Testing and Modeling of Petroleum Based Lubricating Oils by an Improvised System

H. M. KEFAS, M. O. EDOGA, and A. S. KOVO

Department of Chemical Engineering, Federal University of Technology, Yola,

Department of Chemical Engineering, Federal University of Technology, Minna,

Department of Chemical Engineering, Federal University of Technology, Minna, Nigeria

kovoabdulsalami@yahoo.com

Abstract

The effect of temperature, pressure and time was tested on the viscosities of ten lubricant samples using 2³ factorial designs, also an analysis of variance procedure and subsequently a regression model was carried out for each sample.

The result showed that for samples II, V, VI and VIII temperature alone has significant effect on their viscosities while pressure, time and their interactions have no significant effect. For samples I, VII, IX and X, temperature, pressure and time have significant effect and for sample III, all the process variables and their interaction have significant effect except for the interaction between pressure and time. Samples II, V, VI and VIII are of best performance since only temperature affects their viscosities. The coefficient of regression square (R²) is 1.0 for all the samples and this shows a very good correlation between the variables.

The regression model suits the experimented values close and could be used for test for the same formulation without laboratory experiment.

Keywords

            Lubricating oils, Testing, Modelling, Petroleum

Introduction

Lubricating is basically concerned with reducing the frictional resistance that occurs at the surface of the objects when one is moved relative to the other [2]. When one surface moves relative to the other, the interference between these opposing protuberances or asperities generates friction. This friction in liquid is called viscosity. Where there is friction there is wear, shear, and heat generation and in extreme cases, welding of the two surfaces may occur, causing seizure of the moving parts [2]. The overall importance of lubrication is to minimize frictional effect between metals by an oil film, act as cooling medium by absorbing dissipating excessive heat generation and remove dirt’s from engine parts thus keeping them clean [4]. The characteristics and performance of lubricating oils depend on crude oil source, refining method, base stocks and chemical additives. Petroleum products have been found to excel as lubricants. They have high metal wetting ability as well as the viscosity characteristics required of a lubricating film [2]. The basic petroleum lubricant simply referred to are base oil available in variety of types and grade i.e. (100N, 150N, 250N, 500N and BS). The most important single property of lubricating oil is its viscosity, other properties are important for other reasons [1]. It has been known that certain factors affect the viscosity of oil in an operating engine. These factors include temperature, pressure, time, speed etc. A rise in oil temperature is accompanied by a decrease in its viscosity and in lifting ability of oil leading to increased wear of the crankshaft and bearing shells [3]. To test the effect of some of these factors on the viscosity of a lubricant is important as it helps in knowing the performance of a product in an engine system. A good way of carrying out this test is by a fractional design. Fractional design is a statistical approach, which allows for simultaneous variations of process variables and more importantly all possible combinations of these variables at all chosen levels of investigating [6]. The number of possible combinations, “N” of these process variable is denoted by N=n, where “n” represents the number of possible levels of each variable [6]. These levels are usually obtained by using unifactor approach that is by varying one factor at a time while other factors are fixed. The levels at which best range of performance is obtained are normally chosen. “K” represents the number of process variables that are to be considered for any particular experiment [6]. In this present study, a two level factorial experiment is considered in which various combinations of K factor are involved i.e. N = 2^k. The process variables (factors) that are considered for the lubricating oils are temperature, pressure and time. The present factor in design expression, N = n^k, therefore is 2³ = 8, resulting in eight different operating conditions at which the oil would be subjected to. Also, an analysis of variance procedure to establish the extend to which these process variables affects the viscosity of each lubricant and a regression model relating the process variables and viscosity for test will be done.

Experimental Procedure

Materials

A hydrostatic bench 9092 equipment, thermostat and bath (to maintain required temperature) and viscometer were used for the test. The hydrostatic bench consists of a cylinder, piston, loads and Bourdon Gauge to measure pressure.

Procedure

Each sample was poured into the cylinder and subjected by a piston and loads to produce the required pressure. The subjected oil was then placed into bath at the required temperature and timed. The viscosity was then measured for that combination and recorded.

Results and Discussions

Table 1. Various Combinations Used for the Fractional Design

Process variables			Dependent variable, V
P1	P2	P3	1	2	3	4	5	6	7	8	9	10
40	1	4	91.70	138.44	144.05	201.42	205.31	198.47	180.98	174.52	171.07	174.35
100	1	41	10.22	13.91	15.12	20.44	21.25	20.63	18.39	18.06	18.12	18.73
40	2	4	91.59	137.27	143.40	201.35	205.18	198.19	180.91	174.49	171.01	174.29
100	2	4	10.11	13.87	15.06	20.41	21.13	20.62	18.35	18.04	18.09	18.69
40	1	6	91.43	137.40	143.06	201.24	205.14	198.12	180.88	174.43	170.98	174.25
100	1	6	10.09	13.84	15.02	20.39	21.09	20.61	18.33	17.62	18.08	18.67
40	2	6	91.36	137.04	142.43	201.20	205.07	198.09	180.81	174.39	170.93	174.19
100	2	6	10.05	13.76	14.97	20.36	21.09	20.57	18.30	17.48	18.05	18.64

Legend:

P₁ - Temperature (°C); P₂ - Pressure (bar); P₃ - Time (hr); ∑X_i = 1, where X₁: 500N oil, X₂: Paranox 5501 (additive package), and X₃: Shelins 261 (viscosity improver).                                                      

Table 1 shows the various combinations used for the 2³ factorial design. From the table, it could be seen that there is little variation in the viscosities of the lubricants.

Table 2a. Analysis of variance procedure

V	Source	d.f.	SS	MS	F	Pr > F	R^2	C.V
1	Model Error corrected	6 1	13248 0.00011	2208 0.00011	10^6	0	1.0	0.02087
2	Model Error corrected	6 1	30601 0.09031	5100 0.09031	56472	0.0032	0.999997	0.39704
3	Model Error corrected	6 1	32868 0.00001	5478 0.00001	10^6	0	1	0.00447
4	Model Error corrected	6 1	65451 0.00011	10909 0.00011	10^6	0	1	0.00957
5	Model Error corrected	6 1	67738 0.00045	11290 0.00045	10^6	0	1	0.01875
6	Model Error corrected	6 1	63091 0.00980	10575 0.00980	10^6	0	1	0.09048
7	Model Error corrected	6 1	52843 0.00001	8807 0.00001	10^6	0	1	0.00355
8	Model Error corrected	6 1	49083 0.00151	8181 0.00151	10^6	0	1	0.04046
9	Model Error corrected	6 1	46764 0.00001	7794 0.00001	10^6	0	1	0.00374
10	Model Error corrected	6 1	48415 0.00001	8069 0.00001	10^6	0	1	0.03665

Table 2b. The effect of process variable

V	Source	d.f.	SS = MS	F	Pr > F
1	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	13248 0.01901 0.04961 0.00101 0.00781 0.00361	10^6 169 441 9 69 32	0.0 0.0489 0.0303 0.2048 0.0760 0.1112
2	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	30600 0.34031 0.26281 0.24851 0.14851 0.07411	10^6 3.8 2.9 2.8 1.6 0.8	0.0 0.3028 0.3375 0.3454 0.4216 0.5314
3	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	32867 0.24151 0.57781 0.17111 0.39161 0.00011	10^6 19321 46225 13689 31329 9	0.0 0.0046 0.0030 0.0054 0.0036 0.2048
4	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	65451 0.00361 0.02311 0.00031 0.00661 0.00011	10^6 32 205 2.8 59 1	0.0 0.1112 0.0443 0.3440 0.0826 0.5000
5	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	67738 0.01280 0.02880 0.00080 0.0080 0.00405	10^6 28 64 1.8 1.8 9	0.0 0.1180 0.0792 0.4097 0.4097 0.2048
6	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	63090 0.01620 0.03380 0.00845 0.01805 0.00605	10^6 1.7 3.5 0.9 1.8 0.6	0.0 0.4208 0.3145 0.5236 0.4043 0.5760
7	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	52843 0.00661 0.01051 0.00031 0.00151 0.00001	10^6 529 841 25 121 1	0.0 0.0277 0.0219 0.1257 0.0577 0.5000
8	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	49083 0.00661 0.17701 0.00101 0.08201 0.00211	10^6 4.4 1117 0.7 54 1.4	0.0 0.2840 0.0587 0.5635 0.6859 0.4471
9	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	46764 0.00361 0.00781 0.00031 0.00101 0.00001	10^6 289 625 25 81 1	0.0 0.0374 0.0255 0.1257 0.0704 0.5000
10	P1 P2 P3 P1P2 P1P3 P2P3	1 1 1 1 1 1	48415 0.00451 0.1201 0.00031 0.00101 0.00001	10^6 361 961 25 81 1	0.0 0.0335 0.0205 0.1257 0.0704 0.5000

Table 2b shows the effect of process variable (temperature, pressure and time) cum their interactions on the viscosity of the lubricants.

Table 3. Regression Model Equation for the Lubricating Oil Samples

Lubricant sample \ Source	Intercept	P1	P2	P3	P1P2	P1P3	P2P3
1	147.06	-1.36	-3.63e-1	-2.15e-1	7.50e-4	1.04e-3	4.25e-2
2	225.79	-2.1	-2.2	-7.88e-1	1.18e-2	4.54e-3	1.93e-1
3	234.23	-2.19	-1.07	-7.96e-1	9.75e-3	7.38e-3	7.50e-3
4	322.67	-3.02	-1.09e-1	-1.32e-1	4.17e-4	9.58e-4	7.50e-3
5	328.81	-3.07	-3.52e-1	-1.51e-1	6.67e-4	3.33e-4	4.50e-2
6	318.28	-2.97	-5.17e-1	-2.58e-1	2.17e-3	1.58e-3	8.50e-2
7	289.71	-2.71	-7.42e-2	-6.46e-2	4.17e-4	4.58e-4	-2.50e-3
8	278.22	-2.59	1.58e-1	1.36e-1	-7.50e-4	-3.38e-3	-3.25e-2
9	273.35	-2.55	-8.42e-2	-6.13e-2	4.17e-4	3.75e-4	2.50e-3
10	278.45	-2.6	-8.92e-2	-6.88e-2	4.17e-4	3.75e-3	2.50e-3

From the table, the results of samples 1, 7, 9 and 10 shows that temperature, pressure and time have significant effect on the viscosity of the component while the interactions between the process variables have no significant effect on the lubricants.

The results of samples 2, 5, 6 and 8 shows that only temperature has significant effect on the viscosity of  the lubricants while pressure, time and the interaction between the process variables have no significant effect.

The result of sample 3 shows that the entire process variable and their interactions have significant effect except for the interaction between pressure and time that has no significant effect.

The result of sample 4 shows that temperature and time have significant effect on the viscosity of the lubricant while pressure and the interactions between the process variables have no significant effect on it.

From table 2a, the coefficient of regression square (r²) is 1.0 (100%) for all the lubricants. The result shows a very good correlation between the variables of the samples. The coefficient of variation (C.V) for the lubricants is less than one for all the lubricants, this shows that it is significant and implies that there is a very small variation in the effect of the process variable on the viscosities of the mixtures.

Table 3 shows the regression model relating the viscosity and process variable for each sample. Substituting the actual values of the process variables into the model gave a very close approximate result of the test values of the viscosity from the table. Therefore, the model can serve to test the viscosity of the same formulated lubricant at any level of investigation of the process variables without carrying out a laboratory experiment.

Conclusions

The effect of temperature, pressure and time was tested on the viscosities of various lubricants, an analysis of variance procedure to establish the extent to which the process variables affect the oil viscosities and a regression model was done each sample.

It can be concluded that, samples 2, 5, 6, and 8 are not much affected by the process variables. Temperature above has significant effect on their viscosities. The effect of the process variables on the viscosity of sample 4 is not much when compared to those of sample 1, 7, 9, 10 and 3. The coefficient of regression square (r²) is 1.0. This shows a very good correlation between the variables of the lubricant samples.

The regression model suits the test and could be used for the same formulation without any laboratory work.

Investigations have so far been carried out using hydrostatic bench equipment to examine the effect of process variables on the viscosities of lubricants. It is our recommendation that the lubricants be tested using an internal combustion engine so as to know the real suitability and performance of the lubricants.

References

[1] Lansdown A. R., A practical guide to lubricant selection, Pergamon Press, 1^st Edition, 1982, p. 25-26.

[2] Mahmood I. H., Comparative studies of the level of contaminants in lube oils between Yola and Kaduna, Unpublished B. Eng. Thesis, F.U.T., Yola, 1997, p. 1-2.

[3] Khovakh M., Motor vehicle engines, Mir publishers Moscow, 1979, p. 548.

[4] Aibe M. A., Characterization and improvement of Nigerian lubricating oils, Unpublished B. Eng. Thesis, F.U.T., Minna, 1998.

[5] Scheffe H., Simplex lattice design for experiments with mixtures, Journal of the Royal Statistical Society, B, 1963, 25(4), p. 235-263.

[6] Eterigho J. E., Formulation of hydraulic brake fluid using castor oil as base stock, M. Eng. Thesis, 2001.

[7] Robert G. D. S., James H. T., Principles and procedures of statistics, a biometrical approach, 2^nd Edition, 1981, p. 27.

[8] Loveday R., Statistics, second edition of a second course in statistics, University Press, Cambridge, 1969, p. 192.

[9] Iriom G., Wilks S. S., Hunter J.S., Introductory engineering statistics, John Wiley and Sons, 3^rd Edition, New York, 1982, p. 472-477.