** **

** **

**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*

**Abstract**

The effect of temperature, pressure and time was tested
on the viscosities of ten lubricant samples using 2^{3} 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 (R^{2}) 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 2^{3} = 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 |
|||||||||||

P |
P |
P |
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:

P_{1} -
Temperature (°C); P_{2} - Pressure (bar); P_{3} - Time (hr); ∑X_{i}
= 1, where X_{1}: 500N oil, X_{2}: Paranox 5501 (additive
package), and X_{3}: Shelins 261 (viscosity improver).

Table 1 shows the various combinations used for the 2^{3}
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 |
C.V |

1 |
Model Error corrected |
6 1 |
13248 0.00011 |
2208 0.00011 |
10 |
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 |
0 |
1 |
0.00447 |

4 |
Model Error corrected |
6 1 |
65451 0.00011 |
10909 0.00011 |
10 |
0 |
1 |
0.00957 |

5 |
Model Error corrected |
6 1 |
67738 0.00045 |
11290 0.00045 |
10 |
0 |
1 |
0.01875 |

6 |
Model Error corrected |
6 1 |
63091 0.00980 |
10575 0.00980 |
10 |
0 |
1 |
0.09048 |

7 |
Model Error corrected |
6 1 |
52843 0.00001 |
8807 0.00001 |
10 |
0 |
1 |
0.00355 |

8 |
Model Error corrected |
6 1 |
49083 0.00151 |
8181 0.00151 |
10 |
0 |
1 |
0.04046 |

9 |
Model Error corrected |
6 1 |
46764 0.00001 |
7794 0.00001 |
10 |
0 |
1 |
0.00374 |

10 |
Model Error corrected |
6 1 |
48415 0.00001 |
8069 0.00001 |
10 |
0 |
1 |
0.03665 |

*Table
2b. The effect of process variable*

V |
Source |
d.f. |
SS = MS |
F |
Pr > F |

1 |
P P P P P P |
1 1 1 1 1 1 |
13248 0.01901 0.04961 0.00101 0.00781 0.00361 |
10 169 441 9 69 32 |
0.0 0.0489 0.0303 0.2048 0.0760 0.1112 |

2 |
P P P P P P |
1 1 1 1 1 1 |
30600 0.34031 0.26281 0.24851 0.14851 0.07411 |
10 3.8 2.9 2.8 1.6 0.8 |
0.0 0.3028 0.3375 0.3454 0.4216 0.5314 |

3 |
P P P P P P |
1 1 1 1 1 1 |
32867 0.24151 0.57781 0.17111 0.39161 0.00011 |
10 19321 46225 13689 31329 9 |
0.0 0.0046 0.0030 0.0054 0.0036 0.2048 |

4 |
P P P P P P |
1 1 1 1 1 1 |
65451 0.00361 0.02311 0.00031 0.00661 0.00011 |
10 32 205 2.8 59 1 |
0.0 0.1112 0.0443 0.3440 0.0826 0.5000 |

5 |
P P P P P P |
1 1 1 1 1 1 |
67738 0.01280 0.02880 0.00080 0.0080 0.00405 |
10 28 64 1.8 1.8 9 |
0.0 0.1180 0.0792 0.4097 0.4097 0.2048 |

6 |
P P P P P P |
1 1 1 1 1 1 |
63090 0.01620 0.03380 0.00845 0.01805 0.00605 |
10 1.7 3.5 0.9 1.8 0.6 |
0.0 0.4208 0.3145 0.5236 0.4043 0.5760 |

7 |
P P P P P P |
1 1 1 1 1 1 |
52843 0.00661 0.01051 0.00031 0.00151 0.00001 |
10 529 841 25 121 1 |
0.0 0.0277 0.0219 0.1257 0.0577 0.5000 |

8 |
P P P P P P |
1 1 1 1 1 1 |
49083 0.00661 0.17701 0.00101 0.08201 0.00211 |
10 4.4 1117 0.7 54 1.4 |
0.0 0.2840 0.0587 0.5635 0.6859 0.4471 |

9 |
P P P P P P |
1 1 1 1 1 1 |
46764 0.00361 0.00781 0.00031 0.00101 0.00001 |
10 289 625 25 81 1 |
0.0 0.0374 0.0255 0.1257 0.0704 0.5000 |

10 |
P P P P P P |
1 1 1 1 1 1 |
48415 0.00451 0.1201 0.00031 0.00101 0.00001 |
10 361 961 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 |
P |
P |
P |
P |
P |
P |

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 (r^{2})
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 (r^{2}) 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**

** **

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[3]
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publishers Moscow, 1979, p.
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[4]
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