Characteristics of helical flow in slim holes and calculation of hydraulics for ultra-deep wells

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1 6 Pet.Sci.(00)7:6-3 DOI 0.007/s Characteristics f helical flw i slim hles ad calculati f hydraulics fr ultra-deep wells Fu Jiahg, Yag Yu, Che Pig ad Zha Jihai 3 State Key Labratry f Oil ad Gas eservir Gelgy ad Explitati, Suthwest Petrleum Uiversity, Chegdu, Sichua 60500, Chia Chagqig Egieerig Techlgy esearch Istitute, Chuaqig Drillig Egieerig Cmpay Limited, Xi a, Shaaxi 700, Chia 3 Drillig Techlgy esearch Istitute, SINOPEC Shegli Oilfield, Dgyig, Shadg 5707, Chia Chia Uiversity f Petrleum (Beijig) ad Spriger-Verlag Berli Heidelberg 00 Abstract: Due t the slim hle at the lwer part f the ultra-deep ad deep wells, the eccetricity ad rtati f drill strig ad drillig fluid prperties have great effects the aular pressure drp. This leads t the fact that cvetial cmputatial mdels fr predictig circulatig pressure drp are iapplicable t hydraulics desig f deep wells. With the adpti f helical flw thery ad H-B rhelgical mdel, a cmputatial mdel f velcity ad pressure drp f -Newtia fluid flw i the eccetric aulus was established fr the cases where the drill strig rtates. The effects f eccetricity, rtati f the drill strig ad the dimesis f aulus pressure drp i the aulus were aalyed. Drillig hydraulics was give fr a ultra-deep well. The results shw that the aular pressure drp decreases with a icrease i eccetricity ad rtary speed, ad icreases with a decrease i aular flw area. There is a great differece betwee static mud desity ad equivalet circulatig desity durig deep well drillig. Key wrds: Ultra-deep well, slim hle, aular velcity, aular pressure drp, hydraulics Itrducti With further explrati ad develpmet f il ad gas, mre ad mre deep ad ultra-deep wells are beig drilled. Hydraulics desig f deep ad ultra-deep wells are sigificatly differet frm cvetial wells due t cmplicated casig prgram ad slim hles at the lwer part f the wells. I the small aulus i a deep well, bth eccetricity ad rtati f the drill strig have great effects aular pressure drp; ad there is a great differece betwee the drillig fluid desity ad equivalet circulatig desity (ECD). The characteristics f circulatig fluid flwig i the slim hles f deep wells may cause sme difficulties i ptimiati f the deep well hydraulics. A umber f studies f the flw mechaism f -Newtia fluids i slim hles have bee made ver the years (Delwiche et al, 99; McCa et al, 995; Cui ad Liu, 996; Zheg, 998; Wag et al, 000; Ya ad Samuel, 008). Hwever, the mdels prpsed by previus researchers d t take it accut the effects f pipe rtati, eccetricity, ad the aular dimesis aular pressure drp simultaeusly. Lg et al (005) ad Demirdal ad Cuha (007) studied the effects f -Newtia fluids ad rhelgical mdels aular *Crrespdig authr. fujiahg@6.cm eceived May 6, 009 pressure drp. Sighal et al (005), Chag et al (007) ad Cui et al (008) studied the effects f eccetricity aular pressure drp. Marke et al (99), Cartals et al (996), He (005) ad Ma (006) studied the effects f eccetricity ad drill strig rtati aular pressure drp by experimetal mdels. N great prgress i the effects f drill strig rtati the velcity ad pressure fields i the arrw aulus has bee made. Helical flw characteristics i slim hles. Basic characteristics Cmpared with cvetial drillig, deep slimhle drillig is characteried by the slim hle ad very slim aulus. Therefre, the aular dimesis, ad the rtati ad eccetricity f the drill strig have sigificat effects the pressure drp ad velcity distributi i the aulus. The cmputatial mdel f fluid flw ad related techlgy adpted i cvetial drillig are t applicable t the cases f deep slimhle drillig. It is critical t develp a pressure drp mdel ad a velcity distributi mdel fr a accurate predicti f drillig fluids flwig i the drill strig ad the slim aulus. Figs. ad are the crss-sectial views f the aulus ad the drill strig, respectively. The ier radius ad uter radius f the aulus are i ad, ad

2 Pet.Sci.(00)7:6-3 7 the ier radius f the drill strig is d. The drill strig rtates at a agular speed f Ω while the brehle wall r casig wall keeps still. The eccetric distace betwee the drill strig ad the aulus is e ad ε is the dimesiless eccetricity, e. i e Ω (θ) θ i θ O 0 Fig. Flw crss secti i the eccetric aulus Ω r B si si d g 3 r i r rpi i 3 r r B r gsi si d r r 3 p r 3 r rpi B g sisi d r r 3 pi r rp i 3 r () Budary cditi: The agular velcity at the ier wall f the aulus is i ad the agular velcity at the uter wall f the aulus is 0. P is the pressure gradiet, Pa/m; η is the apparet viscsity f H-B flw, Pa s; r pi is the iteral budary f the flw cre i the aulus, m; r p is the exteral budary f the flw cre i the aulus, m; r is the radial crdiate, m; θ is the agle i degrees; Ω is the agular speed f the drill strig, rad/s; ρ is the fluid desity, kg/m 3 ; α is the icliati; B ad C are itegrati cstats; g is the accelerati f gravity, m/s..3 Apparet viscsity distributi i the aulus The apparet viscsity η(r) f the fluids at ay psiti i the aulus ca be derived frm cstitutive equatis f a H-B fluid, the axial velcity, ad the agular velcity. d O r with B C K G r Pr 3 r r B C Gr Pr 0 3 r r (3) G gsisi Fig. Flw crss secti iside the drill strig. Velcity distributi i the aulus Based the ctiuity equati ad equati f mti whe fluid flws i the lamiar flw regime ad the cstitutive equati f a Herschel-Bulkley (H-B) fluid, i the plar crdiate system (see Fig. ), the axial velcity u(r) ad the agular velcity ω(r) f the drillig fluid at ay psiti (r, θ) i the aulus ca be deduced as fllws: r P r C d r i r r pi i r r P r C ur d r r p r r rpi P r C d r r pi r r i r p () where is the liquidity idex; K is the csistecy cefficiet; τ 0 the is yield pit, Pa..4 Aular pressure gradiet Based the defiiti f flw rate, the crrelati betwee the flw rate ad the pressure gradiet i the aulus ca be deduced by itegratig ver the whle aular crss secti t flw. The pressure gradiet P the ca be expressed as fllws: Q P (4) b b b3d 0 with r r r C rpi pi r d i, Pr b b r rp p r d, Pr r (5) r r C r (6)

3 8 Pet.Sci.(00)7:6-3 r r C rpi p pi r 3 d i r, Pr b where Q is the flw rate, m 3 /s; r pi (θ) ad r p (θ) are the ier ad uter radii f flw cre at a circumferetial agle f θ, m; C(θ) is the itegral cstat f axial velcity at a radm circumferetial agle; η(r, θ) is the apparet viscsity f flw crss secti at a circumferetial agle f θ, Pa s. Eq. (4) is the mdel fr cmputig the pressure gradiet f the lamiar helical flw f H-B fluids i the eccetric aulus. r (7) u xr 0 xd 0 P K x P K x r r 0 d u xr 0 xd 0 r r 0 d (0) ().5 Velcity distributi iside the drill strig.5. Agular velcity distributi The agular velcity ω f the helical flw f the H-B fluid iside the drill strig is: r g si si d r r (8) r d d 3 r0 0 g sisi dr 0 r r 0 d 3 (9) where ω is the agular velcity at the flw cre, rad/s; r 0 is the radius f the flw cre, m..5. Axial velcity distributi The velcity f the axial flw iside the drill strig is: with G P x 9 4 where u is the axial flw velcity iside the drill strig, m/s; u 0 is the flw velcity iside the flw cre, m/s..6 Pressure gradiet iside the drill strig Based the defiiti f flw rate, the relatiship betwee the flw rate ad the pressure gradiet iside the drill strig ca be deduced by itegratig ver the whle flw crss secti f the drill strig. The pressure gradiet P is as fllws: Q K P x d xd 0 x d 4 d 0 x xd 0 d 0 x 3 () A iitial pressure gradiet value is assumed ad the the pressure gradiet P ca be calculated by iterati. 3 Aular velcity distributi ad factrs ifluecig the pressure gradiet I deep slimhle drillig, the distributis f velcity ad pressure are differet frm thse i cvetial drillig due t the very slim aulus. Therefre, it is very imprtat t study the effects f aular dimesis, drill strig rtati ad eccetricity the distributis f aular velcity ad pressure. Basic iput data fr calculati are as fllws: ) Drillig fluid prperties Drillig fluid desity:.34 g/cm 3 ; rhelgical parameters: 600=59.5, 300=00.0, 00=76, 00=47.4, 600=3.6, 3=.3. ) Dimesis f the aulus Hle sie: 4.5 mm; uter diameter f the drill strig: 63.50, 8.55, 85.50, ad mm, respectively. 3) Drillig parameters Flw rate: 5 L/s; rtary speed: 60 ad 0 r/mi, respectively. 3. Calculati f aular velcity Fig. 3(a) ad Fig. 3(b) shw the aular velcity distributis respectively fr the cases f 63.5-mm ad 07-mm drill strig (ier diameter f the aulus). The hle sie is 4.5 mm (uter diameter f the aulus), the dimesiless eccetricity is 0.5 ad the rtary speed is 60 r/mi. The aular dimesi has a great effect the distributis f axial velcity ad agular velcity ver all crss sectis. The greater the diameter f the drill stem is, i.e. the smaller the aular clearace is, the higher the maximum axial velcity is. Fig. 3(b) ad Fig. 3(c) depict the effects f the eccetricity f the drill strig the distributis f axial velcity ad agular velcity. The greater the dimesiless eccetricity f the drill strig is, the bigger the differece i velcity at the wider clearace ad the arrwer clearace is. If the drill strig is lcated the ceter f the wellbre (see Fig. 3(c)), the axial velcity ad agular velcity arud drill strig chage slightly. Fig. 3(b) ad Fig. 3(d) shw that the rtary speed f the drill strig has little effect the axial velcity, but a great effect the agular velcity. The higher the rtary speed, the greater the agular velcity is.

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6 Pet.Sci.(00)7:6-3 3 Table Hydraulics desig fr Well CK N. Well depth m Bit sie mm Flw ratet L/s Mud desity g/cm 3 Nle cmbiati mm Stadpipe pressure MPa Bit pressure drp MPa Aular pressure drp MPa Impact frce kn Nle jet velcity m/s Hydraulic pwer kw ECD g/cm 3 aular pressure. Fr drillig deep wells i pressure-sesitive frmatis, cmplicated situatis such as lst circulati durig drillig ad well kick durig wiper trip shuld be preveted. As a large hydraulic pressure lss ccurs i bth the drill pipe ad the aulus, ptimiati f hydraulics parameters shuld be udertake whe drillig the lwer part f deep wells. 5 Cclusis ) Helical flw thery ad the H-B rhelgical mdel are used t establish a three-dimesial mdel fr predictig velcity distributi i a eccetric aulus. The velcity distributi i the eccetric aulus prvides a basis fr crrect calculati f aular pressure drp. ) The cmputatial mdel f pressure drp fr - Newtia fluids i the eccetric aulus is established, ad the effects f the eccetricity, rtati f the drill strig ad the aular dimesis aular pressure drp are aalyed. The aular pressure gradiet decreases with a icrease i the dimesiless eccetricity, ad icreases with a decrease i the aular flw area. 3) Fr ultra-deep wells with slim hles, there is a high pressure drp i the aulus ad a great differece betwee the equivalet circulati pressure ad the hydrstatic fluid pressure, which brigs challeges fr safe drillig. Ackwledgemets This wrk is supprted by the Natial 863 Prgram (006AA06A9-). efereces Car tals U, Kig I, Dupuis D, et al. Field validated hydraulic mdel predictis give guidelies fr ptimal aular flw i slimhle drillig. Paper SPE 353 preseted at SPE/IADC Drillig Cferece held i New Orleas, Luisiaa, March -5, 996 Cha g Y, Ba Z J, Cui H Q, et al. Pressure gradiet f usteady flw f fluid i a eccetric aulus with the ier cylider reciprcatig axially. Jural f Daqig Petrleum Istitute (6): (i Chiese) Cui H Q ad Liu X S. Velcity distributi f -Newtia helical flw i eccetric auli. Acta Petrlei Siica (): (i Chiese) Cui H Q, Zhag S Y, Xiu D Y, et al. Pressure gradiet f Newtia fluid flw i a aulus with the ier cylider executig plaetary mti. Jural f Chia Uiversity f Petrleum (6): (i Chiese) Del wiche A, Lejeue M, Mawet P, et al. Slimhle drillig hydraulics. Paper SPE 4596 preseted at the 67th Aual Techical Cferece ad Exhibiti f SPE held i Washigt, D.C., Octber 4-7, 99 Dem irdal B ad Cuha J C. Pressure lsses f -Newtia fluids i drillig peratis. Paper SPE 087 preseted at the 007 Iteratial Oil Cferece ad Exhibiti held i Veracru, Mexic, Jue 7-30, 007 He C C. Cmputer simulati f pwer-law fluid ad Bigham fluid i a eccetric aulus. Drillig Fluid & Cmpleti Fluid (3): (i Chiese) L g Z H, Wag Z M ad Gu X L. Crrecti cefficiet methd f drillig circulatig pressure lss calculati ad its applicati. Natural Gas Idustry (7): (i Chiese) Ma M F. Aular pressure lss ad hle cleaig f hrital wells. West-Chia Explrati Egieerig (): (i Chiese) Mar ke C D, He X J ad Saase A. The ifluece f drillig cditis aular pressure lsses. Paper SPE 4598 preseted at SPE Aual Techical Cferece ad Exhibiti held i Washigt, D.C., Octber 4-7, 99 McC a C, Quigley M S, Zamra M, et al. Effects f high-speed pipe rtati pressures i arrw auli. SPE Drillig & Cmpleti (): Si ghal N, Shah S N ad Jai S. Fricti pressure crrelatis fr Newtia ad -Newtia fluids i ccetric auli. Paper SPE 9480 preseted at the SPE Prducti ad Operatis Sympsium held i Oklahma City, OK, U.S.A., April 7-9, 005 Wa g H G, Su Y N, Bai Y M, et al. Experimetal study f slimhle aular pressure lss ad its field applicatis. Paper SPE/IADC 5965 preseted at SPE/IADC Drillig Cferece held i New Orleas, Luisiaa, February 3-5, 000 Ya D P ad Samuel G. Aular-pressure-lss predictis fr varius stadff devices. Paper SPE 544 preseted at the IADC/SPE Drillig Cferece held i Orlad, Flrida, U.S.A., March 4-6, 008 Zhe g Y. Exact sluti fr helical flw f a -Newtia fluid i a aulus. Acta Petrlei Siica (): 9-96 (i Chiese) (Edited by Su Yahua)