DRILL COLUMN-RISER-WELLBORE CONTACT FORCES IN A FLOATING DRILLING RIG IN WAVES

Transcription

1 DRILL COLUMN-RISER-WELLBORE CONTACT FORCES IN A FLOATING DRILLING RIG IN WAVES Celso Kazuyuki Morooka Unicamp - Universidade Estadual de Campinas Ricardo Cassio Soares Bueno Petrobras - Petroleo Brasileiro S.A. Abstract - When the drill column works rotating inside a well and riser during an offshore drilling, contacts between the drill column and riser or, drill column and wellbore is undesirable. Specially, in deepwater the magnification of those forces which arise from the contact, they could provoke damage into the drilling equipment such as BOP, riser and wellbore. The correct evaluation of damage possibilities is very important in order to estimate the safety of the drilling operation. Furthermore, it will be very useful for accurate planning of drilling operations. In the present paper, behavior in waves of the floating drilling rig is evaluated, dynamics and displacements of the riser is considered and, finally contact forces between drill column-riser and drill column-wellbore is calculated. The methodology to calculate the contact forces using finite elements for modeling the drill column is here described. Results for a deepwater drilling case is presented and a interesting result for the contact force dynamics is shown. Finally, the practical application of the methodology here proposed has shown good results and it make possible the overall analysis of the floating rig, drill column and wellbore environments. It is a very important tool for the safety assessment of the drilling operations. INTRODUCTION The increase in the water depth of recent offshore oil discoveries and the necessity of drilling and producing those deepwater reservoirs conducted to several technological problems. In particular, deepwater drilling and completion are usually done by using floating vessels like drillship and semi-

2 126 Offshore Engineering submersible floating drilling rig. On those floating systems longer drilling/completion riser with larger capacity riser tensioning system is required for deepwater. The floating drilling rig operating at the open sea with a riser-drill columnwellbore system under effects of the environment (wind, current and waves) is induced by loads which can result in contact forces between the parts of that system. 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 the wear rate expected in the riser, wellhead equipment and casings. Many models^* have been used to predict the forces inside the wellbore, but those approaches are no longer valid, specially for offshore operations. The present work proposes a methodology to estimate the contact forces generated by the drill column against the wellbore and the marine riser system. A new procedure for overall analysis of the drill column behavior inside the riser and wellbore is described. For this purpose, motions of the drilling rig and displacements of the riser under wind, current and waves effects are initially calculated. Following, those results are used in obtaining the contact forces based on from finite element analysis procedure. An example of application is shown for a drilling rig operating in a deepwater Brazilian offshore oilfield. Finally, the present methodology is expected to be important in the safety analysis of the wellhead equipment and also in planning drilling operations. The results also suggest that the forces should be used in the dynamic analysis of marine riser system. METHODOLOGY Floating Drilling Rig Motion Six degree of freedom are considered for floating drilling rig motions. The motions 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

3 Offshore Engineering 127 drag, [C] restoring matrix of the floating drilling rig platform, [D] is linearized restoring matrix due to the mooring system, x(t) is time dependent motions of the floating drilling rig and the dots means its derivatives and, f,(t) is time dependent hydrodynamic exciting fluid force. In case of dynamic positioning system (DPS) motion calculation no mooring system restoring exists. Frequency domain solution^ for Equation (1) is straightforward and it is used in the present analysis. Hydrodynamic added mass, damping and wave exciting forces can be obtained from source-sink method. For drillships, strip method also based on potential theory can be used. Non-linear viscous drag is usually obtained from experiments^. The linear wave 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 following riser differential equation for small deformations: a I T(z),9ul, m(z)jgu _ fr(z,t) (2)

4 128 Offshore Engineering where, u (z) is riser horizontal displacements at coordinate z, EI(z) is modulus of elasticity xarea moment of inertia of riser as function of z, T(z) is effective riser 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 coordinate of riser. In above Equation (2), T(z) is the effective riser tension*^ and, it is important to 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 in case of static problem the inertia term in Equation (2) is not included. And, linearized frequency domain solution is possible for dynamic problem by solving Equation (2) for harmonic riser excitations. Figure 1 shows schematically a drillship in operation at the sea under environmental loads. Contact Forces Calculation The Quasi-Static Approach The calculated static plus time varying geometry of the riser is sliced on time for the quasi-static approach. The drill columnriser-wellbore contact forces are calculated for each time step by static Finite Element Method (FEMf calculation. Then, the riser geometry for each time step is reproduced from the riser response static and dynamic analysis. The riser configuration for each time step is added to the wellbore geometry. That shows the entire trajectory which the drill column follows during the drilling procedure (Figure 1). This configuration is generated for each time step and it is used in the FEM calculations. Considerations on the FEM Model The previously calculated riser column configuration with the floating drilling rig position and the designed wellbore trajectory are considered and, both are divided into several finite elements. Same procedure is repeated for the drill column. The purpose of the present calculation is to obtain the still unknown drill column configuration and, consequently contact points with magnitude of forces. General purpose FEM routine^ is used for the drill column calculations.

5 Offshore Engineering 129 In the present calculation, non-linear approach are applied to drill column calculations. The solution is obtained throughout step by step calculation of static equilibrium of the system, by the Newton-Raphson full interactive procedure. The drill column is modeled as elastic beams and the stiffness contributions are all kept. The boundary conditions at the bit and the stabilizers are shown in the Figure 2. The upper boundary condition at the rotary table has full restriction of freedom. The contact points are assumed to occur only at the tool-joints then, each beam element has the exactly same length of each joint of the drillpipe. Drill C o 1 1 a r C'en t.r. Bit ' L1 L.- >-^ /77^ K1 I-W/V-:, -VWVVv^ ' KO K1 L-A/WV i 1 Vv\/VW\- KO ;.qj / K1 > AAMr~ Figure 2 - Boundary Condition at the bottom end of the drill column (drill bit/stabilizers) Contact elements with a specified spring-stiffness are arranged on the wellbore elements. The adopted springs are schematically presented in the Figure 2 showing the manner which works the present FEM calculations. It shows how the mechanism of contact between the drill column element nodes and the riser or 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 negligible value works. At the moment of the contact when the drill column touches the wellbore/riser internal wall, this spring value changes for a very harder one (Ki). Then, in the present approach, a node will continue to have displacements despite very small. The spring constants of contact elements where adjusted tentatively, by try and error procedure, in order to avoid excessive "penetration" of the wall by the nodes and, represent as much as possible the real physics of the problem. However, there is option to set the KO

6 130 Offshore Engineering spring with different stiffness in order to simulate the lithology along the wellbore. If two dimensional calculation is considered by FEM and, the riser and wellbore wall is considered as composed by right and left hand side walls as indicated in the Figure 3, then firstly the right hand side of the riser and wellbore wall is placed at the actual position. Now, the drill column from the initially up right position is displaced by the lower end (bit) to its actual position and, the upper end (rotary table) to the displaced offset position of the drillship. In order to put the drill column into the limits of the wellbore and riser internal diameters, the left hand side of the wall is placed into the true position. Finally, the upper drill column axial tension is correctly adjusted and, the final configuration of the drill column with the contact forces and its position are reached. d ril Is t rin g (displaced) riser n all ( left ha n d s id e ) displacement ( offset ) S.VV.L. riser wall (right hand side) M.L wellbore wall (right hand side) wellbore wall (left h a ii d side) displacement ( at the hit) Figure 3 - Contact forces calculation by FEM scheme for drill column-riser-wellbore system

7 RESULTS Offshore Engineering 131 A dynamically positioning system (DPS) drillship is considered in the following results. 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 drillship motion response is entered into the riser analysis. LENGTH, L (m) DRAFT, D (m) BREATH, B (M) DISPLACEMENT (ton) RADIUS OF GYRATION [roll]( m) METACENTER HEIGHT [Gmt] (m) CENTER OF GRAVITY [ VCG] (m) , T.68 Table 1 - Principal Dimensions of the Drillship DE,PTH (m) up to 1000 VELOCITY (knots) Table 2 - Current profile at the offshore drillsite

8 132 Offshore Engineering 1.00 SWAY MOTION Beam Sea (%=90 ) 0.50 n on VJ.UU i i i i i i i i i i o.c X/L on v?u.uu nn n u.uu no PHASE (degree) i I i I i I i I. I 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 the riser analysis. This situation corresponds to the maximum allowed horizontal displacement of the drillship in normal operation by the rules*. This condition coincides with the operational limit for yellow alarm of the drilling operation, which means that the normal drilling has to be stopped and the drillfloor crew must be ready for disconnection procedures of the drillship from the well. Based on previous experience in the same site, added mass coefficient 1.0 and drag coefficient 0.8 was chosen to apply in the Morison type equation to calculate current and waves loads acting directly on theriser*.the current profile used was observed in the Campos Basin, Offshore Brazil and it is presented at the Table 2. The top tension with an overpull around 10% and mud weight of 9 Ibs/gal are previously defined from the design.

9 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'' " 11(30') 6 5/8 " ft x 10"* ft" 41.76x!OS b/ff 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' Ib 705 Ib Ib b Ib Table 4 - Marine Riser Dimensions The well located at the sea bottom in a 550 m waterdepth has a high inclination angle of 60 degrees. The Table 3 shows the dimensions of drill column used and, Table 4 the marine riser principal dimensions. In the quasi-static analysis, the wave condition is set with a wave height of 1.75 m (5.7 ft.) and a wave period of 5.8 seconds which are predominant at the site. In the calculations, the wave was considered harmonic and one period is 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* order was used in the calculations.

10 134 Offshore Engineering O.O-i \ \ ct h- m ] Q l o f^ or LLJ > ^ %: O o i= a: LU > \ 1 nnnn n I ' I '! ' I ' I LATERAL DISPLACEMENTS (ft) 1 nnnn n ; ' I I ' : ' I ( LATERAL DISPLACEMENT (ft) Figure 5 - Drill Column before left hand side wall displacement Figure 6 - Final configuration of drill column Figure 5 shows the drill column geometry before moving the left hand side of the riser/wellbore into actual position during FEM calculation. And, Figure 6 shows the final configuration of the drill column extending from the rotary table at the drillship to the drillbit at the bottom of the well. Observe in the Figure 6 that the 60 degree well-path is reproduced BS 8 O CONTACT FORCES O O O MEASURED DEPTH (FT) _ i CO H CZ o MEASURED DEPTH (FT) Figure 7 - Contact forces between drill drill column and riser/wellbore at t=0,58 sec Figure 8 - Contact forces between and riser/wellbore at t =1,74 sec

11 Offshore Engineering 13 5 Figures 7 and 8 show the contact forces along the depth at two different time steps (0.58 sec. and 1.74 sec). The positive values means that the contact occurs on the right hand side of the riser/wellbore wall. As it can be observed the maximum force happens at the region of theflexiblejoint (wellhead) and, it is almost twice of the maximum force inside the well, as it was noted, for all cases of present calculation. Comparing FEM calculations with simplified equilibrium calculations for the constant inclination part (60 degree slope) of the well, very close results was observed which validates the results from the present method. As already mentioned, existent models are efficient for calculations inside the wellbore. On those models, the drill column is modeled without stiffness and also assume that it has always the same wellbore curvature ratio Calculations here carried out without the gravitational load (weight) in order to verify the forces only due to the stiffness has shown results 3% less than the originals inside the well. It confirms that the contribution of the stiffness is really very small. However, in the riser portion the geometry of the drill column is very different if compared with the riser one (different curvature ratio). Then, those methods are no longer valid., _J ( o: O O TIME (SEC) 6.0 Figure 9 - Time series of maximum contact forces The maximum forces time series has shown sinusoidal-like appearance as expected. However, decreasing the time step with more slices of time is desirable in order to have better idea of the time varying behavior of the contact forces (Figure 9).

12 136 Offshore Engineering As it can be observed from the results, the present method could be applied on several problem analysis verified during drilling/completion such as casing and riser wear, optimization of directional drilling paths, nonlinear bucking of the BHA (bottom hole assembly), torque and drag calculations and to set the completion packer energized by weight. The present method is normally computer time consuming procedure. In the present calculations 24 hours of computing time was used to run each time step in a 40 Megaflops Workstation. In other words, 240 hour for the entire analysis (equivalent 180 days in 486 PC computer) was used. However, the computing time can be decreased a lot once the contact points are known (first run) and, considering it in the following steps of calculations. In this case, some contact elements will not be necessary because there is no chance to close. It could reduce the computer time in more than 50%. Moreover, the recent computer advances increasing the performance of computers was not taken into account in the present analysis. CONCLUSIONS A new procedure to evaluate contact forces between drill column-riserwellbore was here proposed for offshore drilling. Comparisons with other models for drill column-wellbore analysis confirms the validity of the present method and, the application of the present methodology for offshore drilling was shown. From the calculations, it was observed that the values of the forces inside the riser have a magnitude that suggest that they should be included in the dynamic analysis of riser. In despite of large computer effort required for application of the present methodology, it is very suitable to be used for design and planning of offshore drilling/completion. NOMENCLATURE [a] Ae(i) [B] [C] [D] EI(z) fs(t) fr(z,t) L - floating drilling rig platform added mass (inertia) matrix - external (internal) pressure at coordinate z - damping matrix which includes the equivalent linearized viscous drag - restoring matrix of the floating drilling rig platform - linearized restoring matrix due to the mooring system - modulus of elasticity \area moment of inertia of riser as function of z - time dependent hydrodynamic exciting fluid force - loads on the riser at coordinate z and time t - ship lenght

13 Offshore Engineering 13 7 m(z) [M] Pe(i) t T(z) TZ(Z) u(z) x(t) Y z - mass of riser at coordinate z - floating drilling rig platform mass (inertia) matrix - external (internal) pressure at coordinate z - time - effective riser tension at coordinate z - actual riser tension at coordinate z - riser horizontal displacements at coordinate z - time dependent motions of the floating drilling rig - sway motion - axial coordinate of riser % - incident wave direction X - wave lenght - wave amplitude Abbreviations BOP - blow out preventor DPS - dynamic positioning system FEM - finite element method ID - inner diameter LMRP - lower marine riser package ML - mud line (sea floor) OD - outer diameter SWL - still water level Units 1 knot = m/s 1 Ib = kg 1 ft = m Igal = 3.785x]0"'m" REFERENCES [1] Bueno, R., "Methodology of Drill String / Riser / Well Interaction Analysis by Finite Elements", M. Sc. dissertation, UNICAMP-Brazil, [2] Johansic, C.A.; Friesen,D.B.; Dawson, R, "Torque and Drag in Directional Wells"- Journal of Petroleum Technology"; pp , [3] Morooka, C.K. and Maeda, H., "Motions of Floating Bodies in Multidirectional Ocean Waves", Brazil Offshore'89, 1989.

14 13 8 Offshore Engineering [4] Morooka, C.K.; Nishimoto, K. ; Rodrigues, R.S.; Cordeiro, A.L., "Transportation and Installation of the Template Octos 1000", Brasil Offshore'89, [5] Takezawa, S.; Hirayama, T.; Morooka,C.K., "A Practical Calculation Method of a Moored Semi-Submersible Rig Motion in Waves", Journal of SNAJ, vol. 155, , [6] Young, R D., "Mathematics of the Marine Riser"; Energy Technology Conference and Exhibition; Houston, Texas, [7] Young, R D et. all.,"derp Users Manual", Stress Engineering, Houston, TX, [8] Chakrabarti, S.K. and Frampton, R.E., "Review of Riser Analysis Techniques", Applied Ocean Research, vol. 4, 2:73-90, [9] Swanson Engineering, "ANSYS 5.0 Users Manual", [10]API-RP-2Q, "Recommended Practice for Design and Operation of Marine Drilling Riser Systems", 2nd Edition, [ll]milheim, K. ; Jordan, S.; Ritter,C J, "Bottom Hole Assembly Analysis Using the Finite Element Method"; - Journal of Petroleum Technology, SPE, , 1978.