Optimization Design of a Riser-Drill String Coupling ...

Research ArticleOptimization Design of a Riser-Drill String Coupling SystemBased on CAE Techniques

Shiyao Qin1 Ruiming Wang1 Deyi Fu 1 and Gaowei Wang2

1State Key Laboratory of Operation and Control of Renewable Energy amp Storage Systems (China Electric Power ResearchInstitute Co Ltd) Beijing 100192 China2School of Mechanical Engineering University of Science and Technology Beijing China

Correspondence should be addressed to Deyi Fu fudeyieprisgcccomcn

Received 27 October 2020 Revised 9 November 2020 Accepted 30 December 2020 Published 30 January 2021

Academic Editor Yuqiang Xu

Copyright copy 2021 Shiyao Qin et al -is 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

In a riser-drill string coupling system the drill string extends from platform to downhole and its exterior tube is divided by mudline into two parts riser for upside and borehole for downside Due to such a pipe-in-pipe structure an improved dynamic modelis proposed to take the multipoint interactions between the inner and outer pipes into consideration -e dynamic responses ofthis system are analyzed by Computer Aided Engineering (CAE) techniques specifically it is numerically simulated in Abaqusthen both the parametric sensitivity analysis and the main effect analysis are carried out in Isight to determine the optimizationparameters and the optimization strategy Moreover six-sigma algorithm in Isight is applied to simultaneously drive theneighborhood cultivation genetic algorithm (NCGA) to conduct multiobjective optimization and drive the Monte Carlo methodto analyze the stability of the obtained optimal solution Based on the above investigations a software package is developed via thesecondary developments of both Abaqus and Isight By this way the optimization design of the riser-drill string coupling systembased on dynamic analysis can be conducted effectively and efficiently

1 Introduction

-e exploitation of offshore petroleum resources is facedwith complex ocean environment hence the reliability ofequipment and the operation safety should be of highstandard Offshore drilling is different from onshoredrilling since drilling rigs and drilling mud reach wellheadthrough a riser system whose length is determined by thesea depth A riser system can be viewed as an extension ofborehole since its bottom side joins with a blowout pre-venter which is installed on the wellhead -e topside ofthe riser system is connected with a drilling platform or adrilling vessel via telescopic joint and flexible joint -eriser and borehole constitute an outer pipe within which adrill string system rotates Above the mud line the pipe-in-pipe structure deflects under the effects of ocean loadswhich triggers the intermittent contacts and frictions be-tween the inner and outer pipes along the whole drillingtube system

-e investigations of the dynamics of the offshoredrilling tube system trace back to 1970s As the beginningonly the riser system was considered According to both thefourth-order differential equation of Euler-Bernoulli beamand the Morison equation Burke [1] built up a dynamicmodel of a riser system for 800 ft sea depth Based onBurkersquos work scholars applied finite element method toanalyze the riser dynamics for two-dimensional [2 3] orthree-dimensional conditions [4 5] -ereafter rather thanusing the Euler-Bernoulli beam Yazdchi and Crisfeld [6]applied Reissner-Simo beam to develop the mathematicalmodel of the riser system to enhance the analysis of sheardeformation of the riser Instead of using the beam modelsNair and Baddour [7] divided the riser system into pieceswhich were connected by a series of spring-damper unitsIn addition Wang et al [8] analyzed the drilling tubevibration under the influences of the drilling mud flowingLiu et al [9] discussed the wear of deepwater drilling riserBy further considering the contact nonlinearity between

HindawiMathematical Problems in EngineeringVolume 2021 Article ID 6659632 11 pageshttpsdoiorg10115520216659632

drill string and riser the pipe-in-pipe structure for thedrilling tube system raises the interests of scholars Buenoand Morooka [10] designed an interaction model to cal-culate the contact force between drill string and riserHarrison and Helle [11] proposed an equivalent model tocalculate the combined stiffness of the inner and outerpipes Liu et al [12] introduced the gap-element to analyzethe nonlinear mechanics of drill string Mao et al [13 14]designed an experimental system to measure the dynamicresponses of a riser system Guo et al [15] discussed thevibration suppression of a variable-length drilling risersystem-e precise dynamic analysis of the riser-drill stringcoupling system is the precondition of its correspondingoptimization design Housner and Dixon [16] primarilyconducted the optimization design to reduce the steelvolumes of the pipe-in-pipe structure and thus to save thepotential cost Chang et al [17] analyzed both the envi-ronmental influences and the operational factors for op-timizing offshore drilling riser In order to promote thecalculation efficiency Zheng and Yang [18] applied ap-proximation method to optimize a compliant vertical ac-cess riser Qin et al [19] carried out optimization design ofa deepwater riser based on parametric sensitivity analysisand its optimal objective is to minimize the total tensionYang et al [20] presented an efficient optimization strategyfor the design of the offshore riser by considering the fa-tigue life constraints Aiming at minimizing the rotationangle of the lower flexible joint Wang et al [21] focused onthe optimization of the top tension of the riser

According to the aforementioned investigations in thispaper a complete optimization flow about the riser-drillstring coupling system is expected to be developed which isbased on the analyses of the dynamic responses of the pipe-in-pipe structure model -e multiobjective optimizationmethod will be applied and the reliability analysis will beintegrated into the optimization design-emain purpose isto secure the safety and stability of the designed offshoredrilling tube system when it works under the varied ocean

environmental loads and the perturbations of systemparameters

-e rest of this paper is organized as follows Section 2introduces the mathematical modeling of the riser-drillstring coupling system and the gap-element is introduced tosimulate the intermittent interactions between the inner andouter pipes -e dynamic responses of the drilling tubesystem are numerically simulated by using Abaqus InSection 3 the parametric sensitivity analyses and the maineffect analyses are conducted to explore the optimizationparameters and to determine the optimization strategy -emultiobjective optimization by using a combination ofoptimization algorithms is carried out successively InSection 4 based on the secondary developments of bothAbaqus and Isight a software package is developed whichcan be specially applied for the optimization design of theriser-drill string coupling system At last concluding re-marks are provided in section 5

2 Mathematical Modeling andNumerical Simulation

-e developed physical model for a part of a riser-drill stringcoupling system is shown in Figure 1-e deformation of thepipe-in-pipe structure under the effects of ocean loads isdepicted in subplot (a) and a gap-element unit used tosimulate the interactions between the inner and outer pipesis displayed in subplot (b)

During the mathematical modeling on the one handEkman drift theory [22] Airy wave theory [22] andMorisonequation (1) are applied to describe the ocean loads acting onthe riser Meanwhile the shear force tension gravity andinertia force of the riser are also considered On the otherhand the force analysis of the drill string is similar to theriser but without considering the direct influences of theocean loads In addition the interactions between the drillstring and the riser are described by the gap-elements-erefore the differential equations for the drilling tubesystem with the pipe-in-pipe structure can be written as

z2

zz2 EI

z2y

zz21113890 1113891 + P

z2y

zz2 + 1 minus Bf1113872 1113873mg

zy

zz+ m

z2y

zt2 +

12CdDρ uw + uc minus

zy

zt1113888 1113889 uw + uc minus

zy

zt

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868

+14D

2πρ Cmaw minus Cm minus 1( 1113857z2y

zt21113890 1113891 + H y minus yprime minus G( 1113857Fcminusf 0

z2

zzprime2 EIprime

z2yprime

zz rsquo21113890 1113891 + Pprime

z2yprime

zzprime2+ mprimeg

zyprime

zzprime+ mprime

z2yprime

zt2 + H y minus yprime minus G( 1113857Fcminusf 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)

2 Mathematical Problems in Engineering

where H(y minus yprime minus G) is a Heaviside function wheny minus yprime minus Gge 0 the interaction between the inner and outerpipes happens and the corresponding interaction force iscalculated as Fcminusf

H y minus yprime minus G( 1113857 0 y minus yprime minus Glt 0( 1113857

1 y minus yprime minus Gge 0( 1113857

⎧⎨

⎩

Fcminusf K(z) y minus yprime minus G( 1113857 + μ(z)K(z) y minus yprime minus G( 1113857

(2)

In addition the boundary conditions for the drilling tubesystem can be summarized as

y(0 t) 0

EI(0)z2y(0 t)

zz2 kb

zy(0 t)

zz

y(L t) S

EI(L)z2y(L t)

zz2 kt

zy(L t)

zz

yprime(0 t) A sin(Ωt)

zyprime(0 t)

zzprime 0

yprime(L t) S

zyprime(L t)

zzprime 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

-e initial conditions of the drilling tube system aredescribed as

y(z 0) 0

zy(z 0)

zt 0

yprime zprime 0( 1113857 0

zyprime zprime 0( 1113857

zt 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)

In addition the borehole is assumed to be vertical andstatic Two independent coordinate systems are applied todescribe the movements of the riser system (x minus y minus z) andthe drill string system (xprime minus yprime minus zprime) respectively All thesystem parameters are listed in Table 1

Based on the developed mathematical model Abaqusis applied to carry out the numerical simulation Spe-cifically the beam element B31 is used to construct boththe inner and outer pipes the edge-to-edge contact modelis chosen to simulate the interactions of pipes -econnector element CONN3D2 with joint-rotationproperty is used to describe the upper and lower flexiblejoints -e ocean loads are set by the Aqua module withthe sea current velocity decreasing exponentially from thesea level to the mud line Additionally to eliminate thedisturbance of transient dynamic behavior each nu-merical simulation lasts 100 periods of the sea wave andonly the last 20 periods are used to analyze the systemdynamics which ensures this system reaching its dynamicstable status A numerical simulation case is shown inFigure 2 In subplot (a) the dynamic stable status of thewhole riser-drill string coupling system is displayedwhere its lateral size is enlarged 5 times for more clearobservation -e maximal deflection region is marked asred which locates around the 13 sea depth Subplot (b) isan enlarged view to show the drill string-riserinteractions

Ocean load

Drill String

Mud

Riser

Gap-element I-1

Gap-element I

Gap-element I+1

xy

zxrsquo

zrsquoyrsquo

Mudx(xrsquo)

y(yrsquo)

k

k

μ

μ

Figure 1 Physical model of a riser-drill string coupling system

Mathematical Problems in Engineering 3

(a) (b)

Figure 2 Numerical simulation using Abaqus

Table 1 Nomenclature list

Kw Factor of wind speedz Distance from mud line (m)hw Amplitude of sea wave (m)ω Circular frequency of sea wave (rads)D External diameter of riser (m)m Mass of riser per unit length (kg)EIprime Flexural stiffness of drill string (Nm2)mprime Mass of drill string per length (kg)S Top drift of riser (m)kb Stiffness of lower joint (Nmrad)vw Wind speed (ms)L Water depth (m)Tw Period of sea wave (s)Cd Drag coefficientρ Sea-water density (kgm3)Bf Buoyancy factorPprime Tension of drill string (N)K Contact stiffness (Nm)A Amplitude of drill bit (m)kt Stiffness of top joint (Nmrad)vt Current speed (ms)φ Geographic latitude (deg)Lw Sea wavelength (m)Cm Inertial coefficientEI Flexural stiffness of riser (Nm2)P Tension of riser (N)g Gravitational acceleration (ms2)μ Friction coefficientΩ Frequency of drill bit (rads)G Initial gap between pipes (m)


3 Optimization Design Based onDynamic Responses

In this section the finite element model developed inAbaqus is embedded into Isight via its data interface spe-cialized for Abaqus and thus the optimization parametersdesigned by Isight can be sent to Abaqus meanwhile thedynamic responses of the riser-drill string system simulatedby Abaqus can also be transferred into Isight for furtheroptimization

31 Parametric Sensitivity Analyses Based on the numericalsimulation introduced in Section 2 parametric sensitivityanalyses for the riser-drill string coupling system can becarried out Six system parameters are considered diameterof riser thickness of riser top drift of riser hanging load ofdrill string top tension of riser and rotational stiffness offlexible joint For the purpose of comparison the dynamicresponses of a standard case are simulated primarily [15]and then the six system parameters are modified successivelyto compare their influences on the system dynamic re-sponses All the obtained results of numerical simulationsare plotted in Figures 3ndash5 Figure 3 shows the distributionsof (a) the deflection (b) bending moment (c) Mises stressand (d) the rotation angle for the riser respectively Figure 4displays the distributions of (a) the deflection (b) bendingmoment and (c)Mises stress for the drill string respectivelyFigure 5 shows the time histories of rotation angles of (a) theupper and (b) lower flexible joints respectively Accordingto the distinguishing influences of these six system pa-rameters the optimization strategies such as thickening theriser wall increasing the riser diameter decreasing the topdrift increasing the hanging load of drill string increasingthe top tension of riser and increasing the rotationalstiffness of flexible joint are suggested Since by applyingthese optimization strategies the tube deflection is re-stricted both the bending moment and Mises stress de-crease and the rotations of the riser and the flexible jointsare also limited effectively

32 Main Effect Analysis According to field practices fourmain constraint conditions for the system dynamic re-sponses should be considered during optimization designthemaximalMises stress is less than 67 of yield stress of thepipe material the maximal deflection of the tube system isless than 2 of the sea depth the maximal rotation angles ofthe upper and lower flexible joints are controlled within 5degand 2deg respectively Based on the proposed constraintconditions the correlations between the optimization pa-rameters and the constraint conditions are investigatedSpecifically the design of experiment method (DOE) and theLatin Hypercube sampling technique are applied -e sixoptimization parameters are set to vary within plusmn50 aroundtheir standard values 1000 sampling cases are tested -eobtained correlations are shown in Table 2 Specifically themaximal Mises stress is mainly determined by the hangingload of drill string and they are positive correlation -emaximal deflection is mainly determined by the top drift of

riser meanwhile large top tension of the riser and largehanging load of the drill string can also restrict the pipedeflection -e increasing diameter and the top tension ofthe riser can decrease the maximal rotation angle of theupper flexible joint In particular since the rotation angle ofthe lower flexible joint is negative the optimization target isto decrease its absolute value For this purpose decreasingthe top drift of riser or increasing the top tension of riser orthe hanging load of drill string or the rotational stiffness ofthe lower joint is effective to control the rotation of the lowerflexible joint

Meanwhile several contradiction effects are also ob-served in Table 2 For instance the increasing hanging loadof drill string will be of benefit for the controls of the riserdeflection and the rotations of the upper and lower jointsbut it will also lead to high Mises stress Such contradictioneffects among different optimization objectives approve thenecessity of the application of multiobjective optimizationsince its basic principle is to search the optimal solutions viabalancing these contradictory optimization objectives Inorder to conduct multiobjective optimization multipleobjectives are also needed According to these four con-straint conditions the corresponding optimization objec-tives are inferred as simultaneously minimizing the pipedeflection the Mises stress and the rotation angles of boththe upper and lower flexible joints

33 Multiobjective Optimization By considering the sixoptimization parameters four constraint conditions andfour optimization objectives the optimization of the riser-drill string coupling system is a multiparameter multi-constraint and multiobjective optimization Moreover inorder to further secure the stability of the obtained opti-mization solutions the influences of the parameter per-turbation should be considered during optimization design-erefore a combination of optimization algorithms isdesigned Specifically NCGA is chosen to conduct theoptimization design Monte Carlo method is applied todetermine the reliability of the obtained optimization so-lutions Both the NCGA and the Monte Carlo method areintegrated by the six-sigma method since it is able to si-multaneously drive the NCGA and Monte Carlo method tosecure that all the confirmed optimization designs satisfy theminimal requirement for reliability To conduct the multi-objective optimization effectively the pipe-in-pipe modeldeveloped in Abaqus is directly imported into Isight inwhich a variety of optimization algorithms have already beenintegrated

For a practical multiobjective optimization design of ariser-drill string coupling system all the optimization pa-rameters are allowed to fluctuate within plusmn10 around theoptimization designs and the minimal requirement forreliability is set as 98 By applying the combination of theoptimization algorithms 1000 parameter combinations areanalyzed and the obtained results are projected to a three-dimensional phase space (see Figure 6) All the 1000 designsare divided into three types failed designs general designsand optimization designs Specifically the failed designs (red


dots) may violate constraint conditions or dissatisfy reli-ability requirement or cannot converge -e general designs(black dots) satisfy the constraints and reliability require-ment but they are not optimal from a mathematical point ofview while the optimization designs (blue dots) are sug-gested according to comprehensive comparisons among allthe feasible solutions Moreover all the optimization designs(blue points) constitute a Pareto front which is a surface inthe three-dimensional phase space -is Pareto front indi-cates a basic distribution trend of the optimization designsbased on multiobjective optimization

4 Secondary Developments of Abaqusand Isight

From dynamic analysis to multiobjective optimization thewhole procedure of the optimization design of a riser-drillstring coupling system has been introduced in detail whichcan be further summarized as the flow chart shown inFigure 7

Following this flow chart a software package is developedvia the secondary developments of both Abaqus and IsightFigure 8 displays the framework of the newly developed

0 20 30 4010Riser deflection (m)

0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25

Diameter + 10Hanging load + 50

ickness + 100Top dri ndash 100

Standard caseStiffness + 200

(a)

0ndash200 100ndash100Riser bending moment (kNm)

0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(b)

0 40 6020Riser Mises stress (MPa)

0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(c)

0

500

1000

1500

2000

Sea d

epth

(m)

0 10ndash5 5Rotation angle of riser (deg)

Top tension + 25




(d)

Figure 3 Comparison of dynamic responses for the riser system with different parameters


software package which consists of 10 function modulesSpecifically four function modules are developed based onAbaqus including parametric modeling data analysis dy-namic simulation and data saving Six other optimizationmodules are extracted from Isight including DOE NCGAand Monte Carlo analysis of the pipe-in-pipe structure modelbuilt in Abaqus and the corresponding NCGA Monte Carlo

and six-sigma analysis of the approximation model which isdeveloped by using the radial basis neural network analysis ofall the obtained results of numerical simulations In particularthe accuracy of the approximation model mainly depends onthe quality and quantity of the obtained simulation resultshence it can be upgraded continuously as more numericalsimulations are conducted

Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)

0 20 40ndash20Drill string deflection (m)

(a)

Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)

0 2 4 6ndash2Drill string bending moment (kNm)

(b)

Top tension + 25




100 200 3000Drill string Mises stress (MPa)

ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)

(c)

Figure 4 Comparison of dynamic responses for the drill string with different parameters


When a new study case is analyzed by using thissoftware package the parametric modeling is appliedprimarily and a pipe-in-pipe structure model can be di-rectly built up based on the input system parameters seeFigure 9(a) After conducting the numerical simulationsnine dynamic responses about the drilling tube system aredisplayed see Figure 9(b) Subsequently both the devel-oped pipe-in-pipe structure model and the obtained resultsof numerical simulations are imported into the

optimization modules and the optimization design startsby calling the corresponding Isight template which hasalready been integrated into this software package seeFigure 9(c) However the optimization design based on thepipe-in-pipe structure model is generally time-consumingUnder such circumstances the optimization module usingthe approximation model can be used to replace the cor-responding optimization of the structure model seeFigure 9(d)

100 200 300 4000Simulation time (s)

ndash4ndash2

02468

Ang

le o

f upp

er jo

int (

deg)

Top tension + 25




(a)

300200100 4000Simulation time (s)

ndash3ndash25

ndash2ndash15

ndash1ndash05

005

Ang

le o

f low

er jo

int (

deg)

Top tension + 25




(b)

Figure 5 Comparison of time series for the upper and lower joints with different parameters

Table 2 Effect correlations between the input and output variables

OutputInput

Riserdiameter

Riserthickness

Topdrift

Hangingload

Toptension

Stiffness of lowerjoint

Stiffness of upperjoint

Maximal Mises stress 006 minus012 005 095 minus014 003 004Maximal deflection minus018 minus009 079 minus026 minus041 001 minus005Maximal angle of upperjoint minus065 001 minus017 minus034 minus052 minus001 minus017

Maximal angle of lowerjoint 004 002 minus062 041 055 024 006


Six sigma

NCGA Monte Carlo

Minimalrequirement

Parameter range

Yes

No

Parameter perturbation

Optimal design

Degree of reliability

Optimizationparameters

Constraintconditions

Optimizationobjectives

Dynamic model Dynamic responses

Parametric sensitivity analysis Principal effect analysis

Abaqus

Isight

Figure 7 Flow chart of the software package for optimization design

Deflection (m)

40

0

ndash30

05

80

0

Ang

le o

f low

er jo

int (

deg)

Angle of upper joint (deg)

Figure 6 Pareto front obtained by multiobjective optimization


5 Concluding Remarks

In this paper the dynamic model of a riser-drill stringcoupling system with pipe-in-pipe structure was proposed-e interactions between the inner and outer pipes wereconsidered into the dynamic model via introducing a seriesof gap-elements Based on the numerical simulations inAbaqus the parametric sensitivity analyses were carried outIn order to secure the offshore drilling tube system working

in safe conditions the operations such as thickening theriser wall increasing the riser diameter limiting the topdrift increasing the hanging load of drill string enhancingthe top tension of riser and increasing the rotationalstiffness of the flexible joints were suggested

According to the main effect analyses the top drift ofriser the top tension of riser and the hanging load of drillstring were proved as the three most significant parametersfor the system optimization design A combination of

Figure 9 Main function modules of the software package

1 Parametric modeling

3 Dynamic simulation2 Data analysis

4 Data saving5 DOE6 NCGA7 Monte Carlo 8 Monte Carlo of approximation model9 NCGA of approximation model

10 Six sigma of approximation model

8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1

Figure 8 Interface for the optimization design of a riser-drill string coupling system


optimization algorithms including NCGA Monte Carlomethod and six-sigma method was designed based onwhich a group of optimization designs were explored andthey constituted a Pareto front which indicated a basicdistribution trend of the optimization designs

Based on the secondary developments of both Abaqusand Isight a software package was developed specially forthe optimization design of offshore drilling tube system Tenfunction modules including parametric modeling dynamicanalysis and optimization design had been integrated intothis software package

For the future work the coupling effect of drilling fluidin the pipe-in-pipe structure will be taken into consider-ation the fatigue damage of the drilling tube system isexpected to be analyzed by using Fe-safe meanwhile thesoftware package will also be upgraded correspondinglyWith the further improvements of this software package it isexpected to be of benefit for offshore drilling engineers toconduct the optimization designs of offshore drilling tubesystems with high reliability and high efficiency

Data Availability

All data models or codes generated or used during the studyare available from the corresponding author upon request

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is work was supported by the National Key Research andDevelopment Program of China (2018YFB0904005) Scienceand Technology Project of State Grid(SGDK0000NYJS1803505) the National Natural ScienceFoundation of China (Grant no 51904018) and the Fun-damental Research Funds for the Central Universities(Grant no FRF-TP-18-054A1)

References

[1] B G Burke ldquoAn analysis of marine risers for deep waterrdquo inProceedings of the Offshore Technology Conference HoustonTX USA April 1973

[2] M H Patel S Sarohia and K F Ng ldquoFinite-element analysisof the marine riserrdquo Engineering Structures vol 6 no 3pp 175ndash184 1984

[3] B Yue K C Man and D Walters ldquoTension and expansionanalysis of pipe-in-pipe risers part B finite element model-ingrdquo in Proceedings of the International Offshore and PolarEngineering Conference Anchorage AK USA June 2013

[4] M M Bernitsas J E Kokarakis and A Imron ldquoLarge de-formation three-dimensional static analysis of deep watermarine risersrdquo Applied Ocean Research vol 7 no 4pp 178ndash187 1985

[5] Y Bae and M M Bernitsas ldquoImportance of nonlinearities instatic and dynamic analyses of marine risersrdquo in Proceedingsof the International Offshore and Polar EngineeringConference Hague Netherlands June 1995

[6] M Yazdchi and M A Crisfeld ldquoNonlinear dynamic behaviorof flexible marine pipes and risersrdquo International Journal forNumerical Methods in Engineering vol 54 pp 1265ndash13082001

[7] W R Nair and R E Baddour ldquo-ree-dimensional dynamicsof a flexible marine riser undergoing large elastic deforma-tionsrdquo Multibody System Dynamics vol 10 pp 393ndash4232003

[8] Y Wang D Gao and J Fang ldquoStatic analysis of deep-watermarine riser subjected to both axial and lateral forces in itsinstallationrdquo Journal of Natural Gas Science and Engineeringvol 19 pp 84ndash90 2014

[9] X Liu G Chen Y Chang L Zhang and K Liu ldquoStudy ondeepwater drilling riser wearrdquo in Proceedings of the OffshoreTechnology Conference Asia Kuala Lumpur Malaysia March2017

[10] R C S Bueno and C K Morooka ldquoAnalysis method forcontact forces between drillstring-well-riserrdquo in Proceedingsof the International Petroleum Conference and Exhibition ofMexico Veracruz Mexico October 1994

[11] R I Harrison and Y Helle ldquoUnderstanding the response ofpipe-in-pipe deepwater riser systemsrdquo in Proceedings of theInternational Offshore and Polar Engineering ConferenceLisbon Portugal July 2007

[12] J-B Liu H Ding and X Zhang ldquoApplication of gap elementto nonlinear mechanics analysis of drillstringrdquo Journal ofZhejiang University Science vol 3 no 4 pp 440ndash444 2002

[13] L Mao Q Liu S Zhou G Wang and Q Fu ldquoDeep waterdrilling riser mechanical behavior analysis considering actualriser string configurationrdquo Journal of Natural Gas Science andEngineering vol 33 pp 240ndash254 2016

[14] L Mao Q Liu S Zhou W Jiang Z Liu and T PengldquoVortex-induced vibration mechanism of drilling riser undershear flowrdquo Petroleum Exploration and Development vol 42no 1 pp 112ndash118 2015

[15] F Guo Y Liu F Luo and YWu ldquoVibration suppression andoutput constraint of a variable length drilling riser systemrdquoJournal of the Franklin Institute vol 356 no 3 pp 1177ndash11952019

[16] M Housner andM Dixon ldquoOptimized design of pipe-in-pipesystemsrdquo in Proceedings of the Offshore TechnologyConference Houston TX USA February 2003

[17] Y Chang G Chen and L Xu ldquoInfluential factors for thedesign of ultra-deepwater drilling risersrdquo Petroleum Explo-ration and Development vol 36 no 4 pp 523ndash528 2009

[18] W Zheng and H Yang ldquoDynamic response optimization of acompliant vertical access riserrdquo Ship Science amp Technologyvol 32 no 2 pp 115ndash119 2010

[19] W Qin Z Kang and Y Kang ldquoFree standing hybrid riserglobal parametric sensitivity analysis and optimum designrdquo inProceedings of the International Conference on Ocean Offshoreand Arctic Engineering Rotterdam Netherlands October2011

[20] H Yang H Li and H Park ldquoOptimization design for steelcatenary riser with fatigue constraintsrdquo International JournalOffshore and Polar Engineering vol 21 no 4 pp 302ndash3072011

[21] Y Wang D Gao and J Fang ldquoOptimization analysis of theriser top tension force in deepwater drilling aiming at theminimum variance of lower flexible joint deflection anglerdquoJournal of Petroleum Science and Engineering vol 146pp 149ndash157 2016

[22] O M Faltinsen Sea Loads on Ships and Offshore StructuresCambridge University Press Cambridge England 1998


drill string and riser the pipe-in-pipe structure for thedrilling tube system raises the interests of scholars Buenoand Morooka [10] designed an interaction model to cal-culate the contact force between drill string and riserHarrison and Helle [11] proposed an equivalent model tocalculate the combined stiffness of the inner and outerpipes Liu et al [12] introduced the gap-element to analyzethe nonlinear mechanics of drill string Mao et al [13 14]designed an experimental system to measure the dynamicresponses of a riser system Guo et al [15] discussed thevibration suppression of a variable-length drilling risersystem-e precise dynamic analysis of the riser-drill stringcoupling system is the precondition of its correspondingoptimization design Housner and Dixon [16] primarilyconducted the optimization design to reduce the steelvolumes of the pipe-in-pipe structure and thus to save thepotential cost Chang et al [17] analyzed both the envi-ronmental influences and the operational factors for op-timizing offshore drilling riser In order to promote thecalculation efficiency Zheng and Yang [18] applied ap-proximation method to optimize a compliant vertical ac-cess riser Qin et al [19] carried out optimization design ofa deepwater riser based on parametric sensitivity analysisand its optimal objective is to minimize the total tensionYang et al [20] presented an efficient optimization strategyfor the design of the offshore riser by considering the fa-tigue life constraints Aiming at minimizing the rotationangle of the lower flexible joint Wang et al [21] focused onthe optimization of the top tension of the riser

According to the aforementioned investigations in thispaper a complete optimization flow about the riser-drillstring coupling system is expected to be developed which isbased on the analyses of the dynamic responses of the pipe-in-pipe structure model -e multiobjective optimizationmethod will be applied and the reliability analysis will beintegrated into the optimization design-emain purpose isto secure the safety and stability of the designed offshoredrilling tube system when it works under the varied ocean

environmental loads and the perturbations of systemparameters

-e rest of this paper is organized as follows Section 2introduces the mathematical modeling of the riser-drillstring coupling system and the gap-element is introduced tosimulate the intermittent interactions between the inner andouter pipes -e dynamic responses of the drilling tubesystem are numerically simulated by using Abaqus InSection 3 the parametric sensitivity analyses and the maineffect analyses are conducted to explore the optimizationparameters and to determine the optimization strategy -emultiobjective optimization by using a combination ofoptimization algorithms is carried out successively InSection 4 based on the secondary developments of bothAbaqus and Isight a software package is developed whichcan be specially applied for the optimization design of theriser-drill string coupling system At last concluding re-marks are provided in section 5

2 Mathematical Modeling andNumerical Simulation

-e developed physical model for a part of a riser-drill stringcoupling system is shown in Figure 1-e deformation of thepipe-in-pipe structure under the effects of ocean loads isdepicted in subplot (a) and a gap-element unit used tosimulate the interactions between the inner and outer pipesis displayed in subplot (b)

During the mathematical modeling on the one handEkman drift theory [22] Airy wave theory [22] andMorisonequation (1) are applied to describe the ocean loads acting onthe riser Meanwhile the shear force tension gravity andinertia force of the riser are also considered On the otherhand the force analysis of the drill string is similar to theriser but without considering the direct influences of theocean loads In addition the interactions between the drillstring and the riser are described by the gap-elements-erefore the differential equations for the drilling tubesystem with the pipe-in-pipe structure can be written as

z2

zz2 EI

z2y

zz21113890 1113891 + P

z2y

zz2 + 1 minus Bf1113872 1113873mg

zy

zz+ m

z2y

zt2 +

12CdDρ uw + uc minus

zy

zt1113888 1113889 uw + uc minus

zy

zt

1113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868

+14D

2πρ Cmaw minus Cm minus 1( 1113857z2y

zt21113890 1113891 + H y minus yprime minus G( 1113857Fcminusf 0

z2

zzprime2 EIprime

z2yprime

zz rsquo21113890 1113891 + Pprime

z2yprime

zzprime2+ mprimeg

zyprime

zzprime+ mprime

z2yprime

zt2 + H y minus yprime minus G( 1113857Fcminusf 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(1)





⎧⎨

⎩


(2)


y(0 t) 0

EI(0)z2y(0 t)

zz2 kb

zy(0 t)

zz

y(L t) S

EI(L)z2y(L t)

zz2 kt

zy(L t)

zz


zyprime(0 t)

zzprime 0

yprime(L t) S

zyprime(L t)

zzprime 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)


y(z 0) 0

zy(z 0)

zt 0



zt 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)



Ocean load

Drill String

Mud

Riser

Gap-element I-1

Gap-element I

Gap-element I+1

xy

zxrsquo

zrsquoyrsquo

Mudx(xrsquo)

y(yrsquo)

k

k

μ

μ



(a) (b)



















0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(a)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(b)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(c)

0

500

1000

1500

2000

Sea d

epth

(m)


Top tension + 25




(d)





Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(a)

Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(b)

Top tension + 25





ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)

(c)






ndash4ndash2

02468

Ang

le o

f upp

er jo

int (

deg)

Top tension + 25




(a)


ndash3ndash25

ndash2ndash15

ndash1ndash05

005

Ang

le o

f low

er jo

int (

deg)

Top tension + 25




(b)



OutputInput

Riserdiameter

Riserthickness

Topdrift

Hangingload

Toptension






Six sigma

NCGA Monte Carlo

Minimalrequirement

Parameter range

Yes

No


Optimal design







Abaqus

Isight


Deflection (m)

40

0

ndash30

05

80

0

Ang

le o

f low

er jo

int (

deg)













8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1






Data Availability




Acknowledgments


References



























⎧⎨

⎩


(2)


y(0 t) 0

EI(0)z2y(0 t)

zz2 kb

zy(0 t)

zz

y(L t) S

EI(L)z2y(L t)

zz2 kt

zy(L t)

zz


zyprime(0 t)

zzprime 0

yprime(L t) S

zyprime(L t)

zzprime 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)


y(z 0) 0

zy(z 0)

zt 0



zt 0

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(4)



Ocean load

Drill String

Mud

Riser

Gap-element I-1

Gap-element I

Gap-element I+1

xy

zxrsquo

zrsquoyrsquo

Mudx(xrsquo)

y(yrsquo)

k

k

μ

μ



(a) (b)



















0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(a)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(b)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(c)

0

500

1000

1500

2000

Sea d

epth

(m)


Top tension + 25




(d)





Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(a)

Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(b)

Top tension + 25





ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)

(c)






ndash4ndash2

02468

Ang

le o

f upp

er jo

int (

deg)

Top tension + 25




(a)


ndash3ndash25

ndash2ndash15

ndash1ndash05

005

Ang

le o

f low

er jo

int (

deg)

Top tension + 25




(b)



OutputInput

Riserdiameter

Riserthickness

Topdrift

Hangingload

Toptension






Six sigma

NCGA Monte Carlo

Minimalrequirement

Parameter range

Yes

No


Optimal design







Abaqus

Isight


Deflection (m)

40

0

ndash30

05

80

0

Ang

le o

f low

er jo

int (

deg)













8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1






Data Availability




Acknowledgments


References
























(a) (b)



















0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(a)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(b)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(c)

0

500

1000

1500

2000

Sea d

epth

(m)


Top tension + 25




(d)





Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(a)

Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(b)

Top tension + 25





ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)

(c)






ndash4ndash2

02468

Ang

le o

f upp

er jo

int (

deg)

Top tension + 25




(a)


ndash3ndash25

ndash2ndash15

ndash1ndash05

005

Ang

le o

f low

er jo

int (

deg)

Top tension + 25




(b)



OutputInput

Riserdiameter

Riserthickness

Topdrift

Hangingload

Toptension






Six sigma

NCGA Monte Carlo

Minimalrequirement

Parameter range

Yes

No


Optimal design







Abaqus

Isight


Deflection (m)

40

0

ndash30

05

80

0

Ang

le o

f low

er jo

int (

deg)













8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1






Data Availability




Acknowledgments


References






































0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(a)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(b)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(c)

0

500

1000

1500

2000

Sea d

epth

(m)


Top tension + 25




(d)





Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(a)

Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(b)

Top tension + 25





ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)

(c)






ndash4ndash2

02468

Ang

le o

f upp

er jo

int (

deg)

Top tension + 25




(a)


ndash3ndash25

ndash2ndash15

ndash1ndash05

005

Ang

le o

f low

er jo

int (

deg)

Top tension + 25




(b)



OutputInput

Riserdiameter

Riserthickness

Topdrift

Hangingload

Toptension






Six sigma

NCGA Monte Carlo

Minimalrequirement

Parameter range

Yes

No


Optimal design







Abaqus

Isight


Deflection (m)

40

0

ndash30

05

80

0

Ang

le o

f low

er jo

int (

deg)













8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1






Data Availability




Acknowledgments


References





























0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(a)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(b)


0

500

1000

1500

2000

Sea d

epth

(m)

Top tension + 25




(c)

0

500

1000

1500

2000

Sea d

epth

(m)


Top tension + 25




(d)





Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(a)

Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(b)

Top tension + 25





ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)

(c)






ndash4ndash2

02468

Ang

le o

f upp

er jo

int (

deg)

Top tension + 25




(a)


ndash3ndash25

ndash2ndash15

ndash1ndash05

005

Ang

le o

f low

er jo

int (

deg)

Top tension + 25




(b)



OutputInput

Riserdiameter

Riserthickness

Topdrift

Hangingload

Toptension






Six sigma

NCGA Monte Carlo

Minimalrequirement

Parameter range

Yes

No


Optimal design







Abaqus

Isight


Deflection (m)

40

0

ndash30

05

80

0

Ang

le o

f low

er jo

int (

deg)













8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1






Data Availability




Acknowledgments


References


























Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(a)

Top tension + 25




ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)


(b)

Top tension + 25





ndash1000

ndash500

0

500

1000

1500

2000

Sea d

epth

(m)

(c)






ndash4ndash2

02468

Ang

le o

f upp

er jo

int (

deg)

Top tension + 25




(a)


ndash3ndash25

ndash2ndash15

ndash1ndash05

005

Ang

le o

f low

er jo

int (

deg)

Top tension + 25




(b)



OutputInput

Riserdiameter

Riserthickness

Topdrift

Hangingload

Toptension






Six sigma

NCGA Monte Carlo

Minimalrequirement

Parameter range

Yes

No


Optimal design







Abaqus

Isight


Deflection (m)

40

0

ndash30

05

80

0

Ang

le o

f low

er jo

int (

deg)













8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1






Data Availability




Acknowledgments


References



























ndash4ndash2

02468

Ang

le o

f upp

er jo

int (

deg)

Top tension + 25




(a)


ndash3ndash25

ndash2ndash15

ndash1ndash05

005

Ang

le o

f low

er jo

int (

deg)

Top tension + 25




(b)



OutputInput

Riserdiameter

Riserthickness

Topdrift

Hangingload

Toptension






Six sigma

NCGA Monte Carlo

Minimalrequirement

Parameter range

Yes

No


Optimal design







Abaqus

Isight


Deflection (m)

40

0

ndash30

05

80

0

Ang

le o

f low

er jo

int (

deg)













8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1






Data Availability




Acknowledgments


References
























Six sigma

NCGA Monte Carlo

Minimalrequirement

Parameter range

Yes

No


Optimal design







Abaqus

Isight


Deflection (m)

40

0

ndash30

05

80

0

Ang

le o

f low

er jo

int (

deg)













8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1






Data Availability




Acknowledgments


References

































8

6

2

10

4

Dynamics

7

5

1

9

3

Part-1






Data Availability




Acknowledgments


References



























Data Availability




Acknowledgments


References
























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Optimization Design of a Riser-Drill String Coupling ...

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