paper2004_faro1.pdf

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GENETIC ALGORITHMS APPLIED FOR PATTERN GENERATION FOR DOWNHOLEDYNAMOMETER CARDS

L. Schnitman1; B.C.Brandao1; H.Lepikson1; J.A.M. Felippe de Souza2; J.F.S.Correa3

1Universidade Federal da Bahia- Brazil

2Universidade da Beira Interior, Covilh Portugal

3Petrobras UN-BA - Brazill

[email protected] ; [email protected] ; [email protected]; ;[email protected];

[email protected]

Abstract: Rod-pumping is a largely used technique for oil extraction. Pumpingconditions and malfunctions may be monitored through downhole dynamometer

cards (DC). DCs are a load vs. position plots of the pump. Its monitoring isimportant to sustain acceptable productivity levels. An automated system for DC

shape classification is desired for quicker response avoiding productiondisturbances. PETROBRAS has such a system that relies on a set of pattern tables,which are used to match the DCs. However, the problem of pattern identificationand generation still remains. This article proposes a new method for patterns

generations based on genetic algorithms (GA), so that DCs can be better classifiedby the used method. Copyright @Controlo 2004.

Key-Words: recognition, genetic algorithms, pattern generation, rod-pumping

1. INTRODUCTION

Monitoring oil wells production is a hard task which

requires several details in order to sustain acceptableproductivity levels. Rod-pumping is one of the mostused techniques for oil extraction as well as DCs areone of the main tool for rod-pumping well productionanalysis.

PETROBRAS has such a system that relies on a tableof patterns and uses a specific method to match theDCs. The used method operates satisfactorily,although with a reduced number of shape typesclassifiable. It requires one pattern for eachclassifiable DC shape type. When tested against the

actual table, the pattern that has the closest match is

choosed to indicate the DCs shape type. This articledescribes a new approach for pattern generationbased on genetic algorithms so that previous resultscan be improved in terms of numbers of patterns tobe classified and their respective accuracy.

Section 2 describes the set of theoretical DCs whichare desired to be recognized. In section 3, the actualused method is described. The concepts of GAapplication are introduced in section 4 and section 5presents its application. Section 6 presents somenumerical results. Conclusions are detailed in section

7.

2. DOWNHOLE DYNAMOMETER CARD

DCs shapes indicate certain pumping characteristicsor states. Those cards are acquired periodically from

the wells and stored in a database. They consist of acollection of bidimensional points, where the X axisrepresents the displacement of the pump, and the Yaxis the load. The plotting begins at the lower leftcorner of the card, with the pump unloaded at thebottom of the well, and goes on circle clockwise until

the pump returns to the initial position. A slightlymore detailed description can be found at [7]. Anexample of real DC data is shown in Figure 1.

Figure 1: DC real data

There are many theoretical shapes described in theliterature [1], from which 8, as shown in Figure 2, arethe main interest of this article. All of them describe

clearly a predominant effect and they were selectedby PETROBRAS expert engineer [1].


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1-Normal, unanchored tubing

2-Severe fluid pound

3-Severe gas interference

4-Rod stuck by sand

5-Leaking standing valve

6-Leaking traveling valve

7-Pump tapping at the top

8-Pump tapping at the bottom

Figure 2: DC patterns

Many combinations of conditions and malfunctionsare possible. Of course, its classification becomesmore difficult when more complex operatingconditions occurs. However, they can not be

generalized, therefore are not covered in this article.

3. ACTUAL RECOGNITION METHOD

The objective of the recognition system is to classifya certain DC data as one of the shape typespreviously chosen. For that purpose pattern table is

needed.

For each shape type there is one pattern that iscompared with the DC data in order to generate aconfidencedegree. During operation, the DC data istested against each one of the patterns available so

that the highest confidenceidentifies the closer shape

type.

The DC data may show variations in scale and offset.Thus, the first step is then to normalize the data. It isimportant to note that data comes with a high degree

of redundancy. In order to improve time delay,memory use and storage efficiency, data are

compressed by known method [2]. The main idea ofthe proposed method is based on variation ofdirection beyond a specified threshold so that theoriginal plot can be approximately reconstructed by

interpolation methods [3]. Compressed data arecalled as representative plots (RP) from now on and

represents a set of (X,Y) pairs that represents themain DC data.

Figure 1 presents a didactic example of DC cardwhile Figure 4 present its reconstruction by the RPshown as red circles when a sensibility of 15ois used

for the angle variation detection.

300 350 400 450 500 550 600 650 700300

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600

650

700A circle as a didactic example of DC card

Figure 3: Didactic example of DC card


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Reconstruction based on RP

Figure 4: Reconstruction by the RP (red circles)

Compressed data are then to be tested against therecognition patterns. The patterns consist of a smallnumber of bidimensional points (X,Y) and their

respective variance (V) and relevance (R). Thevariance V of a point is used to account for the

divergence between the position of that patternspoint position and the closest RP. The relevance Rweights the patterns points so that points whichbelongs to regions of the graph that are moresignificant for the shape type have higher weight, andvice-versa.

Consider Pi a specific point (X,Y) of an acquiredDC. The test procedure is as follows:

a) Choose a new point Pifrom the DC

b) Find the point from the RP, RPj,that has theshortest euclidean distance Difrom Pi.Min (Di

2= (RPjx Pix)

2+ (RPjy Piy)

2)

c) Compute a partial confidence ci for thatpoint according to the distance Diusing:

ci= -0,5x+1 where

i

i

V

Dx =

d) After performing a, band conce for everypoint in RP, compute the resulting

confidence C using the partial confidencesand the relevance Riof each Pi, Ri:

=

i

i

iii

R

RcC

e) The highest resulting confidence indicateswhich class the DC belongs to.

The whole procedure can be summarized as:- Normalize data- Compress the data extract RPs- Test against each pattern: compute resulting

confidence for each one of them.- Choose the shape type whose pattern has given

the highest confidence.

Remark 1: It is important to note that this is the

method which is used by PETROBRAS in real cases

so that faults or benefits of the method do not

compose the contents of this paper. On the other

hand, satisfactory results are described by expert

operators. Also, note that its application requires a

known pattern table such that the problem of patterngeneration still remains.

4. GENETIC ALGORITHM

An automatic method for pattern generation is

strongly recommended to enhance the actual method.

Genetic algorithms (GA) are a search algorithm withadequate performance, especially used when formalapproach is hard to be implemented or has noefficient results. They are inspired in the Darwins

theory of evolution. An accessible introduction to

GA can be found at [4][5][6].

Given a search space, an initial population (set ofpossible solutions) and a fitness function used tocompute the solution performance, and adequate GA

may search for regions of maximum or minimum,which is supposed to hold adequate better

performance with respect to the fitness function. TheGA search method is based on the evaluation of thepopulation. It happens through crossover andmutation by a certain number of generations. For

each generation each chromosome (individual) of thepopulation has its adaptation degree performed by the

fitness function. Higher degrees associate higherprobabilities of combining, and therefore, maintaintheir characteristics in future generations which hashigher surviving probability.

This paper uses the GA parameters:

a) Population size: Number of chromosomes,or individual solutions. Big values slowdown significantly the evolution; smallvalues usually lead to prematureconvergence, situation where the algorithmsget stuck at a local extreme with probable

sub-optimal solutions.

b) Probability of crossover: Associated to theprobability of recombination of thechromosomes. This value is usually sethigh, lower values slow down theconvergence.

c) Probability of mutation: Associated to howoften the chromosome will have hischaracteristics randomly altered. This valueis usually kept low. Higher values may leadto a random search.

d) Population overlapping: Associated to anumber of individuals of the old generation

that should be maintained at the new

generation. Keep the best chromosomes is ausual procedure for evolutionary purposes.


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It is called as elitismand guarantees that thenext generation contains at least the bestsolution of the last one.

5. PATTERN GENERATION PROPOSEDMETHOD

The problem of the pattern recognition used methodis how to generate Npatterns to respective N shapetypes that the system should recognize through anautomated way. The objective is to be able tocorrectly classify DCs types.

In order to evaluate the proposed algorithm

performance, a known data base is used. It has 6.428plot samples from different wells and different shapetypes and contains the normalized acquired data ofloadvs.positionplots, the extracted RP and also the

respective DC type based on previous classification.

Each chromosome of the GA is set to be a realnumber array of fixed length. This array is divided ingroups of four numbers, consisting of the Cartesiancoordinates (X,Y), the relevance (R) and the variance

(V). A set of 10 groups represents a patternproposition.

One concludes that evolving all the patterns at thesame time would be less efficient, since it wouldrequire a larger population and the proposed

algorithm convergence may be delayed. Thus, eachpattern has a specific population and higher number

of individuals is used. The proposed approach is toseparately treat each pattern. However, the evolutionis done at the same time in such way that theindividual result of a specific pattern performancemay be used and compared with the other ones.

The algorithm begins by testing the population(patterns propositions) against the whole database. Itresults a confidence table TC, which contains theconfidence values for every sample and everypattern. Each individual confidence value is obtainedas explained in section 3.

The highest confidence value indicates from whichtype the sample is recognized to be into. Since theactual type of the sample is known from the database,it is possible to evaluate right and wrong recognition.A report table is then generated describing the

number of DCs that are rightly recognized and thenumber that are not (see table 2 for an example). Thisway the recognition error ratio is known for eachpattern.

The algorithm starts by picking the pattern with thehighest error ratio and try to evolve a better one

through the GA. A new population is created and the

chosen pattern inserted in it as a chromosome. Thefitness value that is actually used by the GA is

evaluated as the difference between the chromosomematch ratio (1-error ratio) and the highest error ratiofrom the otherN-1patterns that are not being evolvedat the given time.

At each generation, every chromosome of the

population is tested against every sample at thedatabase. For each chromosome a new report table isgenerated. For this, the resulting confidences for eachsample are checked against the stored values fromthe otherN-1patterns in TC. Therefore a new report

table is generated, with corresponding match anderror ratios of each pattern and the fitness value of

each chromosome can be evaluated.

The system is left evolving until:a) There is another pattern that has a higher

error ratio. In that case, the system is set toevolve this pattern. That is, the TC is

updated with the confidence values from thebest chromosome that represents the patternthat was being evolved previously.Therefore the patterns column in TC is

replaced with the new values. A newpopulation is created and the new pattern

inserted in it, and let, as already described,evolving.

b) There have been many generations since thelast time a better chromosome were found.

In that case, the GA seems to be stuck, andthe system is set to evolve the pattern that

has incorrectly detected more DCs of the

pattern that was being evolved. A proceduresimilar to a is used. For an example seetable 2. Five samples from type 1 wereincorrectly recognized as type 6; in that

case, if the system were stuck trying toevolve the pattern 1, the pattern 6 would beset to evolve instead.

c) The system is not changing again but bhas already been attempted. In that case, arandom pattern is chosen to be evolved.

6. RESULTS

Previous values for the GA parameters are used as:- 80% of crossover probability- 0.5% mutation probability- population size of 30 to 50 chromosomes- population overlap of 2

In Table 1, pattern types are associated to Figure 2description while Not found means that the patterncan not be found in the used data base.

Erro! A origem da referncia no foi encontrada.presents the results when the proposed algorithm is

used and previous parameters are sets. It summarizes

the obtained results when compared with expertknowledge stored in the Data Base. Each column


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presents the classification of the respective DC type.For instance, one has 1937 classifications of normalDCs (type 1, see Table 1) which are classified aspattern 1 (1930 of them), pattern 2 (2 of them)and pattern 6 (5 of them). It means that only 7

errors happened.

PatternType

Data Base

Registers

1 1.937

2 4.342

3 17

4 Not found

5 Not found

6 84

7 48

8 Not found

TOTAL 6.428Table 1: Expert knowledge based pre-classified

Data Base

7. CONCLUSIONS

A significant computational effort is required forpattern generation. On the other hand, it should notbe considered for practical solutions. The presented

algorithm is not proposed to be an on-line trainingmethod. Thus, a single pattern table is required forpractical implementation.

The obtained result shows that the algorithmperformance is adequate and patterns are generated in

such a way that the pattern recognition methodenhances its performance while it tries to reproducethe human expert knowledge.

It means that considering a table of expert knowledgeclassification, the algorithm is able do automaticallygenerate a table of patterns which summarizes theexpert knowledge and may be used for automaticclassification of DC.

REFERENCES

[1] Corra, J. F. CartaPad CartasDinamomtricas Padres Apresentado no IISeminrio de Engenharia de Poo, Rio de Janeiro,

1998.

[2] Regattieri, M., Andrade Neto, M., Rocha, A. F.

Results of Data Compression for PlaneCurves Using Neural Networks Proceedingsof IEEE Neural Nets Congress, Orlando, v. , p.

1691-1694, 1994.

[3] Regattieri, M., Zuben, F. J. V., Rocha, A. F.Neurofuzzy Interpolation: II ReducingComplexity of Description 2nd InternationalConference on Neural Networks IEEE San

Francisco, p. 1835-1840, 1993.[4] Forrest, S. Genetic Algoritms ACM

Computing Surveys, Vol. 28, No. 1, 1996.

[5] Obitko, M. Introduction to GeneticAlgorithms 1998,

http://cs.felk.cvut.cz/~xobitko/ga

[6] Wall, M. GAlib: A C++ Library of Genetic

Algorithm Componentsver. 2.4 Doc. rev. B,1996.

[7] TechNote: Pump Card Shapes, http://www.

echometer.com/support/technotes/pumpcards.html

Database Sample (DC Type)

Recognized

Type

1 2 3 4 5 6 7 8

1 1930

2 2 4339

3 174 1

5 1 1

6 5 2 84

7 48

8 1

Total 1937 4342 17 1 1 84 48 1

Error 7 3 0 0 0 0 0 0

% 0,36 0,07 0,00 0,00 0,00 0,00 0,00 0,00

Table 2: Obtained results

Remark 2: Since some types of DC are not found in the Data Base, a single example is artificially generated torepresents each one of them.

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