Concentric Dual-tubing Steam Injection: A New Model for Predicting Steam Pressure in the Annulus

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1 Jounal of Industial Intelligent Infomation Vol., No. 4, ecembe 014 Concentic ual-g Steam Injection: A New Model fo Pedictg Steam Pessue te Hao Gu, Lsong Ceng, Sijun Huang, Suang Ai, Saolei Wei epatment of Petoleum Engeeg, Ca nivesity of Petoleum, Beijg, Ca lsceng@cup.edu.cn, {guao110110, fengyun7407, aisuang4415, leisuew}@163.com Abstact It is not always easy accuately pedict botmole steam pessue, tempeatue quality wen we design concentic dual-g steam jection scemes due te complexity of two-pase flow te annulus, also, pevious meds fo estimatg pessue gadient annuli ae time-consumg. In tis study, a new model is establised based on mass enegy balances calculate steam pessue te annulus. A moe igoous temodynamic beavio of steam/wate mixtue is also taken account. Moe impotantly, one--one coespondence between pessue gadient tempeatue gadient of satuated steam is easonably developed applied fute deivation. Te esults dicate tat te poposed model is moe accuate convenient pedictg steam pessue tan pevious meds. Moeove, te steam pessue te ne g dops faste tan tat of te annulus even te wellead mass flow ate of te fome is lowe. Te vaiation law of steam quality te ne g is diffeent fom tat of te annulus, dependg on te net eat losses of mixtue fluid eac g. Index Tems new model, steam pessue, concentic dualg, annulus, eat tansfe I. INTROCTION Heavy oil eseves ae widely distibuted te wold tey play an impotant ole day s enegy supplies [1]. Howeve, it is not always easy efficiently develop ig-viscosity oil due low mobility unde itial fomation tempeatue. At pesent, temal ecovey meds, especially fo steam jection tecniques, ae extensively used te pocess of eavy oil poduction. Injectg steam wellboe would evitably esult eat excange between te wellboe fluid its suoundg fomation []. In addition, te steam pessue, tempeatue quality would cange as fluid flows wn te wellboe. Teefoe, pedictg wellboe eat losses botmole steam popeties ae two majo tasks wen we design steam jection pojects. Howeve, tee ae always many difficulties designg concentic dual-g steam jection scemes because two-pase flow te annulus is muc moe complex tan tat of pipes, so is te estimation of pessue gadient. Manuscipt eceived ecembe 4, 013; evised Apil 15, Engeeg Tecnology Publisg i: /jiii Te calculation meds fo pessue gadient annuli can be divided two categoies: empiical coelations mecanistic models [3]. Many eseaces ave establised diffeent mecanistic models fo two-pase flow annuli based on flow-pattens, suc as Caetano [4] (1985) model, Annio et al. [5] (00) model Yu et al. [3] model (010). Howeve, te defitions of flow pattens, te tansition citeia te pocess of calculatg flow-paametes ae vey complicated time-consumg. Gisn et al. [6] teated te annuli as pipes on te bases of ydaulic diamete concept, wile it is just an appoximation will be discussed late. Fo eat tansfe between te wellboe fluid its suoundg fomation, Ramey [7] poposed te expession of fluid tempeatue wellboes. His wok laid te foundation fo late eseaces ug e only consideed sgle pase (ideal gas compessible liquid) flow. Satte [8] ok account te effect of condensation pesented a med fo calculatg steam quality, but e ignoed fictional losses ketic enegy effects. Holst Flock [9] studied te effect of fiction on wellboe eat losses. Willite [10] explicitly analyzed tee mecanisms (conduction, natual convection adiation) of eat tansfe te wellboes suggested a med fo detemg ove-all eat tansfe coefficient. Recently, moe moe eseaces combed eat tansfe model wit two-pase flow model, suc as Fontanilla Aziz [11] (198), Alves et al.[1](199), Hasan et al. [13]-[16](1994,007,009),Baona et al. [17](010) Mady et al.[18](01).howeve, tese models ae all ab sg-g steam jection. Baua [19] Higt [0] mentioned concentic dual-g steam jection, but neite set up concete matematical models. In tis wok, we popose a new model wic is moe accuate convenient pedict steam pessue te annulus. In addition, te caacteistics of eat tansfe concentic dual-g ae also analyzed detail. II. MOELING FLI PRESSRE Fig. 1 sows te scematic diagam of concentic dualg steam jection well ove te diffeential lengt of.afte steam eaces te wellead along suface

2 Jounal of Industial Intelligent Infomation Vol., No. 4, ecembe 014 pipeles, it would be simultaneously ente te ne g te annulus between te ne e g. Figue 1. Concentic dual-g steam jection well. A. Pessue Gadient te Inne Tubg Fo two-pase flow te ne g, te pessue calculation model poposed by Beggs Bill [1] is apted. Te goveng equations fo mixtue fluid ove a diffeential lengt of yield te followg equations: Mass balance equation W z Momentum balance equation 0 (1) z d gs () wee W ae te mass flow ate te velocity of mixtue fluid te ne g, espectively; p ae te density te pessue of mixtue fluid, espectively; is te two-pase fiction fac; is te diamete of ne g; g is te gavitational acceleation; is te well angle fom oizontal. Te tid tem of te igt side () can be given by d sg (3) p wee is te supeficial velocity of gas pase te sg ne g. Substitutg (3) (), an expession fo te pessue gadient te ne g can be obtaed, sg gs 1 / p B. Pessue Gadient te Gisn et al. [6] teated te annuli as pipes based on ydaulic diamete concept, oweve, ydaulic diamete is not always a suitable epesentative caacteistic (4) dimension fo two-pase flow te annulus [4]. In tis study, a new semi-analytical model fo estimatg pessue gadient te annulus is fomulated. Te eat canges of mixtue fluid te annulus esult fom two pats: eat losses te fomation, eat losses te ne g o eat absoption fom te ne g. A geneal enegy balance on te fluid can be witten as wee 1 W W d d v g s (5) ae te mass flow ate te velocity of mixtue fluid te e g, espectively; fluid; / ae te specific entalpy of mixtue is te ate of eat tansfe fom te / annulus te fomation; is te ate of eat tansfe fom te ne g te annulus, but if te / value of is negative, it dicates te annulus absobs eat fom te ne g. In (5), te ketic enegy cange fo pe unit mass of mixtue fluid ove te diffeential lengt of d z can be similaly obtaed fom (3) d v d sg (6) p wee sg is te supeficial velocity of gas pase te annulus. sg basic temodynamic pciples, te entalpy gadient can be witten tems of te tempeatue pessue gadients [1]: wee Cpm d dt T p (7) C pm p dt CJmC pm is te eat capacity of mixtue fluid at constant pessue; C is te Joule-Tompson coefficient. Jm Substitutg (6) (7) (5)yields, 1 CJmCpm W (8) dt sg Cpm g s p Te elationsip between tempeatue gadient pessue gadient can be fute ceated. Ejiogu Fioi [], Totlke Faouq Ali [3] poposed diffeent coelations between tempeatue pessue of satuated steam based on steam table. In tis study, te Totlke Faouq Ali s coelation is apted due its ig accuacy validation toug almost te entie steam-satuation envelope, wic is given by T f p lnp lnp lnp ln p 4 T (9) 014 Engeeg Tecnology Publisg 46

3 Jounal of Industial Intelligent Infomation Vol., No. 4, ecembe 014 Te elationsip between tempeatue gadient pessue gadient of satuated steam can be expessed as dt df p (10) Substitutg (10) (8) educes te pessue gadient te annulus 1 g s W df p sg CJmCpm Cpm p (11) In (11), te eat capacity te Joule-Tompson coefficient of two-pase flow system can be estimated by efeg te med suggested by Alves et al. [1]. Teefoe, it is easy calculate te pessue dop te annulus wit usg mecanistic models o empiical coelations, wic depend on complicated flow-pattens o appoximate teatment. But befoe (11) can be used, it is necessay estimate / /. III. MOELING WELLBORE HEAT TRANSFER As fluid flows bot te ne g te annulus, eat tansmission can be sepaated tee pats: (a).heat excange between te fluid te ne g te annulus. (b).heat tansfe fom te fluid te annulus te cement seat. (c).heat tansfe te fomation. If te wellead jection conditions ema constant, eat tansfe side te wellboe can be assumed steady-state wile eat tansfe te fomation can be assumed tansient, Holst Flock [9] discussed te assumption detail. A. Heat Excange between te Fluid te Inne Tubg te Tee would be eat excange between te fluid te ne g te annulus if te fluid tempeatue is not equal. Te ate of eat flow ove te diffeential lengt of d z can be given based on Fouie law ( T T ) (1) wee is te side adius of ne g; T Tae te tempeatue of fluid te ne g te annulus, espectively; is te ove-all eat tansfe coefficient fo ne g, wic can be witten as follows: wee, fti f fti ti ln ti 1 f 1 (13) ae te foced-convection eat tansfe coefficient on side side of ne g, espectively; is te temal conductivity of g wall; ti is te side adius of ne g. Because te foced-convection eat tansfe coefficient ) te temal conductivity of g wall ( fti ( f ) ae vey ig, te ate of eat excange between te fluid te ne g te annulus would be vey fast even te tempeatue diffeence is small. B. Heat Tansfe fom te Fluid te te Cement Seat Similaly, fo steady-state eat tansfe fom te fluid te annulus te cement seat, te ate of eat flow can be expessed as ( T T ) (14) wee, is te side adius of e g; T is te wellboe/fomation teface tempeatue ; is te ove-all eat tansfe coefficient between te e g te cement seat. Willite [10] poposed te med fo calculatg wee,, wic can be given by 1 1 ln fdi di di c (15) co ln ln cas ci cem co fdi is te foced-convection eat tansfe coefficient on side of e g; di is te side adius of e g; ci co ae te side adius side adius of casg, espectively; is te side adius of te wellboe; cas cem ae te temal conductivity of casg cement, espectively; c ae te convective eat tansfe coefficient te adiative eat tansfe coefficient, espectively, wic can also be estimated by efeg te coelations suggested by Willite [10]. Also, because, cas ae lage compaed fdi wit ote tems (15), te expession of educed (16) 1 c cem C. Heat Tansfe te Fomation ln co 1 can be (16) Fo te tansient eat tansfe te fomation, te ate of eat flow is te function of jection time tempeatue diffeence, te geneal expession is et Tei (17) f t wee, e is te temal conductivity of te fomation; T is te itial tempeatue of te fomation at any given ei 014 Engeeg Tecnology Publisg 47

4 Jounal of Industial Intelligent Infomation Vol., No. 4, ecembe 014 dept, Tei T0 azs, T is te suface tempeatue of 0 te fomation, a is te geotemal gadient; f (t) is te tansient eat-conduction time function. Ramey [7], et al. [4] Hasan et al. [5] poposed diffeent empiical expessions, oweve, Hasan et al. med is apted due its accuacy, wic is given by (1 0.3 ), ln (1 ), 1. 5 Combg (14), (17) yields, d T T (18) e ei T (19) e T (0) e T - z e Te med fo pedictg steam quality is pesented Ref. [6]. Equations (4), (11), (1), (0) steam quality model need be coupled solved iteatively fo eac segment. IV. RESLTS AN ISCSSIONS A. Compaison wit Field ata Te field test data obtaed fom Higt [0] is used veify te accuacy eliability of te new model. In te field test, te diametes of te ne e g ae m (1.9.) m ( 7 / 8.), espectively, te diamete of te casg is m (5 1 /.) Fig. sows a compaison of calculated pessue wit te measued field data. As can be seen fom Fig., te simulated esults agee vey well wit te measued values. Also, te maximum elative eo is ab 5.39%. Steam pessue (MPa) Measued annulus Measued ne g Calculated annulus Calculated ne g Well dept (m) Figue. Compaison of calculated pessue wit measued field data B. Example Analysis Te caacteistics of eat tansfe te wellboe ae discussed detail. Table I. is te basic paametes of te wellboe te fomation Table II is te wellead jection conditions. ei TABLE I. BASIC PARAMETERS OF THE WELLBORE AN THE FORMATION Paamete value Paamete value Inside adius of ne g(m) Outside adius of ne g(m) Inside adius of e g(m) Outside adius of e g(m) Inside adius of casg(m) Outside adius of casg(m) Outside adius of te wellboe(m) Suface tempeatue of te fomation(k) Geotemal gadient (K m -1 ) Foced-convection eat tansfe coefficient (W m - K -1 ) Temal conductivity of te g casg wall(w m -1 K ) Temal conductivity of te cement(w m -1 K -1 ) Temal conductivity of te fomation (W m -1 K -1 ) Temal diffusivity of te fomation(m /s) TABLE II. WELLHEA INJECTION CONITIONS Paametes Inne g Steam pessue(mpa) Steam tempeatue (K) Steam quality Mass flow ate(kg/) Fig. 3 sows a compaison of te esults fom te pesent model tat fom Gisn et al. [6] model. In tei study, te annulus was teated as a pipe te ydaulic diamete e di was used eplace (4) estimate te pessue gadient te annulus. Howeve, Fig. 3 dicates tat te esult of te new model sows a good ageement wit field data wile te calculated pessue fom Gisn et al. model is muc smalle tan test data. Teefoe, te ydaulic diamete is not always a suitable epesentative caacteistic dimension fo two-pase flow annuli. Steam pessue te annulus (MPa) Field data Gisn et al. model New model Well dept (m) Figue 3. Compaison of calculated pessue wit Gisn et al. model Fig. 4 is te esults of steam pessue te concentic dual-g. It is found tat te botmole pessue te ne g is smalle tan tat of te annulus 014 Engeeg Tecnology Publisg 48

5 Jounal of Industial Intelligent Infomation Vol., No. 4, ecembe 014 ug te wellead jection pessue is not te case. Moeove, te wellead mass flow ate te ne g is 3000kg/, wic is lowe tan tat of te annulus (5000 kg/), but te pessue te ne g dops faste tan tat of te annulus. Te eason may be tat te adius of ne g is muc smalle te fluid te ne g needs ovecome lage fiction. Te vaiation law of tempeatue is te same wit tat of pessue (Fig. 5). Fom te entie steam jection, te aveage pessue gadient tempeatue gadient te ne g ae MPa/m 0.01K/m, espectively, wile te coespondg values te annulus ae MPa/m K/m, espectively. Steam pessue (MPa) Inne g Well dept (m) Figue 4. Pessue concentic dual-g steam jection well 544 saply wit well dept because te net eat losses ae lage. Howeve, te steam quality te ne g deceases slowly fom te wellead ab 190m, fom 190m te botm, it ceases wit well dept. Te possible explanation fo flection pot is 190m ate tan 30m is as follows: fom 190m 30m, ug te fluid te ne g still loses eat te annulus, te tempeatue diffeence is lowe te eat losses ae not lage enoug esult quality dop, on te contay, te ceased enegy tansfomed fom potential enegy makes te specific entalpy of mixtue fluid cease slowly fom 190m 30m(Fig. 8).Wen te well dept exceeds 30m, te steam quality cease saply sce te fluid te ne g begs absob eat fom te annulus. Rate of eat flow (W/m) Fom ne g annulus Fom annulus fomation Net eat losses te annulus Well dept (m) Figue 6. Rate of eat flow te wellboe Steam tempeatue (K) Inne g Steam quality Inne g Well dept (m) Figue 5. Tempeatue concentic dual-g steam jection well Fig. 6 is te vaiation law of eat tansfe side te wellboe. It is obseved tat fom te wellead ab 30m, eat is tansfeed fom te ne g te annulus te ate of eat flow deceases wit well dept. Tis is because te tempeatue of fluid te ne g is ige tan tat of te annulus te tempeatue diffeence also deceases wit well dept. But wen te well dept exceeds 30m, te fluid te annulus begs elease eat te ne g. In addition, sce te tempeatue of fluid te annulus is muc ige tan fomation tempeatue, eat is always tansfeed fom te annulus suoundg fomation te net eat losses te annulus ae positive. Fig. 7 is te esults of steam quality te concentic dual-g. Te steam quality te annulus deceases Well dept (m) Figue 7. Steam quality concentic dual-g steam jection well Specific entalpy of wet steam (kj/kg) Well dept (m) Figue 8. Specific entalpy of wet steam te ne g 014 Engeeg Tecnology Publisg 49

6 Jounal of Industial Intelligent Infomation Vol., No. 4, ecembe 014 V. CONCLSION In tis pape, a new model is poposed pedict steam pessue te annulus. Te one--one coespondence between pessue gadient tempeatue gadient of satuated steam is easonably developed applied fute deivation. It is because of te impovement tat we can avoid usg mecanistic models o empiical coelations sepaately calculate te pessue dop te annulus wen simultaneously solvg wellboe eat tansfe model. Te caacteistics of eat tansfe concentic dual-g ae also analyzed detail. Te med suggested by tis pape povides a efeence fo te design of steam jection pojects. ACKNOWLEGMENT Te aus wis tank te Reseac Institute of Petoleum Exploation & evelopment, Liaoe Oilfield Company, Peto Ca. Tis wok was suppoted pat by a gant fom National Science Tecnology Majo Pojects of Ca (011ZX ). REFERENCES [1] W. S. Huang, H. P. Cen, Z. Meng, Evaluation tecniques of eseves fo eavy oil oil ss, Poc. Intenational Petoleum Tecnology Confeence, 6-8 Mac 013, pp [] W. L. Ceng, Y. H. Huang,. T. Lu, H. R. Y, A novel analytical tansient eat-conduction time function fo eat tansfe steam jection wells consideg te wellboe eat capacity, Enegy, pp , May 011. [3] T. T. Yu, M. X. Li, C. Saica, A mecanistic model fo gas/liquid flow upwad vetical annuli, SPE Poduction & Opeation, pp , August 010. [4] E. F. Caetano, pwad two-pase flow toug an annulus, P.. dissetation,. of Tulsa (1985). [5] C. V. M. Annio W. T. Rune, An expeimental teoetical vestigation of upwad two-pase flow annuli, SPE Jounal, pp , Septembe 00. [6] S. Gisn G. P. Willite, Numeical model fo evaluatg concentic steam jection wells, Poc. SPE Califonia Region Meetg, 8-10 Apil 1987, pp [7] H. J. JR. Ramey, Wellboe eat tansmission, JPT, pp , Apil 196. [8] A. Satte, Heat losses dug flow of steam wn a wellboe, JPT, pp , July [9] P. H. Holst. L. Flock, Wellboe beavio dug satuated steam jection, Te Jounal of Canadian Petoleum, pp , May, [10] G. P. Willite, Oveal eat tansfe coefficients steam ot wate jection wells, JPT, pp , May [11] J. P. Fontanilla K. Aziz, Pediction of botm-ole conditions fo wet steam jection wells, Te Jounal of Canadian Petoleum, pp. 8-88, 198. [1] I. N. Alves, F. J. S. Alanatl, O. Soam, A unified model fo pedictg flowg tempeatue distibution wellboes pipeles, SPE Poduction Engeeg, pp , Novembe 199. [13] A. R. Hasan C. S. Kabi, Aspects of wellboe eat tansfe dug two-pase flow, SPE Poduction & Facilities, pp , August [14] A. R. Hasan C. S. Kabi, A basic appoac wellboe twopase flow modelg, Poc. SPE Annual Tecnical Confeence Exibition, Novembe 007, SPE [15] A. R. Hasan, C. S. Kabi, X. Wang, A obust steady-state model fo flowg-fluid tempeatue complex wells, Poc. SPE Annual Tecnical Confeence Exibition, Novembe 007, SPE [16] A. R. Hasan, C. S. Kabi, X. Wang, Modelg two-pase fluid eat flows geotemal wells, Poc. SPE Westen Region Meetg, 4-6 Mac 009. [17] M. Baona, J. Azaiez, Z. Cen, A semi-unsteady state wellboe steam/wate flow model fo pediction of sface conditions steam jection wells, JCPT, pp. 13-1, Septembe 010. [18] S. Mady S. Kamy, evelopment of a tansient mecanistic two-pase flow model fo wellboes, SPE Jounal, pp , Septembe 01. [19] S. Baua, Computation of eat tansfe wellboes wit sgle dual copletions, Poc. SPE te 66t Annual Tecnical Confeence Exibition, 6-9 Ocbe [0] M. A. Higt, C. L. Redus, J. K. Lemann, Evaluation of dual-jection meds fo multiple-zone steamfloodg, SPE Resevoi Engeeg, pp , Febuay 199. [1] H.. Beggs J. P. Bill, A study of two-pase flow cled pipes, Jounal of Petoleum Tecnology, pp , May [] G. C. Ejiogu M. Fioi, Higt-pessue satuated steam coelations, Jounal of Petoleum Tecnology, pp , ecembe [3] W. S. Totlke S. M. F. Ali, Satuated-steam popety functional coelations fo fully implicit temal esevoi simulation, SPE Resevoi Engeeg, pp , Novembe,1989. [4] K. Ciu S. C. Taku, Modelg of wellboe eat losses diectional wells unde cangg jection conditions, Poc. SPE te 66t Annual Tecnical Confeence Exibition, 6-9 Ocbe [5] A. R. Hasan C. S. Kabi, Heat tansfe dug two-pase flow wellboes: Pat I -fomation tempeatue, Poc. SPE te 66t Annual Tecnical Confeence Exibition, 6-9 Ocbe [6] S. M. F. Ali, A compeensive wellboe steam/wate flow model fo steam jection geotemal applications, Poc. SPE Califonia Region Meetg, 18-0 Apil Hao Gu was bon te city of Huanggang, Hubei, Ca 1989.M.Gu eceived is Bacelo degee Petoleum Engeeg at Yangtze nivesity 011.In 013, e eceived is maste degee fom Ca nivesity of Petoleum, Beijg. At pesent, e is pusg P. Oil Gas evelopment Engeeg fom Ca nivesity of Petoleum, Beijg. His eseac teest cludes temal ecovey numeical simulation. Lsong Ceng was bon te city of Ygceng, Hubei, Ca 1965.M.Ceng eceived is c degee fom Ca nivesity of Petoleum, Beijg 1994.Now e is te pofesso vice pesident at te epatment of Petoleum Engeeg, Ca nivesity of Petoleum, Beijg. His eseac diection cludes temal ecovey, mecanics of flow toug poous media, te ecovey med fo low-pemeability esevoi. Sijun Huang was bon te city of Zengzou, Henan, Ca 1974.M. Huang eceived is c degee fom Ca nivesity of Petoleum, Beijg 006. He as been a visitg scola A&M nivesity. Now e is a vice pofesso at epatment of Petoleum Engeeg, Ca nivesity of Petoleum, Beijg. His eseac diection cludes eavy oil poduction numeical simulation. 014 Engeeg Tecnology Publisg 50

7 Jounal of Industial Intelligent Infomation Vol., No. 4, ecembe 014 Suang Ai was bon Xian Ng city, Hu Bei, Ca M. Ai olds a BS degee 009 a MS degee 01 Petoleum Engeeg fom Ca nivesity of Petoleum (Beijg), Ca. He is P student Oil Gas evelopment Ca nivesity of Petoleum (Beijg), Ca. He as a stong clation fo tansient flow numeical simulation of unconventional gas esevois. of eavy oil. Saolei Wei, eaned e Maste egee Oil- Gas Field evelopment Engeeg fom Ca nivesity of Petoleum (East Ca) Qgdao, Ca, 01. At pesent, se is pusug e p. Oil-Gas Field evelopment Engeeg Ca nivesity of Petoleum Beijg. He aeas of teest clude esevoi numeical simulation, poduction optimization, temal ecovey 014 Engeeg Tecnology Publisg 51