research article modeling and optimization of beam pumping

Research ArticleModeling and Optimization of Beam Pumping System Based onIntelligent Computing for Energy Saving

Xiaohua Gu1 Taifu Li1 Zhiqiang Liao2 Liping Yang3 and Ling Nie1

1 Department of Electrical and Information Engineering Chongqing University of Science and TechnologyChongqing 401331 China

2 College of Electronic Engineering Xirsquoan Shiyou University Xirsquoan 710065 China3 College of Optoelectronic Engineering Chongqing University Chongqing 400044 China

Correspondence should be addressed to Xiaohua Gu xhgucqueducn

Received 17 November 2013 Accepted 2 April 2014 Published 14 April 2014

Academic Editor Olabisi Falowo

Copyright copy 2014 Xiaohua Gu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Beam pumping system which is widely used in petroleum enterprises of China is one of the most energy-consuming equipment Itis difficult to bemodeled and optimized due to its complication and nonlinearity To address this issue a novel intelligent computingbased method is proposed in this paper It firstly employs the general regression neural network (GRNN) algorithm to obtain thebest model of the beam pumping system and secondly searches the optimal operation parameters with improved strength Paretoevolutionary algorithm (SPEA2) The inputs of GRNN include the number of punching the maximum load the minimum loadthe effective stroke and the computational pump efficiency while the outputs are the electric power consumption and the oil yieldExperimental results show that there is good overlap between model estimations and unseen data Then sixty-one sets of optimumparameters are found based on the obtained model Also the results show that under the optimum parameters more than 534oil yield is obtained and more than 375 of electric power consumption is saved

1 Introduction

Beampumping system is one of themost important oil recov-ery equipment in China the occupancy of which reaches to70 [1] However its system efficiency is very low due to thenegative torque long gear train poor working conditionsand other reasons Researching the energy saving of beampumping system is very important and necessary [2]

Improving the structure of the beam pumping unit is akind of effective methods for energy saving [3 4] Throughoptimizing of the four-bar linkage design and improvingthe balance system the fluctuation of the net torque curvebecomes flat and the loading coefficient of beam pumpingunit is reduced which leads to the increasing of motorrsquosefficiency Nonsynchronous crank balance beam pumpingunit and secondary balanced beam pumping unit are thetypical cases It is reported that the nonsynchronous crankbalance beam pumping unit can save 3sim4 energy in someconditions and the secondary balanced beam pumping unit

can save 14 energy However they are not always energy-saving and their energy-saving levels are related to theworking conditions For instance if the balance parametersare not adjusted properly the efficiency of the secondarybalanced beam pumping unit should not be increasing

Changing the working characteristic of the motor isanother solution of this issue [5ndash8] This way is representedby high-slip motor and ultrahigh-slip motor Under the sameworking condition of the well the average of the power-current curve of ultrahigh-slip motor is much less thanthat of conventional-slip motor The curve is flatter andconsequently the cyclic loading coefficient is greatly reducedand the efficiency of the beam pumping unit is increasedHowever since the efficiency of the high-slip motor is lowerthan that of the conventional-slip motor there is a smallamount of space to cut down the energy consumption andthe energy-saving effect is remarkable only in the light-loadconditions

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2014 Article ID 317130 7 pageshttpdxdoiorg1011552014317130

2 Journal of Applied Mathematics

Ground surface

Beam-pumping unit

Pump

Oil

Liquid face level

Figure 1 The schematic diagram of beam pumping system

The aforementioned two ways which try to improve themechanical or electrical structures of the beam pumpingsystem need large investment and long time It will be moreeconomical to reduce the energy consumption based on theexisting system by optimizing the operation parameters

Only if we can build accurate and reliable process opti-mization model the optimization of operation parameteris meaningful Artificial neural network (ANN) modelingbecause of its strong nonlinear approximation ability issuitable for large-scale parallel processing and complexor unknown mechanism problems [9] Since the beampumping system is very complicated in nature mainly dueto unknown dynamic behaviors nonlinear relations andnumerous involved variables In this paper we proposed tobuild beam pumping system model by general regressionneural network (GRNN) Then to identify the optimumoperating parameters multi-object optimization problem ofminimizing the electric power consumption andmaximizingthe oil yield is solved by strength Pareto evolutionary algo-rithm (SPEA2)

The rest of this paper is organized as follows Section 2briefly introduces the beam pumping system Section 3presents the proposed modeling and optimization methodfor beam pumping systemrsquos energy saving Experimentalresults and discussions are given in Section 4 The conclu-sions are finally drawn in Section 5

2 A Sketch of Beam Pumping System

Beam pumping unit is the widely used traditional pumpingequipment A simple beam pumping system is sketchedin Figure 1 The unit and motor at the surface supply theoscillating motion to the sucker and so to the pump Andthe downhole oil is carried to the ground by the pump Ina rush time the motor works in electrical state or generateselectricity state respectively when the sucker is up or down

The reservoirs are extremely complex including rich oillean oil thin oil and thickened oil The unit is impossible towork in constant speed Additionally there are many factsinfluencing the capacity and energy consumption of the oilpump such as the leakage between the worn piston and thebush and the polytropic stratum elements It is hard or evenimpossible to develop an accurate mathematical model This

Table 1 Parameters used for modeling

Inputs Outputs parametersDecision parameter NP (timemin) EPC (kwh)

Environment parameters

MAXL (kN)MINL (kN)

OY (td)ES (m)CPE ()

paper tries to find the potential law of the beam pumpingsystem by the history production data and then utilize the lawto improve the yield and save the energy consumption

3 Modeling and Optimization ofBeam Pumping System

Different from the mechanical structure or electrical struc-ture modification method needs to replace the originalequipment the solution in this paper is to make the systemwork under the optimal operation parameters which areobtained by intelligent computing method based on thehistory production data of the original equipment

As the analysis in Section 2 the beam pumping systemis complicated and nonlinear Its energy consumption isinfluenced by many factors We first select the decisionparameter and environment parameters and then a GRNNmodel is built up to simulate the beam pumping system andfinally the optimization problem according to saving energyis constructed and solved by SPEA2 algorithm

31 Parameters Selection Themonitored parameters of beampumping system usually contain three-phase voltage three-phase current maximum load the minimum load theo-retical pumpage computational pump efficiency effectivestroke number of punching power factor average powerfactor average active power average reactive power electricpower consumption and oil yield for the example of DaGangoilfield of China Obviously the first eight parameters arerelated to the system status while the rest are related to thesystem efficiency

In these parameters the number of punching (NP) isadjustable and directly related to the status of the beampumping unit It is quite important to the energy consump-tion and the oil yield Consequently we selected it as thedecision parameter Moreover it is not hard to find thatsome of these parameters show close relationship In otherword there is redundancy in the parameters Using all theparameters to model will increase the complexity of algo-rithm as well as reduce the reliability of themodel By analysisof their interrelation we finally choose the maximum load(MAXL) the minimum load (MINL) the effective stroke(ES) and the computational pump efficiency (CPE) as theenvironment parameters and the electric power consumption(EPC) and the oil yield (OY) as the evaluation criterions Allthe parameters used in modeling are shown in Table 1

Journal of Applied Mathematics 3

NP

MAXL

MINL

ES

CPE

EPC

OY

Input layer

Pattern layer

Summation layer

Output layer

Figure 2 GRNNmodel of the beam pumping system

32 Modeling of Beam Pumping System GRNN [10] whichevolved from probabilistic neural network (PNN) [11]belongs to the forward neural networks It has many advan-tages (1) strong nonlinear mapping ability and high error-tolerance (2) strong approaching ability and high learningspeed (3) good performance for the small sample sizeproblem and (4) strong ability to deal with unstable data SoGRNN is quite suitable tomodel the complex nonlinear beampumping system

As Figure 2 shows the GRNN model of beam pumpingsystem comprises of four layers namely input layer patternlayer summation layer and output layer The input neuronsin the first layer are distribution neurons which assigned allthe measured values of X where X = x

1 x2 x

119899 x119894=

(119909

1

119894 119909

2

119894 119909

119901

119894)

119879 119899 is the number of samples and 119901 is thedimension of samples

Most processing is done in the pattern layer and thesummation layer The number of neurons of pattern layer isequal to the number of training samples 119899 and the transformfunction is shown as the following formula

119905

119894= exp[minus

(X minus 120601

119909

119894)

119879

(X minus 120601

119909

119894)

2120590

2] 119894 = 1 2 119899 (1)

where X is the input vector of training sample 120601119909119894is the

input portion of the 119894th training vector represented by the 119894thneuron in the pattern layer and120590 is the smoothing parameterwhich can be adjusted to provide different levels of functionsmoothing Larger values for 120590 cause smoother estimatedfunction

In summation layer arithmetic summations andweighted summations are performed in the neurons Thearithmetic summation of the output value of all pattern layerunits is

119904

119863=

119899

sum

119894=1

119905

119894 (2)

And the weighted summation of the output value of allpattern layer units is

119904

119873119895=

119899

sum

119894=1

119910

119894119895119905

119894 119895 = 1 2 119901 (3)

where119910119894119895is the weight between the 119894th neuron of pattern layer

and the 119895th neuron of summation layer it is equal to the 119895thcomponent of the output vector y

119894of the 119894th training sample

The number of output layer neuron 119904 equals the dimen-sion of output vector of training sample and every neurondivides the output values of summation layer namely

119910

119895=

119904

119873119895

119904

119863

119895 = 1 2 119901 (4)

where 119910119895is the estimation value of 119895th component of output

vector of forecasting sample

33 SPEA2 Optimization of Parameters Once the GRNNmodel of the beam pumping unit production system modelis developed it can be used to obtain the optimal values ofthe input variables SPEA2 [12] is an improved version of thestrengthPareto evolutionary algorithm (SPEA) also proposedby Zitzler andThiele [13] in 1999 It is a multiobjective evolu-tionary algorithm characterized by the concepts of strengthand density Compared to SPEA SPEA2 has an improvedfitness assignment strategy and hence can search the globaloptimum of all objective functions Consequently SPEA2becomes one of the most popular optimization techniques innonlinear multiobjective combinatorial optimization prob-lems In this paper the optimization problem for energysaving is solved using SPEA2 algorithm

The objective functions are

119910EPC = min 119869EPC = 119891 (119909NP 119909MAXL 119909MINL 119909ES 119909CPE)

119910OY = max 119869OY = 119891 (119909NP 119909MAXL 119909MINL 119909ES 119909CPE) (5)

Considering that SPEA2 always searches the minimumfitness themaximumobjective is converted tominimumoneby taking its negative Finally the multiobjective problemof the beam pumping system energy saving is described asfollows

119910 = min 119869 (119909) = min (1198691(119909) minus119869

2(119909)) (6)

In the above expression it has

119909 = (119909NP 119909MAXL 119909MINL 119909ES 119909CPE) isin 119883

119910 = (119910EPC minus119910OY) isin 119884

119883 = (119909

1 119909

2 119909

119899) | 119897

119894le 119909

119894le 119906

119894 119894 = 1 2 5

119871 = (119897

1 119897

2 119897

5)

119880 = (119906

1 119906

2 119906

5)

(7)

where 119871 and 119880 are the lower and the upper boundaries ofoptimal parameters respectively


Table 2 Instances of experiment data from a certain oilfield

Number NP MAXL MINL ES CPE EPC OY1 301 972 447 30746 692602 1197 31052 299 973 449 32502 731920 1200 32873 297 1032 426 30683 707739 1337 3065

Evolutionary search

Optimal design

Designs

Approximate performance

Approximate modelSamples

Real problem

GRNN modeling SPEA2 optimization

Figure 3 Framework of GRNN-SPEA2 strategy

The main loop of the SPEA2 algorithm is as follows

Step 1 119894 = 0 initialize population 119875

0and set archive

population 119875

1015840

0= 0

Step 2 Function evaluation calculate fitness values of allindividuals in 119875

119894cup 119875

1015840

119894

Step 3 Environmental selection copy all nondominatedindividuals in 119875

119894and 119875

1015840

119894to 119875

1015840

119894+1 If size of 1198751015840

119894+1exceeds 119873

(archive size) then reduce 119875

1015840

119894+1by means of the truncation

operator otherwise if size of 1198751015840119894+1

is less than119873 then fill 1198751015840119894+1

with dominated individuals in 119875

119894and 119875

1015840

119894+1

Step 4 Termination if stopping criterion (maximum gener-ations) is satisfied set 119875final = 119875

119894+1and terminate

Step 5 Perform tournament selection with replacement on119875

1015840

119894+1to fill the mating pool Apply recombination and muta-

tion operators to the mating pool and set 1198751015840119894+1

to the resultingpopulation

Step 6 119894 = 119894 + 1 go to Step 2

34 GRNN-SPEA2 Strategy To obtain the optimal parame-ters the modeling and the optimization procedure shouldbe combined The framework of GRNN-SPEA2 strategy isbriefly illustrated in Figure 3

The procedure can be briefly described as follows asapproximating themodel of the real problemGRNN is devel-oped with certain calculated algorithm based on experimentdata The SPEA2 is applied to explore good solutions amongsolution spaces Once the SPEA2 generates a new solutionthe GRNN will be used to determine its fitness value for theSPEA2 to continue its searching process Until the SPEA2satisfies certain termination criterion the strategy will export

Table 3 MSE and RE of GRNNmodel

Performance index EPC OY119864MS 00336 00951119864

11987700148 00071

the best solution and its performance determined by detailevaluation based on real problem

4 Experimental Results and Analysis

41 Experimental Data The proposed method is evaluatedby real production data from a certain oilfield Experimentsemploy 3234 samples which recorded the production statusof 8 beam pumping wells from 612011 to 10182011 Severalinstances of the dataset are listed in Table 2

To void the influence caused by the difference betweenthe absolute values of different parameters the data werenormalized to the range of [minus1 1] before used to model

42 GRNN Modeling In the GRNN modeling process thedata is divided randomly into two subsets one is used totrain the model called training set and the other one is usedevaluate the model called test setThe training set and test setcontain 3150 samples and 84 samples respectively Figure 4shows the comparison of the predicted objectives and the realobjectives

It can be seen from Figure 4 that the predicted values andthe real ones are very close To show the diversitymore clearlythe percentage errors of EPC and OY by GRNN model areshown in Figure 5 From Figure 5 we find that the absolutepercentage error of EPC is less than 005 while that of OYis less than 004 which indicates that the obtained GRNNmodel gets nice description of the real model

Also the commonly used mean square error (MSE) andrelative error (RE) whose formula is given in (8) are used to


0 10 20 30 40 50 60 70 80 906

8

10

12

14

16

18

Sample

EPC

(kwmiddoth

)

PredictedObserved

(a)

0 10 20 30 40 50 60 70 80 90Sample

PredictedObserved

20

25

30

35

40

45

50

55

Yiel

d (t

d)

(b)

Figure 4 Comparison of the predicted and real objectives of GRNNmodel (a) EPC and (b) OY

0 10 20 30 40 50 60 70 80 90

0

001

002

003

004005

Sample

minus001

minus002

EPC

erro

r (

)

(a)

0 10 20 30 40 50 60 70 80 90Sample

0

002

004

Yiel

d er

ror (

)

minus004

minus002

(b)

Figure 5 The percentage error of GRNNmodel

further verify the performance of the model The result is asshown in Table 3 Consider

119864MS =radic

sum (119910 minus 119909)

2

119899 minus 1

119864

119877= sum(

1003816

1003816

1003816

1003816

y minus x1003816100381610038161003816

x)

(8)

where x is the observed value and y is the prediction value 119899is the dimensionality of x and y

From the simulation results it can be found that thesimulated values match well with the measured values Thisproves that the GRNN model of beam pumping system isstable and reliable and could be regarded as a knowledgesource for follow-up parameters optimization

43 Optimal Parameters Searching by SPEA2 As discussed inSection 33 the searching boundaries should be set at first Itis not difficult to understand that the parameters should notfluctuate too drastically and then using the statistical rangeof each parameter as the boundary will be reasonable Theboundaries of the five inputs are shown in Table 4

In experiments the initial population is set to 50Then themaximum generations are set to 20 50 100 and 200 respec-tively to find the optimum generation Figure 6 illustrates theresult of Pareto frontiers when the maximum generation is20 50 100 and 200 respectively From Figure 6 it can beseen that when the maximum generation is 100 the Paretofront is basically stable And hence we set the generation to100 In this case there are 61 sets of optimum solutions Someinstances of the optimum solutions are shown in Table 5

From Table 5 we find that the optimal number of punch-ing is bigger than the original setting which confirms withthe fact that big number of punching will achieve high systemefficiency Comparing the optimized results and the originaldata there are above 375 decreasing of the electric powerconsumption and above 534 increasing of the oil yieldIt verifies the correctness of obtaining optimum decisionparameters

5 Conclusions

This paper presents a novel way to saving the energy con-sumption of beam pumping system by general regressionneural network modeling and improved strength Pareto


107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(a)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Pareto front

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(b)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(c)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(d)

Figure 6 SPEA2 Pareto frontier when the maximum generations are 20 50 100 and 200 (a) Maximum generation is 20 (b) maximumgeneration is 50 (c) maximum generation is 100 and (d) maximum generation is 200

Table 4 Searching boundaries of the parameters

Boundary NP MAXL MINL ES EPCUpper 25 933 423 31 71Lower 35 935 425 32 72

Table 5 Instances of solutions of Pareto optimal set

Number NP (timemin) MAXL (kN) MINL (kN) ES (m) CPE () EPC (kw) OY (td)1 329 933 423 31034 712198 111938 35892 329 934 423 31029 710810 115908 37513 329 935 423 31030 713858 113190 36374 331 935 425 31999 719633 113349 3648

61 328 933 423 31000 713138 110982 3554

evolutionary optimizationThis method need not modify theoriginal equipment but just tries tomake the equipment workin energy-saving status Experimental results on 3234 realsamples from a certain oilfield show that the performanceof the beam pumping system is significantly improved afterusing the optimum parameters Specifically the electricpower consumption decreases more than 375 and the oilyield increases more than 534 It verified that the proposedmethod is an alternative effective solution for energy savingof oilfield

This paper puts forward a feasible solution for the inten-sive production of oilfiled however the achieved result is nota determinate solution but a set of Parato fronts How to findthe robust optimal solution to guide the production will beour future research direction

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


Acknowledgments

Thanks are due to the support byChongqingNational ScienceFoundation (cstc2013jcyA40044) National Natural ScienceFoundation of China (51375520) and Research Founda-tion of Chongqing University of Science and Technology(CK2011B06 and CK2013Z11)

References

[1] L P Bai W Z Ma and Y Yang ldquoThe discussing of energy-saving of motor for beam balanced pumprdquo Oil Machinery vol27 no 3 pp 41ndash44 1999

[2] D S Su X G Liu and W X Lu ldquoOverview of energy-savingmechanismof beam-balanced pumprdquoOilMachinery vol 19 no5 pp 49ndash63 2001

[3] J Zhu J Q Ruan and H F Sun ldquoComparative test study ofenergy-saving pumping and their effectrdquo Oil Field Equipmentvol 35 no 3 pp 60ndash62 2006

[4] D-MGuo F Guan Y-M Zhu andY-Z Liu ldquoImproved designof CYJY12-4 8-73HB offset pumping unit supportrdquo Journal ofJianghan Petroleum Institute vol 27 no 2 pp 258ndash260 2005

[5] Y H Gu W S Xiao X X Zhou S C Zhang and Y H JinldquoFull scale test of ZXCY-Series linear motor pumping unitsrdquoPetroleum Exploration and Development vol 35 no 3 pp 366ndash372 2008

[6] W Li Q Yi J Cao and L Li ldquoThe optimization calculation andanalysis of energy-saving motor used in beam-pumping unitbased on continuous quantum particle swarm optimizationrdquoin Proceedings of the International Conference on Power SystemTechnology (POWERCON rsquo10) pp 1ndash8 2010

[7] M V O Corpoven ldquoReal time expert system (RTES) for rodpumping optimizationrdquo in Proceedings of the Petroleum Com-puter Conference pp 53ndash60 Society of Petroleum Engineers(SPE) Houston Tex USA June 1995

[8] W-G Qi X-L Zhu and Y-L Zhang ldquoStudy of fuzzy neuralnetwork control of energy-saving of oil pumprdquo Proceedings ofthe Chinese Society of Electrical Engineering vol 24 no 6 pp137ndash140 2004

[9] G Zahedi F Parvizian andM R Rahimi ldquoAn expert model forestimation of distillation sieve tray efficiency based on artificialneural network approachrdquo Journal of Applied Sciences vol 10no 12 pp 1076ndash1082 2010

[10] D F Specht ldquoA general regression neural networkrdquo IEEETransactions onNeural Networks vol 2 no 6 pp 568ndash576 1991

[11] D F Specht ldquoProbabilistic neural networksrdquo Neural Networksvol 3 no 1 pp 109ndash118 1990

[12] E Zitzler M Laumanns and L Thiele ldquoSPEA2 improvingthe strength pareto evolutionary algorithm for multi-objectiveoptimizationrdquo in Evolutionary Methods for Design Optimisa-tions and Control Swiss Federal Institute of Technology ZurichSwitzerland 2001

[13] E Zitzler and L Thiele ldquoMultiobjective evolutionary algo-rithms a comparative case study and the strength Paretoapproachrdquo IEEETransactions onEvolutionaryComputation vol3 no 4 pp 257ndash271 1999

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Ground surface

Beam-pumping unit

Pump

Oil

Liquid face level

Figure 1 The schematic diagram of beam pumping system

The aforementioned two ways which try to improve themechanical or electrical structures of the beam pumpingsystem need large investment and long time It will be moreeconomical to reduce the energy consumption based on theexisting system by optimizing the operation parameters

Only if we can build accurate and reliable process opti-mization model the optimization of operation parameteris meaningful Artificial neural network (ANN) modelingbecause of its strong nonlinear approximation ability issuitable for large-scale parallel processing and complexor unknown mechanism problems [9] Since the beampumping system is very complicated in nature mainly dueto unknown dynamic behaviors nonlinear relations andnumerous involved variables In this paper we proposed tobuild beam pumping system model by general regressionneural network (GRNN) Then to identify the optimumoperating parameters multi-object optimization problem ofminimizing the electric power consumption andmaximizingthe oil yield is solved by strength Pareto evolutionary algo-rithm (SPEA2)

The rest of this paper is organized as follows Section 2briefly introduces the beam pumping system Section 3presents the proposed modeling and optimization methodfor beam pumping systemrsquos energy saving Experimentalresults and discussions are given in Section 4 The conclu-sions are finally drawn in Section 5

2 A Sketch of Beam Pumping System

Beam pumping unit is the widely used traditional pumpingequipment A simple beam pumping system is sketchedin Figure 1 The unit and motor at the surface supply theoscillating motion to the sucker and so to the pump Andthe downhole oil is carried to the ground by the pump Ina rush time the motor works in electrical state or generateselectricity state respectively when the sucker is up or down

The reservoirs are extremely complex including rich oillean oil thin oil and thickened oil The unit is impossible towork in constant speed Additionally there are many factsinfluencing the capacity and energy consumption of the oilpump such as the leakage between the worn piston and thebush and the polytropic stratum elements It is hard or evenimpossible to develop an accurate mathematical model This

Table 1 Parameters used for modeling

Inputs Outputs parametersDecision parameter NP (timemin) EPC (kwh)

Environment parameters

MAXL (kN)MINL (kN)

OY (td)ES (m)CPE ()

paper tries to find the potential law of the beam pumpingsystem by the history production data and then utilize the lawto improve the yield and save the energy consumption

3 Modeling and Optimization ofBeam Pumping System

Different from the mechanical structure or electrical struc-ture modification method needs to replace the originalequipment the solution in this paper is to make the systemwork under the optimal operation parameters which areobtained by intelligent computing method based on thehistory production data of the original equipment

As the analysis in Section 2 the beam pumping systemis complicated and nonlinear Its energy consumption isinfluenced by many factors We first select the decisionparameter and environment parameters and then a GRNNmodel is built up to simulate the beam pumping system andfinally the optimization problem according to saving energyis constructed and solved by SPEA2 algorithm

31 Parameters Selection Themonitored parameters of beampumping system usually contain three-phase voltage three-phase current maximum load the minimum load theo-retical pumpage computational pump efficiency effectivestroke number of punching power factor average powerfactor average active power average reactive power electricpower consumption and oil yield for the example of DaGangoilfield of China Obviously the first eight parameters arerelated to the system status while the rest are related to thesystem efficiency

In these parameters the number of punching (NP) isadjustable and directly related to the status of the beampumping unit It is quite important to the energy consump-tion and the oil yield Consequently we selected it as thedecision parameter Moreover it is not hard to find thatsome of these parameters show close relationship In otherword there is redundancy in the parameters Using all theparameters to model will increase the complexity of algo-rithm as well as reduce the reliability of themodel By analysisof their interrelation we finally choose the maximum load(MAXL) the minimum load (MINL) the effective stroke(ES) and the computational pump efficiency (CPE) as theenvironment parameters and the electric power consumption(EPC) and the oil yield (OY) as the evaluation criterions Allthe parameters used in modeling are shown in Table 1


NP

MAXL

MINL

ES

CPE

EPC

OY

Input layer

Pattern layer

Summation layer

Output layer




1 x2 x

119899 x119894=

(119909

1

119894 119909

2

119894 119909

119901

119894)



119905

119894= exp[minus

(X minus 120601

119909

119894)

119879

(X minus 120601

119909

119894)

2120590

2] 119894 = 1 2 119899 (1)




119904

119863=

119899

sum

119894=1

119905

119894 (2)


119904

119873119895=

119899

sum

119894=1

119910

119894119895119905

119894 119895 = 1 2 119901 (3)





119910

119895=

119904

119873119895

119904

119863

119895 = 1 2 119901 (4)








119910 = min 119869 (119909) = min (1198691(119909) minus119869

2(119909)) (6)



119910 = (119910EPC minus119910OY) isin 119884

119883 = (119909

1 119909

2 119909

119899) | 119897

119894le 119909

119894le 119906

119894 119894 = 1 2 5

119871 = (119897

1 119897

2 119897

5)

119880 = (119906

1 119906

2 119906

5)

(7)





Evolutionary search

Optimal design

Designs



Real problem





0and set archive

population 119875

1015840

0= 0


119894cup 119875

1015840

119894


119894and 119875

1015840

119894to 119875

1015840

119894+1 If size of 1198751015840

119894+1exceeds 119873


1015840





119894and 119875

1015840

119894+1




1015840




Step 6 119894 = 119894 + 1 go to Step 2





11987700148 00071









0 10 20 30 40 50 60 70 80 906

8

10

12

14

16

18

Sample

EPC

(kwmiddoth

)

PredictedObserved

(a)

0 10 20 30 40 50 60 70 80 90Sample

PredictedObserved

20

25

30

35

40

45

50

55

Yiel

d (t

d)

(b)


0 10 20 30 40 50 60 70 80 90

0

001

002

003

004005

Sample

minus001

minus002

EPC

erro

r (

)

(a)

0 10 20 30 40 50 60 70 80 90Sample

0

002

004

Yiel

d er

ror (

)

minus004

minus002

(b)



119864MS =radic

sum (119910 minus 119909)

2

119899 minus 1

119864

119877= sum(

1003816

1003816

1003816

1003816

y minus x1003816100381610038161003816

x)

(8)






5 Conclusions



107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(a)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Pareto front

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(b)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(c)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(d)






61 328 933 423 31000 713138 110982 3554






Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










NP

MAXL

MINL

ES

CPE

EPC

OY

Input layer

Pattern layer

Summation layer

Output layer




1 x2 x

119899 x119894=

(119909

1

119894 119909

2

119894 119909

119901

119894)



119905

119894= exp[minus

(X minus 120601

119909

119894)

119879

(X minus 120601

119909

119894)

2120590

2] 119894 = 1 2 119899 (1)




119904

119863=

119899

sum

119894=1

119905

119894 (2)


119904

119873119895=

119899

sum

119894=1

119910

119894119895119905

119894 119895 = 1 2 119901 (3)





119910

119895=

119904

119873119895

119904

119863

119895 = 1 2 119901 (4)








119910 = min 119869 (119909) = min (1198691(119909) minus119869

2(119909)) (6)



119910 = (119910EPC minus119910OY) isin 119884

119883 = (119909

1 119909

2 119909

119899) | 119897

119894le 119909

119894le 119906

119894 119894 = 1 2 5

119871 = (119897

1 119897

2 119897

5)

119880 = (119906

1 119906

2 119906

5)

(7)





Evolutionary search

Optimal design

Designs



Real problem





0and set archive

population 119875

1015840

0= 0


119894cup 119875

1015840

119894


119894and 119875

1015840

119894to 119875

1015840

119894+1 If size of 1198751015840

119894+1exceeds 119873


1015840





119894and 119875

1015840

119894+1




1015840




Step 6 119894 = 119894 + 1 go to Step 2





11987700148 00071









0 10 20 30 40 50 60 70 80 906

8

10

12

14

16

18

Sample

EPC

(kwmiddoth

)

PredictedObserved

(a)

0 10 20 30 40 50 60 70 80 90Sample

PredictedObserved

20

25

30

35

40

45

50

55

Yiel

d (t

d)

(b)


0 10 20 30 40 50 60 70 80 90

0

001

002

003

004005

Sample

minus001

minus002

EPC

erro

r (

)

(a)

0 10 20 30 40 50 60 70 80 90Sample

0

002

004

Yiel

d er

ror (

)

minus004

minus002

(b)



119864MS =radic

sum (119910 minus 119909)

2

119899 minus 1

119864

119877= sum(

1003816

1003816

1003816

1003816

y minus x1003816100381610038161003816

x)

(8)






5 Conclusions



107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(a)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Pareto front

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(b)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(c)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(d)






61 328 933 423 31000 713138 110982 3554






Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Evolutionary search

Optimal design

Designs



Real problem





0and set archive

population 119875

1015840

0= 0


119894cup 119875

1015840

119894


119894and 119875

1015840

119894to 119875

1015840

119894+1 If size of 1198751015840

119894+1exceeds 119873


1015840





119894and 119875

1015840

119894+1




1015840




Step 6 119894 = 119894 + 1 go to Step 2





11987700148 00071









0 10 20 30 40 50 60 70 80 906

8

10

12

14

16

18

Sample

EPC

(kwmiddoth

)

PredictedObserved

(a)

0 10 20 30 40 50 60 70 80 90Sample

PredictedObserved

20

25

30

35

40

45

50

55

Yiel

d (t

d)

(b)


0 10 20 30 40 50 60 70 80 90

0

001

002

003

004005

Sample

minus001

minus002

EPC

erro

r (

)

(a)

0 10 20 30 40 50 60 70 80 90Sample

0

002

004

Yiel

d er

ror (

)

minus004

minus002

(b)



119864MS =radic

sum (119910 minus 119909)

2

119899 minus 1

119864

119877= sum(

1003816

1003816

1003816

1003816

y minus x1003816100381610038161003816

x)

(8)






5 Conclusions



107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(a)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Pareto front

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(b)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(c)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(d)






61 328 933 423 31000 713138 110982 3554






Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 10 20 30 40 50 60 70 80 906

8

10

12

14

16

18

Sample

EPC

(kwmiddoth

)

PredictedObserved

(a)

0 10 20 30 40 50 60 70 80 90Sample

PredictedObserved

20

25

30

35

40

45

50

55

Yiel

d (t

d)

(b)


0 10 20 30 40 50 60 70 80 90

0

001

002

003

004005

Sample

minus001

minus002

EPC

erro

r (

)

(a)

0 10 20 30 40 50 60 70 80 90Sample

0

002

004

Yiel

d er

ror (

)

minus004

minus002

(b)



119864MS =radic

sum (119910 minus 119909)

2

119899 minus 1

119864

119877= sum(

1003816

1003816

1003816

1003816

y minus x1003816100381610038161003816

x)

(8)






5 Conclusions



107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(a)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Pareto front

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(b)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(c)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(d)






61 328 933 423 31000 713138 110982 3554






Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(a)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Pareto front

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(b)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(c)

107 108 109 11 111 112 113 114 115 116 117EPC (kwmiddoth)

Yiel

d (t

d)

minus34

minus345

minus35

minus355

minus36

minus365

minus37

minus375

minus38

minus385

(d)






61 328 933 423 31000 713138 110982 3554






Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Acknowledgments


References





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article modeling and optimization of beam pumping

Documents