This produces a conversion versus timecurve. The constant can then be determined by fittingthe equation to the curve, as shown in figure 4. Forevery oil, these procedures are repeated to obtain theArrhenius equation constants.

4. Evaporation effect on DSC test procedure

The ramping temperature DSC tests were used toobtain the heat flow during the oxidation process. Eventhough the pans used are covered with a single pin holeto minimize the evaporation effect, evaporation stilltakes place. Since evaporation is an endothermic pro-cess, the heat-flow data may be compromised. A seriesof DSC tests under argon atmosphere was conducted toassess the effect of evaporation on the heat-flow data.Comparing the two test results, the effect of evaporationunder oxidative condition can be assessed.

The tests were conducted under 1 atm argon at30ml/min flow rate. The temperature program was setto equilibrate at 160 �C, then increase at a rate of10 �C/min from 160 to 560 �C. The test was conductedon CT5113 oil. Results suggested that the overall effectof evaporation on the heat-flow data was about 3% orless. Other oils showed a similar magnitude of error.Therefore, the test procedure used is acceptable.


The kinetic rate constant k2 is the rate constant forthe primary oxidation products reacting to form high-molecular-weight products P under metal-catalyzedconditions. A Penn State micro-oxidation test procedureis used. The test procedure is described in detail in [13].Briefly, a thin film of oil is placed on a mild steel pelletwhich is heated to a prescribed temperature in a glasstube. Air is circulated into the glass tube to ensure nooxygen diffusion effect on the oxidation rate. The reac-tion is stopped at different times. The reaction productsare extracted by tetrahydrofuran solvent and the solu-tion is analyzed by Gel Permeation Chromatography formolecular-weight determination. The high-molecular-weight fraction is determined. The test result for oil CT5126 at 240 �C is shown in figure 5. The original oil isdefined by the time zero result. As the time of oxidationincreases, part of the oil shifts to higher-molecular-weight products. The area under the curve between theunreacted oil and the high-molecular-weight fractionsgives the quantity Q. The procedure to determine k2 isillustrated in figure 6. Tests at three or more tempera-tures were conducted to obtain Q (amount of primaryoxidation products) and P (high-molecular-weight pro-ducts) at three different test durations. The quantity of Pwas then plotted against Q as a function of time for

Figure 3. DSC data used to determine the activation energy for

oxidation.

Figure 4. Temperature-ramped DSC data used to determine A1.


different temperatures. The slope at each temperatureprovides k2 at each temperature. Again, the Arrheniusequation was used to establish an equation so that the

simulation program can be used at any temperaturewithin the range. To obtain A2 and �E2, plot ln(k)versus 1/temperature.


From the high-molecular-weight products to depositformation depends on the temperature and time. This isdetermined by a modified (simplified) procedure of themicro-oxidation test procedure. The same apparatus isused, except the conditions are set to higher tempera-tures and longer durations. The amount of deposit isdetermined by weighing the steel disc before and after ahexane wash (removing the oil and oil-soluble reactionproducts). The procedure is illustrated in figure 7. Thedeposit formation curve for oil CT 5113 is shown infigure 8. For each test, the amount of evaporation isobtained by the weight difference before and after thetest. The amount of liquid left after each test wasobtained by the weight difference before and after THFextraction. The deposit was obtained by mass balance.The liquid portion went through GPC analysis to obtainthe fraction of the high-molecular-weight product.

Figure 5. Micro-oxidation test results showing the polymer formation

for CT5126 oil.

Figure 6. Procedure to determine k2. Figure 7. Procedure to determine k3.


Figure 8 shows evaporation, liquid, deposit, and high-molecular-weight (HMW) products.

This modified micro-oxidation deposit test was usedto determine k3. Tests were carried out at three or moredifferent temperatures. A deposit versus time plot wasconstructed for each temperature. The maximum slopein each plot is k3 at that temperature. With k3 at severaltemperatures, the pre-exponent constant and the acti-vation energy again can be determined following theprocedure described previously.


To determine the evaporation rate under an oxidativeenvironment, TGA tests under oxygen were used. Figure9 illustrates the procedure. Constant-temperature TGAtests were conducted at three or more different tem-peratures. The maximum slope at each temperature isthe rate constant at that temperature. With the rateconstants from several temperatures, one can obtain thepre-exponent constant and activation energy.

When the pre-exponent constant and the activationenergy are obtained, one can estimate the rate constant

at any other temperature using the following equation:

k ¼ Ae�E

RT

where: k ¼ the rate constant, A ¼ pre-exponent con-stant, �E ¼ activation energy, R ¼ gas constant, andT ¼ temperature

8. The rate constants

Using these bench-test procedures, the rate constantsfor the five lubricants tested were obtained and areshown in table 1. The uncertainty for these rate con-stants is about �10%.

9. Summary

In combination with a computer simulation program,several bench-test procedures were selected to obtain thekinetic constants for oxidation, evaporation, anddeposit formation. These bench-test procedures incor-porated some of the diesel engine operating environment

Figure 8. Deposit test result for CT5113 at 250 �C in air.


suchasmetal catalysis and limitedoxygendiffusion (DSC)but did not include fuel-blow-by, fuel dilution, etc. Otherbench tests were also tried but the results are less than

satisfactory. In order to provide the simulation programrate constants throughout the temperature range, Arrhe-nius correlation equations were used throughout. Theserate constants were then used in the computationaccording to the kinetic model to simulate engine opera-tions.Agreementwith engine test results validates such anapproach and the selection of the bench-test procedures.

Acknowledgement

The authors gratefully acknowledge financial supportfrom the Caterpillar Co. Helpful discussion with FrankKelley is greatly appreciated.

References

[1] S.M. Hsu, Lubr. Eng. 37(12) (1981) 722.

[2] S.M. Hsu, A.L. Cummings and D.B. Clark, SAE 821252, SAE

SP-526, (Base Oils for Automotive Lubricants, 1982) 127.

[3] R.S. Gates and S.M. Hsu, Lubr. Eng. 39(9) (1983) 561.

[4] S.M. Hsu and A.L. Cummings, SAE 831682, SAE SP-558,

Lubricant and Additive Effects on Engine Wear, 1983 51.

[5] R.S. Gates and S.M. Hsu, Lubr. Eng. 40(1), 1984, 27.

[6] C.S. Ku and S.M. Hsu, Lubr. Eng. 40(2) (1984) 75.

[7] C.S. Ku, P.T. Pei and S.M. Hsu, (SAE 902121, SAE Warrendale,

PA 1990).

[8] J.M. Perez, P.T. Pei, Y. Zhang and S.M. Hsu, (SAE 910750, SAE

Warrendale, PA 1991).

[9] Y. Zhang, P.T. Pei, J.M. Perez and S.M. Hsu, Lubr. Eng. 48(3)

(1992) 189.

[10] Y. Zhang, J.M. Perez, P.T. Pei and S.M. Hsu, Lubr. Eng. 48(3)

(1992) 221.

[11] J.X. Sun, P.T. Pei, Z.S. Hu and S.M. Hsu, Lubr. Eng. 54(5)

(1998) 12.

[12] J.M. Perez, F.A. Kelly, E.E. Klaus and V. Bogrodian, (SAE

paper no. 872028, Toronto, Canada, 1987).

[13] S.K. Naidu, E.E. Klaus and J. L. Duda, Ind. Eng. Chem. Prod.

Res. Dev. 25 (1986) 596.

[14] F.E. Lockwood, E.E. Klaus and J.L. Duda, ASLE Trans. 24(2)

(1981), 276.

[15] J.R. Barnes and J.C. Bell, Lubr. Eng. 45(9) (1989) 549.

Figure 9. Procedure to determine k4.

Table 1

List of rate constants.*

Oil CT 5113 CT 5126 CT 5213 CT 5214 CT 5215

Temperature 240 �C 250 �C 240 �C 250 �C 220 �C 245 �C 220 �C 245 �C 220 �C 245 �C

k1 minute-1 0.09 0.14 0.058 0.1 0.08 0.16 0.12 0.24 0.07 0.18

k2 1.5 2.4 2.0 2.9 3 4.8 6 9 4.5 6.8

k3 0.1 0.154 0.05 0.1 0.1 0.154 0.35 0.5 0.095 0.17

k4 0.0052 0.0095 0.0025 0.0052 0.0016 0.006 0.0136 0.028 0.0115 0.023

k5 0.9 1.5 1.9 2.1 1.4 2.0 1.0 1.3 2 2.5

k6 0.05 0.11 0.0375 0.075 0.001 0.014 0.15 0.25 0.0083 0.038

k7 0.0011 0.002 0.001 0.002 0.0028 0.006 0.005 0.01 0.0035 0.00726

k8 0.088 0.14 0.05 0.08 0.13 0.56 0.105 0.42 0.39 1.8

*A 10% experimental uncertainty is estimated for these rate constants.


a chemical kinetics model to predict diesel engine performance

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