Application of Gray Analysis Method in Friction Coefficient Assessment for Extended Reach Well

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1 Advances n Peroleu Explaon and Developen Vol. 8, No. 2, 24, pp DOI:.3968/637 ISSN X [Prn] ISSN [Onlne] Applcaon of Gray Analyss Mehod n Frcon Coeffcen Assessen f Exended Reach Well JIA Janghong [a],* ; YAN Zhenla [a] ; XIA Guangqang [a] [a] Drllng Technology Research Insue, Shengl Peroleu Engneerng Co., Ld, Snopec, Dongyng, Chna. * Crespondng auh. Supped by Naonal 863 Progra Key Technology Developen and Inegraon f Offshe Exended Reach Well Drllng and Copleon (22AA95). Receved 2 Ocer 24; acceped 25 Deceber 24 Publshed onlne 29 Deceber 24 Absrac The frcon & que s a ce ssue n he process of exended reach well drllng. The frcon coeffcen has a grea nfluence on frcon & que predcon. Reasonable and crec deernaon of he frcon coeffcen s an ssue ha us be addressed n he frcon & que analyss and predcon. The nverse odel of frcon coeffcen was esablshed based on exensve acual drllng daa. On hs bass, grey relaonal analyss s used o exple he poenal facs nfluencng he frcon coeffcen and esablsh he assocaon beween frcon coeffcen and he relevan nfluencng facs. The sudyng resul ndcaes ha he an facs affecng frcon coeffcen n ers of pance are he average rae of overall angle change, he ype of drllng flud, well deph, hole daeer, drllng flud densy, drllng flud loss, dynac shear of drllng flud, vercal deph, dsplaceen, drllng flud vscosy, drllng flud plasc vscosy. The research resuls can provde a heecal gude f reducng he frcon and que n he consrucon of exended reach wells. Key wds: Exended reach well; Frcon & que; Grey relaonal analyss; Influencng facs; Drllng flud Ja, J. H., Yan, Z. L., & Xa, G. Q. (24). Applcaon of gray analyss ehod n frcon coeffcen assessen f exended reach well. Advances n Peroleu Explaon and Developen, 8(2), Avalable fro: URL: hp:// DOI: hp://dx.do.g/.3968/637 INTRODUCTION In he drllng engneerng desgn and consrucon process of exended reach well, he predcon and analyss of frcon & que s crcal, whch s drecly relaed o he success of drllng operaon. A presen, exensve research on he frcon & que odel has been carred ou a hoe and abroad, however, due o he coplexy of frcon & que self, he frcon coeffcen s ofen acqured hrough experence n exsng odels, he exsng odel predcon err s bg, he que err even could be e han 5% [-2]. There are wo ehods o deerne he frcon coeffcen ncludng labay experens and feld daa nverson. However, due o he bg dfference beween he ndo sulaed condons and acual drllng condons, he frcon coeffcen aned by he experenal ehod has a large err and repeaably err, also exhbs po sably. Ths ehod can only evaluae and opze he base flud and lubrcan of drllng flud fro one aspec [3-4]. Based on consderable acual drllng daa, he auh presens a ehod f he quanave descrpon on relaed facs affecng frcon coeffcen by opzng he frcon & que calculaon odels and browng fro gray syse hey on he bass of he nverson of acual drllng frcon daa. Ths paper provdes he gudance f reducng he frcon and que n he consrucon of exended reach wells.. FRICTION COEFFICIENT INVERSION. Calculaon Model of Frcon and Tque F exended reach well, behole curvaure s generally low. So he drll colun can be assued o be a sof rope whch has no flexural rgdy, bu could whsand he que. The sof odel s used n he frcon & que calculaon odel. And he calculaon fula s as follows: Copyrgh Canadan Research & Developen Cener of Scences and Culures 58

2 JIA Janghong; YAN Zhenla; XIA Guangqang (24). Advances n Peroleu Explaon and Developen, 8(2), γ 2 N ( ) T + T2 sn + WX + WZ 2 F N f () a T T2 + WY± F M. 5 N f c D Where: T, T 2 - The axal fces on he up and down cross secons of he srng un, kn; γ - The dogleg angle of he ceran un, rad; N - The posve conac fce beween he drll srng un and he behole wall, kn; f a - Coprehensve frcon coeffcen, densonless; f c - Sldng frcon coeffcen, densonless; F - The frconal ressance of he srng un, kn; M - Wellhead que, kn ; WX, WY, WZ - Coponen of he buoyan wegh of he srng un on he prncple, angen and he bnal drecon, respecvely, kn..2 Inpu Paraeers of Frcon Coeffcen Inverson In he frcon coeffcen nverson process, he daa o be enered ncludes: (a) The well rajecy paraeers (well deph, nclnaon, azuh); (b) The BHA daa (he ype of drllng ool, grade, ouer daeer, nner daeer, un wegh, densy, lengh); (c) The well srucure daa (well deph, hole daeer); (d) Measured value of hook load durng rppng operaon (hook load, crespondng deph); (e) The easured que of roary able durng roary drllng process (que of roary able, crespondng deph); (f) The easured value of hook load durng roary drllng process (he hook load, he crespondng hole deph); (g) The easured value of WOB durng roary drllng (WOB, crespondng deph); (h) The easured value of hook load durng slde drllng process (hook load, crespondng deph); () The easured value of WOB durng slde drllng operaon (WOB, crespondng deph); (j) Flud perfance paraeers..3 Boundary Condons of Frcon Coeffcen Inverson The frcon coeffcen beween drll srng and be hole, he sress sae of drll srng and he conac fce beween drll srng and be hole could be oned hrough he easured value of hook load and que of roary able durng operaon. F dfferen drllng condons, he boundary condons are as follows: Trppng Process F M (2) F () W M () Where, W s Wellhead enson, and T s he oal lengh of he drll srng. Drllng Process F W M T F () W M () T Where, W s he wegh on b, T s he drll b que. Roang off Boo Reang Process F F () W M M () T F M T F () W M () T Back Reang Process F M T (6) F () W M () T If he frcon coeffcen s supposed o be an unknown consan n he whole well a ceran hole secon, f every easured value of hook load and que, he frcon coeffcen could be aned hrough he boundary condons enoned above..4 The Inverson Process Wh rppng ou operaon, f exaple, he hook load s F h, he axal fce a drll b s zero, frcon coeffcen ranges fro o, he err exceped (E ER ) s.2. Dealed calculaon s as follows: (a) Assung frcon coeffcen range: u n, u ax ; (b) Hook load calculaon: Make u a (u n + u ax )/2, calculae he hook load F bc, n case F bc < F h, hen u n u a, erwse u ax u a ; (c) Cyclc eraon o nverse he frcon coeffcen, f (u ax - u n )/u a > E ER, reurn o sep (b). Oherwse, u a s he nverson value of frcon coeffcen of rppng ou..5 Inverson Resuls of Frcon Coeffcen The feld daa relaed o exended reach well was colleced. Take he roary drllng f exaple, he frcon coeffcen was nvered hrough erave approach. Durng he nverson process, he frcon coeffcen nsde he casng was assued as.2, he eraon sep sze s, he frcon coeffcen a each pon n open hole s calculaed, and hen he average frcon coeffcen of hs well secon s aned. The resuls are shown n Table. (3) (4) (5) 59 Copyrgh Canadan Research & Developen Cener of Scences and Culures

3 Applcaon of Gray Analyss Mehod n Frcon Coeffcen Assessen f Exended Reach Well Table Inverson Resuls of Exended Reach Well Frcon Coeffcen Well nuber TD () TVD () Dsplaceen () Mud wegh (g/c 3 ) Sulaon hole secon () Average frcon coeffcen Bn 73-HF 3,983 2,892, ,67-3, Bn 435-4HF 5,97 3,699, ,93-5,97.27 Boye-png 2 3,645 2,568, ,332-3,645.2 Fan 6-HF 4,2 2,84, ,6-4,2.34 Fan 6-2HF 3,92 2,783, ,2-3,92.35 Fan 6-3HF 4,96 2,789, ,844-4,96.3 Fan 6-4HF 3,88 2,789,87.3 3,47-3,88.3 Fan 54-7HF 4,26 2,758, ,2-4,26.47 Fan 54-8HF 4,58 2,76,69.3 3,786-4,58.47 Fan 62-2HF 4,522 2,666 2, ,25-4,522.3 Gaopng 4, ,84.4 4,2-4, Nu 87-X7 3,752 3,7, ,49-3,752.9 Xn 4-8HF 4,69 2,582 2, ,852-4,69.49 Yan 227-2HF 4,522 3,653, ,62-4,522.3 Yan 227-5HF 4,74 3,99, ,647-4,74.29 Yan 227-7HF 4,26 3,4, ,69-4,26.22 Yan 227-4HF 4,323, ,25-4, Yan 227-9HF 4,925 3,84, ,26-4,925.4 Zhuang 29-HF 5,34 3,34 3,68.4 5,4-5,34.2 Langye HF 3,969 3,26,.5 3,6-3, Boye-png 4,335 2,969, ,-4, CORRELATION ANALYSIS OF INFLUENTIAL FACTORS ON FRICTION COEFFICIENT 2. Prncples of Gray Crelaon Analyss Grey syse hey holds ha any rando process s a grey varable whch changes n a ceran range of aplude value and e. Gray process s done by sng he raw daa o fnd he law of he nuber [5]. The basc dea of Grey relaonal analyss s based on he slary of geoery curve of each paraeer o judge wheher he conac s closely relaed no, he e slar he shape of he curve, he greaer he degree of relevance beween he crespondng sequences. The degree of slary should be descrbed by crelaon coeffcen and he degree of crelaon. The degree of crelaon descrbes how uch he facs can nfluence he resuls. The bgger he degree of crelaon, he greaer he degree of nfluence [6]. F a praccal syse analyss, he paren facs (a daa sequence of syse behav characerscs) and he sub-facs (an effecve facs nfluencng he syse behav characerscs) should be confred. To perf crelaon analyss, a reference daa colun should be specfed frs. A se of dscree sequence should be requred [7-8]. x (k), k, 2,, ; x (k), k, 2,, ;, 2,, n; x (k) s he sequence of paren facs, x (k) s a sequence of sub-facs. The generaon processng on led gnal daa n a cuulave way should be carred ou befe calculaon o ge e regular daa coluns. The gnal sequence of daa should be ransfed o he densonless f n der o anan densonal conssency and ake all daa coluns have a pon of nersecon. Due o he dfferen daa denson, he facs befe processng are unable o be copared because he facs wh saller nuercal value ay be ou of acon, whle he facs wh bgger value are exaggeraed. Equalzaon ehod s coonly used n densonless reaen [9-]. Equalzaon reaen process s as follows: Copyrgh Canadan Research & Developen Cener of Scences and Culures 6

4 JIA Janghong; YAN Zhenla; XIA Guangqang (24). Advances n Peroleu Explaon and Developen, 8(2), y x x k, 2, 3 n, k, 2, 3, (7) Where, y s he equalzaon sequence f each facs, x (k) s he sequence of sub-facs. y x k x k, 2, 3, (8) Where, y s he equalzaon sequence f each paren facs, x (k) s he paren fac sequence. The crelaon coeffcen s calculaed as follows, n n y y ( k) + a ax ax y y k k ξ y y + a ax ax y y (9) Where, ξ s he crelaon coeffcen of y on y a k oen, whch s he relave dfference of reference curve y and coparson curve y (k) f fac a he k pon. I s called y o y a k pon crelaon coeffcen. I s no convenen o ake a coparson f he crelaon coeffcen s quoed drecly because of he large daa volue and oo dspersve nfaon. I s necessary o conver all he crelaon coeffcen values a each oen o a sngle value. Calculang he Table 2 Basc Daa f Grey Crelaon Analyss Well Nuber Frcon coeffcen Hole sze () TD () k Well rajecy paraeers TVD () Dsplaceen () ean value s a ehod f processng hs nfaon nensvely. α s he resoluon coeffcen, whch s generally beween and, usually aken as.5 Grey crelaon s calculaed as follows: N r ξ ( k ),2,3 n, k,2,3, () N k Where, r s he crelaon degree of Curve y o he Reference curve y, he sequence coposed of crelaon degree r descrbes he nfluence of sub-facs on paren facs. The crelaon degree wh bgger value ndcaes ha has a greaer nfluence on he resuls. 2.2 Resuls of Grey Crelaon Analyss Based on he nverson resuls of frcon coeffcen (shown n Table ), he frcon coeffcen s seleced as a paren fac. he well rajecy paraeers (ncludng he average dogleg of he full hole, axu dogleg, dffculy ndex f enaon), drllng flud paraeers (ncludng drllng flud densy, vscosy, plasc vscosy, dynac shear fce) and he drllng dynac paraeers (ncludng dsplaceen, roae speed, ROP and dynac negraed drllng paraeers) are seleced as he effecve facs ha affec syse behav characerscs, naely sub-facs. Based on he Grey relaonal analyss hey, cned wh feld acual frcon coeffcen of basc daa (Table 2), several facs nfluencng on he frcon coeffcen are analyzed, and he resuls are shown n Table 3. Average rae of over all angle change ( /3 ) Drllng flud ype Densy (g/c 3 ) Drllng flud paraeers Vscosy (s) Plasc vscosy (Pa s) Dynac shearfce (Pa) Flud loss (l) Bn 73-HF ,983 2,892, Bn 435-4HF ,97 3,699, Boye-png ,645 2,568, Fan 6-HF ,2 2,84, Fan 6-3HF ,96 2,789, Fan 6-4HF ,88 2,789, Fan 54-8HF ,58 2,76, Fan 62-2HF ,522 2,666 2, Gao-png , , Nu87-X ,752 3,7, Xn 4-8HF ,69 2,582 2, Yan 227-2HF ,522 3,653, Yan 227-7HF ,26 3,4, Yan 227-4HF ,323 3,453, Zhuang 29- HF ,34 3,34 3, Boye-png ,335 2,969, Fan 6-2HF ,92 2,783, Fan 54-7HF ,26 2,758, Yan 227-5HF ,74 3,99, Yan 227-9HF ,925 3,84, Langye HF ,969 3,26, Noe. In he colun of drllng flud ype, eans ol-based drllng flud, 2 eans waer-based drllng flud. 6 Copyrgh Canadan Research & Developen Cener of Scences and Culures

5 Applcaon of Gray Analyss Mehod n Frcon Coeffcen Assessen f Exended Reach Well Table 3 Grey Crelaon Analyss Facs Crelaon degree Rank Facs Crelaon degree Rank Hole sze () Drllng flud ype Well deph () densy (g/c 3 ) TVD () Vscosy (s).639 Dsplaceen () Plasc vscosy (Pa s).654 Average rae of overall angle change ( /3 ).877 Dynac shear (Pa) Flud loss (l) Table 3 shows ha he an facs affecng he frcon coeffcen n ers of crelaon degree are he average rae of overall angle change, drllng flud ype, well deph, hole sze, drllng flud densy, drllng flud loss, drllng flud dynac shear, vercal deph, dsplaceen, drllng flud vscosy, drllng flud plasc vscosy. Therefe, n exended reach well drllng process, he so well rajecy wh low buld-up rae should be desgned frs, followed by a drllng flud syse wh good lubrcang perfance o reduce he frcon and que hrough he conrol of drllng flud perfance paraeers. CONCLUSION (a) The frcon n drllng s a concep of hybrd frcon ncludng boundary frcon, dry frcon and flud frcon. So he frcon coeffcen durng drllng operaon s a coprehensve frcon coeffcen nfluenced by behole geoery, drllng flud perfance, ppe srng srucure and he rock properes. (b) The que and frcon prle s an pan research feld of he Exended reach well, whch runs hroughou he enre process of drllng desgn, drllng operaon, well copleon operaons, ec. The frcon coeffcen nvered fro feld acual daa shows he consderaon on acual drllng condon and has a good relably. I avods he laon of frcon coeffcen deerned by labay experens. (c) There are any facs affecng he coeffcen frcon. Wh he ad of gray crelaon analyss hey, he auh akes a quanave descrpon on relaed facs affecng frcon coeffcen on he bass of he nverson of frcon coeffcen. The resuls show ha n exended reach well drllng process, he so well rajecy wh low buld-up rae should be desgned frs, followed by a drllng flud syse wh good lubrcang perfance o reduce he frcon que hrough he conrol of drllng flud perfance paraeers. REFERENCES [] Jancsk, C. A., Fresen, D. B., & Dawson, R. (984). Tque and drag n dreconal wells-predcon and easureen. Journal of Peroleu Technology, 36(6), [2] Ho, H. S. (988, Ocer). An proved odelng progra f copung he que and drag n dreconal and deep wells. Paper presened a SPE Annual Techncal Conference and Exhbon, Houson, Texas. [3] Fan, G. D., Huang, G. L., & L, X. F. (23). Calculaon odel of frcon que f hzonal well srng. Drllng & Producon Technology, 36(5), [4] Madla, E. E., & Wojanowcz, A. K. (987, March). Feld ehod of assessng behole frcon f dreconal well casng. Paper presened a Mddle Eas Ol Show, Bahran. [5] B, X. L., Yan, T., Chang, L., & Wang, C. J. (28). Gray crelaon analyss ehod and s applcaon n drll se falure n ol and gas engneerng. Proceedngs of Icnc 28: Fourh Inernaonal Conference on Naural Copuaon. [6] Chen, J. J., Qan, S. J. (23). An energy effcency assessen ehod based on grey crelaon degree analyss f ransp arps. Advanced Maerals Research, 66-68, [7] Cheng, Y. C., Zhang, P., Jao, Y. B., Tao, J. L., Wang, Y. D. (23). Grey crelaon analyss ehod o analyze he nfluence facs of aenuaed perfance of asphal xure under waer-eperaure-radaon cycle acon. Appled Mechancs and Maerals, , [8] Jun, M. (2). Research on Harbn governen webse perfance based on grey crelaon analyss ehod. Paper presened a 2 Ep/Ia Conference on Syse Scence and Sulaon n Engneerng (SSSE 2), Hong Kong, Chna. [9] Wang, L. K., Wang, X. G., Zhong, H. M., & La, D. J. (22). Usng hybrd wegh grey crelaon analyss ehod o evaluae he envronen safey grade of uranu wase rock heap. Proceedngs of 22 Inernaonal Conference on Iage Analyss and Sgnal Processng, [] Wang, T. D., Wang, J. J., & Peng, D. H. (24). Enerprse qualy cred evaluaon based on grey crelaon analyss and TOPSIS ehod. Proceedngs of he 24 Inernaonal Conference on E-Educaon, E-Busness and Infaon Manageen 9, Copyrgh Canadan Research & Developen Cener of Scences and Culures 62

Anisotropic Behaviors and Its Application on Sheet Metal Stamping Processes

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