Journal of Pressure Equipment and Systems 4 (2006) 29-32

The failure probability analysis of ethylene cracking furnace tube based on risk

Wenhe Wang a,*, Shiming Shen a,b a College of Mechanical and Power Engineering of Nanjing University of Technology, Nanjing 210009, China

b Center of Engineering Risk Analysis & Research, SINOPEC, Nanjing 210009, China

Abstract

The ethylene cracking furnace is the primary equipment for the petrochemical industry. The furnace tube is the key component of

cracking in the furnace. Failure can cause serious consequences such as fire and explosion. The Monte Carlo method is used to apply the risk analysis theory of API 581. The qualitative analysis leads to failure probability of the ethylene cracking furnace tubes the fail-ure probability of furnace tube. The results supply a reliable foundation for prolonging risk-based inspection period and risk manage-ment of furnace tube.

Keywords: Ethylene cracking furnace; Furnace tube; Failure probability; Risk. 1. Introduction

The ethylene cracking furnace is important equip-

ment in the enterprises of petrochemical industry; the furnace tube is its important component. The influence factors on failure of tube are various under high tem-perature of tube. The damage of furnace tube includes creep, carburization and corrosion and so on. Damage may result in cracking, break and melting, and bring on leakage of high temperature media, and lead to conse-quently fire and explosion. So failure probability of furnace tube is more concerned.

With the rapid development of risk assessment in petrochemical industry, the risk analysis and assess-ment research for oil refining devices are attracted more and more people’s attention. Failure likelihood (failure probability) is a mainly part in risk analysis of devices [1, 2]. In the paper, Monte Carlo method and risk based inspection of API 581 are applied to com-pute the failure probability of a ethylene cracking fur-nace tube in a petrochemical plant, it provided reliable data for risk assessment, and insured a long period op-eration of the furnace tube.

2. Failure probability analysis methods of the cracking furnace tube

The computation methods of failure probability are

various; there are mainly the first order second mo-ment methods, the response surface method, Monte Carlo method and so on [4-7]. In the paper, Monte

* Corresponding Author. E-mail Address: wangwenhe518@163.com (Wenhe Wang).

Carlo method and risk based inspection of API581 are applied to compute the failure probability of a ethylene cracking furnace tube in a petrochemical plant, and the results of calculation are compared each other for sup-plying the reliable basis for risk analysis of the furnace tube.

2.1. Failure probability analysis of furnace tube based on Monte Carlo method

The Monte Carlo method is also called random si-mulation method, its basic thought is sample with probability density function of the basic random varia-ble, the failure probability is defined by comparing with a sample number of failure and the total sample number [7].The Monte Carlo method is widely applied to the reliability computation of the chemical equip-ment and analysis of failure probability has no limit in the application scope, so long as the limiting condition equation is known, results obtained by Monte Carlo method approach to the fact [8, 9].

2.1.1. Parameters and failure causes of the cracking furnace tube

The material of the furnace tube is the HP series casting condition, its microstructure is the eutectic car-bide and the austenite [11], internal radius Ri=46.95mm, external radius Ro=56.95 mm. The operation parame-ters of the ethylene cracking furnace tube: operation pressure Pi=0.106MPa, inner wall temperature Ti=838℃, outer wall temperature To=1050℃.

By failure mode and effect analysis (FMEA), risk of the furnace tube is the highest in the entire equip-ment, meanwhile, creep and carburization are consi-dered as the mainly causes for rupture of the ethylene

Wenhe Wang et al. / The failure probability analysis of ethylene cracking furnace tube based on risk

30

cracking furnace tube [3].

2.1.2. The failure limiting condition equation of the cracking furnace tube

Cumulated life fraction value is known as evaluation criteria of the cracking furnace tube, according to Lar-son-Miller method and life theory [11], when cumu-lated life fraction value reaches critical life-span frac-tion value, the furnace tube is considered as rupture by creep. In the paper, the critical life-span fraction value is used as a criterion and the failure probability of fur-nace tube is computed [12-14].

By the stress strength interference model, the failure limiting condition equation of furnace tube can be written with the formulas (1) and (2) [9, 10]:

0)( crFtF (1)

M

i iL

LtF

1

)()( (2)

In these parameters, F(t) is life-span fraction for

furnace tubes at time t (hour), Li is rupture life-span under stress σt and temperature t, ∆L is operation pe-riod, Fcr is the critical life-span fraction value.

2.1.3. The failure probability of the furnace tube under creep and carburization

The furnace tube failure probability under interfe-rence of creep and carburization, which is shown as the non-coupled superposition for circumference stress, is only concerned in this paper. Cumulated life-span frac-tion value is as judgment method by Monte Carlo me-thod. the failure probability of furnace tube can be ob-tained under different operation time [3] (Where opera-tion pressure Pi is normally distributed, the variation coefficient is 0.1; Ti and T0 are the temperature of in-ternal and external walls respectively, are the normally distributed, the variation coefficient is 0.01; Number of the sample is 10000 times).

Failure probability at a certain life-span value is shown in table 1.

Fig. 1 shows that the relation between failure proba-bility and operation times of the furnace tube. From Fig. 1, it is seen that the failure probability of the fur-nace tube is increased constantly with the increasing of operation times. If regarding 5% of failure probability as the ultimate life-span, then the service life of fur-nace tube is 6.4 years.

2.2. Failure probability computation of furnace tube based on API 581

The assessment of failure probability based on Risk-based Inspection(RBI) is carried out according to the failure mechanism of the devices (fluid medium in devices, the material of the devices and process para-

meters etc.). In assessment, a very important point is to calculate future failure probability according to the present failure mechanism of the equipment. In API581, there are three assessment methods, qualita-tive, half quantitative and quantitative analysis me-thods [15]. In the paper, the quantitative assessment method of API581 is applied to predict the failure probability of furnace tube according to the failure probability of the apparatus and statistics database of the incident reason, and appropriate factors.

2.2.1 Generic failure probability for furnace tube API581 provides the generic failure probability of the furnace tube about three kinds of size. The failure probability of the furnace tube can be calculated di-rectly by the similar failure probability of long-term creep in the technological module of furnace tube. If the short-term creep is taken place, the failure proba-bility of furnace tube can be obtained by multiplying similar failure probability with coefficient 100.Results are shown in Table 2 [15]. Table 1. Failure probability of tube at certain life (under creep & carburization).

Operation Times (hours)

Failure Probability

33141.94 38048.97 43538.02 55914.96 64005.95 72343.38 91637.16 102716.7 128060.0 142454.6 158088.7 193353.7 281842.3

0.000E+00 4.999E-04 2.900E-03 5.041E-02 8.079E-02

0.1611E+00 0.4135E+00 0.5498E+00 0.7893E+00 0.8669E+00 0.9209E+00 0.9759E+00 0.9990E+00

Fig. 1. Relationship between failure probability and operation times of furnace tube.

Journal of Pressure Equipment and Systems 4 (2006) 29-32

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Table 2. Generic failure probability for furnace tube.

Hole Size Failure Probability(long-term) Failure Probability(short-term)

6.35mm 25.4mm 101.6mm Rupture

0 4.62*10-6 1.32*10-6 6.60*10-7

0 4.62*10-4 1.32*10-4 6.60*10-5

Table 3. Failure probabilities of furnace tube for creep.

Hole Size/mm 25.4 101.6 Rupture

FTMSFST

FTMSFLT

Failure Probability(long-term)/a Failure Probability(short-term)/a

4.62*10-6

4.62*10-4

5.5 0.55

1.32*10-6

1.32*10-4

6.60*10-7

6.60*10-5

2.2.2 Computation of the secondary factor of long-term creep in the technological module

The material of cracking furnace tube is HP-Nb, the tube is made by the centrifugal foundry. The mean Larson Miller parameter of material, Lmavg, can be de-scribed as [11]:

mavg 65.05956-2.17933lnL S (3)

where, S is stress of furnace tube (MPa).The Larson Miller parameter at the current operation condition, lm, is calculated using the following equation:

)()1000

460( CLogtTMT

l im

(4)

where TMT is operating tube metal temperature in de-gree; ti is total time in service in hours and C is the material coefficient which is 57 in here. The failure coefficient can be expressed as:

3 20.6723* 0.2854* 0.5905* 0.3001LT = min(1,10 )X X XF (5)

deltammavg LMlLX /)( (6)

LTF

TMSFLT eF *1355.0 (7)

where LMdelta is the average difference between the mean and minimum Larson Miller curves in API RP530; X can be calculated by formula (6), and then X=0.3 in here. The failure factor FLT can be calculated by formula (5), and then FLT = 0, the technical module subfactor of long-term creep FTMSFLT can be computed using the formula (7), and then FTMSFLT=0.55. 2.2.3. Computation result of failure probability in API581 According to the similar failure probability of the heating furnace in API581, and considering creep fail-

ure causes and the secondary factor of technological module, the heating furnace tube long-term annual failure probability of creep can be obtained, shown as Table 3 [15]. 3. Conclusions

(1) In the situation that failure probability is 5%, and

considering simultaneously the interaction of creep and carburization, the furnace tube operation life is 6.4 years. The results indicated that the creep and carburi-zation are main reasons of the cracking furnace tube rupture.

(2) Because of having not considered the influence of carburization, the result of failure probability com-putation based on API581 is lower than that using Monte Carlo method.

(3) The failure probability of cracking furnace tube calculated by Monte Carlo method is compared with that using API581. The results provide failure possibil-ity data for risk assessment of the cracking furnace tube. References

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