route optimization of pipeline in gas-liquid two-phase...

Research ArticleRoute Optimization of Pipeline in Gas-Liquid Two-Phase FlowBased on Genetic Algorithm

Jun Zhou1 Guangchuan Liang1 Tao Deng2 and Jing Gong3

1Southwest Petroleum University Chengdu 610500 China2China National Petroleum Corporation Guangzhou Petroleum Training Center Guangzhou 510510 China3China University of Petroleum (Beijing) Beijing 102249 China

Correspondence should be addressed to Jun Zhou 201599010096swpueducn and Guangchuan Liang lgcdjr163com

Received 23 October 2016 Accepted 13 December 2016 Published 19 January 2017

Academic Editor Jose Alberto Romagnoli

Copyright copy 2017 Jun Zhou et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper describes the problems in route optimization of two-phase pipelines Combining the hydraulic calculation with routeoptimization theory this paper establishes an automatic route optimization model and adopts the general genetic algorithm (gGA)and steady-state genetic algorithm (ssGA) to solve the model respectively gets the optimal route and discusses the influence ofparameters setting to the result This algorithm was applied in determining pipelines routes in coalbed methane gathering andtransporting system in Shanxi Province China The result shows that the algorithm is feasible which improves the hydraulicproperties by reducing the pressure drop along the line while the pipeline length is still acceptable

1 Introduction

In a recent decade to meet the constant need of energyalthough the global economy has come through a downturnthe oil-gas pipelines construction is still prosperous aroundthe world In 2013 the total length of pipelines under con-struction or planned to be constructed is about 188108 kmand the length of those under construction is 53180 km 114longer than that in the year 2012 47732 km During the con-struction the first step is to determine the pipeline routeThetask is frequent and time-consuming and plenty of attemptshave beenmade Traditionally engineerswould determine theroute manually on a printed map or solve the problem withoptimization theory Early in the year 1971 Shamir [1] useddynamic programming to determine the optimal route onmanual mesh In years 2004 and 2012 Meisingset et al [2]and Marcoulaki et al [3] established the mathematical opti-mizationmodels in terms of minimum investment separatelyfor submarine pipelines and ground pipelines and solved themodels with simulated annealing but those models did notinvolve the hydraulic properties

In the problemof oil-gas pipeline route optimization pipeflowmay be single-phase ormultiphaseMultiphase pipe flow

is different from single-phase pipe flow the pressure drop isclosely related to the height along the line Both uphill sectionand downhill section can be energy-consuming yet theenergy loss in the uphill section cannot be replenished by thegravity effect of downhill section Thus with the same start-ingending location and pipeline length but different routesand different topographic reliefs different pipelines possessdifferent hydraulic properties In literature Xiao et al [4]used 119860lowast algorithm to study the optimal route of gas-liquidtwo-phase flow pipeline yet119860lowast algorithm is not a global opti-mization algorithm which is based on a combined algorithmbetween Dijkstrarsquos algorithm and Best-First-Search algo-rithm In this paper the authors would use a global optimiza-tion algorithm-genetic algorithm (GA) to discuss the optimalroute programming of gas-liquid two-phase flow pipelines

2 Gas-Liquid Two-Phase Pipe Flow

In oil-gas field people would usually use one pipeline totransport the product of several wells As long as two-phaseflow exists in the pipeline the pipeline is defined as two-phasepipeline In an oil-gas mixture transportation pipeline theoil-gas ratio may vary a lot in different parts In drainage

HindawiInternational Journal of Chemical EngineeringVolume 2017 Article ID 1640303 9 pageshttpsdoiorg10115520171640303

2 International Journal of Chemical Engineering

pipes of oil-gas separators the flowing liquid is basicallycrude oil but along the pressure drop some dissolved gaswould come out In venting pipes of oil-gas separators theflow inside is basically natural gas yet along the flowingthere may be water or heavy hydrocarbon condensated Forexample in the coalbed methane gas fields which are largelyexploited the gas came out from the well along the gasflow there would be water condensation then gas-liquid two-phase flow would appear At the same time in gathering andtransporting process it is not economic to use two pipelinesseparately transporting crude oil and natural gas in smallquantities Thus in the surface gathering and transportingsystem mixture transportation pipelines are widely usedMoreover in some specific conditions mixture transporta-tion has some advantages that single-phase pipeline cannotcompare with For instance in some places that are notsuitable for installing gas-liquid separators and processingfacilities (such as urban areas desserts lakes ecologicalreserves and swamplands) mixture transportation pipelinesare necessary Those pipelines tend to go through hills ormountainous areas which does not cause any problemswhen the pipelines are single-phase because the pressureenergy loss during uphill sectionwould be replenishedduringdownhill section Yet in two-phase flow the situation is muchdifferent Since the liquid holdup and the density of the gas-liquid mixture in downhill section are much smaller thanthose in uphill section the pressure cannot be regained thatmuch in downhill section Therefore as far as multiphasepipeline route determination is concerned engineers mustgive high priority to the hydraulic properties of the pipe flowand combine it with the route optimization

The distribution of gas and liquid in the two-phase pipeflow varies a lot and flow patterns vary a lot too Thesewould influence not only the mechanical relationship of thetwo-phase flow but also the heat and mass transfer thusthe gas-liquid two-phase flow is very complicated Currentlythere are plenty of calculationmodels of gas-liquid two-phaseflow with their own advantages and disadvantages Yet theresearch of two-phase models goes beyond our study in thepaper This paper plans to use existing gas-liquid two-phaseBeggs-Brill [5] model to integrate hydraulic simulation withroute optimization algorithm

3 Optimization

Route determination involves many aspects such as likepipelinersquos design construction operation and maintenancewhich include the security of the pipeline hydraulic andthermal conditions environmental conservation historicalsites soil and hydrological conditions and constructionrequirements For route optimization based on intelligencealgorithm the route programming of oil-gas pipelinesmainlydeals with the following factors oil-gas production oil-gasphysical properties the starting point and terminal of thepipeline the starting and ending pressure of the pipelinethe areas that the pipeline goes through heights of differentplaces land types (rocky soil sandy soil etc) forest covered

Costparameters

Optimal routeOptimization

Topography

Pipe simulation

Figure 1 Optimization tools

area source of water rivers roads railroads and impenetra-ble areas The material and labor costs of pipeline construc-tion the pipes regional regulation constructing techniquesconstruction goal (usually minimum investment) and otherfactors influencing the pipeline construction

We need to find the pipeline route from the starting pointto the terminal satisfy the gas-liquid two-phase flow char-acters and other constraint conditions and then make theobject function minimum This paper focuses on the two-phase pipeline route on complex topography using digitaltopographical data to decide the optimal routeThe overviewof the optimization tool is shown in Figure 1

31 Topographical Data

Digital Map Automatic route optimization is carried out ondigital maps using discrete data (see Figure 2) to representthe continuous surface Discrete data is the approximation ofcontinuous surface The higher the resolution is the closerthe approximation is to the real topography and the moreaccurate the route tracing is Yet there is a highest resolutionlimitation This form has a good compatibility and is con-sistent with the grid data of GIS (Geographic InformationSystem)

32 Algorithm On the issue of shortest route the researchersstudied several intelligence algorithms [6ndash8] Among themgenetic algorithmwas established simulating Darwinrsquos evolu-tion theory which can be used to solve the problems of func-tion optimization or machine learning It imitates the proce-dure of inheritance and evolution that is selection replica-tion crossover and variation and introduces the concept ofldquosurvival of the fittestrdquo into the algorithmThe block diagramof genetic algorithm is shown in Figure 3

To carry out the hydraulic calculation of gas-liquid two-phase pipeline we adopt the method of segmentation tocalculate the pressure drop of different sections one by one

The symbol of discretization is shown in Figure 4 Thestarting point is 1198730 ending point is 119873119899 and the nodes dividethe pipeline into many sections The starting and endingpoints of pipe section 119895 are 119873119895 and 119873119895+1 If only hydraulic

International Journal of Chemical Engineering 3

1 15 27 37 45 44

0 12 23 32 38 37

0 10 19 26 31 31

0 8 15 21 25 25

1 7 12 16 20 19

3 6 9 13 15 15

0

9

18

27

36

45

Figure 2 Topographical sample (approximately showing real topography)

Start

Initialize

Fitness value

Selection

Crossover

Mutation

Stop

EndYes

No

Figure 3 The block diagram of genetic algorithm

calculation is conducted it means to do hydraulic simulationon a determined route and to manually set the mesh spacing(usually equal mesh spacing) However in three dimensionsthe route is not determined Therefore at the same time withroute optimization hydraulic calculation must be taken intoconsideration

During the optimization each route represents a pipelineThe nodes on the route divide the pipeline into pipe sectionswith different lengths as shown in Figure 5 Calculationaccuracy can be guaranteed when the mesh spacing is smallenough

In route optimization assuming that there is a groundarea with limited boundaries starting point is A (1199090 1199100 1199110)and ending point is B (119909119899 119910119899 119911119899)There aremany routes goingfrom A to B Assuming that the investment of pipeline isproportional to the pipeline length the route optimization isto find a route that canminimize the construction investmentor optimize other object functions

The initial population contains 119898 routes the route 119894 ingeneration 119896 is expressed as

119903119894119896 = (1199091198941198960 1199101198941198960 1199111198941198960) (1199091198941198961 1199101198941198961 1199111198941198961)sdot sdot sdot (119909119894119896(119899minus1) 119910119894119896(119899minus1) 119911119894119896(119899minus1)) (119909119894119896119899 119910119894119896119899 119911119894119896119899) (1)

The length of route 119894 in generation 119896 is expressed as

119871119894119896 = 1003817100381710038171003817100381711990311989411989610038171003817100381710038171003817= 119899minus1sum119895=0

radic(119909119894119896(119895+1)

minus 119909119894119896119895

)2 + (119910119894119896(119895+1)

minus 119910119894119896119895

)2 + (119911119894119896(119895+1)

minus 119911119894119896119895

)2 (2)

Taking hydraulic conditions into consideration we havethe following

The pressure drop between adjacent nodes is 119889119901119894119896119895 so thepressure drop along the route 119894 in generation 119896 is expressed as

119863119875119894119896= 119899minus1sum119895=0

119889119901119894119896119895radic(119909119894119896(119895+1)

minus 119909119894119896119895

)2 + (119910119894119896(119895+1)

minus 119910119894119896119895

)2 + (119911119894119896(119895+1)

minus 119911119894119896119895

)2 (3)

Pressure drop 119889119901119894119896119895 can be calculated by many methodsFitness function is expressed as

Fitness119894119896 = 1119863119875119894119896 (4)

Due to the grid data in genetic algorithm we use integercoding roulette wheel selection single-point crossover andsingle-point variation for calculatation repeat the procedurein Figure 3 till the best individual is found

33 Realization Due to the complexity of terrain pipelineoptimization it is often unable to obtain the best path Aswe all know under the plane condition straight line betweentwo points is the shortest [9] To test the program we firstoptimize the shortest path between two points on the plane


N0

N1

Njminus1

Nj

Nn

Figure 4 Discretization sketch of gas-liquid two-phase pipeline

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20123456789

1011121314151617181920

N0

N1

Nj

Nn

Y

X

Nj+1

Figure 5 Discretization sketch of pipeline route

Supposing the population size and the maximum num-ber of iterations are 200 and 1000 respectively crossoverprobability andmutation probability are 095 and 02 respec-tively Figure 6 shows the algorithm convergence as can beseen from the figure the algorithm converges quickly andapproaches the best solution after 250 iterations Figure 7shows the path graphs under different generations and thepath approaches a straight line between two points after 500iterations

34 Test Results and Discussion General and steady-stategenetic algorithms with roulette wheel selection arithmeticcrossover and uniform mutation are adopted The computeris Samsung R408 Intel Pentium dual T3400 216Hz 1 GRAM

Generate the digital map with topographical model func-tion

119911 (119909 119910)= ℎsum119894=1

ℎ119894 times expminus (1003816100381610038161003816119909 minus 1199091198881198941003816100381610038161003816119906119894 )119901119894 minus (1003816100381610038161003816119910 minus 1199101198881198941003816100381610038161003816

V119894)119902119894 (5)

Parameters of topographical function are shown inTable 1

BestOptimal value

2530354045505560657075808590

Eval

uatio

n va

lue

50 100 150 200 250 300 350 400 450 5000Number of iterations

Figure 6 Performance of the GA in finding the best solution

Table 1 Parameters of topographical function

119894 119909119888 119910119888 119901 119902 119906 V ℎ1 25 87 15 15 30 20 572 64 28 2 35 65 12 193 34 53 3 2 21 13 minus324 77 92 2 2 6 25 385 94 55 3 3 11 14 246 65 24 15 15 13 9 minus227 15 11 3 2 11 16 minus148 93 14 3 3 13 11 minus17

Here is the route programming of complex topographywith grid data The example digital map is in Figure 8 Meshnumber is 20 times 20 and mesh size is 5 times 5

For genetic algorithms crossover probability (CP) andmutation probability (MP) are extremely important param-eters which directly affect the optimization quality of thealgorithm In this paper to analysis the sensitivity of the twoGAs to the parameters CP ranges from 04 to 10 and MPranges from 00005 to 03 Figure 9 shows the averages resultsof ten independent operations at different probabilities Twogenetic algorithms are sensitive to CP and MP Both of them


The 100th iterationThe 300th iterationThe 500th iteration

The 700th iterationThe 1000th iteration

0

5

10

15

20

Y

5 10 15 200X

Figure 7 Routes sketch of different generations in optimization

4375

1450

2463

3475

4488

55002

4

6

8

10

12

14

16

18

20

Y

4 6 8 10 12 14 16 18 202X

minus2600

minus1588

minus5750

Figure 8 Digital profile of topographical surface

Table 2 Best result obtained from ssGA and gGA

GN GA SS GACP MP 09 0005 10 01Average evaluation value (over ten times) 17219 17309Best evaluation value (over ten times) 16318 16734

can obtain best function evaluation values whenCP is big Yetthe MP of GN GA is small but that of SS GA is big

The optimal results of two GA are shown in Table 2 Theaverage and best result of GN GA both are a little smallerthan those of SS GA The best evaluation value is 16318 InFigure 10 the red curve is optimal route and it bypasses thelow areas in the middle

Table 3 Parameter of pipeline simulation

Parameter Parameter valueVolume flow rate of gas m3d 4000Volume flow rate of liquid m3d 03Starting pressure MPa 15Pipe diameter m 02

Table 4 Calculation results

Real value Calculation resultPipeline length 5433804m 5570194mPipeline pressure drop 1021MPa 0644MPa

4 Example Analysis

The existing pipeline data and simulation parameter is shownin Table 3

The calculation model of gas-liquid two-phase pipe flowis Beggs-Brill [8] model to calculate liquid holdup andpressure drop For more detailed information of the modelplease refer to Appendix A

The topographical data comes from digital map whosefile format is TIF shown in Figure 11 and the pixel size in gridinformation is 21m times 13621m The elevation model of thisblock (red box in Figure 11) is shown in Figure 12 with anarea of 275625 km2 and mesh number of 250 times 250

In Figure 12 point A is the starting point point Bthe ending point and dotted line the existing pipeline Itis obvious in the figure that the line passes through highmountains in the middle With the model in this paper wecan get the optimal route represented by solid line From thestarting point the line goes down and bypasses the hills to theending pointThe route under three-dimension topography isshown in Figure 13

The calculation results are presented in Table 4 Table 4lists out the pipeline length and pressure drop of both optimalroute and real route From Figures 14 and 15 the variation ofexisting pipeline elevation is big while the optimal pipelineelevation goes gently Pipeline length increased to 5570194mfrom 5433804m by 245 yet which is still acceptable andthe pressure drop along the line reduced to 0644MPa from1021MPa by 3692 This greatly improves the hydraulicproperties of the pipeline

5 Conclusions

(1) This paper establishes a pipeline route determinationmodel combined hydraulic calculation in complextopography With the digital topographical data theoptimal route can be automatically determined

(2) Genetic algorithm can be used to select an optimalroute for gas-liquid two-phase pipeline The parame-ters of genetic algorithm would have an influence onoptimization result If topographical data andpipelineparameters are known with a program the optimal


0405

0607

080910 170

175

180

185

190

195

200

205

0302

01005

0010005

000200005

(a)

0405

060708

0910

170

175

180

185

190

195

00005

0002

0005

001005

0102

03

(b)

Figure 9 Effect of variations of CP and MP on the performance of gGA (a) and ssGA (b)

2 4 6 8 10 12 14 16 18 20

1875

1250

2313

3375

4438

5500

X

2

4

6

8

10

12

14

16

18

20

Y

minus3000

minus1938

minus8750

Figure 10 Result of route curves

route can be determined As the example in paper thismethod can reliably seek out the route

(3) This paper gives a structure of pipeline route designIt is a reference for the engineers They can add otherexpenses according to the real situation

Appendix

A Beggs-Brill Liquid HoldupRelative Expression

Beggs-Brill relative expression (BB relative expression) can beused to calculate the liquid holdup When dip angle 120579 = 0the calculation result is the liquid holdup of horizontal pipeswhen 120579 = 0 the result is the liquid holdup of inclined pipeswhich has a correction factor

Figure 11 Topography file in TIF of some block

Before calculating liquid holdup first identify flow pat-tern and Table 5 presents the rules of flow pattern identifica-tion

The equation to calculate liquid holdup of horizontal pipeis

119867119871 (0) = 119886119877119887119871Fr119888

119877119871 = 119876119897119876119897 + 119876119892

Fr = 1199082119892119889

(A1)


Table 5 Rules of flow pattern identification

Flow pattern Identification rules Calculating method of 119871119877119871 Fr

Separated flow lt001 lt1198711ge001 lt1198712

Transition flow ge001 gt1198712 amp lt1198713 1198711 = 316 times 11987711987103021198712 = 9252times10minus4times119877minus246841198711198713 = 001 times 119877minus145161198711198714 = 05 times 119877minus6738119871Intermittent flow ge001 amp lt04 gt1198712 amp lt1198711

ge04 gt1198713 amp le1198714Dispersion flow lt04 ge1198711

ge04 gt1198714

Optimal routeExisting pipeline

0

50

100

150

200

250

B

9400

9750

1010

1045

1080

1115

1150

1185

1220

A

Y

50 100 150 200 2500X

Figure 12 Pipeline route in contour map

050

100

150

200

250

800900

10001100

12001300

1400

0

50

100

150200

250

A

B

YX

Z

Figure 13 Pipeline route in 3D topographical map

Elevation of existing pipelineElevation of optimal pipeline

1000 2000 3000 4000 5000 60000Pipe length (m)

1060

1080

1100

1120

1140

1160

1180

1200

Elev

atio

n (m

)

Figure 14 Elevation along the line

0 1000 2000 3000 4000 500004

06

08

10

12

14

16

Pres

sure

(MPa

)

Pipe length (m)

Optimal pipelineExiting pipeline

Figure 15 Pressure along the line


Table 6 Different coefficient of a b and c

Flow pattern a b cSeparated flow 0980 04846 00868Intermittent flow 0845 05351 00173Dispersion flow 1065 05824 00609

Table 7 Coefficient values

Flow pattern 119889 119890 119891 119892Uphill separated flow 0011 minus3768 3539 minus1614Uphill intermittent flow 296 0305 minus04473 00978Uphill dispersion flow 119862 = 0 120601 = 1Downhill flow 470 minus03692 01244 minus05056

In the equation 119877119871 is volume liquid holdup and Fr isFroude dimensionless number

With different flow pattern we use different coefficient tocalculate 119886 119887 and 119888 The results are listed in Table 6

Correction factor is

120593 = 1 + 119862 [sin (18120579) minus 13 sin3 (18120579)] (A2)

When 120579 = 90∘119862 = (1 minus 119877119871) ln (119889119877119890119871119873119891119871119908Fr119892)

119873119871119908 = 119882119904119871 ( 120588119871119892120590)025 (A3)

In the equation 119873119871119908 is liquid apparent velocity indexThe coefficients 119889 119890 119891 and 119892 depend on flow patterns as

shown in Table 7The correction factor 120601 represents the liquid holdup ratio

of inclined pipe to horizontal pipe

120601 = 119867119871 (120579)119867119871 (0) (A4)

B Beggs-Brill Pressure DropRelative Expression

B1 Pressure Drop Gradient Calculating

minus 119889119901119889119897= [119867119871120588119871 + (1 minus 119867119871) 120588119866] 119892 sin 120579 + 120582 (21199081198721205871198893)

1 minus [119867119871120588119871 + (1 minus 119867119871) 120588119892] 119908119908119904119892119901 (B1)

In the equation 119867119871 is liquid holdup dimensionless 119901is average absolute pressure of flow in the pipe Pa is 120582-hydraulic friction coefficient of gas-liquid mixed pipelinedimensionless 120588119892 is density of gas and liquid kgm3 119872 ismass flow rate of the gas-liquid mixture kgs 119908 is the flow

velocity of gas-liquid mixture ms 119908119904119892 is apparent velocityof gas ms 119889 is inner diameter of pipes m and 120579 is dip angledegree

Among all those calculating methods of gas-liquid mix-ture transportation pipeline with topographic relief BB pres-sure drop calculating method is the only one taking downhillenergy recovery into consideration If liquid holdup equals 1or 0 the method turns into calculating single-phase liquid orgas pipeline

B2 Laws of Two-Phase Hydraulic Friction Coefficient Assu-ming hydraulic friction coefficient of homogeneous flow is1205820 the hydraulic friction coefficient ratio of two-phase flowto homogeneous flow is 1205821205820

( 1205821205820) = 119890119899

119898 = 119877119871[119867119871 (120579)] 119899= minus ln119898

00523 minus 3182 ln119898 + 08725 (ln119898)2 minus 001853 (ln119898)4

(B2)

When 1 lt 119898 lt 12 119899 = ln(22119898 minus 12)For hydraulically smooth pipes the hydraulic friction

coefficient of homogeneous flow is 1205820 which can be lookedup in Moody graph or calculated by the following equations

1205820 = [2 lg( Re045223 lg Re0 minus 38215)]minus2

Re0 = 119889119908120588119891120583 = 119889119908 [120588119871119877119871 + 120588119892 (1 minus 119877119871)]

[120583119871119877119871 + 120583119892 (1 minus 119877119871)] (B3)

Figure 16 is the program chart of BB method to getpressure drop

Nomenclature

119894 Route number in genetic algorithm119895 Pipe section number119896 Generation 119896 in genetic algorithm119873119895 Node number(119909119895 119910119895) The coordinates of node 119873119895119911119895 The elevation of node 119873119895119903119894119896 Nodes set of the route 119894 in generation 119896119871119894119896 Length of route 119894 in generation 119896119863119875119894119896 The pressure drop along the route 119894 in

generation 119896119889119901119894119896119895 The pressure drop along pipe section 119895

between nodes 119873119895 and 119873119895+1


Start

Input data

Identify flow pattern

Calculate correction factor according to flow pattern

Calculate liquid holdup of inclined pipe

Calculate pressure drop of two-phase flow

End

Hydraulic friction coefficient

Assume the ending pressure P1

Calculate the ending pressure P2

Output the ending pressure

Yes

No|P1 minus P2| lt 120576

Calculate L1 L2 L3 L4

Figure 16 The program chart of BB method

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors appreciate the financial support from the YoungScholars Development Fund of SWPU (201599010096)

References

[1] U Shamir ldquoOptimal route for pipelines in two-phase flowrdquoSociety of Petroleum Engineers Journal vol 11 no 03 pp 215ndash222 1971

[2] H Meisingset J Hove and G Olsen ldquoOptimization of pipelineroutesrdquo in Proceedings of the 14th International Offshore andPolar Engineering Conference Toulon France May 2004

[3] E C Marcoulaki I A Papazoglou and N Pixopoulou ldquoInte-grated framework for the design of pipeline systems usingstochastic optimisation and GIS toolsrdquo Chemical EngineeringResearch and Design vol 90 no 12 pp 2209ndash2222 2012

[4] J J Xiao A J Al-Muraikhi and A M Qahtani ldquoAutomatedroute finding for production flowline to minimize liquid inven-tory and pressure lossrdquo in Proceedings of the SPE Annual Techn-ical Conference and Exhibition (ATCE rsquo06) Texas USA Septem-ber 2006

[5] D H Beggs and J P Brill ldquoA experimental study of two-phaseflow in inclined pipesrdquo Journal of Petroleum Technology vol 25no 5 pp 607ndash617 1973

[6] Z Huang S Chen L Kang and Y Chen ldquoSolving the shortestpath on curved surface based on simulated annealing algo-rithmrdquo Journal Wuhan University vol 46 no 3 pp 273ndash2762000

[7] D D Yang and R Ran ldquoGenetic algorithm based shortest pathplanning on curved surfacerdquo Computer Simulation vol 23 no8 pp 168ndash169 2006

[8] J Y Luo ldquoThe study on PSO algorithm to seek shortest path oncurved surfacerdquo Journal of Min Jiang University vol 25 no 5pp 14ndash17 2007

[9] J Zhou X Li T Deng M Cheng and J Gong ldquoLayout optimi-zation of branchpipeline network on curved surface using gene-tic algorithmrdquo in Proceedings of the 10th International PipelineConference (IPC rsquo14) Calgary Canada October 2014

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pipes of oil-gas separators the flowing liquid is basicallycrude oil but along the pressure drop some dissolved gaswould come out In venting pipes of oil-gas separators theflow inside is basically natural gas yet along the flowingthere may be water or heavy hydrocarbon condensated Forexample in the coalbed methane gas fields which are largelyexploited the gas came out from the well along the gasflow there would be water condensation then gas-liquid two-phase flow would appear At the same time in gathering andtransporting process it is not economic to use two pipelinesseparately transporting crude oil and natural gas in smallquantities Thus in the surface gathering and transportingsystem mixture transportation pipelines are widely usedMoreover in some specific conditions mixture transporta-tion has some advantages that single-phase pipeline cannotcompare with For instance in some places that are notsuitable for installing gas-liquid separators and processingfacilities (such as urban areas desserts lakes ecologicalreserves and swamplands) mixture transportation pipelinesare necessary Those pipelines tend to go through hills ormountainous areas which does not cause any problemswhen the pipelines are single-phase because the pressureenergy loss during uphill sectionwould be replenishedduringdownhill section Yet in two-phase flow the situation is muchdifferent Since the liquid holdup and the density of the gas-liquid mixture in downhill section are much smaller thanthose in uphill section the pressure cannot be regained thatmuch in downhill section Therefore as far as multiphasepipeline route determination is concerned engineers mustgive high priority to the hydraulic properties of the pipe flowand combine it with the route optimization

The distribution of gas and liquid in the two-phase pipeflow varies a lot and flow patterns vary a lot too Thesewould influence not only the mechanical relationship of thetwo-phase flow but also the heat and mass transfer thusthe gas-liquid two-phase flow is very complicated Currentlythere are plenty of calculationmodels of gas-liquid two-phaseflow with their own advantages and disadvantages Yet theresearch of two-phase models goes beyond our study in thepaper This paper plans to use existing gas-liquid two-phaseBeggs-Brill [5] model to integrate hydraulic simulation withroute optimization algorithm

3 Optimization

Route determination involves many aspects such as likepipelinersquos design construction operation and maintenancewhich include the security of the pipeline hydraulic andthermal conditions environmental conservation historicalsites soil and hydrological conditions and constructionrequirements For route optimization based on intelligencealgorithm the route programming of oil-gas pipelinesmainlydeals with the following factors oil-gas production oil-gasphysical properties the starting point and terminal of thepipeline the starting and ending pressure of the pipelinethe areas that the pipeline goes through heights of differentplaces land types (rocky soil sandy soil etc) forest covered

Costparameters

Optimal routeOptimization

Topography

Pipe simulation

Figure 1 Optimization tools

area source of water rivers roads railroads and impenetra-ble areas The material and labor costs of pipeline construc-tion the pipes regional regulation constructing techniquesconstruction goal (usually minimum investment) and otherfactors influencing the pipeline construction

We need to find the pipeline route from the starting pointto the terminal satisfy the gas-liquid two-phase flow char-acters and other constraint conditions and then make theobject function minimum This paper focuses on the two-phase pipeline route on complex topography using digitaltopographical data to decide the optimal routeThe overviewof the optimization tool is shown in Figure 1

31 Topographical Data

Digital Map Automatic route optimization is carried out ondigital maps using discrete data (see Figure 2) to representthe continuous surface Discrete data is the approximation ofcontinuous surface The higher the resolution is the closerthe approximation is to the real topography and the moreaccurate the route tracing is Yet there is a highest resolutionlimitation This form has a good compatibility and is con-sistent with the grid data of GIS (Geographic InformationSystem)

32 Algorithm On the issue of shortest route the researchersstudied several intelligence algorithms [6ndash8] Among themgenetic algorithmwas established simulating Darwinrsquos evolu-tion theory which can be used to solve the problems of func-tion optimization or machine learning It imitates the proce-dure of inheritance and evolution that is selection replica-tion crossover and variation and introduces the concept ofldquosurvival of the fittestrdquo into the algorithmThe block diagramof genetic algorithm is shown in Figure 3

To carry out the hydraulic calculation of gas-liquid two-phase pipeline we adopt the method of segmentation tocalculate the pressure drop of different sections one by one

The symbol of discretization is shown in Figure 4 Thestarting point is 1198730 ending point is 119873119899 and the nodes dividethe pipeline into many sections The starting and endingpoints of pipe section 119895 are 119873119895 and 119873119895+1 If only hydraulic


1 15 27 37 45 44

0 12 23 32 38 37

0 10 19 26 31 31

0 8 15 21 25 25

1 7 12 16 20 19

3 6 9 13 15 15

0

9

18

27

36

45


Start

Initialize

Fitness value

Selection

Crossover

Mutation

Stop

EndYes

No








119871119894119896 = 1003817100381710038171003817100381711990311989411989610038171003817100381710038171003817= 119899minus1sum119895=0

radic(119909119894119896(119895+1)

minus 119909119894119896119895

)2 + (119910119894119896(119895+1)

minus 119910119894119896119895

)2 + (119911119894119896(119895+1)

minus 119911119894119896119895

)2 (2)



119863119875119894119896= 119899minus1sum119895=0

119889119901119894119896119895radic(119909119894119896(119895+1)

minus 119909119894119896119895

)2 + (119910119894119896(119895+1)

minus 119910119894119896119895

)2 + (119911119894119896(119895+1)

minus 119911119894119896119895

)2 (3)


Fitness119894119896 = 1119863119875119894119896 (4)




N0

N1

Njminus1

Nj

Nn


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20123456789

1011121314151617181920

N0

N1

Nj

Nn

Y

X

Nj+1





119911 (119909 119910)= ℎsum119894=1


V119894)119902119894 (5)


BestOptimal value

2530354045505560657075808590

Eval

uatio

n va

lue










0

5

10

15

20

Y

5 10 15 200X


4375

1450

2463

3475

4488

55002

4

6

8

10

12

14

16

18

20

Y

4 6 8 10 12 14 16 18 202X

minus2600

minus1588

minus5750










4 Example Analysis






5 Conclusions




0405

0607

080910 170

175

180

185

190

195

200

205

0302

01005

0010005

000200005

(a)

0405

060708

0910

170

175

180

185

190

195

00005

0002

0005

001005

0102

03

(b)


2 4 6 8 10 12 14 16 18 20

1875

1250

2313

3375

4438

5500

X

2

4

6

8

10

12

14

16

18

20

Y

minus3000

minus1938

minus8750




Appendix






119867119871 (0) = 119886119877119887119871Fr119888

119877119871 = 119876119897119876119897 + 119876119892

Fr = 1199082119892119889

(A1)







ge04 gt1198714


0

50

100

150

200

250

B

9400

9750

1010

1045

1080

1115

1150

1185

1220

A

Y

50 100 150 200 2500X


050

100

150

200

250

800900

10001100

12001300

1400

0

50

100

150200

250

A

B

YX

Z



1000 2000 3000 4000 5000 60000Pipe length (m)

1060

1080

1100

1120

1140

1160

1180

1200

Elev

atio

n (m

)


0 1000 2000 3000 4000 500004

06

08

10

12

14

16

Pres

sure

(MPa

)

Pipe length (m)











120593 = 1 + 119862 [sin (18120579) minus 13 sin3 (18120579)] (A2)

When 120579 = 90∘119862 = (1 minus 119877119871) ln (119889119877119890119871119873119891119871119908Fr119892)

119873119871119908 = 119882119904119871 ( 120588119871119892120590)025 (A3)




120601 = 119867119871 (120579)119867119871 (0) (A4)



minus 119889119901119889119897= [119867119871120588119871 + (1 minus 119867119871) 120588119866] 119892 sin 120579 + 120582 (21199081198721205871198893)

1 minus [119867119871120588119871 + (1 minus 119867119871) 120588119892] 119908119908119904119892119901 (B1)





( 1205821205820) = 119890119899

119898 = 119877119871[119867119871 (120579)] 119899= minus ln119898


(B2)




Re0 = 119889119908120588119891120583 = 119889119908 [120588119871119877119871 + 120588119892 (1 minus 119877119871)]

[120583119871119877119871 + 120583119892 (1 minus 119877119871)] (B3)


Nomenclature





Start

Input data





End





Yes




Competing Interests


Acknowledgments


References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 15 27 37 45 44

0 12 23 32 38 37

0 10 19 26 31 31

0 8 15 21 25 25

1 7 12 16 20 19

3 6 9 13 15 15

0

9

18

27

36

45


Start

Initialize

Fitness value

Selection

Crossover

Mutation

Stop

EndYes

No








119871119894119896 = 1003817100381710038171003817100381711990311989411989610038171003817100381710038171003817= 119899minus1sum119895=0

radic(119909119894119896(119895+1)

minus 119909119894119896119895

)2 + (119910119894119896(119895+1)

minus 119910119894119896119895

)2 + (119911119894119896(119895+1)

minus 119911119894119896119895

)2 (2)



119863119875119894119896= 119899minus1sum119895=0

119889119901119894119896119895radic(119909119894119896(119895+1)

minus 119909119894119896119895

)2 + (119910119894119896(119895+1)

minus 119910119894119896119895

)2 + (119911119894119896(119895+1)

minus 119911119894119896119895

)2 (3)


Fitness119894119896 = 1119863119875119894119896 (4)




N0

N1

Njminus1

Nj

Nn


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20123456789

1011121314151617181920

N0

N1

Nj

Nn

Y

X

Nj+1





119911 (119909 119910)= ℎsum119894=1


V119894)119902119894 (5)


BestOptimal value

2530354045505560657075808590

Eval

uatio

n va

lue










0

5

10

15

20

Y

5 10 15 200X


4375

1450

2463

3475

4488

55002

4

6

8

10

12

14

16

18

20

Y

4 6 8 10 12 14 16 18 202X

minus2600

minus1588

minus5750










4 Example Analysis






5 Conclusions




0405

0607

080910 170

175

180

185

190

195

200

205

0302

01005

0010005

000200005

(a)

0405

060708

0910

170

175

180

185

190

195

00005

0002

0005

001005

0102

03

(b)


2 4 6 8 10 12 14 16 18 20

1875

1250

2313

3375

4438

5500

X

2

4

6

8

10

12

14

16

18

20

Y

minus3000

minus1938

minus8750




Appendix






119867119871 (0) = 119886119877119887119871Fr119888

119877119871 = 119876119897119876119897 + 119876119892

Fr = 1199082119892119889

(A1)







ge04 gt1198714


0

50

100

150

200

250

B

9400

9750

1010

1045

1080

1115

1150

1185

1220

A

Y

50 100 150 200 2500X


050

100

150

200

250

800900

10001100

12001300

1400

0

50

100

150200

250

A

B

YX

Z



1000 2000 3000 4000 5000 60000Pipe length (m)

1060

1080

1100

1120

1140

1160

1180

1200

Elev

atio

n (m

)


0 1000 2000 3000 4000 500004

06

08

10

12

14

16

Pres

sure

(MPa

)

Pipe length (m)











120593 = 1 + 119862 [sin (18120579) minus 13 sin3 (18120579)] (A2)

When 120579 = 90∘119862 = (1 minus 119877119871) ln (119889119877119890119871119873119891119871119908Fr119892)

119873119871119908 = 119882119904119871 ( 120588119871119892120590)025 (A3)




120601 = 119867119871 (120579)119867119871 (0) (A4)



minus 119889119901119889119897= [119867119871120588119871 + (1 minus 119867119871) 120588119866] 119892 sin 120579 + 120582 (21199081198721205871198893)

1 minus [119867119871120588119871 + (1 minus 119867119871) 120588119892] 119908119908119904119892119901 (B1)





( 1205821205820) = 119890119899

119898 = 119877119871[119867119871 (120579)] 119899= minus ln119898


(B2)




Re0 = 119889119908120588119891120583 = 119889119908 [120588119871119877119871 + 120588119892 (1 minus 119877119871)]

[120583119871119877119871 + 120583119892 (1 minus 119877119871)] (B3)


Nomenclature





Start

Input data





End





Yes




Competing Interests


Acknowledgments


References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










N0

N1

Njminus1

Nj

Nn


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20123456789

1011121314151617181920

N0

N1

Nj

Nn

Y

X

Nj+1





119911 (119909 119910)= ℎsum119894=1


V119894)119902119894 (5)


BestOptimal value

2530354045505560657075808590

Eval

uatio

n va

lue










0

5

10

15

20

Y

5 10 15 200X


4375

1450

2463

3475

4488

55002

4

6

8

10

12

14

16

18

20

Y

4 6 8 10 12 14 16 18 202X

minus2600

minus1588

minus5750










4 Example Analysis






5 Conclusions




0405

0607

080910 170

175

180

185

190

195

200

205

0302

01005

0010005

000200005

(a)

0405

060708

0910

170

175

180

185

190

195

00005

0002

0005

001005

0102

03

(b)


2 4 6 8 10 12 14 16 18 20

1875

1250

2313

3375

4438

5500

X

2

4

6

8

10

12

14

16

18

20

Y

minus3000

minus1938

minus8750




Appendix






119867119871 (0) = 119886119877119887119871Fr119888

119877119871 = 119876119897119876119897 + 119876119892

Fr = 1199082119892119889

(A1)







ge04 gt1198714


0

50

100

150

200

250

B

9400

9750

1010

1045

1080

1115

1150

1185

1220

A

Y

50 100 150 200 2500X


050

100

150

200

250

800900

10001100

12001300

1400

0

50

100

150200

250

A

B

YX

Z



1000 2000 3000 4000 5000 60000Pipe length (m)

1060

1080

1100

1120

1140

1160

1180

1200

Elev

atio

n (m

)


0 1000 2000 3000 4000 500004

06

08

10

12

14

16

Pres

sure

(MPa

)

Pipe length (m)











120593 = 1 + 119862 [sin (18120579) minus 13 sin3 (18120579)] (A2)

When 120579 = 90∘119862 = (1 minus 119877119871) ln (119889119877119890119871119873119891119871119908Fr119892)

119873119871119908 = 119882119904119871 ( 120588119871119892120590)025 (A3)




120601 = 119867119871 (120579)119867119871 (0) (A4)



minus 119889119901119889119897= [119867119871120588119871 + (1 minus 119867119871) 120588119866] 119892 sin 120579 + 120582 (21199081198721205871198893)

1 minus [119867119871120588119871 + (1 minus 119867119871) 120588119892] 119908119908119904119892119901 (B1)





( 1205821205820) = 119890119899

119898 = 119877119871[119867119871 (120579)] 119899= minus ln119898


(B2)




Re0 = 119889119908120588119891120583 = 119889119908 [120588119871119877119871 + 120588119892 (1 minus 119877119871)]

[120583119871119877119871 + 120583119892 (1 minus 119877119871)] (B3)


Nomenclature





Start

Input data





End





Yes




Competing Interests


Acknowledgments


References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












0

5

10

15

20

Y

5 10 15 200X


4375

1450

2463

3475

4488

55002

4

6

8

10

12

14

16

18

20

Y

4 6 8 10 12 14 16 18 202X

minus2600

minus1588

minus5750










4 Example Analysis






5 Conclusions




0405

0607

080910 170

175

180

185

190

195

200

205

0302

01005

0010005

000200005

(a)

0405

060708

0910

170

175

180

185

190

195

00005

0002

0005

001005

0102

03

(b)


2 4 6 8 10 12 14 16 18 20

1875

1250

2313

3375

4438

5500

X

2

4

6

8

10

12

14

16

18

20

Y

minus3000

minus1938

minus8750




Appendix






119867119871 (0) = 119886119877119887119871Fr119888

119877119871 = 119876119897119876119897 + 119876119892

Fr = 1199082119892119889

(A1)







ge04 gt1198714


0

50

100

150

200

250

B

9400

9750

1010

1045

1080

1115

1150

1185

1220

A

Y

50 100 150 200 2500X


050

100

150

200

250

800900

10001100

12001300

1400

0

50

100

150200

250

A

B

YX

Z



1000 2000 3000 4000 5000 60000Pipe length (m)

1060

1080

1100

1120

1140

1160

1180

1200

Elev

atio

n (m

)


0 1000 2000 3000 4000 500004

06

08

10

12

14

16

Pres

sure

(MPa

)

Pipe length (m)











120593 = 1 + 119862 [sin (18120579) minus 13 sin3 (18120579)] (A2)

When 120579 = 90∘119862 = (1 minus 119877119871) ln (119889119877119890119871119873119891119871119908Fr119892)

119873119871119908 = 119882119904119871 ( 120588119871119892120590)025 (A3)




120601 = 119867119871 (120579)119867119871 (0) (A4)



minus 119889119901119889119897= [119867119871120588119871 + (1 minus 119867119871) 120588119866] 119892 sin 120579 + 120582 (21199081198721205871198893)

1 minus [119867119871120588119871 + (1 minus 119867119871) 120588119892] 119908119908119904119892119901 (B1)





( 1205821205820) = 119890119899

119898 = 119877119871[119867119871 (120579)] 119899= minus ln119898


(B2)




Re0 = 119889119908120588119891120583 = 119889119908 [120588119871119877119871 + 120588119892 (1 minus 119877119871)]

[120583119871119877119871 + 120583119892 (1 minus 119877119871)] (B3)


Nomenclature





Start

Input data





End





Yes




Competing Interests


Acknowledgments


References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0405

0607

080910 170

175

180

185

190

195

200

205

0302

01005

0010005

000200005

(a)

0405

060708

0910

170

175

180

185

190

195

00005

0002

0005

001005

0102

03

(b)


2 4 6 8 10 12 14 16 18 20

1875

1250

2313

3375

4438

5500

X

2

4

6

8

10

12

14

16

18

20

Y

minus3000

minus1938

minus8750




Appendix






119867119871 (0) = 119886119877119887119871Fr119888

119877119871 = 119876119897119876119897 + 119876119892

Fr = 1199082119892119889

(A1)







ge04 gt1198714


0

50

100

150

200

250

B

9400

9750

1010

1045

1080

1115

1150

1185

1220

A

Y

50 100 150 200 2500X


050

100

150

200

250

800900

10001100

12001300

1400

0

50

100

150200

250

A

B

YX

Z



1000 2000 3000 4000 5000 60000Pipe length (m)

1060

1080

1100

1120

1140

1160

1180

1200

Elev

atio

n (m

)


0 1000 2000 3000 4000 500004

06

08

10

12

14

16

Pres

sure

(MPa

)

Pipe length (m)











120593 = 1 + 119862 [sin (18120579) minus 13 sin3 (18120579)] (A2)

When 120579 = 90∘119862 = (1 minus 119877119871) ln (119889119877119890119871119873119891119871119908Fr119892)

119873119871119908 = 119882119904119871 ( 120588119871119892120590)025 (A3)




120601 = 119867119871 (120579)119867119871 (0) (A4)



minus 119889119901119889119897= [119867119871120588119871 + (1 minus 119867119871) 120588119866] 119892 sin 120579 + 120582 (21199081198721205871198893)

1 minus [119867119871120588119871 + (1 minus 119867119871) 120588119892] 119908119908119904119892119901 (B1)





( 1205821205820) = 119890119899

119898 = 119877119871[119867119871 (120579)] 119899= minus ln119898


(B2)




Re0 = 119889119908120588119891120583 = 119889119908 [120588119871119877119871 + 120588119892 (1 minus 119877119871)]

[120583119871119877119871 + 120583119892 (1 minus 119877119871)] (B3)


Nomenclature





Start

Input data





End





Yes




Competing Interests


Acknowledgments


References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















ge04 gt1198714


0

50

100

150

200

250

B

9400

9750

1010

1045

1080

1115

1150

1185

1220

A

Y

50 100 150 200 2500X


050

100

150

200

250

800900

10001100

12001300

1400

0

50

100

150200

250

A

B

YX

Z



1000 2000 3000 4000 5000 60000Pipe length (m)

1060

1080

1100

1120

1140

1160

1180

1200

Elev

atio

n (m

)


0 1000 2000 3000 4000 500004

06

08

10

12

14

16

Pres

sure

(MPa

)

Pipe length (m)











120593 = 1 + 119862 [sin (18120579) minus 13 sin3 (18120579)] (A2)

When 120579 = 90∘119862 = (1 minus 119877119871) ln (119889119877119890119871119873119891119871119908Fr119892)

119873119871119908 = 119882119904119871 ( 120588119871119892120590)025 (A3)




120601 = 119867119871 (120579)119867119871 (0) (A4)



minus 119889119901119889119897= [119867119871120588119871 + (1 minus 119867119871) 120588119866] 119892 sin 120579 + 120582 (21199081198721205871198893)

1 minus [119867119871120588119871 + (1 minus 119867119871) 120588119892] 119908119908119904119892119901 (B1)





( 1205821205820) = 119890119899

119898 = 119877119871[119867119871 (120579)] 119899= minus ln119898


(B2)




Re0 = 119889119908120588119891120583 = 119889119908 [120588119871119877119871 + 120588119892 (1 minus 119877119871)]

[120583119871119877119871 + 120583119892 (1 minus 119877119871)] (B3)


Nomenclature





Start

Input data





End





Yes




Competing Interests


Acknowledgments


References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















120593 = 1 + 119862 [sin (18120579) minus 13 sin3 (18120579)] (A2)

When 120579 = 90∘119862 = (1 minus 119877119871) ln (119889119877119890119871119873119891119871119908Fr119892)

119873119871119908 = 119882119904119871 ( 120588119871119892120590)025 (A3)




120601 = 119867119871 (120579)119867119871 (0) (A4)



minus 119889119901119889119897= [119867119871120588119871 + (1 minus 119867119871) 120588119866] 119892 sin 120579 + 120582 (21199081198721205871198893)

1 minus [119867119871120588119871 + (1 minus 119867119871) 120588119892] 119908119908119904119892119901 (B1)





( 1205821205820) = 119890119899

119898 = 119877119871[119867119871 (120579)] 119899= minus ln119898


(B2)




Re0 = 119889119908120588119891120583 = 119889119908 [120588119871119877119871 + 120588119892 (1 minus 119877119871)]

[120583119871119877119871 + 120583119892 (1 minus 119877119871)] (B3)


Nomenclature





Start

Input data





End





Yes




Competing Interests


Acknowledgments


References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Start

Input data





End





Yes




Competing Interests


Acknowledgments


References












RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









route optimization of pipeline in gas-liquid two-phase...

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