7/28/2019 An Improved Method for Computing Wellbore Position Uncertainty and Its http://slidepdf.com/reader/full/an-improved-method-for-computing-wellbore-position-uncertainty-and-its 1/12 THE SPE I MAGE LI BRARY SPE 36863 SPE 36863 An I mpr oved Method f or Comput i ng Wel l bore Posi t i on Uncert ai nt y and i t s Appl i cat i on t o Col l i si on and Tar get I nt er secti on Pr obabi l i t y Anal ysi s Andr ew G. Br ooks, SPE, and Har r y W i l son, SPE, Baker Hughes I NTEQ Copyr i ght 1996, Soci et y of Pet r ol eum Engi neer s, I nc. Thi s paper was prepar ed f or presentat i on at t he 1996 SPE Eur opean Pet r ol eum Conf er ence hel d i n Mi l an, I t al y, 22- 24 Oct ober 1996. Thi s paper was s el ect ed f or pr esent at i on by an SPE Pr ogr am Comm i t t ee f ol l owi ng r evi ew of i nf or mat i on cont ai ned i n an abst r act subm i t t ed by t he aut hor ( s) . Cont ent s of t he paper , as pr esent ed, have not been r evi ewed by t he Soci et y of Pet r ol eum Engi neer s and ar e subj ect t o cor r ect i on by t he aut hor ( s) . The mat er i al , as pr esent ed, does not necessar i l y r ef l ect any posi t i on of t he Soci et y of Pet r ol eum Engi neer s, i t s of f i cer s, or member s. Paper s pr esent ed at t he SPE meet i ngs ar e subj ect t o publ i cat i on r evi ew by Edi t or i al Comm i t t ees of t he Soci et y of Pet r ol eum Engi neer s. Per m i ssi on to copy i s restri cted t o an abst r act of not mor e t han 300 wor ds. I l l ust r at i ons may not be copi ed. The abst r act shoul d cont ai n conspi cuous acknowl edgment of wher e and by whom t he paper i s pr esent ed. Wr i t e Li br ar i an, SPE, P. O. Box 833836, Ri char dson, Texas 75083- 3836, U. S. A. , f ax 01- 214- 952- 9435. Abst r act As moder n dr i l l i ng pr oj ect s cont i nue t o i ncl ude i ncr eased use of ext ended- r each wel l bor es di r ect ed t o smal l er t ar get s, t he need f or an accur at e assessment of uncer t ai nt y i n bot t om - hol e l ocat i on i s becom i ng i ncreasi ngl y cri t i cal . I ncor r ect assessment of t he pr obabi l i t y of i nt er sect i ng t he t ar get can l ead t o an equal l y i ncor r ect assessment of t he vi abi l i t y of t he pr oj ec t . Most publ i shed met hods f or comput i ng wel l bor e posi t i on uncer t ai nt y ar e based on t he anal ysi s of syst emat i c er r or s i n i ncl i nat i on, azi mut h and measur ed dept h. The under pi nni ng of such anal yses i s t hat t hese var i ous er r or t er ms ar e uncor r el at ed const ant s, but t hi s assumpt i on may not al ways be j ust i f i ed. The t echni que has t her ef or e been gener al i zed t o make use of mor e f undament al i nput er r or t er ms. and to t ake account of t he pr obabi l i st i c nat ur e of such t er ms, t her eby cal cul at i ng an el l i psoi dal pr obabi l i t y f i el d f or each poi nt al ong t he wel l . Exampl es ar e pr esent ed whi ch i l l ust r at e t he advant ages of t hi s met hod, i ncl udi ng t he abi l i t y t o t ake i nt o account t he r ot at i on of an el ect r oni c magnet i c sur vey i nst r ument such as an MWD t ool . When one sur vey t ool i s f ol l owed i n t he hol e by anot her , some er r or t er ms may behave i n a syst emat i c f ashi on acr oss t he ti e- on poi nt whi l e ot her s combi ne r andom l y. Si nce t he comput ed uncer t ai nt y i n bot t om - hol e l ocati on depends on t he degr ee of corr el ati on between one set of er r or s and t he next , a f l exi bl e means i s suggest ed f or accommodat i ng such t i e- ons.
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7/28/2019 An Improved Method for Computing Wellbore Position Uncertainty and Its
An I mpr oved Method f or Comput i ng Wel l bore Posi t i on Uncer t ai nt y and i t sAppl i cat i on t o Col l i si on and Tar get I nt er secti on Pr obabi l i t y Anal ysi s
Andr ew G. Br ooks, SPE, and Har r y Wi l son, SPE, Baker Hughes I NTEQ
Copyr i ght 1996, Soci et y of Pet r ol eum Engi neer s, I nc.
Thi s paper was prepar ed f or presentat i on at t he 1996 SPE Eur opeanPet r ol eum Conf er ence hel d i n Mi l an, I t al y, 22- 24 Oct ober 1996.
Thi s paper was sel ected f or pr esent at i on by an SPE Progr am Commi t t eef ol l owi ng r evi ew of i nf or mat i on cont ai ned i n an abst r act submi t t ed byt he aut hor ( s) . Cont ent s of t he paper , as pr esent ed, have not beenr evi ewed by t he Soci et y of Pet r ol eum Engi neer s and ar e subj ect t ocor r ect i on by the aut hor ( s) . The mat er i al , as pr esent ed, does notnecessar i l y r ef l ect any posi t i on of t he Soci et y of Pet r ol eumEngi neer s, i t s of f i cer s, or member s. Paper s pr esent ed at t he SPEmeet i ngs ar e subj ect t o publ i cat i on r evi ew by Edi t or i al Commi t t ees of
t he Soci et y of Pet r ol eum Engi neer s. Per mi ssi on t o copy i s r est r i ct edt o an abst r act of not mor e t han 300 wor ds. I l l ust r at i ons may not becopi ed. The abst r act shoul d cont ai n conspi cuous acknowl edgment of wher e and by whom t he paper i s present ed. Wr i t e Li br ar i an, SPE, P. O.Box 833836, Ri char dson, Texas 75083- 3836, U. S. A. , f ax 01- 214- 952- 9435.
Abst r act
As moder n dr i l l i ng pr oj ect s cont i nue t o i ncl ude i ncr eased use of ext ended- r each wel l bor es di r ect ed t o smal l er t ar get s, t he need f or anaccur at e assessment of uncer t ai nt y i n bot t om- hol e l ocat i on i s becomi ngi ncreas i ngl y cr i t i cal .
I ncor r ect assessment of t he pr obabi l i t y of i nt er sect i ng t he t ar get canl ead t o an equal l y i ncor r ect assessment of t he vi abi l i t y of t hepr oj ect.
Most publ i shed met hods f or comput i ng wel l bor e posi t i on uncer t ai nt y ar ebased on t he anal ysi s of syst emat i c er r or s i n i ncl i nat i on, azi mut h andmeasur ed dept h. The under pi nni ng of such anal yses i s t hat t hesevar i ous er r or t er ms are uncor r el at ed const ant s, but t hi s assumpt i onmay not al ways be j ust i f i ed. The t echni que has t her ef or e beengener al i zed t o make use of mor e f undament al i nput er r or t er ms. and t o
t ake account of t he pr obabi l i st i c nat ur e of such t er ms, t her ebycal cul at i ng an el l i psoi dal pr obabi l i t y f i el d f or each poi nt al ong t hewel l . Exampl es are pr esent ed whi ch i l l ust r at e t he advant ages of t hi smet hod, i ncl udi ng t he abi l i t y t o t ake i nt o account t he r ot at i on of anel ect r oni c magnet i c sur vey i nst r ument such as an MWD t ool .
When one survey t ool i s f ol l owed i n t he hol e by anot her , some er r ort er ms may behave i n a syst emat i c f ashi on acr oss t he t i e- on poi nt whi l eother s combi ne r andoml y. Si nce t he comput ed uncert ai nt y i n bot t om- hol el ocat i on depends on t he degr ee of cor r el at i on between one set of err or s and t he next , a f l exi bl e means i s suggest ed f or accommodat i ngsuch t i e- ons.
7/28/2019 An Improved Method for Computing Wellbore Position Uncertainty and Its
Si nce a pr obabi l i t y can be assi gned t o t he hypot hesi s t hat a poi nt i na pl anned or dr i l l ed wel l bor e occupi es a gi ven vol ume of space, t hi smet hod can al so be used t o det er mi ne the pr obabi l i t y t hat a par t i cul arpoi nt i n t he wel l mi ght i nt er sect an adj acent wel l bor e or an ar bi t r ar yt ar get vol ume. Thi s makes possi bl e i mpr oved comput at i on of t hepr obabi l i t i es of wel l bor e col l i si on or t ar get penet r at i on.
I nt r oducti on
The cal cul at i on of wel l bor e posi t i on uncer t ai nt y has been addr essed byWal st r om et al and by Wol f f and deWardt . I t i s commonl y accept ed t odayt hat such uncer t ai nt y i s domi nat ed by syst emat i c err or s, t hus mostpopul ar model s are based on t he syst emat i c anal ysi s out l i ned by Wol f f and deWar dt . Wi t h ext ensi ve f i el d usage of t hese model s over t heyears, some l i mi t at i ons have become appar ent . These i ncl ude t hedet er mi ni st i c nat ur e of t he syst emat i c model as or i gi nal l y descr i bed,t he def i ni t i on of most i nst r ument er r or s i n t er ms of f i xed i ncl i nat i onand azi mut h uncer t ai nt i es, f ai l ur e t o i ncl ude r andom er r or s as wel l assyst emat i c, and t he i nabi l i t y t o assi gn a pr obabi l i t y t o bor ehol eposi t i on. A modi f i ed t r eat ment of uncer t ai nt y whi ch over comes t hese
l i mi t at i ons i s descr i bed her e. Al t hough sever al of t hese i mpr ovement shave been used f or many year s by a number of compani es, unt i l nowt her e has been l i t t l e document at i on of t hem i n t he l i t er at ur e.
Cal cul at i on of Wel l bor e Posi t i on Uncer t ai nt y
Wel l bor e sur veys ar e t ypi cal l y per f or med at a number of di scr et esurvey st at i ons al ong the cour se of t he wel l by measur i ng component sof t he ear t h' s gr avi t y f i el d and ei t her t he l ocal magnet i c f i el d or ar ot at i on vect or . An i nst r ument per f ormance model i s used t o conver tt hese r aw measurement s t o i ncl i nat i on I , and azi mut h A, whi ch t ogetherwi t h the al ong- hol e dept h L, make up a t hree- component measur ementvect or p. A wel l bor e t r aj ect or y model i s t hen empl oyed t o conver t t heset of measur ement vect or s i nt o a posi t i on vect or r i n a nor t h, east ,and ver t i cal ( N, E, V) coor di nat e syst em.
An i nst r ument per f or mance model i ncl udes pot ent i al sour ces of er r or oruncer t ai nt y i n t he measur ement .
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7/28/2019 An Improved Method for Computing Wellbore Position Uncertainty and Its
