7 nd ntrntionl Confrnc on Softwr, Multimdi nd Communiction Enginring (SMCE 7) SBN: 978--6595-458-5 Thorticl Study on th Whil Drilling Elctromgntic Signl Trnsmission of Horizontl Wll Y-huo FAN,,*, Zi-ping NE nd Xing-yng SUN Univrsity of Elctronic Scinc nd Tchnology of Chin, Sichun, Chngdu, 67 Chin Rsrch nstitut of Rdiowv Propgtion, Xinxing, Hnn, 45 *Corrsponding uthor Kywords: EM-MWD, Equivlnt trnsmission lin, Horizontl lctric dipol. Abstrct. Elctromgntic wv trnsmission is on kind of wirlss signl trnsmission of whil drilling, hs bn rsrch hotspot. Th prvious studis minly on vrticl wll, but this tchnology oftn usd in horizontl wll, so it is ncssry for study on th lctromgntic wv trnsmission from horizontl wll to surfc. Bsd on th fild of th horizontl lctric dipol in conducting hlf-spc nd th quivlnt trnsmission lin thory, th thorticl modl is stblishd. Svrl groups of horizontl sction nd vrticl sction with diffrnt lngths r clcultd. Th rsults of clcultion r nlyzd. ntroduction As drilling, th msurmnt informtion of down-hol is trnsmittd to th surfc in rl tim, it cn provid th bsis nd guidnc for th nxt oprtion. Th informtion trnsmission minly contin wird nd wirlss, lctromgntic wv trnsmission is on kind of wirlss trnsmission wy. Thory rsrch of lctromgntic wv trnsmission cn b dividd into two ctgoris, on is bsd on low frquncy fild chrctristics of th quivlnt pproximtion mthod of quivlnt trnsmission lin mthod. th othr is bsd on solving th fild qutions boundry vlu problms of numricl mthods. But th prvious studis minly on vrticl wll, but this tchnology oftn usd in horizontl wll. n ordr to found th thory modl of th lctromgntic wv trnsmission for horizontl, w ssum tht th formtion is homognous mdium, tht th currnt distribution on th drill pip is not ffctd by th intrfc of formtion nd th bnding of th drill pip. Th quivlnt trnsmission lin modl is usd to clcult th currnt distribution on th drill pip, thn bsd on th fild of horizontl lctric dipol nd vrticl lctric dipol in conducting hlf-spc clcult th rcivd signl on surfc. Th Equivlnt Trnsmission in Modl z d σ m ε m σ ε V s ρ Figur. Th quivlnt trnsmission lin modl. 4
n Figur, th rdius of th drill string, th quivlnt rdius of th trnsmission lin d, th lngth of th drill string, th lngth of th lctrod, th lctricl conductivity nd th dilctric constnt, th subscript m indicts th drill string, nd th subscript rprsnts th formtion. Th sris rsistnc r, inductnc l g, shunt conductnc g nd cpcitnc c of th unit trnsmission lin r s follows [] r m () l g d n () g d n () i c d n th currnt nd voltg distribution on th drill pip cn b xprssd s z z z V V V (5) z z z V V (6) Z whr V, V cn b dtrmind by boundry conditions, for EM- MWD systm trminl is opn, th xcittion nd trminl conditions r () Vs / ZT, ( ), ZT is input impdnc of trnsmitting ntnn, put into th Eq. 6, thn (4) V Z (7) h Z V (8) Thus z z z (9) Z z z V z () For trminl opn circuit, by Eq.6 nd Eq.7, if z, thn th input impdnc Z T V () Z T Z cth () () Du to th lngth of is short thn th skin dpth of th formtion, so th clcultion of th impdnc of th qusi sttic pproximtion mthod [] 5
l Z ln K l whr, K. 69. Thus, th input impdnc of th trnsmitting ntnn is () Z T Z Z () T T Fild of Elctric Dipol in Conducting Hlf-spc Th horizontl lctric dipol in conducting hlf-spc s th figur shows. z z (ρ,φ,h) h O O l x(x ) x Figur. Th horizontl lctric dipol in conducting hlf-spc. Undr qusi-sttic conditions, th Hrtz vctor in th uppr hlf spc cn b writtn s l ( zh) h J( d 4j (4) x ) l cos ( zh) h z J( ) d 4j (5) / for Eq nd Eq th ( k ), k ( j / ). n ordr to fcilitt th clcultion, th us of Wit mirror img thory [] d thr d / k,thn if d (6) (7) k k b (8) for th EM-MWD, it is possibl to pproximt.96, b.4. thn Will b th typ into Eq4 nd Eq 5, thn intgrl h kh bh (9) x l kh 4j C C () 6
l kh cos d ( z h) bh z h z 4j C C thr bh () C () ( z h bh) C ( d z h bh) () th fild for surfc kh l cos b h E b kbh C C (4) kh l sin C C E ( ) C d C (5) kh l cos 6bh 4 bh d bh Ez 5 4 C d C C For th fild of th vrticl lctric dipol in conducting hlf-spc [4] (6) E jl jbk h h k h 5 (7) Rcivd Signl Clcultion for Horizontl Wll Th lctromgntic wv trnsmission in horizontl wlls is shown in th figur. Th horizontl wll modl is mor complx thn th vrticl wll, in ordr to fcilitt study, w ssum tht th formtion is homognous, tht th currnt distribution on th drill pip is not ffctd by th intrfc of formtion nd th bnding of drill pip. V r b v Th rciv signl cn b clcultd by h Figur. Th horizontl wll. Vr b t E d t v h thr E E E, thn () 7
j () l h () h h v v jbkh E dl 5 h k kh h h ( l)cos b h E b kbh dl C C () n ordr to discuss th influnc of th horizontl sction, th clcultion prmtrs r slctd s shown in Tbl, Th rsults r shown in Tbl. Tbl. Prmtr slction tbl. σ Ω m ε ε r. -6 Ω μ μ.m A 9m f Hz Tbl. Comprison of clcultion rsults. Th lngth v m 5 5 5 5 5 5 Th lngth h m 5 5 5 V h dbv -68. -66. -65. -95. -9. -9.9 -.5 -.4-9. V v dbv -44.4-49.9-6.9-58. -6.9-77.9-7. -77.8-9.8 Totl V r dbv -44. -48.8-58.5-58. -6.8-76.4-7. -77.9-9. V r Vrticl wll dbv -44.4-5. -6.9-58. -6.9-77.9-7. -77.9-9.8 From Tbl, th contribution of th currnt on th horizontl sction to Totl V r is rltd to th lngth of th vrticl sction nd th lngth of th horizontl sction. Whn th vrticl sction is longr thn th lngth of th horizontl sction, th V h is smllr thn V v. Th V r for Vrticl wll in Tbl. With th lngth drill pip is qul to th totl lngth of th vrticl sction nd horizontl sction. Th Tbl show tht th diffrnt lngth of vrticl nd horizontl, horizontl wlls nd vrticl wlls production sitution is slightly diffrnt. t cn b concludd tht th currnt drill pip nr th wllhd ply th min contribut to V r. Th conclusion is on th ssumption tht th formtion is homognous, th currnt distribution of drill pip r smll ffctd by drill pip bnding. Th fct condition for th formtion of non uniform formtion, so to furthr rsrch on lctromgntic wv trnsmission problms with horizontl wll, th complx thorticl modl must b foundd. Summry Bsd on th fild of th horizontl lctric dipol in conducting hlf-spc nd th quivlnt trnsmission lin thory, th thorticl modl is stblishd. Th clcultion shows tht th horizontl sction contribution to signl is smllr thn vrticl sction, th ffcts of th horizontl sgmnt in th clcultion cn b no spcil trtmnt. Acknowldgmnt This rsrch ws finncilly supportd by CETC. Rfrncs [] Fn Y H, Ni Z P, i T. EM chnnl thory modl nd chrctristics nlysis for MWD. Chins Journl of Rdio Scinc, 8():99~94. [] Wit, J. R. Th lctromgntic filds of horizontl dipol in th prsnc of conducting hlf-spc, Cn. J. Phys, 9(96):7-8. 8
[] Arthur D. Wtt, VF Rdio Enginring, first d, Prgmon Prss (Oxford nd Nw York), 967. [4] P. Bnnistr. Th qusi-nr filds of dipol ntnns. EEE Trnsctions on Antnns & Propgtion, 967, 5(5):68-66. 9