Early Warning Analysis of Oil-Gas Field Equipment Failure Based on Statistical Model of Failure Rate

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1 2016 Iteratoal Cogress o Computato Algorthms Egeerg (ICCAE 2016) ISBN: Early arg Aalyss of Ol-Gas Feld Equpmet Falure Based o Statstcal Model of Falure Rate eb Y 1, Zhexog Ke 2 & Shucheg u 1 1 Cha Natoal Petroleum Corporato, Bejg, Cha 2 School of Machery, Storage ad Trasportato Egeerg, Cha Uversty of Petroleum-Bejg, Bejg, Cha ABSTRACT: Ths paper proposed a method used to estmate mechacal equpmet falure for ol-gas feld eterprses. Frst, ths method establshed a mxed falure dstrbuto model of mechacal equpmet modules. Accordg to the collected statstcal data of module defect, ths method the appled MLE (Maxmum Lkelhood Estmato) algorthm ad EM algorthm to calculate the mxed falure dstrbuto parameters of mechacal equpmet modules, so as to form the mxed dstrbuto fucto of falure rate. The feasblty of ths method was verfed through examples. At last, the cocept of rsk early warg maagemet for mechacal equpmet falure was proposed based o the estmated dstrbuto fucto of mechacal equpmet falure rate. As a result, there are scetfc grouds for the equpmet mateace & repar cycle regulated by grass-roots staff ad the equpmet replacemet & scrappg strategy set by maagemet-level users. Keywords: statstcal model of falure rate; falure rate of mechacal equpmet; rsk early warg 1 INTRODUCTION th cotuous crease of ol-gas resources Cha, ol-gas eterprses have etered rapd developmet phase. Usage quattes of correspodg ol-gas well felds ad mechacal equpmet are cotuous crease. The safety ad stable operato of ths kd of equpmet ca drectly affect the plag, costructo, ad safety of ol-gas felds. Therefore, mechacal equpmet used ol-gas felds has occuped a mportat part the daly equpmet maagemet of ol-gas feld eterprses. Due to faclty or techcal problems occurred the costructo or operato process of ol-gas felds, there ca be dowtme rsks caused by accdetal falure durg the producto ru of ol-gas well felds ad part mechacal equpmet. I most cases, ths kd of rsks ca drectly or drectly cause the occurrece of related major accdets ol-gas feld eterprses. Hece, t ca make a bg dfferece coductg assessmet ad aalyss of ol-gas feld producto system equpmet. The goal of safe producto ol-gas feld eterprses ca be evetually reached by ehacg scetfc maagemet o related equpmet falure well felds ad statos [1]. Key lks the ol-gas feld producto system are composed of dfferet types of rotatg equpmet. Assessmet o the relablty of correspodg producto system wll deped o accurate calculato of correspodg equpmet falure. Therefore, deep aalyss ad research o the method used to estmate correspodg mechacal equpmet are eeded. Geerally, equpmet falure ca be dvded to early falure, accdetal falure ad agg falure. At preset, most scholars are coductg correspodg research o accdetal falure [2] ad agg falure [3]. These two kds of falure are maly used aalyss of equpmet falure caused by oe kd of reasos or statstcal aalyss of falure rate wthout full lfe cycle of equpmet. Equpmet falure rate s used to descrbe a set of the same equpmet type. As equpmet shares dfferet operatg years, operatg codtos ad usages, dfferet reasos for equpmet falure (such as early falure, accdetal falure ad agg falure) ca coexst most cases. hle coductg estmato o the falure rate of full lfe crcle, parameter dstrbuto features of varous falure frequeces shall be fully cosdered. hle coductg estmato o full lfe crcle falure rate of equpmet, loger statstcal data perod ca lead to larger data sze. As a 325

2 Fgure 1. The relatoshp of the equpmet falure rate ad operatg years. result, correspodg statstcal falure rate ca show hgher practcablty ad accuracy. However, as the formatozed maagemet level for falure rate data of mechacal equpmet ol-gas feld eterprses s low ad t s lmted to coduct aalyss accordg to data records ad statstcs, serous cesored data exst the fal results of equpmet falure data aalyss. Based o orgal statstcal falure data of equpmet, ths paper proposed a mxed dstrbuto model of equpmet falure accordg to the stuato that dfferet equpmet falure causes coexsted ad, dfferet parameter dstrbuto patters were caused by varous occurrg frequeces of those falure causes. Ths model ca apply a accurate parameter estmato method to aalyze the maxmum lkelhood fucto patter correspodg to blateral tmg cesored data whle usg EM algorthm to obta the mxed falure rate fucto through parameter estmato order to solve problems of short statstcal cycle, complete agg falure data, ad cesored data. I the ed, by aalyzg effectve equpmet falure records of ol-gas feld eterprses, ths model ca make quattatve smulato o the falure rate fucto of mechacal equpmet. By coductg rsk early warg of equpmet falure rate dfferet tme perods, ths model ca also provde scetfc grouds for the equpmet mateace & repar cycle regulated by grass-roots staff ad the equpmet replacemet & scrappg strategy set by maagemet-level users. 2 STATISTICAL ANALYSIS PRINCIPLES OF OIL AND GAS FIELD MECHANICAL EQUIP- MENT FAILURE RATE The relatoshp betwee falure rate of ol-gas feld producto equpmet ad operatg years ca be smlar to a bathtub curve. Ths curve ca be dvded to three perods: early falure perod, accdetal falure perod, ad agg falure perod [4]. (1) Early falure perod refers to the tal cometo-use perod of equpmet. Falure ths perod s caused by teral materal defect, desg defect or maufacturg defect of product. The falure rate gets lower wth the passage of tme, showg egatve growth. (2) A type feature of accdetal falure perod s the falure rate ca stay a low level ad mata a stable varato perod for a log tme. Falure ths perod s caused by radom varato stress codtos. The falure rate shows radom dstrbuto. (3) The falure rate correspodg to agg falure perod gets hgher quckly wth the passage of tme. Falure ths perod s caused by equpmet abraso ad agg. The falure rate shows postve growth. See Fgure 1 for the bathtub curve betwee falure rate of equpmet ad operatg years. I cosderato of the actual usage of mechacal equpmet ol-gas feld eterprses, most equpmet have completed suffcet abraso ad got through early falure perod. Therefore, statstcal aalyss s maly coducted for accdetal falure rate ad agg falure rate of mechacal equpmet used ol-gas feld eterprses. As the frequeces of accdetal falure ad agg falure are dfferet, there are dffereces betwee ther correspodg parameter dstrbuto patters. The specfc dffereces are: (1) Statstcs betwee accdetal falures s depedet ad the falure rate s approxmate to a costat where expoetal dstrbuto (E(t λ)) ca be appled; (2) agg falure rate gets hgher wth the passage of tme ad ebull dstrbuto ((t a,b)) s usually appled for aalyss. I cocluso, ths paper proposed a method to estmate statstcal aalyss of falure rate of mechacal equpmet combato wth the operatg propertes of mechacal equpmet used ol-gas feld eterprses. See Fgure 2 for the specfc algorthm process. Aalyss of ths algorthm maly cludes fve steps. The cotet of each step s as follows: 1) Step 1: Complete collecto ad processg of statstcal falure data of mechacal equpmet used ol-gas feld eterprses to form essetal data cludg equpmet type, stallato tme, falure occurrece tme, falure cause, repar record, ad replacemet record. 2) Step 2: Make aalyss of falure causes based o 326

3 Data put Aalyss of the reasos for equpmet falure Establsh mxed dstrbuto model of equpmet falure hether statstcal tme terval s log eough Complete data parameter estmato (MLE method) Cesored data parameter estmato method (EN method) Mxed falure rate of equpmet Fgure 2. Estmato flowchart of rotatg equpmet falure rate. put basc data ad coduct prelmary classfcato of accdetal falure ad agg falure of mechacal equpmet. Calculate the proporto p that agg falure occupes. 3) Step 3: Italze the mxed dstrbuto model of accdetal falure ad agg falure, ad fer the mxed falure rate fucto of mechacal equpmet accordg to the proportoal relatoshp betwee accdetal falure ad agg falure. See Secto 3 for the specfc process of fucto dervato. 4) Step 4: Make comprehesve judgemet o statstcal perod of mechacal equpmet falure, so as to obta soluto of falure rate fucto soluto. he statstcal perod of falure s log ad statstcal falure data s complete, tradtoal MLE method ca be drectly appled to estmate ukow parameters of mxed dstrbuto model. he statstcal perod of falure s short ad there s serous cesored data, EM method ca be appled for parameter estmato o cesored data. See Secto 4 for specfc process of fucto soluto. 5) Step 5: Brg parameter estmato results to mxed falure rate fucto of mechacal equpmet to obta falure rate fucto of mechacal equpmet. I the ed, coduct statstc predctve aalyss of falure rate of mechacal equpmet. 3 MIXED DISTRIBUTION MODEL OF EQUIP- MENT FAILURE 3.1 Uversal mxed dstrbuto model Mechacal equpmet used ol-gas felds are composed of several compoets. Take cetrfugal pump as a example. Cetrfugal pump s maly made of pump body, mpeller, sealg rg, rotato axs, ad axle sealg box. Some cetrfugal pumps are eve equpped wth gude roller, ducer, ad balace dsk. Each compoet of falure rate cotas ts ow features. Dfferet compoets have dfferet falure probabltes ther lfe crcles. All together, they ca form the etre accumulated dstrbuto fucto of falure probablty of mechacal equpmet. Assume some cetrfugal pump s composed of dfferet compoets ad each compoet s ts lfe crcle (t refers to the tme perod). Set the accumulated dstrbuto fucto of falure correspodg to each compoet as G 1 (t), G 2 (t),..., G (t) ad the correspodg mxed proportos are p 1, p 2,, p. See Formula (1) for the accumulated dstrbuto fucto of equpmet falure G(t) gve below: G t p G t p G t (1) 1 1 Amog whch, p>0 ad 1 1 p 1. G (t) refers to the mxed dstrbuto model [6]. Assume that the relablty fucto ad probablty desty fucto of mxed dstrbuto model G(t) are respectvely R(t) ad g(t). See Formula (2) for the specfc forms gve below: R( t) p R ( t) 1 g( t) p g ( t) 1 (2) The, the equpmet falure rate fucto h(t) after mxg s show as follows: gt () p g () t 1 ( ) ( ) ( ) v t h t Rt () 1 pr() t 1 h t (3) Amog whch, v () t refers to the mxed falure rate fucto of equpmet wth a sze rage as follows: pr() t 0 v ( t) 1 (4) Rt () 3.2 Soluto prcples for model of mxed falure rate I some statstcal perod of etre equpmet falure record oe ol-gas feld ut, accdetal falure ad agg falure of equpmet compoet ca geerally coexst due to dfferet operatg years of dfferet equpmet compoets, certa dffereces betwee dvdual compoets, ad dffereces operatg codtos. Moreover, occurrece frequeces of accdetal falure ad agg falure ca also be dfferet ad they respectvely correspod to expoetal dstrbuto (E(t λ)) ad ebull dstrbuto ((t a,b)). Assume that the mxed proporto of equpmet agg falure s p (0<p<1). I combato of the relablty 327

4 fucto formulas of ad E for equpmet facltes ad accordg to Formula (2), we ca calculate the relablty fucto of mxed dstrbuto model of equpmet: R( t) pr ( t) (1 p) R ( t) pexp ( t / a) (1 p)exp( t/ ) E b (5) Combg ths formula wth Formula (4), we ca calculate the falure rate fucto after mxg. By calculatg the mxed falure rate fucto accordg to Formula (3), we ca obta the followg formula through smplfcato: b b1 1 p( ) 1 b () a t ht t b t p (1 p)exp[( ) ] a (6) It ca be see from the calculato results of the formula gve above that there are 3 ukow varables the mxed falure rate fucto h(t):, a ad b. Method to solve parameters wll be troduced Secto 4. 4 ESTIMATION ON PARAMETERS OF MIXED FAILURE RATE MODEL To some extet, accdetal falure ad agg falure of equpmet ca be totally separated the statstcal falure data of ol-gas feld producto equpmet, ad the proportoal relatoshp p of these two types ca be drectly calculated through formulas. Accordg to Formula (6), further calculato of mxed falure rate fucto ca be obtaed by calculatg the ukow parameter of the expoetal dstrbuto correspodg to accdetal falure ad the ukow parameters a ad b of the ebull dstrbuto correspodg to agg falure [7]. 4.1 Estmato methods for MLE parameters expoetal dstrbuto I geeral, accdet falure ca be repared by equpmet mateace ad there s o assocato betwee each falure. I ths case, falure rate s approxmate to a costat. Parameter estmato value ca be obtaed through tradtoal MLE method as show Formula (7): t1 t2 N (7) ( ) / Amog whch, N refers to the total umber of accdetally faled equpmet compoets; refers to the total operatg tme of accdetally faled equpmet compoets; refers to the total operatg t 2 t 1 tme of ormal operatg compoets durg equpmet operato; refers to the average total operatg tme of compoets durg statstcal falure cycle. 4.2 Estmato methods for EM parameters ebull dstrbuto Ol-gas feld equpmet s composed of dfferet compoets ad there are major dffereces betwee the agg falure perods of each compoet. As a result, parameter estmato s requred a gve perod. Assume there re compoets of ol-gas feld operatg system sufferg from agg falure ther lfe cycle X. The statstcs of correspodg tmes of agg falure s as follows: t... t... t... t t... t 1 s1 s r r1 However, accordg to the statstcal aalyss of the actual sample collecto stuato, the sequetal agg momet data s actually show as follows: T t t... t t T 1 s s1 r1 r 2 Ths sample s called a cesored sample whle T1 ad T2 are respectvely the left cesored tme ad the rght cesored tme. Set T ( t, t,... t, t ) to s s1 r1 r obta the maxmum lkelhood fucto of cesored sample:! L a b T g t a b G t a b G t a b ( s 1)!( r)! r (, ) s s1 (,, )( ( s,, )) (1 r ( r,, )) It s very hard to solve the ebull dstrbuto parameters ths statstcal perod; EM algorthm eeds to be troduced to complete parameter soluto. EM (Expectato-Maxmzato) algorthm s a terato algorthm to solve maxmum lkelhood estmato of parameter. Its calculato process s smple ad stable. Covergece ca be relably obtaed. Each terato cludes E step (Expectato) ad M step (Maxmzato). At frst, set ( ab, ), T refers to observed complete dstrbuto data, ad Z refers to potetal data of costructo. L ( T) s used to represet the observato posteror dstrbuto of ad L (, ) T Z meas to add posteror dstrbuto. L (, ) Z T refers to codtoal dstrbuto desty () fucto. Set as the estmato value of No.(+1) terato. The two steps of No. (+1) terato are show as follows: E step: Take log L ( T, Z) as the dstrbuto of Z to solve expectato: Q T E L T Z T ( ) ( ) (, ) Z[log (, ), ] L T Z L Z T dz () log (, ) (, ) 328

5 Table 1. Falure causes ad classfcato of equpmet ol feld. Falure cause Exteral factors (broke by exteral force, broke traffc offece, broke by a crashg object, etc.) Natural rsk damage (lghtg stroke damage, ar humdty, strog wd ad heavy ra, etc.) Exprato of atural lfetme of equpmet Falure type Accdetal falure Agg falure Table 2. Comparso of two cases. Scheme Data perod Data type Tmes of accdetal falure Tmes of agg falure Mxed proporto Estmato method Scheme Complete data % MLE method Scheme Blateral cesored data % EM method M step: Use () Q(, T) to calculate the dervatos of ( ab, ). Fd a pot ( 1) ( 1) ( 1) ( a, b ) to make: Q T Q T ( 1) ( ) ( ) (, ) max (, ) ( ) ( 1) Hece, the No.1 terato s completed. Iterate the above E ad M, ad stops after ( 1) ( ) hours to obta parameter ( ab, ). Thus, the estmato value of accdetal falure parameter, agg falure parameter values a ad b ca be calculated whe put equpmet gets falure data. Accordg to the three calculated parameters ad combato of Formula (6), the equpmet falure rate of ol feld equpmet ca be calculated. 5 ANALYSIS OF MIXED MODEL ALGORITHM ACCURACY OF FAILURE RATE BASED ON OIL FIELD CASES Ths secto coducted calculato aalyss of the falure rate obtaed from the complete falure recordg data of the producto & operato mechacal equpmet used a ol extracto work zoe of a brach ol feld compay of PetroCha, amg to verfy the effectveess of applyg EM algorthm as the statstcal falure rate method whch s metoed above. By statg the falure recordg data collected the ol extracto work zoe of ths ol feld ad aalyzg dfferet reasos for the falure recorded the orgal recordg data, two falure types were fgured out to expla the causes of falure: agg falure ad accdetal falure. See Table 1 for the specfc classfcato method. I order to verfy the effectveess of the falure statstcal method metoed above, two comparso schemes were desged accordg to complete recordg data. See Table 2 for the detals. As the data sze collected from the orgal falure record s huge, oly total statstcal umbers of compoet falure are gve here. Uder the two schemes as show Table 2, ebull probablty was used to ft equpmet accdetal falure data (correspodg expoetal dstrbuto ca be regarded as the ebull dstrbuto of shape parameter b=1) ad agg falure data. As degrees of fttg were both hgher tha 0.8, expoetal dstrbuto (E(t λ)) ad ebull dstrbuto ((t a,b)) ca be used to smulate these two types of falure data respectvely. 1) Comparso valdato of parameter estmato mxed dstrbuto model of equpmet falure rate MLE method was appled to process the statstcal falure data of Scheme 1 ad EM algorthm was used to process the blateral tmg cesored agg falure data of Scheme 2. See Table 3 for the results of parameter estmato. Table 3. The results of parameter estmato. Parameter Scheme 1 Scheme 2 λ a b From the results as show Table 3, t ca be see that parameter of expoetal dstrbuto λ correspodg to accdetal falure had low sestvty to statstcal tme terval of falure ad sze of falure data sample. Besdes, after processg the blateral tmg cesored data te years by EM algorthm Scheme 2, the result of the obtaed shape parameter b was close to that obtaed by MLE method Scheme 1. 2) Falure rate curves of the two schemes After brgg the results of parameter estmato calculated Table 3 to the falure rate fucto Formula (6) Secto 3.2 metoed above, the varato of the mxed falure rates correspodg to these two schemes chagg wth tme the work zoe of ths ol feld could be see ad show Fgure 3. It ca be see that the tred of the tme-varyg falure rate ths work zoe accorded wth the law of equpmet bathtub curve. Moreover, the dfferece betwee the elemet falure rate calculated Scheme 2 by applyg the statstcal falure data 10 years ad that calculated Scheme 1 by applyg the statstcal falure data 30 years s lttle, further verfyg that ths EM algorthm ca be used operatoal 329

6 Fgure 3. Mxed falure rate of ol feld equpmet uder the two cases. Fgure 4. The early warg of ol feld equpmet based o the dstrbuto of falure rate. aalyss of equpmet falure rate whe cesored data s suffcet ol-feld equpmet falure record. 6 FOREARNING MANAGEMENT OF MECHANICAL EQUIPMENT FAILURE RISK BASED ON FAILURE RATE DISTRIBUTION EM algorthm used to deal wth the serous cesored stuato of curret falure record data ol felds has bee metoed above ad, further verfcato about the feasblty of ths algorthm was made at last. The statstcal probablty results of ths algorthm ca further provde quatfcato proof for the mateace & repar cycle, scrappg, ad replacemet of mechacal equpmet ol-gas eterprses ad help chage curret equpmet maagemet patter whch s cled to daly admstratve staff s workg experece. However, there s huge workg load makg artfcal statstcs of the tremedous ad complex equpmet falure data at the ste. Therefore, the establshmet of automatzed equpmet falure rsk early warg maagemet system s eeded to obta deeper data aalyss, so as to mprove the utlzato effect of falure record data. Automatzed equpmet falure rsk early warg maagemet system maly aalyzes the equpmet falure rate dstrbuto dfferet tme cycles through the falure rate aalyss model embedded the system ad realzes the falure rate exceedg early warg by presettg precauto value. The system ca provde scetfc grouds for the equpmet mateace & repar cycle regulated by grass-roots staff ad the equpmet replacemet & scrappg strategy set by maagemet-level users. As show Fgure 4, the rsk early warg maagemet prcples of equpmet falure based o equpmet falure rate dstrbuto are show as follows: (1) he tme frame was T A, mechacal equpmet falure rate was value A ad the correspodg falure rate was obvously hgher tha average level, meag the curret mateace ad repar level s suffcet to elmate equpmet falure rsk. As a result, grass-roots staff shall coduct more routg specto ad mateace maagemet o equpmet. (2) he tme frame was T B, mechacal equpmet falure rate was value B ad the correspodg falure rate was a hgh level, meag curret agg falure probablty s hgh ad, the routg specto ad mateace maagemet coducted by grass-roots staff o equpmet caot guaratee ormal operato of equpmet. As a result, maagemet-level users eed to set up a equpmet replacemet ad scrappg pla. I combato of the dstrbuto dagram of estmated mechacal equpmet falure rate, values of correspodg tme T A ad T B ca be ferred ad, effectve rsk early warg of equpmet falure ca be realzed after grass-roots staff ad maagemet-level users cofrm the A value ad B value of equpmet falure rate. Therefore, based o the research results show ths paper, grass-roots staff 330

7 ad maagemet-level users ca make effectve use of fte data to obta prelmary aalyss of equpmet falure rate ad realze rsk early warg of equpmet falure dfferet tme frames, so as to mprove the maagemet level o mechacal equpmet used ol-gas felds. 7 CONCLUSIONS Ths paper proposed a method to estmate the falure rate of mechacal equpmet used ol ad gas felds. It ca coduct correspodg falure rate smulato based o lmted falure record. Based o the curret stuato that the statstcal tme rage of mechacal equpmet falure data used ol-gas feld eterprses s short ad the statstcal data s complete, the applcato of ths research method ca effectvely smulate the falure rate dstrbuto of mechacal equpmet varato wth tme. Ths paper proposed a rsk early warg maagemet cocept for mechacal equpmet falure ad provded scetfc grouds for the equpmet mateace & repar cycle regulated by grass-roots staff ad the equpmet replacemet & scrappg strategy set by maagemet-level users, so as to effectvely guaratee ormal operato of safety producto ol-gas feld eterprses. REFERENCES [1] Zhou, C.Y Research o the maagemet system based o relablty mateace of mechacal equpmet. Mechacal Egeer, 11: [2] ag, G.X Relablty Aalyss of Early Fault Perod ad Radom Falure Perod Machg Ceter. Dala: Dala Uversty of Techology. [3] L Icorporatg agg falures power system relablty evaluato. IEEE Tras o Power System, 17: [4] Ca, Y.Z Research o mateace decso for hghway electromechacal equpmet based o bathtub curve law. North Traffc, 10: [5] Pa, F.Q Structural lft ad developmet of cetrfugal pump. Equpmet Maufacturg Techology, 5: [6] Lg, Y Parameter Estmato of Hybrd Model. Shagha: East Cha Normal Uversty. [7] Lg, D ebull Dstrbuto Model ad Appled Research o Its Mechacal Relablty. Chegdu: Uversty of Electroc Scece ad Techology of Cha. 331