GENETIC ALGORITHMS APPLIED FOR PATTERN GENERATION FOR DOWNHOLE DYNAMOMETER CARDS

Transcription

1 GENETIC ALGORITHMS APPLIED FOR PATTERN GENERATION FOR DOWNHOLE DYNAMOMETER CARDS L. Schntman 1 ; B.C.Brandao 1 ; H.Lepkson 1 ; J.A.M. Felppe de Souza 2 ; J.F.S.Correa 3 1 Unversdade Federal da Baha- Brazl 2 Unversdade da Bera Interor, Covlhã Portugal 3 Petrobras UN-BA - Brazll lezer@ufba.br ; Bruno.Brandao@c.uncamp.br ; herman@ufba.br; ; felppe@dem.ub.pt; jfcorrea@petrobras.com.br Abstract: Rod-pumpng s a largely used technque for ol extracton. Pumpng condtons and malfunctons may be montored through downhole dynamometer cards (DC). DCs are a load vs. poston plots of the pump. Its montorng s mportant to sustan acceptable productvty levels. An automated system for DC shape classfcaton s desred for qucker response avodng producton dsturbances. PETROBRAS has such a system that reles on a set of pattern tables, whch are used to match the DCs. However, the problem of pattern dentfcaton and generaton stll remans. Ths artcle proposes a new method for patterns generatons based on genetc algorthms (GA), so that DCs can be better classfed by the used method Key-Words: recognton, genetc algorthms, pattern generaton, rod-pumpng 1. INTRODUCTION Montorng ol wells producton s a hard task whch requres several detals n order to sustan acceptable productvty levels. Rod-pumpng s one of the most used technques for ol extracton as well as DCs are one of the man tool for rod-pumpng well producton analyss. PETROBRAS has such a system that reles on a table of patterns and uses a specfc method to match the DCs. The used method operates satsfactorly, although wth a reduced number of shape types classfable. It requres one pattern for each classfable DC shape type. When tested aganst the actual table, the pattern that has the closest match s choosed to ndcate the DCs shape type. Ths artcle descrbes a new approach for pattern generaton based on genetc algorthms so that prevous results can be mproved n terms of numbers of patterns to be classfed and ther respectve accuracy. Secton 2 descrbes the set of theoretcal DCs whch are desred to be recognzed. In secton 3, the actual used method s descrbed. The concepts of GA applcaton are ntroduced n secton 4 and secton 5 presents ts applcaton. Secton 6 presents some numercal results. Conclusons are detaled n secton DOWNHOLE DYNAMOMETER CARD DCs shapes ndcate certan pumpng characterstcs or states. Those cards are acqured perodcally from the wells and stored n a database. They consst of a collecton of bdmensonal ponts, where the X axs represents the dsplacement of the pump, and the Y axs the load. The plottng begns at the lower left corner of the card, wth the pump unloaded at the bottom of the well, and goes on crcle clockwse untl the pump returns to the ntal poston. A slghtly more detaled descrpton can be found at [7]. An example of real DC data s shown n Fgure 1. Fgure 1: DC real data There are many theoretcal shapes descrbed n the lterature [1], from whch 8, as shown n Fgure 2, are the man nterest of ths artcle. All of them descrbe clearly a predomnant effect and they were selected by PETROBRAS expert engneer [1].

2 1-Normal, unanchored tubng 2-Severe flud pound 3-Severe gas nterference 4-Rod stuck by sand 5-Leakng standng valve Many combnatons of condtons and malfunctons are possble. Of course, ts classfcaton becomes more dffcult when more complex operatng condtons occurs. However, they can not be generalzed, therefore are not covered n ths artcle. 3. ACTUAL RECOGNITION METHOD The objectve of the recognton system s to classfy a certan DC data as one of the shape types prevously chosen. For that purpose pattern table s needed. For each shape type there s one pattern that s compared wth the DC data n order to generate a confdence degree. Durng operaton, the DC data s tested aganst each one of the patterns avalable so that the hghest confdence dentfes the closer shape type. The DC data may show varatons n scale and offset. Thus, the frst step s then to normalze the data. It s mportant to note that data comes wth a hgh degree of redundancy. In order to mprove tme delay, memory use and storage effcency, data are compressed by known method [2]. The man dea of the proposed method s based on varaton of drecton beyond a specfed threshold so that the orgnal plot can be approxmately reconstructed by nterpolaton methods [3]. Compressed data are called as representatve plots (RP) from now on and represents a set of (X,Y) pars that represents the man DC data. Fgure 1 presents a ddactc example of DC card whle Fgure 4 present ts reconstructon by the RP shown as red crcles when a sensblty of 15 o s used for the angle varaton detecton. 700 A crcle as a ddactc example of DC card Leakng travelng valve Pump tappng at the top Fgure 3: Ddactc example of DC card 8-Pump tappng at the bottom Fgure 2: DC patterns

3 Reconstructon based on RP Remark 1: It s mportant to note that ths s the method whch s used by PETROBRAS n real cases so that faults or benefts of the method do not compose the contents of ths paper. On the other hand, satsfactory results are descrbed by expert operators. Also, note that ts applcaton requres a known pattern table such that the problem of pattern generaton stll remans. 4. GENETIC ALGORITHM Fgure 4: Reconstructon by the RP (red crcles) Compressed data are then to be tested aganst the recognton patterns. The patterns consst of a small number of bdmensonal ponts (X,Y) and ther respectve varance (V) and relevance (R). The varance V of a pont s used to account for the dvergence between the poston of that pattern s pont poston and the closest RP. The relevance R weghts the patterns ponts so that ponts whch belongs to regons of the graph that are more sgnfcant for the shape type have hgher weght, and vce-versa. Consder P a specfc pont (X,Y) of an acqured DC. The test procedure s as follows: a) Choose a new pont P from the DC b) Fnd the pont from the RP, RP j, that has the shortest eucldean dstance D from P. Mn (D 2 = (RP j x P x) 2 + (RP j y P y) 2 ) c) Compute a partal confdence c for that pont accordng to the dstance D usng: D c = -0,5x+1 where x = V d) After performng a, b and c once for every pont n RP, compute the resultng confdence C usng the partal confdences and the relevance R of each P, R : c R C = R e) The hghest resultng confdence ndcates whch class the DC belongs to. The whole procedure can be summarzed as: - Normalze data - Compress the data extract RPs - Test aganst each pattern: compute resultng confdence for each one of them. - Choose the shape type whose pattern has gven the hghest confdence. An automatc method for pattern generaton s strongly recommended to enhance the actual method. Genetc algorthms (GA) are a search algorthm wth adequate performance, especally used when formal approach s hard to be mplemented or has no effcent results. They are nspred n the Darwn s theory of evoluton. An accessble ntroducton to GA can be found at [4][5][6]. Gven a search space, an ntal populaton (set of possble solutons) and a ftness functon used to compute the soluton performance, and adequate GA may search for regons of maxmum or mnmum, whch s supposed to hold adequate better performance wth respect to the ftness functon. The GA search method s based on the evaluaton of the populaton. It happens through crossover and mutaton by a certan number of generatons. For each generaton each chromosome (ndvdual) of the populaton has ts adaptaton degree performed by the ftness functon. Hgher degrees assocate hgher probabltes of combnng, and therefore, mantan ther characterstcs n future generatons whch has hgher survvng probablty. Ths paper uses the GA parameters: a) Populaton sze: Number of chromosomes, or ndvdual solutons. Bg values slow down sgnfcantly the evoluton; small values usually lead to premature convergence, stuaton where the algorthms get stuck at a local extreme wth probable sub-optmal solutons. b) Probablty of crossover: Assocated to the probablty of recombnaton of the chromosomes. Ths value s usually set hgh, lower values slow down the convergence. c) Probablty of mutaton: Assocated to how often the chromosome wll have hs characterstcs randomly altered. Ths value s usually kept low. Hgher values may lead to a random search. d) Populaton overlappng: Assocated to a number of ndvduals of the old generaton that should be mantaned at the new generaton. Keep the best chromosomes s a usual procedure for evolutonary purposes.

4 It s called as eltsm and guarantees that the next generaton contans at least the best soluton of the last one. 5. PATTERN GENERATION PROPOSED METHOD The problem of the pattern recognton used method s how to generate N patterns to respectve N shape types that the system should recognze through an automated way. The objectve s to be able to correctly classfy DC s types. In order to evaluate the proposed algorthm performance, a known data base s used. It has plot samples from dfferent wells and dfferent shape types and contans the normalzed acqured data of load vs. poston plots, the extracted RP and also the respectve DC type based on prevous classfcaton. Each chromosome of the GA s set to be a real number array of fxed length. Ths array s dvded n groups of four numbers, consstng of the Cartesan coordnates (X,Y), the relevance (R) and the varance (V). A set of 10 groups represents a pattern proposton. One concludes that evolvng all the patterns at the same tme would be less effcent, snce t would requre a larger populaton and the proposed algorthm convergence may be delayed. Thus, each pattern has a specfc populaton and hgher number of ndvduals s used. The proposed approach s to separately treat each pattern. However, the evoluton s done at the same tme n such way that the ndvdual result of a specfc pattern performance may be used and compared wth the other ones. The algorthm begns by testng the populaton (patterns propostons) aganst the whole database. It results a confdence table TC, whch contans the confdence values for every sample and every pattern. Each ndvdual confdence value s obtaned as explaned n secton 3. The hghest confdence value ndcates from whch type the sample s recognzed to be nto. Snce the actual type of the sample s known from the database, t s possble to evaluate rght and wrong recognton. A report table s then generated descrbng the number of DC s that are rghtly recognzed and the number that are not (see table 2 for an example). Ths way the recognton error rato s known for each pattern. The algorthm starts by pckng the pattern wth the hghest error rato and try to evolve a better one through the GA. A new populaton s created and the chosen pattern nserted n t as a chromosome. The ftness value that s actually used by the GA s evaluated as the dfference between the chromosome match rato (1-error rato) and the hghest error rato from the other N-1 patterns that are not beng evolved at the gven tme. At each generaton, every chromosome of the populaton s tested aganst every sample at the database. For each chromosome a new report table s generated. For ths, the resultng confdences for each sample are checked aganst the stored values from the other N-1 patterns n TC. Therefore a new report table s generated, wth correspondng match and error ratos of each pattern and the ftness value of each chromosome can be evaluated. The system s left evolvng untl: a) There s another pattern that has a hgher error rato. In that case, the system s set to evolve ths pattern. That s, the TC s updated wth the confdence values from the best chromosome that represents the pattern that was beng evolved prevously. Therefore the pattern s column n TC s replaced wth the new values. A new populaton s created and the new pattern nserted n t, and let, as already descrbed, evolvng. b) There have been many generatons snce the last tme a better chromosome were found. In that case, the GA seems to be stuck, and the system s set to evolve the pattern that has ncorrectly detected more DC s of the pattern that was beng evolved. A procedure smlar to a s used. For an example see table 2. Fve samples from type 1 were ncorrectly recognzed as type 6; n that case, f the system were stuck tryng to evolve the pattern 1, the pattern 6 would be set to evolve nstead. c) The system s not changng agan but b has already been attempted. In that case, a random pattern s chosen to be evolved. 6. RESULTS Prevous values for the GA parameters are used as: - 80% of crossover probablty - 0.5% mutaton probablty - populaton sze of 30 to 50 chromosomes - populaton overlap of 2 In Table 1, pattern types are assocated to Fgure 2 descrpton whle Not found means that the pattern can not be found n the used data base. Erro! A orgem da referênca não fo encontrada. presents the results when the proposed algorthm s used and prevous parameters are sets. It summarzes the obtaned results when compared wth expert knowledge stored n the Data Base. Each column

5 presents the classfcaton of the respectve DC type. For nstance, one has 1937 classfcatons of normal DCs (type 1, see Table 1) whch are classfed as pattern 1 (1930 of them), pattern 2 (2 of them) and pattern 6 (5 of them). It means that only 7 errors happened. Pattern Type Data Base Regsters Not found 5 Not found Not found TOTAL Table 1: Expert knowledge based pre-classfed Data Base 7. CONCLUSIONS A sgnfcant computatonal effort s requred for pattern generaton. On the other hand, t should not be consdered for practcal solutons. The presented algorthm s not proposed to be an on-lne tranng method. Thus, a sngle pattern table s requred for practcal mplementaton. The obtaned result shows that the algorthm performance s adequate and patterns are generated n such a way that the pattern recognton method enhances ts performance whle t tres to reproduce the human expert knowledge. It means that consderng a table of expert knowledge classfcaton, the algorthm s able do automatcally generate a table of patterns whch summarzes the expert knowledge and may be used for automatc classfcaton of DC. REFERENCES [1] Corrêa, J. F. CartaPad Cartas Dnamométrcas Padrões Apresentado no II Semnáro de Engenhara de Poço, Ro de Janero, [2] Regatter, M., Andrade Neto, M., Rocha, A. F. Results of Data Compresson for Plane Curves Usng Neural Networks Proceedngs of IEEE Neural Nets Congress, Orlando, v., p , [3] Regatter, M., Zuben, F. J. V., Rocha, A. F. Neurofuzzy Interpolaton: II Reducng Complexty of Descrpton 2nd Internatonal Conference on Neural Networks IEEE San Francsco, p , [4] Forrest, S. Genetc Algortms ACM Computng Surveys, Vol. 28, No. 1, [5] Obtko, M. Introducton to Genetc Algorthms 1998, [6] Wall, M. GAlb: A C++ Lbrary of Genetc Algorthm Components ver. 2.4 Doc. rev. B, [7] TechNote: Pump Card Shapes, echometer.com/support/technotes/pumpcards.html Recognzed Type Database Sample (DC Type) Total Error % 0,36 0,07 0,00 0,00 0,00 0,00 0,00 0,00 Table 2: Obtaned results Remark 2: Snce some types of DC are not found n the Data Base, a sngle example s artfcally generated to represents each one of them.