A Chemical Kinetics Model to Predict Diesel Engine ... - Springer Link

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

A chemical kinetics model to predict diesel engine performance. Part II. Bench-test procedures Stephen M. Hsua and Chun-I Chenb a

National Institute of Standards and Technology, Gaithersburg, MD b University 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 specific aspect in a particular application, such as wear, oxidation stability, sludge and deposit formation. User experience dictates the usefulness of these bench tests. Very few correlations of bench-test results and engine test results or field experience are available in the literature. This lack of correlation stems from the fact that most machinery is complex and its operation involves not only wear but also oxidation, corrosion, evaporation, and decomposition of the lubricant. Since most bench tests can only simulate a single aspect of the complex interaction, the correlation if it exists, does not always work. There are always exceptions to the rules. When several bench tests are used to evaluate the same lubricant and each bench test simulates a particular aspect of the machinery operation, the issue becomes how to interpret the combined test results. One approach is to treat each bench test as a fail/pass. So if a lubricant passes three out of four tests, it fails. This approach has limited success but the conclusion is often not borne out by actual engine test experience. The establishment of the pass/fail criterion is also difficult. In an engine, oxidation, wear, volatility, degradation, cor-

rosion, etc. all interact with each other. A bad corrosion problem may accelerate the wear and oxidation to induce early failure. Another approach is to correlate the actual machinery test results with the results from several bench tests by assuming a simple linear functional relationship. Attempts in doing this usually encounter the difficulty of determining the proper functional relationship among the various bench-test results. While the pursuit of a single ‘‘black box test’’ to predict actual engine performance continues, this paper describes a new way to look at the bench tests as a way to measure fundamental reaction kinetic constants useful in a step-wise computer simulation which incorporates the necessary interaction patterns of various chemical and mechanical parameters. This approach, though difficult, provides a rational basis to link different aspects of the oxidation/degradation processes together to predict the lubricant performance in an engine. This new way of looking at combining various bench tests proves to be useful in predicting lubricant performance in a diesel engine, 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 1023-8883/03/0200-0091/0 # 2003 Plenum Publishing Corporation

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

variety of temperatures, pressures, and loading conditions. The engine operation can be represented by three reactors in series: the oil sump (reactor 3); the piston top ring groove zone (reactor 2); and the piston cylinderliner interface (reactor 1). Simplified first-order kinetic equations have been developed to describe the lubricant degradation processes as shown in figure 1(13). If the reaction rates can be determined independently in a set of controlled laboratory bench tests which take into account the key chemistries, metal-surface catalysis, and engine-operating environment, then this set of kinetic equations can be solved using a numerical technique as a function of time to simulate the engine operation. The key reactions occurring in an engine are: evaporation, thermal degradation, oxidation, oxidative volatility, polymerization, and deposit formation. Evaporative loss can come from several sources: vaporization due to high vapor pressure at high temperatures; thermal decomposition of the oil into smaller molecules hence lower boiling points (higher vapor pressure); oxidation of molecules producing small molecules and fragments. The reaction model shown in figure 1 serves as the basis for the development of specific bench-test procedures. The lubricant (RH) evaporates at a rate of k4 and reacts with oxygen at a rate of k1 to form the primary oxidation products (Q). The oxidized products also

Figure 1. Simplified chemical reaction model and the rate equations.

evaporate and further oxidize to form high-molecularweight products (P) which eventually form deposits (D). The extent of reactions is determined by the relative magnitudes of the rate constants (k’s). Given this kinetic model, we need to select bench-test procedures that can provide a reasonable measure of the rate constants expected in a diesel engine environment. Since the engine operates over a range of temperatures and pressures depending on the loading sequence and driving conditions, it is necessary to correlate the benchtest results as a function of temperature. This is accomplished by using an Arrhenius equation to describe the change of the reaction constant as a function of temperature. For evaporation under engine-operating conditions, thermal gravimetric analysis under oxygen atmospheres on steel pans was selected [4]. This test gives a more open evaporation under oxidative conditions. The tests were conducted in a constant temperature mode at three or more temperatures appropriate for the range of temperatures encountered in the 1K engine test. These temperatures typically range from 160 to 250 C. The maximum slope of the weight-loss curve is taken as the constant at that temperature. These rate constants were then correlated with an Arrhenius equation over the temperature range. So in the computer simulation, evaporation rates were available to the simulation program over the temperature range. The particular temperatures selected for a particular lubricant for the thermal gravimetric analysis are not important. Depending on the volatility of the lubricant, adjustments can be made so that the evaporation rate constants are measured across the volatility range of the lubricant. For oxidation stability, the oxidation induction times as measured by pressurized Differential Scanning Calorimetry was selected [9] based on the small volume of lubricant required, short test time, and minimum oxygen diffusion resistance. The test condition also has a good correlation with diesel performance [9]. These tests were conducted over a temperature range, typically from 180 to 260 C. The test conditions are: 0.8 mg sample size, isothermal temperature, steel pan with steel cover, one hole, 15 psi oxygen pressure at 30 ml/min. The use of steel pans is important because it takes into account the steel catalytic effect without oxygen diffusion limitations. For high-molecular-weight products and deposit rate constants, a modified micro-oxidation test was selected [12,13]. A detailed test procedure and equipment have been described elsewhere [13]. Briefly, the test consists of low carbon steel pellets (1.91 cm diameter) with the top surface machined into a depression with a 15 edge angle which counteracts the surface tension of the lubricant and provides relatively uniform thin lubricant film. Forty micro-liters of lubricant was injected and the pellet was placed into a glass tube. The glass tube was placed in a constant-temperature aluminum bath. A


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constant flow of dry air at 20 ml/min was passed over the surface of the fluid and then out of the system. Again, a range of temperatures was necessary to provide the kinetic constants required by the simulation program. The temperature range selected for the Caterpillar 1K test was from 220 to 270 C. Each test was conducted in two sequences. One in argon to assess the evaporative loss of the lubricant so that the temperature can be adjusted as well as to establish a baseline for the deposit weight. Then the test was run in air at the same temperature. The test was conducted in 10, 20, and 30 min duration. At the end of each test, the steel pellet was rinsed in hexane and then rinsed with 10 ml of tetrahydrofuran (THF). The extracted THF fraction was then analyzed in a gel permeation chromatography unit for molecular-weight analysis. For deposit tests, the test duration was adjusted to 20, 30, and 40 minutes and after the hexane rinse, the deposit was weighed on an analytical balance as described in [12]. In this manner, the rate constants (k’s) can be obtained from independent bench tests designed to measure individual reaction rate constants. The following sections describe in detail how each rate constant is determined from the bench-test results.

3. Determination of k1 Oxidation induction times as measured by the DSC test under oxygen atmosphere are used to determine the primary oxidation reaction rate constant k1 (RH reacting to primary oxidation products, Q). Cold-rolled steel pans with a special design [9] are used to simulate the metal-catalyzed reaction rates in the engine. But no specific environmental conditions are included in the test such as fuel, engine blow-by, sulfuric acid effects. The oxidation rate constant needs to be determined as a function of multiple temperatures so that the rate constant can be expressed as an Arrhenius equation in terms of an activation energy (E) and a pre-exponential constant (A). Isothermal DSC tests at three or more temperatures were used to determine the activation energy. Figure 2 shows the data on CT5113 oil at four temperatures, i.e., 200, 225, 250, and 260 C. After obtaining the induction time, a ln (induction time) versus 1/temperature plot can be constructed, as shown in figure 3. The slope from the plot can be used to determine the activation energy. Results from the regression indicate that the activation energies for both oils are about the same. The activation energy for the initiation step of the oxidation process of CT 5126 is about 135 kJ/mol (32 kcal/mol) and is about 160 kJ/mol (38 kcal/mol) for CT 5113. Naidu [13] reported a value of 75 kJ/mol (20 kcal/mol) for the primary oxidation step of TMPTM. Lockwood [14] reported a value of 94 kJ/mol (22 kcal/mol) for the primary oxidation step of TMPTH. These values are only about one-half to

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

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 pentaerythritol oxidation. Since the oils used in this study are advanced formulations designed for ultrahigh temperature operation, the activation energy results are reasonable and within the range of expected values. The pre-exponential constant A is determined by running a ramping temperature DSC test. In this test condition, the temperature is increased continuously at 10 C per minute. The exact rate of temperature ramping is not significant and sometimes the ramping rate needs to be adjusted for a particular lubricant. This is shown in figure 4. The resulting heat flow versus temperature curve indicates the oxidation rate from temperature 1 to temperature 2. The lubricant basically is oxidized completely over this temperature range. The conversion of un-oxidized lubricant to 100% oxidized lubricant can be obtained by dividing a particular point on the heat-flow

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Figure 3. DSC data used to determine the activation energy for oxidation. Figure 4. Temperature-ramped DSC data used to determine A1.

curve by the total area of the curve, i.e., fractional conversion. This produces a conversion versus time curve. The constant can then be determined by fitting the equation to the curve, as shown in figure 4. For every oil, these procedures are repeated to obtain the Arrhenius equation constants.

4. Evaporation effect on DSC test procedure The ramping temperature DSC tests were used to obtain the heat flow during the oxidation process. Even though the pans used are covered with a single pin hole to minimize the evaporation effect, evaporation still takes place. Since evaporation is an endothermic process, the heat-flow data may be compromised. A series of DSC tests under argon atmosphere was conducted to assess the effect of evaporation on the heat-flow data. Comparing the two test results, the effect of evaporation under oxidative condition can be assessed. The tests were conducted under 1 atm argon at 30 ml/min flow rate. The temperature program was set to equilibrate at 160 C, then increase at a rate of 10 C/min from 160 to 560 C. The test was conducted on CT5113 oil. Results suggested that the overall effect of evaporation on the heat-flow data was about 3% or less. Other oils showed a similar magnitude of error. Therefore, the test procedure used is acceptable.

5. Determination of k2 The kinetic rate constant k2 is the rate constant for the primary oxidation products reacting to form highmolecular-weight products P under metal-catalyzed conditions. A Penn State micro-oxidation test procedure is used. The test procedure is described in detail in [13]. Briefly, a thin film of oil is placed on a mild steel pellet which is heated to a prescribed temperature in a glass tube. Air is circulated into the glass tube to ensure no oxygen diffusion effect on the oxidation rate. The reaction is stopped at different times. The reaction products are extracted by tetrahydrofuran solvent and the solution is analyzed by Gel Permeation Chromatography for molecular-weight determination. The high-molecularweight fraction is determined. The test result for oil CT 5126 at 240 C is shown in figure 5. The original oil is defined by the time zero result. As the time of oxidation increases, part of the oil shifts to higher-molecularweight products. The area under the curve between the unreacted oil and the high-molecular-weight fractions gives the quantity Q. The procedure to determine k2 is illustrated in figure 6. Tests at three or more temperatures were conducted to obtain Q (amount of primary oxidation products) and P (high-molecular-weight products) at three different test durations. The quantity of P was then plotted against Q as a function of time for


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

6. Determination of k3 From the high-molecular-weight products to deposit formation depends on the temperature and time. This is determined by a modified (simplified) procedure of the micro-oxidation test procedure. The same apparatus is used, except the conditions are set to higher temperatures and longer durations. The amount of deposit is determined by weighing the steel disc before and after a hexane wash (removing the oil and oil-soluble reaction Figure 5. Micro-oxidation test results showing the polymer formation products). The procedure is illustrated in figure 7. The for CT5126 oil. deposit formation curve for oil CT 5113 is shown in figure 8. For each test, the amount of evaporation is obtained by the weight difference before and after the different temperatures. The slope at each temperature test. The amount of liquid left after each test was provides k2 at each temperature. Again, the Arrhenius obtained by the weight difference before and after THF equation was used to establish an equation so that the extraction. The deposit was obtained by mass balance. The liquid portion went through GPC analysis to obtain the fraction of the high-molecular-weight product.

Figure 6. Procedure to determine k2.


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

Figure 8 shows evaporation, liquid, deposit, and highmolecular-weight (HMW) products. This modified micro-oxidation deposit test was used to determine k3. Tests were carried out at three or more different temperatures. A deposit versus time plot was constructed for each temperature. The maximum slope in each plot is k3 at that temperature. With k3 at several temperatures, the pre-exponent constant and the activation energy again can be determined following the procedure described previously.

7. Determination of k4 To determine the evaporation rate under an oxidative environment, TGA tests under oxygen were used. Figure 9 illustrates the procedure. Constant-temperature TGA tests were conducted at three or more different temperatures. The maximum slope at each temperature is the rate constant at that temperature. With the rate constants from several temperatures, one can obtain the pre-exponent constant and activation energy. When the pre-exponent constant and the activation energy 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 constant, E ¼ activation energy, R ¼ gas constant, and T ¼ temperature 8. The rate constants Using these bench-test procedures, the rate constants for the five lubricants tested were obtained and are shown in table 1. The uncertainty for these rate constants is about 10%. 9. Summary In combination with a computer simulation program, several bench-test procedures were selected to obtain the kinetic constants for oxidation, evaporation, and deposit formation. These bench-test procedures incorporated some of the diesel engine operating environment

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S.M. Hsu, C.-I. Chen/Chemical kinetics model to predict engine performance. Part II. Bench-test procedures Table 1 List of rate constants.* Oil Temperature k1 minute-1 k2 k3 k4 k5 k6 k7 k8

CT 5113 240 C 250 C 0.09 1.5 0.1 0.0052 0.9 0.05 0.0011 0.088

0.14 2.4 0.154 0.0095 1.5 0.11 0.002 0.14

CT 5126 240 C 250 C

CT 5213 220 C 245 C

CT 5214 220 C 245 C

CT 5215 220 C 245 C

0.058 2.0 0.05 0.0025 1.9 0.0375 0.001 0.05

0.08 3 0.1 0.0016 1.4 0.001 0.0028 0.13

0.12 6 0.35 0.0136 1.0 0.15 0.005 0.105

0.07 4.5 0.095 0.0115 2 0.0083 0.0035 0.39

0.1 2.9 0.1 0.0052 2.1 0.075 0.002 0.08

0.16 4.8 0.154 0.006 2.0 0.014 0.006 0.56

0.24 9 0.5 0.028 1.3 0.25 0.01 0.42

0.18 6.8 0.17 0.023 2.5 0.038 0.00726 1.8

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

satisfactory. In order to provide the simulation program rate constants throughout the temperature range, Arrhenius correlation equations were used throughout. These rate constants were then used in the computation according to the kinetic model to simulate engine operations. Agreement with engine test results validates such an approach and the selection of the bench-test procedures. Acknowledgement The authors gratefully acknowledge financial support from the Caterpillar Co. Helpful discussion with Frank Kelley is greatly appreciated. References


such as metal catalysis and limited oxygen diffusion (DSC) but did not include fuel-blow-by, fuel dilution, etc. Other bench tests were also tried but the results are less than

[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.