56 DOI 10.1007/s118-013-0368-8 Research regardng coal-bed wellbore stablty based on a dscrete element model Zhu Xaohua, Lu Wej and Jang Jun School of Mechancal Engneerng, Southwest Petroleum Unversty, Chengdu, Schuan 610500, Chna Chna Unversty of Petroleum (Bejng) and Sprnger-Verlag Berln Hedelberg 01 Abstract: order to perform thorough and systematc research regardng coal-bed wellbore stablty problems, a new dscrete element model whch fully consders the features of cleat coal-beds s establshed based on the bed collapse/fracture pressure are determned; n addton, the relatonshps between ppe trppng speed and ppe sze, cleat sze, etc. and wellbore stablty are analyzed n the coal-bed drllng and ppe trppng processes. The case studes show the followng results: the wellbore collapses (collapse pressure:.33 ) or fractures (fracture pressure: 1.7 ) n certan drectons as a result of swab or surge pressure wellbore stablty, and f the drllng flud pressure s too low, the wellbore s prone to collapse when enough, the butt cleat sze has no nfluence on the wellbore fracture; the factors nfluencng coal-bed stablty nclude the movement length, ppe sze, borehole sze. Key words: Coal-bed methane, wellbore stablty, dscrete element model, ppe trppng; wellbore collapse 1 Introducton Coal-bed methane s an mportant alternatve energy source; ts reserves are equal n amount to those of conventonal natural gas, but at present the producton of coal-bed methane s not very actve. The exploraton for coalbed methane began n Amerca as early as the 1980s, but untl 010 coal-bed methane producton only accounted for producton. The coal-bed methane ndustry n Chna began relatvely late, but ts development has been very rapd, as there were more than 5,9 coal-bed methane wells n Chna by the end of 011, and the surface coal-bed methane 8 m 3 ; however, the coal-bed of Chna s total conventonal natural gas producton (San and Ejefodom, 011; Shen et al, 01). The coal beds n Chna are characterzed by low pressure, low permeablty, low saturaton and strong ansotropy, so horzontal drllng s becomng a favorable choce n coal-bed methane development. The gas producng rates of horzontal wells have reached 10 tmes those of vertcal wells drlled n the same coal seams, wth an average beng -5 tmes (Matthews, 005; Shen et al, 01). However, coal-bed wellbore *Correspondng author. emal: zxhth113@163.com Receved February 3, 01 stablty problems are very sgnfcant (especally n multlateral horzontal coal-bed methane wells), due to low tensle strength, low elastc modulus, developed fractures (cleat gaps), strong pressure senstvty, etc. of coal-beds (Gentzs et al, 009a; Kem et al, 011; Huang et al, 013). In vew of the problems of wellbore stablty, many researchers have performed a large number of studes: Zhang et al (006) studed the effect of the sze of horzontal wellbores n coal-beds usng the realstc falure process analyss (RFPA D ). Zhu et al (007) analyzed the wellbore and poroelastc theores. Whttles et al (007) descrbed the applcaton of computatonal modellng to the predcton of the stablty of methane dranage boreholes durng the extracton lfe of an actve longwall coal panel. Desman et al (008) used the Hoek-Brown falure crteron wth the geologcal strength ndex (GSI) to capture the nfluence of both cleatng and mcro-fractures on coal strength. Gentzs (009b; 009c) used STABVewTM D and 3D to analyze the wellbore nstablty problems occurrng durng drllng and producton. Desman et al (010) and Hawkes (007) examned wellbore stablty based on mechancal propertes factors on mult-lateral horzontal coal-bed methane wells based on the Hoek-Brown crteron. Qu et al (010; 011a; 011b) dd some research on the mechansm of coal-bed wellbore nstablty and drllng flud densty wndows n
57 coal-bed methane drllng based on fracture mechancs theory and the 3D dscrete element method. Besdes, Connell and Jeffrey (005), Moschovds et al (005), Palmer et al (005a; 005b), Yan (005), Dexter (006), Gentzs and Bolen (008) examned the effect of seam thckness, seam depth, gas content, permeablty, coheson of the coal, overburden stress, wellbore length, reservor pressure, drllng flud densty, water rate, mechancal skn and well trajectory on wellbore stablty and gas producton. Coal blocks are dscontnuous due to the hgh development of cleats n coal-beds, and the mechancal characterstcs of coal blocks are dscontnuous and nonlnear. However, the foundaton of the current wellbore stablty theory s the contnuum theory, thus t s mpossble to descrbe the stress stran condton of cleat coal-bed boreholes. As a result, the nstablty mechansm of wellbores n coal-beds s unclear, and at present a comparatvely accurate theoretcal model has yet to be developed. In order to perform thorough and systematc research on wellbore stablty n coal-beds, a new dscrete element model whch fully consders the features of cleat coal-beds s establshed based on the Krsch equaton. Wth ths model, the safe ppe trppng speed, drllng flud densty wndow and the coal-bed collapse/fracture pressure are determned; n addton, the relatonshps between ppe trppng speed and ppe sze, cleat sze, etc. and wellbore stablty are analyzed n the processes of coal-bed drllng and ppe trppng. Establshment of a dscrete element model There are two approxmately perpendcular cleat systems (a butt cleat system and a face cleat system) n a coal-bed, ther respectve cleat surfaces are located across from each other, dvdng the coal-bed nto many matrx blocks (Laubach et al, 1998; Yn et al, 01), as Fg. 1 shows. 3 1 Face cleat Butt cleat Fg. 1 Cleat system n a coal-bed b a the planes s perpendcular to the wellbore axs, and the plane stran condton can be appled to the vertcal and horzontal wells (or devated wells). The dscrete element method s not only a numercal analyss method, but also a pattern for thnkng of rock mechancs. The nteracton between each block obeys macroscopc Newton s laws whle dvdng the coal-bed nto many matrx blocks; however, the block tself obeys mcroscale deformaton elastc-plastc mechancs. Accordng to the Krsch equaton, the stress of the matrx block can be expressed as follows: r 1 r r p r r 1 3r r (1 ) cos r r r 1 r p r r 1 3r (1 ) cos r 1 r 3r r (1 ) sn r r where r s the radal stress; s the tangental stress; s the shear stress; p s the drllng pressure; r s the wellbore radus; r and are the polar coordnates; and and are the prncpal stresses. Convertng Eq. (1) from the cylndrcal coordnate system to the Cartesan coordnate system, the stress dstrbuton around the wellbore n the Cartesan coordnate system can be expressed as follows: cos sn sn sn cos sn sn cos Each sngle coal matrx block s clamped between two the block s more lkely to slp along the cleat face, resultng n wellbore collapse; when the drllng flud pressure s whch the wellbore rock suffered wll turn from compressve to tensle, and f the tangental stress s hgher than the tensle strength of the wellbore rock, then the wellbore wll undergo tensle falure. Therefore, block one s sngled out and analyzed wth respect to the stresses, as shown n Fg.. The compressve or tensle stress between block two and one (or between four and one) s obtaned as follows: (1) () As we all know that the wellbore length s much larger than the wellbore dameter. The stress state around the wellbore s plane stran condton n both vertcal and horzontal wells (and devated wells) except for the toe of the wellbore. So, we assume that the plane stran condton on 1= cos 1+ sn 1 sn1 1= cos 1+ sn 1 sn1 where s the butt cleat oblque angle. (3)
58 t 1 31 1 t 1 coheson of cleats; and S td s the tensle strength of the cleats. y x 1 r Wellbores are very easly broken because they are senstve to pressure fluctuatons caused by trppng out (wthdrawng the drll strng, negatve swab pressures) and trppng n (rensertng the drll strng, postve surge pressures) (Lal, 1983; Sorgun and Ozbayoglu, 010). Therefore, the effect of pressure fluctuatons must be consdered when studyng wellbore stablty. The wdely used method developed by Burkhardt (Burkhardt, 1961). Accordng to the research of Ossanya and Schafftzel (1996), the matrx block sze s small (about 10 ). Compared wth the borehole sze, the matrx block sze s much smaller. Thus, the opposte sdes of the block can be consdered as beng equal to each other. The stress value of the actng surface s also consdered as the mean stress, such as 1 and 1. Therefore, the correspondng polar coordnates are as follows: 1= + / 1= 1= + / 1= + / The 1 and 1 can be calculated whle substtutng Eq. () or Eq. (5) nto Eq. (1) and Eq. (). The crtcal shear stress when the matrc block slps along the cleat face s: 1=tan m ( 1 ) (6) 1=tan m ( 1 ) where m s the frcton angle of the face cleat. The compressve stress 31 s: 31= cos + sn + sn 31= + (7) 31= + / where s the face cleat oblque angle. Accordng to Newton s laws, the crtcal condton where the matrc block does not slp s: ( ) ( + + ) = 31 1 1 m td And the crtcal condton under whch the matrc blocks do not undergo tensle falure s: Fg. Stress analyss of a matrx block mn ( ),( ) 1 1 td where b s the face cleat sze; a s the butt cleat sze; C m s the () (5) (8) (9) sw 0.196 m (10) ( c ) (11) where p sw m s the drllng 3 ; v s the reverse dschargng speed of the f s the frcton factor; L s the ppe length n the wellbore, m; D s the dameter of the annulus, cm; d s the ppe outer dameter, cm; K c s the consstency ndex; and V s the ppe trppng speed, m/s. Surge pressure may break down weak formatons and lead to wellbore fracture or lost crculaton. Swab pressure or gas nto the borehole, reducng overbalance pressure, thus potentally resultng n a well control stuaton. The drllng s sw (1) The drllng flud pressure has a close relatonshp wth the ppe trppng speed, as shown n Table 1,.e. the surge and swab pressures wll ncrease when the ppe trppng speed s ncreased. Therefore, Eq. (1) can also be wrtten as follows: 1 s 1 3 (1 ) cos 1 s 1 3 (1 ) cos 1 3 (1 ) sn s sw (13) where p s Case studes
59 wellbore stablty, the relatonshps between ppe trppng speed and ppe sze, cleat sze, etc. and wellbore stablty are analyzed based on the above establshed dscrete element model durng coal-bed drllng and ppe trppng processes. In the case studes both the face cleat oblque angle and the butt cleat oblque angle are equal to 5º, the other basc calculaton parameters are shown n Table 1. Table 1 Basc calculaton parameters the formaton fracture pressure p p =p s =1.69. Ths to 1.69 the wellbore s stable; n other words, g/cm 3. Therefore, n order to retan wellbore stablty, t s necessary to avod hgher ppe trppng speeds n the ppe n the drllng process. C m a b S td D d m degree L m g/cm 3 9 6 1 10 10 1.1 15.9 15. 10 100 1.17 Takng a well of a length of 1,00 m as an example (vertcal length: 600 m, horzontal length: 600 m, length of 15. drllng collar: 00 m, length of 17 drll Table Ppe trppng speed V, m/s 0.5 1.0 1.5.0.5 3.0 3.5.0.5 0.55 0.91 1.3 1.77.67 3.60.7 5.69 6.80 p sw,.1 Effect of the ppe trppng speed on wellbore stablty and determnaton of collapse and fracture pressure speed s.5 m/s (p s =.33 ), the swab pressure caused by the ppe movement wll lead to wellbore collapse n the 315º and 135º drectons, therefore, n ths case the formaton collapse pressure p t =p s =.33. As shown n Fg., when the trppng n speed s m/s (p s =1.69 ), the surge pressure caused by the ppe movement wll lead to wellbore fracture n the 0º and 180º drectons, therefore, n ths case Fg. Effect of the trppng n speed on wellbore stablty (a=b=10 ). Effect of the ppe sze on wellbore stablty n the ppe trppng process From Eqs. (10) and (11) we know that durng ppe trppng the factors nfluencng pressure fluctuaton are the drllng flud propertes, annulus dameter, ppe sze, ppe trppng speed, etc. The smaller these are, the more stable the wellbore wll be. As shown n Fg. 5, the larger the ppe sze s, the lower the probablty of the wellbore stablty wll be. Therefore, durng ppe trppng, n order to reduce the probablty of wellbore nstablty we should use the smaller szed ppe, whle keepng the other nfluental factors the same. Fg. 3 Effect of the trppng out speed on wellbore stablty (a=b=10 ) Fg. 5 Effect of the ppe sze on wellbore stablty (V=.5 m/s, a=b=10 )
530.3 Effect of the cleat sze on wellbore stablty The cleat sze affects both wellbore collapse and wellbore fracture. As shown n Fg. 6, when the drllng flud pressure s suffcently low, the wellbore wll collapse wth a decreasng rato of face cleat sze to butt cleat sze. The wellbore s n a stable state when a=b=10, but once a=b=0 the wellbore collapses n the 315º and 135º drectons. If the drllng flud pressure s suffcently hgh, only the face cleat sze has an effect on the wellbore fracture whle the butt cleat sze does not, as shown n Fg. 7. Fg. 7 pressure s too hgh (p =9.67 ). Effect of other factors on wellbore stablty From Eqs. (8) and (9) and Table we know that, n the processes of coal-bed drllng and ppe trppng, the mentoned factors, but also the prncpal stresses, borehole and tensle strength of cleats, etc. The effect of these factors on wellbore stablty can also be nvestgated usng the same method and theoretcal model, thus they are not descrbed n ths paper. 5 Conclusons In ths study, a new dscrete element model whch fully consders the features of cleat coal-beds s establshed based on the Krsch equaton. Wth ths model, the safe ppe trppng speed, drllng flud densty wndow and coal-bed collapse/fracture pressure are determned, and n addton the relatonshps between ppe trppng speed and ppe sze, cleat sze, etc. and wellbore stablty are analyzed n the processes of drllng coal-bed and ppe trppng. Through the analyses, the followng recogntons and conclusons are acheved: 1) Wth the above establshed model, the coal-bed collapse/fracture pressure and drllng flud densty wndow are determned. In ths paper, the collapse pressure s shown to be.33 and the fracture pressure s 1.69. Ths to 1.69, the wellbore s stable; n other words, the correspondng drllng flud densty wndow s 0.7-1.81 g/ cm 3. ) Wellbore nstablty probablty ncreases as the ppe trppng speed ncreases, and when the ppe trppng speed reaches a certan value the wellbore wll collapse or fracture n certan drectons. In ths paper, when the trppng out speed of the 15. drll collar s.5 m/s, the wellbore may collapse n the 315º and 135º drectons, and when the trppng n speed s m/s, the wellbore may fracture n the 0º and 180º drectons. 3) In the ppe trppng process, the factors nfluencng dameter, ppe sze, ppe trppng speed, etc. The smaller the dameter of the annulus, ppe sze, ppe trppng speed and wellbore wll collapse wth a decrease n the rato of the face cleat sze to butt cleat sze. If the drllng flud pressure s wellbore fracture, whle the butt cleat sze does not. References Bur khardt J A. Wellbore pressure surges produced by ppe movement. Journal of Petroleum Scence and Technology. 1961. 13(6): 595-605 Con nell L D and Jeffery R G. Hstory matchng for optmzaton of gas dranage from horzontal wells contanng sand propped hydraulc fractures. 005 Internatonal Coalbed Methane Symposum, 16-0 May 005, Tuscaloosa, Alabama De sman N, Gentzs T and Chalaturnyk R J. Unconventonal geomechancal testng on coal for coalbed reservor well desgn: the Alberta Foothlls and Plans. Internatonal Journal of Coal Geology. 008.75(1): 15-6 De sman N, Ivars D M, Darcel C, et al. Emprcal and numercal approaches for geomechancal characterzaton of coal seam reservors. Internatonal Journal of Coal Geology. 010. 8(3-): 0-1 Dexter D. Investgatve CBM modelng for horzontal and other well types. The Conf. Board of Canada Mtg. Calgary, AB. 1-15 February 006 Gen tzs T and Bolen D. The use of numercal smulaton n predctng coalbed methane producblty from the Gates coals, Alberta Inner Foothlls, Canada: comparson wth Mannvlle coal CBM producton n the Alberta Synclne. Internatonal Journal of Coal Geology. 008. 7(3-): 15-36 Gen tzs T, Desman N and Chalaturnyk R J. Effect of drllng fluds on coal permeablty: mpact on horzontal wellbore stablty. Internatonal Journal of Coal Geology. 009a. 78(3): 177-191
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