MODEL OF CEMENTING ANNULUS GAS CHANNELING BASED ON THE LATTICE BOLTZMANN THEORY

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1 Journal of Theoretcal and Appled Informaton Technology 20 th February 203. Vol. 48 No JATIT & LLS. All rght reerved. ISSN: E-ISSN: MODEL OF CEMENTING ANNULUS GAS CHANNELING BASED ON THE LATTICE BOLTZMANN THEORY WANCHUN ZHAO, 2 WEIWEI YUAN, 3 CHEN WANG, 2 TINGTING WANG Key Laboratory of Enhanced Ol and Ga Recovery of Educaton Mntry, Northeat Petroleum Unverty, Daqng 6338, Helongjang, Chna 2 Northeat Petroleum Unverty, Daqng 6338, Helongjang, Chna 3 CNOOC Energy Technology & Servce-Olfeld Technology Servce Co.,Tanjn , Chna ABSTRACT The phenomenon of the cementng annulu mcro clearance ga channelng drectly nfluence cement job qualty and olfeld producton, o accurately decrbng the flow rule of cementng annulu mcro clearance ga channelng the core and "bottleneck" problem of controllng ga channelng effectvely. From the perpectve of the mcro partcle moton and baed on the lattce Boltzmann method, the flow model of cementng annulu mcro clearance ga partcle etablhed. Select a block of Daqng Olfeld to calculate and mulate the dtrbuton rule of flow velocty of mcro clearance ga partcle under dfferent annulu preure dfference. The calculaton reult reveal the eence of the cementng ga channelng ga partcle flowng n mcro rng clearance, and new dea are found out for the tudy of the problem about ubequent cementng ga channelng. Keyword: Annulu Mcro Clearance, Lattce Boltzmann, Cementng Ga Channelng, Partcle Flow. INTRODUCTION In the proce of ga well cementng the mcroannulu and mcro-fracture ext between the cang and cement heath due to the preureout WOC, the volumetrc hrnkage of the cement column, the ntal ettng of mud, a well a the nterfacal bond and other reaon []. Through calculaton, the ze of mcro-annulu from a few mcron to ten of mcron [2] (Fgure ), and thee weaknee wll provde channelng crculaton way for formaton ga nto the annulu. For many year, the mot tude on ga channelng flow n the mcro clearance bae on macrocopc cale, and a large number of tude are carred out on the annular ga channelng mechanm after cementng, predcton method and preventng ga channelng and o on at home and abroad, but the problem of ga channelng of the cementng faled to be olved fundamentally[3]. However, there a great dfference between the flow of ga n the mcro clearance and macrocopc channel, and there a bg devaton between the reult of the macrocopc decrpton and the actual engneerng. Therefore, to mplement the tudy on the mechanm of ga flow n the mcrocopc channel of cang annulu ha mportant gnfcance n the apect of the ubequent cementng pluggng lqud degn, the cementng parameter optmzaton degn and o on. Inpred by the theory of mechancal eal n the MESM, Boltzmann method ued to tudy the flow charactertc of the clearance ga. Lattce- Boltzmann method developed from the mot mple cellular automaton and have been uccefully appled to tudy feld of complex flow pattern at preent [4-8], but there not report on the lattce-boltzmann method ued to the flow tudy of the cementng annulu mcro clearance. Therefore, combned wth the Lattce-Boltzmann method the author tudy the ga channelng flow n the cementng annulu mcro clearance and from the mcrocopc vew analyze the eental connotaton of ga channelng, whch provde the relable centfc ba for the ubequent cementng degn and parameter degn. Cement heath Formaton Cang Mcro clearance Ga Fgure : The Schematc Dagram Of Ga Channelng Flow In The Mcro Clearance 888

2 Journal of Theoretcal and Appled Informaton Technology 20 th February 203. Vol. 48 No JATIT & LLS. All rght reerved. ISSN: E-ISSN: MATHEMATICAL MODEL A known to all, the Naver - Stoke equaton ued to decrbe macrocopc flud moton motly. In order to etablh the relatonhp between macro varable and mcro varable, aume that any tme a t, the functon of the partcle denty dtrbuton n any poton r of the annular mcro clearance a f ( r, t).accordng to the prncple of conervaton of ma and momentum, the macro denty, momentum and preure of the ga flow are expreed a: ρ = f () = ρ v = f e (2) 2 = p = c ρ (3) A hown n Fgure 2 the model of the quare grd two-dmenonal nne velocty (a2-dmenonal pace, nne dcrete peed), the entre ga flow feld dvded nto quare grd, n whch each node adjacent to the eght node urroundng, coupled wth t own, there are nne movng drecton every partcle totally. Fgure 2: The Model Of The Two-Dmenonal Nne Velocty (Q2D) All the velocty vector of nne drecton conttute a collecton a ga equaton e, whch can be expreed a: e 0 0 0, = L = A hown n fgure 2 how the rule of the ga flow n a two-dmenonal annular mooth mcrochannel. In th paper, baed on the Lattce- Boltzmann BGK equaton : eq f ( r + eδ t, t + δt) f = f f τ (5) Among them, f the functon of the partcle denty dtrbuton n r poton and n t moment at the peed e ; τ dmenonle relaxaton tme; f (eq) (r,t) the functon of a partal equlbrum dtrbuton correpondng tme and poton. The correpondng local equlbrum dtrbuton functon : (eq) f 2 2 e ( ) (, ) = + u e + u u r t ω ρ (6) c 2c 2c Among them, ω the weghtng coeffcent; ρ and u are repectvely macrocopcal denty and peed, c the peed of ound n a grd. In addton, c the mgraton rate of the ga partcle, and c = δ x / δ t, wheren δ x δ t are repectvely the trell tep and tme tep. The mgraton rate of the ga partcle c and the lattce ound velocty meet relatonal expreon c = c / 3. For the weght coeffcent ω, there : ( =, 2,3, 4) ω ( 5,6,7,8) = = 36 4 ( = ) For mcrocale ga flow, the charactertc quantty Knuden number ( kn ), and how to gve the relaxaton tme accordng to kn correctly the key of the Lattce-Boltzmann ga flow mulaton. In th paper, the formula of the relaxaton tme : (7) 2λ τ = + NKn (8) 2 π ( ) π ( ) π c(co,n ); =, 2,3, (2 ) π (2 ) π e = 2 c(co,n ); = 5, 6, 7,8 4 4 (0, 0) = (4) Among them, N = L / δx ndcate a charactertc length grd number, λ the contant related to the model, and n the D2Q model, λ = BOUNDARY CONDITION Accordng to the experment of the Knuden molecular level, when the ga partcle reach the 88

3 Journal of Theoretcal and Appled Informaton Technology 20 th February 203. Vol. 48 No JATIT & LLS. All rght reerved. ISSN: E-ISSN: mcro clearance of the outer urface of cang and the nner urface of cement heath at a certan ncdent peed, partcle lp manly reflect for: the partcle backward rebound and forward rebound, hown a Fgure 3. Aume that the rato of the number of partcle forward rebound a, and the rato of the number of partcle backward rebound a. Accordng to the model n Fgure 3 rebound rule can be expreed a: TABLE : The Annulu Dfferental Preure And Sze Of The Mcro Clearance Between The Cang And Cement Sheath The annulu dfferental preure ( MPa ) The ze of the mcro clearance ( µ m ) Fgure 3: The Rebound Rule Of The Irregular Sold Wall Upper boundary condton Lower boundary condton f ( r, t + δt) = f 2 4 f ( r, t + δt) = ( a) f + af f ( r, t + δt) = ( a) f + af f ( r, t + δt) = f CASE CALCULATION f ( r, t + δt) = ( a) f + af f ( r, t + δ t) = ( a) f + af In th paper, combned wth the ga channelng of the cementng annular clearance n a block of Daqng ga feld and baed on the Lattce- Boltzmann method, the rule of ga flow n the proce of the ga channelng mulated. Aume that the heat flux n the wall of the annular clearance unform and the temperature contant. The parameter of annulu mcro clearance are hown a n Table. And n the proce of the ga flow, the meh of the flow feld dvded nto 50 50, the tme tep 0-5, the drvng peed of ga entrance 0.0 m/, the Reynold number of the flow feld 0.0, the ga velocty at the ext contant, the ga partcle dtrbute unformly, the ntal temperature of the entre flow feld 300K, the boundary of the annular clearance the dffue reflecton boundary, the calculaton reult hown a n Fgure 4-. u/u y/h p=.0mpa p=3.0mpa p=5.0mpa p=0.0mpa p=20.0mpa Fgure 4: The Velocty Dtrbuto Under The Dfferent Dfferental Preure u/u H=2.04 H= H=.5 H=22. H= y/h Fgure 5: The Annulu Preure Dtrbuton Under The Dfferent Dfferental Preure 80

Journal of Theoretcal and Appled Informaton Technology 20 th February 203. Vol. 48 No.2 2005-203 JATIT & LLS. All rght reerved. ISSN: 2-8645 www.jatt.org E-ISSN: 87-35 5.

7 µ m () In th paper, the Lattce-Boltzmann method frtly ued to mulate the flow rule of the ga channelng n the cementng annular clearance of the ol feld cementng, and analyze the rule of ga flow

(2) The calculaton reult how that: wth the ncreae of the annular mcro clearance and ga flow velocty, when the annulu mcro clearance ncreae, the Knuden number mprove and the phenomenon of ga lp

4 Journal of Theoretcal and Appled Informaton Technology 20 th February 203. Vol. 48 No JATIT & LLS. All rght reerved. ISSN: E-ISSN: CONCLUSION Fgure 6: The Velocty Dtrbuton Under The Sze Of Mcro Clearance I 45.7 µ m () In th paper, the Lattce-Boltzmann method frtly ued to mulate the flow rule of the ga channelng n the cementng annular clearance of the ol feld cementng, and analyze the rule of ga flow velocty and flow preure dtrbuton under the dfferent ze of annular mcro clearance. (2) The calculaton reult how that: wth the ncreae of the annular mcro clearance and ga flow velocty, when the annulu mcro clearance ncreae, the Knuden number mprove and the phenomenon of ga lp dappear. Ga develop from the lp zone to the tranton zone and the ga flow velocty ncreae, whch content wth the explcaton of the macrocopc flow. Fgure 7: The Velocty Dtrbuton Under The Sze Of Mcro Clearance I 22. µ m ACKNOWLEDGEMENTS Th work wa upported by The Natonal Natural Scence Foundaton(504032),The Chna Natonal Petroleum Corporaton Innovaton Foundaton (20D ),Natural Scence Foundaton of Helongjang Provnce of Chna (QC20006), Foundaton of Helongjang Provnce Educatonal Commttee (KY28) REFERENCES: Fgure 8: The Velocty Dtrbuton Under The Sze Of Mcro Clearance I.5 µ m Fgure : The Velocty Dtrbuton Under The Sze Of Mcro Clearance I 6.88 µ m [] Tanqun L, Zhongfu Wang, Dejun Chen, The mcro clearance plugged cementng technology n Daqng Olfeld deep ga well, Block Faulted Ol And Ga Feld, Vol. 5, No.3,2008, pp [2] Chengjn Yu, Chengln L, The calculaton of the mcro clearance between cang and cement heath, Ol drllng technology, Vol. 3, No.4, 6, pp [3] Fubn Han, The ga channelng control cementng upportng technology n Qnghen ga feld deep ga well, Natural ga ndutry, No. 2, Vol. 2, No.2, 200, pp [4] Hualong Wang, Zhenhua Cha, Zhaol Guo, Lattce Boltzmann mulaton of ga tranfuon n compat porou meda, Computatonal phyc, Vol. 26, No. 3,200, pp [5] ZLong Deng, YongPng Chen, Chengbn Zhang etc, The tudy of the Lattce-Boltzmann method of ga flow n the mcro channel,journal of Engneerng Thermophyc, Vol. 32, No., 202, pp

5 Journal of Theoretcal and Appled Informaton Technology 20 th February 203. Vol. 48 No JATIT & LLS. All rght reerved. ISSN: E-ISSN: [6] Janbang Ceng, Longj L key, Quan Lao etc, The Lattce-Boltzmann method mulaton of the nterface charactertc under the meocopc cale, Chnee Scence Bulletn, Vol. 55, No. 24, 200, pp [7] YHua Zhu, Guo Tao, We Fang etc, The Lattce-Boltzmann mulaton of the 3D porou medum permeablty,loggng Technology, Vol. 32, No., 2008, pp [8] Hubao Luan, L Chen, Wenjng Zhou etc, The applcaton of the Lattce-Boltzmann method dtrbuton functon recontructon operator, Journal of Engneerng Thermophyc, Vol. 32, No. 6, 20, pp

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