Abstract

The performance and reliability based analysis of process air compressor in the petrochemical industry was carried out. The lognormal model was used for reliability analysis, while the Weibull probability distribution and chi test technique were used to analyzed the sample test questions. The failure based results indicated that for every 1% increase in the lognormal probability, the failure rate increased by 2.4% when compare with that of the Weibull distribution. The Reliability indicates that the reliability of the system for 50days of operation is 36.8%. This increased to 38.8% at the MTBF of 365days. Therefore, there exist a relationship between the system reliability and the failure rate. Base on the chi square test at 0.05 and 0.01 levels of significance it was concluded that “Most Machinery failures are lubrication oriented”. Therefore, careful preventive maintenance process that is condition based should be followed in order to improve the plant energy efficiency.

1. Introduction

The concept of reliability is as old as man himself. Man has long been concerned with the problem of unreliability of products used. Will “this” function satisfactorily? Will “that” last long? These are some of the familiar questions he has been asking all along. According to Reskytor ¹ reliability is the property of an object to retain in time, within the predetermined limits, all the parameters ensuring the performance of the required functions in the preset service conditions. The American National Aeronautics and Space Administration (ANASA) defines reliability as the probability of a device performing adequately for the period of time intended under the operating conditions encountered, while Balaguru ² conceives that reliability of a unit (or product) is the probability that the unit performs its intended function adequately for a given period of time under the stated operating condition or environment.

Common to all definitions is that “Reliability” is associated with; probability, intended function, time and operating conditions. If (t) is the time till the failure of the unit occurs, then the probability that it will not fail in a given environment before time (t). Thus, reliability is always a function of time. It also depends on the environmental conditions which may or may not vary with time. Since it is a probability, its numerical value is always between one and zero.

However before delving into the topic Using reliability analysis to improve the performances of rotor dynamic system, an understanding of the term “failure” is needed.

According to Lewis ³ a system or a machine is said to fail when it ceases to perform its intended function. On the other hand, Shigley and Charles ⁴ consider a machine or machine component to have failed when it is no longer capable of performing its required function in a satisfactory manner.

Bain ⁵ defined failure as any change in a machine part or component which causes it to be unable to perform its intended function satisfactorily, also failure as the inability of a component to retain in time, within the predetermined limits all the parameters ensuring the performance of the required function in the present service conditions ¹. Failure can also be defined as an event arising from complete loss of operationally.

A process air compressor is a device that converts power using either electric motor, diesel or gas engine into potential energy stored in pressurized air. The compressed air then is held in the tank until called into use. According to design and principle of operation, they can be classified as positive displacement compressors and negative displacement compressors. Process air compressors are used in petrochemical industry. In present scenario of the demand of energy efficiency is increasing, optimization and effective maintenance plan will enhance sustainable performance ⁶. In petrochemical plant, compressors are running in a corrosive and high temperature conditions ⁷. Jennings ⁸ and Crowder ⁹ used fault tress technique to rank the various risk associated with the petrochemical industry machinery and their corresponding consequences without considering the probability prediction of time-to-failure of the plant. Ayyab and Chia ¹⁰ used reliability goal and subsystem criteria to evaluate the stressed machinery subsystem of the plant without the consideration of the impact of performance indicators and probabilistic review of the plant with time.

Therefore, the research seeks to use probability models to analyze the reliability and time-to-failure of the process air compressor in the petrochemical industry.

2. Methodology

Compressors in three process plants namely; Olefins Plant, Ethylene Plant, Propylene Plant with Power Plant and utilities in a Petrochemicals Plant were covered. These plants have been in operation since 1993 and there have not been a work on the performance of the operating compressors.

A random sample of production personnel (chief operator, panel operator, field operator) and maintenance personnel (mechanical superintendent, supervisor) involve in the operation and maintenance of the machinery in question were taken from which the questionnaire was structured.

Data was acquired through a set of questionnaires and extracts from log books. 30 questionnaires were distributed to respondents in Production and Maintenance Departments of the plant, who are involved in the operation and maintenance of the Petrochemicals Plant.

Out of the 30 questionnaires administered, 12 were completed and returned. This represents an overall response of 40%. Analysis and discussion of data is based on the 12 completed questionnaires. The overall responses were analyzed.

The study adopted a descriptive and inferential analysis on randomly selected sample.

3. Theoretical Formulation and Analysis

There are different types of statistical models used in analyzing any engineering data. The accuracy of such analysis depends on whether the chosen model is appropriate; choice of a wrong model can lead to serious errors. Some of these equations and statistical models are:

The exponential distribution has limited application as a time to failure model because of “no wear out” or aging is not realistic for many services; The Weibull takes care of this limitation and has the following properties ¹¹.

a. Increasing hazard rate

b. Decreasing hazard

c. Constant hazard rate.

It fits into large number of failure characteristics of equipment. The most general form of Weibul Law is given by (Lewis 1987)

(1)

(2)

From equation 3.1 and 3.2, we have

(3)

where is the location parameter, is the shape parameter, is the reliability of the plant, is the failure rate of the plant.

A study on the form of the instantaneous failure rate shows that:

Also according to Gaka and Tabaszewski, ¹² hazard rate can be expressed as:

(4)

Where is the shape of the distribution, is the scaling parameter that determines the spread of the values

(5)

(6)

(7)

(8)

(9)

(10)

Where Tt is the time to failure at a given instant, is the time to failure at infinity, is the sample response from the questionnaire, is the total sample response, is the percentiles for Weibull distribution test.

The lognormal model has many uses in engineering. It can be derived as the appropriate model where failure of a unit occurs when damage has reached a specific level. The model has been used to model stress failure mechanism, such as failure caused by rupture. In such models it is assumed that the rupture was caused when crack in the structure reached a given size and the growth of the crack at any instant is a random proportion of its size at that time.

It is also used in the analysis of mechanical fatigue of wear.

From Spiegel and Stephen ¹³, the probability density function is given by;

(11)

Where is the shape parameter, the scaling parameter.

The mean time between failures MTBF, between , and the n+1th failure as given by ³ is

(12)

Where is the time that the nth failure occurred, is the time to failure.

This is used when the time to failure of a system is made up of redundant units and where redundant units are switched on when the operating units fail. It is also used when failure is caused by accumulation of damage. However, for the purpose of this study, the Weibull, lognormal, the chi-square test and the F-test are used for analysis.

3.4. The Chi-square Test

Is a measure of discrepancy existing between the observed and the expected frequencies. The symbol is the Greek letter Chi. The test was first used by Gupta ¹⁴-. It is defined as:

(13)

Where is the observed frequencies, is the expected frequencies.

(14)

Where is the expected frequency, is the total for the row containing the cell, is the total for the column containing the cell, is the total number of observation

(15)

Where is the number of row, is the number of column.

(16a)

Or

(16b)

(17)

(18a)

Where is the mean time between failures, is the mean time to failures.

Or

To determine the value of , the steps required are:

i. Take the differences between the observed and the expected frequency and obtain the square of these differences i.e. obtain the values of.

ii. Divide the values of obtained in step (II) by the respective expected frequencies and from equation (13) we obtain the total as

This gives the value of, which can range from zero to infinity. If is zero it means that the observed and the expected frequencies completely coincide. The greater the discrepancy between the observed and the expected frequencies the greater shall the value of.

4. Results and Discussions

The Weibull distribution and the chi-square test was used to test the two hypothesis, while the lognormal was used to analyze the reliability of the systems. In addition, the MTBF, MTTR and the availability of the machines was determined. The Weibull distribution model was used to test hypothesis 1, failure data of a compressor (25-k-1A) each treated as a system obtained from maintenance and operation logs were used.

Failure data of compressor (25-k-1A) was treated as a system, located in power plant and utilities was analyzed using the Weibull distribution model. Table 1 show the time to failure of the compressor.

The steps for determining the parameters of the Weibull representing the data, using probability plotting, are outlined in the following instructions. First, rank the times-to-failure in ascending order as shown next.

Consider the same data set from Table 1 given above (with six failures at 16, 34, 53, 75, 93 and 120 hours). Estimate the parameters and the correlation coefficient using rank regression on Y, assuming that the data the 2-parameter Weibull distribution we have Table 2.

Figure 1 and Figure 2 show the results of the weibull distribution and lognormal probability. The figures show a linear progression such that as the failure rate and log time increases as the machinery time to failure increases. This is an indication that if the machinery is not adequately maintained, the air compressor will fail before the life cycle. It further show that for every 1% increase in the lognormal probability, the failure rate increases by 2.4%.

The result shows a weibull analysis of the air compressor for 6 different sample time to failure as predicted from design. The result indicates that for a period of 25 operating hour, minor failure may occur in the sub system and the overall life cycle can be extended if effective maintenance is sustained.

Further analysis show that from equation 7 we have that

The value of W obtained is compared to the 0.05 and 0.95 critical values computed from the above equation.

Similarly,

The result show that the value of W lies between the two numbers, therefore machinery failure rate is dependent on its running hours that is Weibull distribution is accepted. Appendix II shows the percentiles of Weibull distribution for the W test to validate the result output. It therefore demands that an effective condition monitoring technique be put in place to monitor the operation and performance as the operation hour increases. Cost effectiveness and production optimization can be achieved if a proactive maintenance strategy is maintained.

The hazard rate for the process air compressor using Weibull distribution is estimated from

At time at at time at at time at

This shows that the hazard rate of the compressor for the period under review is increasing since .

30 questionnaires were administered with relevant question to detect the cause of failure. The data generated in this respect shows that distribution between lubrication related and non-lubrication related failures are in the ratio of 4:8.

The result shows that out of 12 respondents, 33.0% are lubrication related failures, while 67% are not lubrication related. Chi-square Test will be used for the sample question. The Chi-square Test is a measure of discrepancy existing between the observed and the expected frequencies. The symbol is the Greek letter Chi. The analysis of the result from the questionnaires were analyzed using the expected frequency formulation and result shown in Table 3.

Hence the degree of freedom (df);

Test the theory at 0.05 level where using Appendix (IV).

Since 0.85 less than 7.80 we cannot reject the theory at0.05 level of significance.

To test the theory at 0.01 level of significance, we have for

Since 0.85 is less than 11.34, we can say that most machinery failures are lubrication oriented of 0.01 level of significance. Thus, base on the chi square test at 0.05 and 0.01 levels of significance we can also say that “Most Machinery failures are lubrication oriented”.

The lognormal distribution is used to analyze the reliability of the process air compressor (25-K-1A), whose failure is characterized by wear as a result of poor lubrication. The time to failure of the compressor is shown in Table 1.

From Figure 1, .

Therefore

To estimate the value of we used , where is the estimated values of .

Therefore at , we have that.

The mean value

The standard deviation

From the analysis, the probability of anytime to failure can be obtained. For example, the probability that the time to failure of the compressor of (3.1 months) is obtained by taking the logarithms of 3.1 i.e., in (3.1) = 1.2 is located on the Y axis and the corresponding values on X-axis gives the value of P as 10.5%.

The probability of failure of the pump can be obtained from

where .

The probability of failure can be obtained from normal distribution Tables (Appendix (V)) depending on the value of from which the reliability can be determined.

The reliabilities after 4 years, 5 years and 6 years of operation was estimated as follows:

i. Reliability after four (4) years of operation

Probability of failure after 4 years

However, Reliability (R) = 1- Probability of failure

Therefore R (t) after 4years

ii. Reliability after 5 years

Probability of failure after 5 years

Therefore R (t) after 5years .

iii. Reliability after 6 years

Probability of failure after 6 years

However, Reliability (R) = 1- Probability of failure

Therefore R (t) after 6years

Figure 3 show that the reliability of the equipment decreases with operating time. This result therefore provides a guide on the choice of maintenance plan to be adopted to prevent or minimizes system breakdown and failure. Predictive maintenance that is condition based will help to prevent and protect the plant, thereby sustain production and minimize downtime.

A test case was analysed for the systems operating for the period of one year (365days) using equations 16 – 18 we have that the reliability ranges from 0 to 100, and there is gradual increase in failure with time of the plant operation. Figure 4 shows a plot of reliability with the mean time between failures for a process air compressor within 365days of operation. This plot also affirms the fact that failure rate may be influenced by the running hours and maintenance style of the equipment.

The result plotted in Figure 4 shows the reliability of the plant at different MTBF values. This indicates that the reliability of the system for 50days of operation is 36.8%. This increased to 38.8% at the MTBF of 365days. Therefore, there exist a relationship between the system reliability and the failure rate. That is, as the system reliability increases the failure rate gradually decreases.

5. Conclusion

From appropriate equations and statistical tools used in testing the performance and reliability of air compressor. The investigation shows that machinery failures in Indorama Petrochemical Company is as a result of continuous running without inspection, Poor lubrication; and Poor implementation of preventive maintenance programs.

6. Recommendation

The following recommendations were made

i. Adequate preventive maintenance as specified by the manufacturer should be carried out.

ii. Strict adherence to Turn Around Maintenance Schedules (TAM).

iii. Changing of oil as at when due, oil analysis should be carried to determine when lubricants should be changed.

iv. Proper Handling of Lubricants to avoid contamination.

v. The material management department should work hand- in-hand with the user department to ensure that the right spares are supplied.

References