drill column-riser-wellbore contact … matrix due to the mooring system, x(t) ... drillship in...

DRILL COLUMN-RISER-WELLBORE CONTACT FORCES

IN A FLOATING DRILLING RIG IN WAVES

Celso Kazuyuki MorookaUnicamp - Universidade Estadual de CampinasRicardo Cassio Soares BuenoPetrobras - Petroleo Brasileiro S.A.

Abstract - When the drill column works rotating inside a well and riser duringan offshore drilling, contacts between the drill column and riser or, drill columnand wellbore is undesirable. Specially, in deepwater the magnification of thoseforces which arise from the contact, they could provoke damage into thedrilling equipment such as BOP, riser and wellbore. The correct evaluation ofdamage possibilities is very important in order to estimate the safety of thedrilling operation. Furthermore, it will be very useful for accurate planning ofdrilling operations. In the present paper, behavior in waves of the floatingdrilling rig is evaluated, dynamics and displacements of the riser is consideredand, finally contact forces between drill column-riser and drill column-wellboreis calculated. The methodology to calculate the contact forces using finiteelements for modeling the drill column is here described. Results for adeepwater drilling case is presented and a interesting result for the contactforce dynamics is shown. Finally, the practical application of the methodologyhere proposed has shown good results and it make possible the overall analysisof the floating rig, drill column and wellbore environments. It is a veryimportant tool for the safety assessment of the drilling operations.

INTRODUCTION

The increase in the water depth of recent offshore oil discoveries and thenecessity of drilling and producing those deepwater reservoirs conducted toseveral technological problems. In particular, deepwater drilling andcompletion are usually done by using floating vessels like drillship and semi-

Transactions on the Built Environment vol 29, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509

126 Offshore Engineering

submersible floating drilling rig. On those floating systems longerdrilling/completion riser with larger capacity riser tensioning system is requiredfor deepwater.

The floating drilling rig operating at the open sea with a riser-drill column-wellbore system under effects of the environment (wind, current and waves) isinduced by loads which can result in contact forces between the parts of thatsystem. And, it can cause damages at parts of the system such as in riser joints,BOP and casing-hangers while drilling^.

The magnitude of the forces generated by the drill column against the riser,the wellhead or wellbore must be correctly estimated in order to predict thewear rate expected in the riser, wellhead equipment and casings. Manymodels^* have been used to predict the forces inside the wellbore, but thoseapproaches are no longer valid, specially for offshore operations.

The present work proposes a methodology to estimate the contact forcesgenerated by the drill column against the wellbore and the marine riser system.A new procedure for overall analysis of the drill column behavior inside theriser and wellbore is described. For this purpose, motions of the drilling rigand displacements of the riser under wind, current and waves effects areinitially calculated. Following, those results are used in obtaining the contactforces based on from finite element analysis procedure. An example ofapplication is shown for a drilling rig operating in a deepwater Brazilianoffshore oilfield.

Finally, the present methodology is expected to be important in the safetyanalysis of the wellhead equipment and also in planning drilling operations.The results also suggest that the forces should be used in the dynamic analysisof marine riser system.

METHODOLOGY

Floating Drilling Rig Motion

Six degree of freedom are considered for floating drilling rig motions. Themotions can be calculated from the following differential equation:

[M+a] x(t) + [B] x(t) + [C+D] x(t) = f*(t) (1)

where, [M +a] is floating drilling rig platform mass with added mass (inertia)matrix, [B] is damping matrix which includes the equivalent linearized viscous


Offshore Engineering 127

drag, [C] restoring matrix of the floating drilling rig platform, [D] is linearizedrestoring matrix due to the mooring system, x(t) is time dependent motions ofthe floating drilling rig and the dots means its derivatives and, f,(t) is timedependent hydrodynamic exciting fluid force.

In case of dynamic positioning system (DPS) motion calculation no mooringsystem restoring exists. Frequency domain solution^ for Equation (1) isstraightforward and it is used in the present analysis. Hydrodynamic addedmass, damping and wave exciting forces can be obtained from source-sinkmethod. For drillships, strip method also based on potential theory can beused. Non-linear viscous drag is usually obtained from experiments^. The linearwave theory is adopted in the present study.

offset

Figure 1 - Drillship in operation under environmental loads

Riser Analysis

The horizontal equation of riser motion can be represented by the followingriser differential equation for small deformations:

a I T(z),9ul , m(z)jgu _ fr(z,t) (2)



where, u (z) is riser horizontal displacements at coordinate z, EI(z) is modulusof elasticity xarea moment of inertia of riser as function of z, T(z) is effectiveriser tension at coordinate z, t is time, m(z) is mass of riser at coordinate z,fr(z,t) is loads on the riser at coordinate z and time t and, z is axial coordinateof riser.

In above Equation (2), T(z) is the effective riser tension*^ and, it is importantto consider this in order to obtain the correct solution of riser equation. Then,

T(z) = T,(z) + pc(z)A,(z)- pi(z)A;(z) ( 3 )

where, T%(z) is actual riser tension at coordinate z, p^) is external (internal)pressure at coordinate z, A \) is external (internal) pressure at coordinate z.

Analytical and numerical methods are possible to solve Equation (2) with (3)and obtain solutions for both static and dynamic problems. Observe that incase of static problem the inertia term in Equation (2) is not included. And,linearized frequency domain solution is possible for dynamic problem bysolving Equation (2) for harmonic riser excitations. Figure 1 showsschematically a drillship in operation at the sea under environmental loads.

Contact Forces Calculation

The Quasi-Static Approach The calculated static plus time varying geometryof the riser is sliced on time for the quasi-static approach. The drill column-riser-wellbore contact forces are calculated for each time step by static FiniteElement Method (FEMf calculation.

Then, the riser geometry for each time step is reproduced from the riserresponse static and dynamic analysis. The riser configuration for each time stepis added to the wellbore geometry. That shows the entire trajectory which thedrill column follows during the drilling procedure (Figure 1). Thisconfiguration is generated for each time step and it is used in the FEMcalculations.

Considerations on the FEM Model The previously calculated riser columnconfiguration with the floating drilling rig position and the designed wellboretrajectory are considered and, both are divided into several finite elements.Same procedure is repeated for the drill column. The purpose of the presentcalculation is to obtain the still unknown drill column configuration and,consequently contact points with magnitude of forces. General purpose FEMroutine^ is used for the drill column calculations.



In the present calculation, non-linear approach are applied to drill columncalculations. The solution is obtained throughout step by step calculation ofstatic equilibrium of the system, by the Newton-Raphson full interactiveprocedure. The drill column is modeled as elastic beams and the stiffnesscontributions are all kept. The boundary conditions at the bit and the stabilizersare shown in the Figure 2. The upper boundary condition at the rotary tablehas full restriction of freedom. The contact points are assumed to occur onlyat the tool-joints then, each beam element has the exactly same length of eachjoint of the drillpipe.

DrillC o 1 1 a r

C'en t.r.

' 1

Bit

L

.-£>-^ /77

K1I-W/V-:,

-VWVVv^ 'KO

K1L-A/WV i1

Vv\/VW\-KO--- -- £;.qj

/ K1>— AAMr~ •

KO

L

Figure 2 - Boundary Condition at the bottom end of thedrill column (drill bit/stabilizers)

Contact elements with a specified spring-stiffness are arranged on the wellboreelements. The adopted springs are schematically presented in the Figure 2showing the manner which works the present FEM calculations. It shows howthe mechanism of contact between the drill column element nodes and the riseror the wellbore wall works in the calculations. In general, there is a gap(clearance) before the contact when a very soft spring (Ko) with a negligiblevalue works. At the moment of the contact when the drill column touches thewellbore/riser internal wall, this spring value changes for a very harder one(Ki). Then, in the present approach, a node will continue to havedisplacements despite very small. The spring constants of contact elementswhere adjusted tentatively, by try and error procedure, in order to avoidexcessive "penetration" of the wall by the nodes and, represent as much aspossible the real physics of the problem. However, there is option to set the



spring with different stiffness in order to simulate the lithology along thewellbore.

If two dimensional calculation is considered by FEM and, the riser andwellbore wall is considered as composed by right and left hand side walls asindicated in the Figure 3, then firstly the right hand side of the riser andwellbore wall is placed at the actual position. Now, the drill column from theinitially up right position is displaced by the lower end (bit) to its actualposition and, the upper end (rotary table) to the displaced offset position of thedrillship. In order to put the drill column into the limits of the wellbore andriser internal diameters, the left hand side of the wall is placed into the trueposition. Finally, the upper drill column axial tension is correctly adjusted and,the final configuration of the drill column with the contact forces and itsposition are reached.

d ril Is t rin g( d i s p l a c e d ) d i s p l a c e m e n t

( offset )riser n all( left ha n d s id e )

S.VV.L.

w e l l b o r e w a l l(left h a ii d s i d e )

r i s e r w a l l( r i g h t h a n d s i d e )

M .L

w e l l b o r e w a l l( r i g h t h a n d s i d e )

d i s p l a c e m e n t( at the h i t )

Figure 3 - Contact forces calculation by FEM scheme fordrill column-riser-wellbore system



RESULTS

A dynamically positioning system (DPS) drillship is considered in the followingresults. The principal dimensions of the drillship is shown in the Table 1 and,the Figure 4 shows the sway response of the drillship in waves. This drillshipmotion response is entered into the riser analysis.

LENGTH, L (m)

DRAFT, D (m)

BREATH, B (M)

DISPLACEMENT (ton)

RADIUS OF GYRATION

METACENTER HEIGHT

CENTER OF GRAVITY [

[roll] (

[Gmt]

VCG]

m)

(m)

(m)

144.0

750

23.5

21,747

6.82

044

T.68

Table 1 - Principal Dimensions of the Drillship

DE

600

,PTH (m)

5

20

40

60

80

100

150

200

250

300

400

500

up to 1000

VELOCITY (knots)

1.03

1.03

0.98

0.97

0.97

0.87

0.66

041

0.31

0.20

0.31

043

0.39

Table 2 - Current profile at the offshore drillsite



1.00 —

0.50 —

n onVJ.UU

o.c

180.00 —

on nnv?U.UU

n nou.uu

-90.00 —

-180.00 —

SWAY MOTION

Beam Sea (%=90°)

i i i i i i i i i i

30 1.00 2.00 3.00 4.00 5.00

X/L

PHASE (degree)

i I i I i I i I . I

1.00 2.00 3.00 4.00 5.00

X/L

Figure 4 - Sway response in waves (RAO) of the drillship

The static offset of the drillship is adopted as 3% of the water depth for theriser analysis. This situation corresponds to the maximum allowed horizontaldisplacement of the drillship in normal operation by the rules*. This conditioncoincides with the operational limit for yellow alarm of the drilling operation,which means that the normal drilling has to be stopped and the drillfloor crewmust be ready for disconnection procedures of the drillship from the well.

Based on previous experience in the same site, added mass coefficient 1.0 anddrag coefficient 0.8 was chosen to apply in the Morison type equation tocalculate current and waves loads acting directly on the riser*°. The currentprofile used was observed in the Campos Basin, Offshore Brazil and it ispresented at the Table 2. The top tension with an overpull around 10% andmud weight of 9 Ibs/gal are previously defined from the design.


Offshore Engineering 13 3

Grade of steel

OD

ID

Range

Tool-joint OD

Cross area

Momentum of inertia

Young's coefficient

Floating factor (10 ppg mud)

"S-135"

5.0''

4.276 "

11(30')

6 5/8 "

0.037 ft2

6.88 x 10"* ft"

41.76x!OS|b/ff

0.847

Table 3 - Drill Column Dimensions

OD x thickness(t)

Choke and Kill OD x t

Length

Dry weight w/ floater

Wet weight w/ floater

Wet weight Telescopic joint

Wet weight L.M.R.P.

Wet weight BOP

18 5/8" x 5/8"

4.5" x 0.674"

50'

1 1.750 Ib

705 Ib

21.725 Ib

78.2101b

237.000 Ib

Table 4 - Marine Riser Dimensions

The well located at the sea bottom in a 550 m waterdepth has a highinclination angle of 60 degrees. The Table 3 shows the dimensions of drillcolumn used and, Table 4 the marine riser principal dimensions.

In the quasi-static analysis, the wave condition is set with a wave height of1.75 m (5.7 ft.) and a wave period of 5.8 seconds which are predominant atthe site. In the calculations, the wave was considered harmonic and one periodis divided into ten time slices of 0.58 seconds.

A very small value for the soft spring Ko and, a hard spring K, of 10* orderwas used in the calculations.



0.0-.

cT-2000.0 -h-m£] -4000.0-Q— lo -6000.0 -forLLJ> -8000.0-

1 nnnn n

\

\

I ' I ' ! ' I ' I0.0 2000.0 4000.0 6000.0 8000.0LATERAL DISPLACEMENTS (ft)

O.O-i

-2000.0-

%:

£ -4000.0-O

o -6000.0 -i=a:LU> -8000.0 -

1 nnnn n

\

; ' I • I ' : ' I0.0 2000.0 4000.0 6000.0 8000. (LATERAL DISPLACEMENT (ft)

Figure 5 - Drill Column before lefthand side wall displacement

Figure 6 - Final configuration ofdrill column

Figure 5 shows the drill column geometry before moving the left hand side ofthe riser/wellbore into actual position during FEM calculation. And, Figure 6shows the final configuration of the drill column extending from the rotarytable at the drillship to the drillbit at the bottom of the well. Observe in theFigure 6 that the 60 degree well-path is reproduced.

3000-1

BS 8 O

CONT

ACT FO

RCES

§

8O O

O

-20000 -4000 -8000 -12000 -16000

MEASURED DEPTH (FT)

Figure 7 - Contact forces between drilldrill column and riser/wellbore

at t=0,58 sec

3000 -

2000-_ iCO0 1000 -HCZ

0-1000-o

-2000-0 -4000 -8000 -12000 -16000

MEASURED DEPTH (FT)

Figure 8 - Contact forces betweenand riser/wellbore at t =1,74 sec



Figures 7 and 8 show the contact forces along the depth at two different timesteps (0.58 sec. and 1.74 sec). The positive values means that the contactoccurs on the right hand side of the riser/wellbore wall. As it can be observedthe maximum force happens at the region of the flexible joint (wellhead) and, itis almost twice of the maximum force inside the well, as it was noted, for allcases of present calculation.

Comparing FEM calculations with simplified equilibrium calculations for theconstant inclination part (60 degree slope) of the well, very close results wasobserved which validates the results from the present method.

As already mentioned, existent models are efficient for calculations inside thewellbore. On those models, the drill column is modeled without stiffness andalso assume that it has always the same wellbore curvature ratio Calculationshere carried out without the gravitational load (weight) in order to verify theforces only due to the stiffness has shown results 3% less than the originalsinside the well. It confirms that the contribution of the stiffness is really verysmall. However, in the riser portion the geometry of the drill column is verydifferent if compared with the riser one (different curvature ratio). Then, thosemethods are no longer valid.

,2400.0 -

00_J

(01 1 1 •

o:O

2200.0-

2000.0

OO 1 800.0

0.0 2.0 4.0TIME (SEC)

6.0

Figure 9 - Time series of maximum contact forces

The maximum forces time series has shown sinusoidal-like appearance asexpected. However, decreasing the time step with more slices of time isdesirable in order to have better idea of the time varying behavior of thecontact forces (Figure 9).



As it can be observed from the results, the present method could be applied onseveral problem analysis verified during drilling/completion such as casing andriser wear, optimization of directional drilling paths, nonlinear bucking of theBHA (bottom hole assembly), torque and drag calculations and to set thecompletion packer energized by weight.

The present method is normally computer time consuming procedure. In thepresent calculations 24 hours of computing time was used to run each timestep in a 40 Megaflops Workstation. In other words, 240 hour for the entireanalysis (equivalent 180 days in 486 PC computer) was used. However, thecomputing time can be decreased a lot once the contact points are known (firstrun) and, considering it in the following steps of calculations. In this case,some contact elements will not be necessary because there is no chance toclose. It could reduce the computer time in more than 50%. Moreover, therecent computer advances increasing the performance of computers was nottaken into account in the present analysis.

CONCLUSIONS

A new procedure to evaluate contact forces between drill column-riser-wellbore was here proposed for offshore drilling. Comparisons with othermodels for drill column-wellbore analysis confirms the validity of the presentmethod and, the application of the present methodology for offshore drillingwas shown.

From the calculations, it was observed that the values of the forces inside theriser have a magnitude that suggest that they should be included in thedynamic analysis of riser. In despite of large computer effort required forapplication of the present methodology, it is very suitable to be used for designand planning of offshore drilling/completion.

NOMENCLATURE

[a] - floating drilling rig platform added mass (inertia) matrixAe(i) - external (internal) pressure at coordinate z[B] - damping matrix which includes the equivalent linearized viscous drag[C] - restoring matrix of the floating drilling rig platform[D] - linearized restoring matrix due to the mooring systemEI(z) - modulus of elasticity \area moment of inertia of riser as function of zfs(t) - time dependent hydrodynamic exciting fluid forcefr(z,t) - loads on the riser at coordinate z and time tL - ship lenght



m(z) - mass of riser at coordinate z[M] - floating drilling rig platform mass (inertia) matrixPe(i) - external (internal) pressure at coordinate zt - timeT(z) - effective riser tension at coordinate zTZ(Z) - actual riser tension at coordinate zu(z) - riser horizontal displacements at coordinate zx(t) - time dependent motions of the floating drilling rigY - sway motionz - axial coordinate of riser

% - incident wave directionX - wave lenght£ - wave amplitude

AbbreviationsBOP - blow out preventorDPS - dynamic positioning systemFEM - finite element methodID - inner diameterLMRP - lower marine riser packageML - mud line (sea floor)OD - outer diameterSWL - still water level

Units1 knot = 0.51444 m/s1 Ib = 0.45359 kg1 ft = 0.3048 mIgal = 3.785x]0"'m"

REFERENCES

[1] Bueno, R., "Methodology of Drill String / Riser / Well InteractionAnalysis by Finite Elements", M. Sc. dissertation, UNICAMP-Brazil,1994.

[2] Johansic, C.A.; Friesen,D.B.; Dawson, R , "Torque and Drag inDirectional Wells"- Journal of Petroleum Technology"; pp 987-992, 1984.

[3] Morooka, C.K. and Maeda, H., "Motions of Floating Bodies inMultidirectional Ocean Waves", Brazil Offshore'89, 1989.


13 8 Offshore Engineering

[4] Morooka, C.K.; Nishimoto, K. ; Rodrigues, R.S.; Cordeiro, A.L.,"Transportation and Installation of the Template Octos 1000", BrasilOffshore'89, 1989.

[5] Takezawa, S.; Hirayama, T.; Morooka,C.K., "A Practical CalculationMethod of a Moored Semi-Submersible Rig Motion in Waves", Journal ofSNAJ, vol. 155, 159-171, 1984.

[6] Young, R D., "Mathematics of the Marine Riser"; Energy TechnologyConference and Exhibition; Houston, Texas, 1978.

[7] Young, R D et. all.,"DERP Users Manual", Stress Engineering,Houston, TX, 1992.

[8] Chakrabarti, S.K. and Frampton, R.E., "Review of Riser AnalysisTechniques", Applied Ocean Research, vol. 4, 2:73-90, 1982.

[9] Swanson Engineering, "ANSYS 5.0 Users Manual", 1993.

[10]API-RP-2Q, "Recommended Practice for Design and Operation of MarineDrilling Riser Systems", 2nd Edition, 1984.

[ll]Milheim, K. ; Jordan, S.; Ritter,C J , "Bottom Hole Assembly AnalysisUsing the Finite Element Method"; - Journal of Petroleum Technology,SPE, 265-274, 1978.


drill column-riser-wellbore contact … matrix due to the mooring system, x(t) ... drillship in...

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