Multistring analysis of wellhead movement and uncemented casing strength in offshore oil and gas wells

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1 Pet.Sc.(214)11: DOI 1.17/s Multstrng analyss of wellhead movement and uncemented casng strength n offshore ol and gas wells Lu Xuquan 1, Chen Guomng 1, Chang Yuanjang 1, Zhang Le 1, Zhang Weguo 2 and Xe Hua 2 1 Centre for Offshore Engneerng and Safety Technology, Chna Unversty of Petroleum, Qngdao, Shandong 26658, Chna 2 Shenzhen Branch of Chna Offshore Ol Corporaton, Shenzhen, Guangdong 51867, Chna Chna Unversty of Petroleum (Bejng) and Sprnger-Verlag Berln Hedelberg 214 Abstract: movement and uncemented casng strength n offshore ol and gas wells. Parameters consdered n the theoretcal method nclude operatng load durng drllng and completon and the temperature feld, pressure feld and the end effect of pressure durng gas producton. The fnte element method for multstrng analyss s developed to smulate random contact between casngs. The relevant fnte element analyss scheme s also presented accordng to the actual procedures of drllng, completon are four offshore wells n the South Chna Sea. The calculated wellhead growths durng gas producton are compared wth measured values. The results show that the wellhead subsdes durng drllng and growth are n good agreement wth measured values and the devatons of calculaton are wthn 1%. The maxmum von Mses stress on the uncemented ntermedate casng occurs durng the runnng of the ol tube. The maxmum von Mses stress on the uncemented producton casng, calculated wth the theoretcal method occurs at gas producton. Fnte element solutons for von Mses stress are recommended and the uncemented casngs of four wells satsfy strength requrements. Key words: Offshore ol and gas wells, drllng and completon, gas producton, wellhead movement, uncemented casng strength, gap element 1 Introducton Wellhead assembles are often nstalled on platforms n offshore ol and gas wells. A secton of casngs can not be cemented due to the gap between the platform wellhead and seafloor (Song et al, 212). The wellhead poston and the uncemented casng strength change wth operatng load and envronmental load durng drllng, completon and gas producton. For example, the wellhead grew up durng gas producton n a gas feld of the South Chna Sea and the maxmum growth reached.13 m. Calculaton of the wellhead movement s crtcal for the desgn of the platform layout and producton ppelnes around the Chrstmas tree. Strength assessment of the uncemented casngs s mportant for wellbore ntegrty (Samuel and Gonzales, 1999; Wu et al, 28; Xu et al, 21). However, there s lttle research *Correspondng author: emal: offshore@126.com Receved December 26, 212 on wellhead movement and uncemented casng strength at method for calculatng the wellhead movement durng drllng and completon. The wellhead movement durng drllng and accordng to the proposed theoretcal method and compared wth measured values. The result showed that the calculated values were n good agreement wth measured data. Then a theoretcal method for calculatng the wellhead growth durng gas producton was establshed consderng the temperature feld (Aasen and Aadnoy, 24; 29; McSpadden and Glover, 29). However, the nfluence of the pressure feld on wellhead growth durng gas producton was neglected. In ths paper, the theoretcal method for calculatng the wellhead movement and the uncemented casng strength was mproved Another problem s that the theoretcal method mentoned above does not nvolve random contact between casngs on

2 132 Pet.Sc.(214)11: chosen to analyze contact among strngs. Nonlnear sprngs and gap elements are often adopted to smulate random sprng analogue was chosen for smulatng random contact between ppes (Bueno and Morooka, 1994; Luk et al, 29; Yao et al, 21; Dong et al, 211). When the gap between ppes s open, the sprng stffness vanshes, whle for a closed gap the sprng stffness becomes nfnte. Compared wth a gap element, the nonlnear sprng model often leads to low calculaton effcency and dffculty n convergence (L, and Wess (1979). It proved to be effcent n smulatng random contact among drllstrngs, rsers and wellbores (L, 22; Lu et al, 22; Zhang et al, 22). So the fnte element analyss software ABAQUS adopted gap element ITT for random contact smulaton between ppes (Chang and model for calculatng wellhead movement and uncemented casng strength s presented n ths paper consderng random contact between ppes. The relevant fnte element analyss scheme s also establshed accordng to the actual procedures of drllng, completon and gas producton. Fnally, the wellhead movement and uncemented casng strength of four wells n the South Chna Sea are calculated usng the proposed methods, and the calculated wellhead growths durng gas producton are compared wth measured values. 2 Mechancal analyss model Offshore drllng and completon operatons manly nclude runnng surface conductor, ntermedate casng, producton casng, lner, ol tube, nstallng and removng the BOP, and nstallng the Chrstmas tree. Fg. 1 llustrates the wellbore structure after drllng and completon. The whole wellbore comprses wellhead, surface conductor, ntermedate casng, producton casng, lner and ol tube. The wellhead s nstalled on the lower deck of platform. The surface conductor and lner are not connected to the wellhead and have no effect on wellhead movement. However, the surface conductor apples a hoop constrant on the wellhead to prevent t from lateral deformaton. The surface conductor and the whole wellbore above the mudlne are supported laterally by the centralzer structure of platform. The ntermedate casng, producton casng and ol tube are connected at the wellhead as a mult-strng system whch determnes the wellhead movement. The ntermedate casng and producton casng consst of the lower cemented part and the upper uncemented part. The cemented casngs are consoldated wth sol by the cement sheath and cannot move axally. So the cemented uncemented casngs that determne the wellhead movement. So ths paper focuses on the mechancal analyss of the uncemented ntermedate casng, uncemented producton casng and the ol tube. The mechancal analyss model for wellhead movement and uncemented casng strength shown n Fg. 2 was establshed accordng to the actual load condtons of uncemented casngs. Fg. 2 shows that loads actng on the uncemented casngs and the ol tube nclude the temperature and pressure felds, axal force and contact load between casngs. The Lower deck of platform Sea water Intermedate casng Producton casng Wellhead Fg. 1 Well structure dagram of offshore ol and gas wells Central lne of the Wellbore Axal temperature feld Packer Ol pressure Ol tube Wellhead measurements whle the axal load and contact load between casngs should be calculated. The followng theoretcal method wll descrbe the detals of the calculaton process of the axal load durng drllng, completon and gas producton. The wellhead movement and the uncemented casng strength are then assessed based on the calculated axal load. The whole procedures of drllng, completon and gas producton movement and the uncemented casng strength can be 3 Theoretcal method Surface conductor Mudlne Sol Cement sheath Ol tube Lner hanger Lner Casng pressureinternal External pressure Contact force Axal load Producton casng Radal temperature feld Intermedate casng Fg. 2 Mechancal analyss model for wellhead movement and uncemented casng strength Surface conductor 3.1 Calculaton of wellhead movement and casng axal load durng drllng and completon EA K (1) L,vertcal where K s the axal stffness of the th casng, N/m; E s the elastc modulus, Pa; A s the cross sectonal area of the th casng, m 2 ; L,vertcal s the vertcal component of the

3 Pet.Sc.(214)11: uncemented length of the th casng, m. The mult-strng system s taken as parallel sprngs when the ntermedate casng, producton casng and the ol tube are connected at the wellhead. The axal stffness of the multstrng system s gven by Nj Nj EA K j,sys K (2) 1 1 L,vertcal where K j,sys s the axal stffness of the mult-strng system durng the jth operaton, N/m; N j s the number of casngs related to the wellhead movement durng the jth operaton. The wellhead movement durng each operaton s wrtten as Wj Wj z j N j K (3) j,sys EA 1 L,vertcal z j s the wellhead movement durng the jth operaton, m; W j s the jth operatng load, N. The varaton of axal load on the casng durng each operaton s wrtten as A K L,vertcal F (4), j Wj W N j j K j,sys A L 1,vertcal F,j s the varaton of axal load on the th casng head durng the jth operaton, N. The axal load on each casng head after drllng and completon s gven by n F F,d, j j1 F,d s the varaton of axal load on the th casng head after drllng and completon, N; n s the total number of operatons durng drllng and completon. 3.2 Calculaton of wellhead movement and axal load on the casng durng gas producton The orgn of coordnates s at the wellhead, and the z axs s along the well track. The axal deformaton of each casng McSpadden and Glover, 28; Yan et al, 21) l t ( z)dz,t L l,t s the axal deformaton of the th casng due to the wellbore temperature feld, m; L s the uncemented length of the th casng, m; casngs, ºC t (z) s the temperature varaton of the th casng at z durng gas producton, ºC. The axal deformaton of each casng due to the wellbore l D p ( z) d p ( z) 2 dz L 2 1,p ED ( d ) l,p s the axal deformaton of the th casng due to wellbore pressure feld, m; s the Posson rato; d s the (5) (6) (7) nner dameter of the th casng, m; D s the outer dameter of the p 1 (z) s the nternal pressure varaton of the th casng at zp 2 (z) s the external pressure varaton of the th casng at z durng gas producton, Pa. Then the axal load on the wellhead due to the casng axal deformaton s expressed as l l N,t,p Ftp EA 1 L,vertcal L 2 1 N t z ED ( d ) EA 1 L,vertcal D p ( z) d p ( z) [ ( ) 2 ]dz where F tp s the axal load on the wellhead, N; N s the total number of casngs related to the wellhead movement. The casng pressure and ol pressure are zero durng drllng and completon. However, they ncrease durng gas producton and mpose load on the wellhead. The wellhead load due to the end effect of casng pressure and ol pressure s gven by F r p ( r R ) p 2 end tube tube casng2 tube casng where F end s the wellhead load due to the end effect of pressure, N; r tube s the nner dameter of the ol tube, m; p tube s the ol pressure, Pa; r casng2 s the nner dameter of the producton casng, m; R tube s the outer dameter of the tube, m; p casng s the casng pressure, Pa. Accordng to the calculated wellhead load due to the pressure and ol pressure, the wellhead movement durng gas producton s wrtten as F F F F z p tp end tp end N K EA sys L 1,vertcal (8) (9) (1) z p s the wellhead movement durng gas producton, m; K sys s the axal stffness of the multstrng system, N/m. The axal load varaton of each casng durng gas producton s wrtten as EA F K ( z l l ) ( z l l ),p p,t,p p,t,p L,vertcal (11) F,p s the axal load varaton of the th casng durng gas producton, N. The axal load on each casng head after drllng, completon and gas producton s gven by F F F,d,p where F s the axal load on the th casng head, N. The axal load on each casng at z s wrtten as ( ) ( )d (12) (13)

4 134 Pet.Sc.(214)11: where F (z) s the axal load on the th casng at z, N; W (z) s the unt weght of the th casng at z, N/m. 3.3 Strength assessment of uncemented casngs The axal stress on the casng, radal stress and hoop stress can be calculated by the followng equatons accordng to the measured pressure and calculated axal force (Tan and Gao, 25; Wu and Knauss, 26; wu et al, 28). 4F a (14) ( D d ) Dd p p d p D p D d 4r D d r 2 Dd p p d p D p D d 4r D d (15) (16) where a s the axal stress on casngs, Pa; r s the radal stress, Pa; s the hoop stress, Pa; D s the outer dameter of casngs, m; d s the nner dameter of casngs, m; F s the axal load on casngs, N; r s the dstance between the calculaton pont and the casng center, m; p 2 s the external pressure on casngs, Pa; p 1 s the nternal pressure on casngs, Pa. As the axal stress, radal stress and hoop stress on casngs are obtaned, the von Mses stresss on the casng s wrtten as 1 2 eff [ a r a r ] S 2 4 Fnte element method 4.1 Basc equatons (17) The stffness matrx and external load column vector can be determned based on the wellbore structure and the operatng load n fnte element analyss. However, the random contact force between casngs s complex and can not be determned drectly. The contact force between casngs s wrtten as r g g r g g 1 1 (18) where r s the contact force of the th contact par, N; g s 1 the nertal gap of the th contact par, m; g s the gap after deformaton, m. ABAQUS/Standard s used to solve nequaltes of contact force. Beam element PIPE31 s adopted to smulate casngs. Contact element ITT31 s adopted to smulate random contact between casngs. 4.2 Soluton process The wellhead movement and uncemented casng strength durng each operaton should be calculated snce the wellbore structure and the operatng load always change durng drllng, completon and gas producton. The fnte element analyss scheme shown n Fg. 3 s establshed accordng to the actual procedures of drllng, completon and gas producton. The nternal and external pressure on each casng s appled by DLOAD command n ABAQUS. 5 Case study 5.1 Calculaton parameters The wellhead movement and the uncemented casng strength of four gas wells n the South Chna Sea were calculated wth the proposed methods. The water depth was 198 m and the temperature was 2 ºC. The formaton temperature gradent was 4.8 ºC/1 m. The weght of BOP and Chrstmas tree were 5 tonnes and 6.6 tonnes respectvely. Detaled parameters of each casng are lsted n Table 1. Wellbore structures are lsted n Table 2. The temperature and pressure felds are lsted n Table 3. The ol tube of well A1H are shown n Fg. 4. Ppe Surface conductor Table 1 Detaled parameters of each casng Outer dameter m Inner dameter m Unt weght kg/m Materal Yeld strength MPa X Intermedate casng N8 552 Producton casng L8 552 Ol tube L8 552 Table 2 Wellbore structure Well The length of the ol tube, m The length of the The length of the uncemented producton casng, m producton casng, m The length of the ntermedate casng, m The length of the uncemented ntermedate casng, m The length of the surface conductor, m A1H A2H A3H A4H

5 Pet.Sc.(214)11: Operatons Analyss scheme Run the surface conductor Kll all elements except surface conductor elements and defne lateral constrants on the conductor Run the ntermedate casng Actvate ntermedate casng elements and relevant contact elements Cement the ntermedate casng Defne constrants on the cemented part of the ntermedate casng Install the BOP Apply a compressve force equal to the BOP weght on the wellhead Run the producton casng Actvate producton casng elements and relevant contact elements Cement and land the producton casng Defne constrants on the cemented part of the producton casng and apply a runnng load on the top of the producton casng. Couple the producton casng head and the ntermedate casng head va a JOINT elements Run the ol tube Actvate ol tube elements and relevant contact elements Install the packer Defne constrants on the ol tube at the packer Remove the BOP Apply a tensle force equal to the BOP weght on the wellhead Install the Chrstmas tree Apply a compresson force equal to the Chrstmas tree weght on the wellhead Gas producton Apply the temperature and pressure felds Well Bottom hole temperature, ºC Fg. 3 Fnte element analyss scheme Table 3 Wellhead temperature, ºC Bottom hole pressure, MPa Ol pressure, MPa Casng pressure, MPa A1H A2H A3H A4H Temperature, C Ol tube Producton casng Intermedate casng Well depth, m Fg. 4 The detaled temperature felds of uncemented casngs and ol tube n well A1H 5.2 Mechancal characterstcs of the multstrng system Mechancal characterstcs of the multstrng system were smulate the random contact between casngs. The producton casng was chosen consderng that the uncemented part of the producton casng was long and makes the prmary contrbuton to the wellhead movement. The contact load on the uncemented producton casng n well A1H s shown n Fg. 5. Fg. 5 shows that the contact load between the uncemented producton casng and the ntermedate casng s low n the vertcal secton and hold secton whle the contact load s hgh n the buld secton. The maxmum value of the contact load s needed for the producton casng to bend n order to

6 136 Pet.Sc.(214)11: S, S11 (Avg: 75%) e e e e e e e e e e e e+.2 +.e+. nstallng the Chrstmas tree, and gas producton respectvely. Fg. 6 shows that the theoretcal soluton s close to the and completon due to the weght of the producton casng, ol tube and the Chrstmas tree. The maxmum wellhead subsdence s about.15 m. The wellhead rses durng gas producton due to the varatons of temperature and pressure completon proved to be n good agreement wth measured values by McCabe (1989) n the North Sea gas feld. The comparsons between the calculated wellhead growths and measured values durng gas producton are lsted n Table Theoretcal soluton Fnte element soluton Fg. 5 Contact load on the uncemented producton casng 5.3 Calculaton of the wellhead movement On the bass of methods proposed n ths paper, the wellhead movement was calculated for four gas wells of Panyu gas feld n the South Chna Sea. The calculated wellhead movement of well A1H s shown n Fg. 6. Operatons from 1 to 7 n Fg. 6 stand for runnng the ntermedate casng, nstallng the BOP, runnng the producton casng, runnng the ol tube, removng the BOP, Wellhead movement, m Operatons Fg. 6 Calculated wellhead movement of well A1H Wellhead growth 8 Well Measured data, m Table 4 Comparson between calculated wellhead growths and measured data Theoretcal soluton, m The devaton of theoretcal soluton, % Fnte element soluton, m The devaton of A1H A2H A3H A4H Table 4 shows that the wellhead growths durng gas element solutons for wellhead growth are n good agreement wth the measured values and the devatons of calculaton are theoretcal solutons because the nteracton between casngs The temperature and pressure felds are two factors governng the wellhead growth. The pressure feld ncludes ol pressure and casng pressure, and the casng pressure s wellhead temperature and ol pressure on the wellhead growth of well A1H s calculated, as shown n Fgs. 7 and 8. Fgs. 7 and 8 show that the wellhead growth ncreases wth the wellhead temperature and ol pressure. Compared wth the ol pressure, the wellhead temperature has greater 5.4 Strength assessment of the uncemented casngs The axal load on each casng should be calculated before assessng the strength of the uncemented casngs. Fg. 9 llustrates the calculated axal loads on the ntermedate and producton casngs n well A1H. Operatons from 1 to 7 n Fg. 9 stand for runnng the ntermedate casng, nstallng the BOP, runnng the producton casng, runnng the ol tube, removng the BOP, nstallng the Chrstmas tree, and gas producton respectvely. Fg. 9 shows that the theoretcal solutons are smlar to the fnte element solutons for the casng axal load. The ntermedate casng head s under compresson all the tme and the maxmum compressve load occurs at runnng the ol tube. The producton casng head s under tenson durng

7 Pet.Sc.(214)11: Wellhead growth, m Axal load of casng head, MN Theoretcal soluton of the ntermedate casng Theoretcal soluton of the producton casng Fnte element soluton of the ntermedate casng Fnte element soluton of the producton casng Wellhead temperature, C Operatons Fg. 9 Calculated axal loads on each casng head durng dfferent operatons Fg Wellhead growth, m Von Mses stress, MPa Theoretcal soluton of the ntermedate casng Theoretcal soluton of the producton casng Fnte element soluton of the ntermedate casng Fnte element soluton of the producton casng Operatons Ol pressure, MPa Fg. 8 drllng and completon and under compresson durng gas producton. The maxmum tensle load on the producton casng occurs at removng the BOP. Von Mses stresses on the uncemented casngs durng dfferent operatons, shown n Fg. 1, were calculated accordng to the axal load on each casng. Fg. 1 shows that the maxmum von Mses stress on the ntermedate casng occurs at runnng the ol tube because the axal compressve force s hghest at ths tme (as shown n Fg. 9). The maxmum von Mses stress on the producton casng calculated wth the theoretcal method occurs at removng the BOP whle that maxmum value calculated wth the fnte element method occurs at the stage of gas producton. The producton casng head s under compresson durng gas producton, and the uncemented producton casng s so long that the bottom of the producton casng bends. However, the casng bendng s not consdered n the theoretcal method, so the dfference between the von Mses stresses on the producton casngs calculated wth two Fg. 1 Von Mses stresses durng dfferent operatons solutons for von Mses stress are recommended. Table 5 lsts the calculated strength of the uncemented casngs n four wells. The result shows that all the uncemented casngs satsfy strength requrements. Every uncemented casng keeps structural ntegrty durng drllng, completon and gas producton. Table 5 The calculated strengths of uncemented casngs Well Ppe Materal Mnmum yeld strength MPa Maxmum von Mses stress MPa Safety factor Intermedate casng N A1H Producton casng L Intermedate casng N A2H Producton casng L Intermedate casng N A3H Producton casng L Intermedate casng N A4H Producton casng L

8 138 Pet.Sc.(214)11: Conclusons 1) A theoretcal method and a fnte element method for calculatng wellhead movement and uncemented casng strength are proposed n ths paper. Compared wth the exstng theoretcal method, the proposed theoretcal method consdered the nfluence of pressure feld and ts effect on the wellhead movement and the uncemented casng strength durng gas producton. On the bass of the gap element presented to smulate random contact between casngs. The relevant fnte element analyss scheme was also presented accordng to the actual procedures of drllng, completon and gas producton. 2) The wellhead subsdes durng drllng and completon and the maxmum wellhead subsdence s about.15 m. The wellhead rse durng gas producton s between.5 m wellhead growth are n good agreement wth measured values and the devatons of calculaton are wthn 1%. 3) The theoretcal solutons are smlar to the fnte element solutons for the axal load on casngs. The ntermedate casng head s under compresson all the tme and the maxmum compressve load occurs at the runnng of the ol tube. The producton casng head s under tenson durng drllng and completon and under compresson durng gas producton. The maxmum tensle load on the producton casng occurs on the removal of the BOP. 4) Von Mses stresses on the uncemented casngs change durng drllng, completon and gas producton. The maxmum von Mses stress on the ntermedate casng occurs durng the runnng of the ol tube. The maxmum von Mses stress on the producton casng calculated wth the theoretcal method occurs on removng the BOP whle that calculated safety consderaton, the fnte element solutons for von Mses stress are recommended. Uncemented casngs of the four wells n Chna South Sea satsfy strength requrements. 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