Coupled numerical simulation of multi-layer reservoir developed by lean-stratified water injection

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1 J Petrol Explor Prod Technol (016) 6: DOI /s REVIEW PAPER - PRODUCTION ENGINEERING Coupled numericl simultion of multi-lyer reservoir developed by len-strtified ter injection Dpeng Go 1,,3 Jigen Ye Yueu Liu 1 Songqi Pn,3 Yunpeng Hu He Yun Received: 5 July 015 / Accepted: 13 Februry 016 / Published online: 6 Februry 016 The Author(s) 016. This rticle is published ith open ccess t Springerlink.com Abstrct Len-strtified ter injection is one of the most importnt technologies to increse production nd develop potentils for the oilfield ith extreme high ter content. Hoever, trditionl models cnnot entirely solve the inner boundry conditions of len-strtified ter injection. Therefore, e estblished the injection ellbore constrint equtions, hich ere coupled ith the oil/ter to-phse numericl reservoir models, nd then the seven digonl form sprse coefficient mtrix s solved by block precondition of generlized miniml residul lgorithm. Considering the specific sitution of len-strtified ter injection ells, reservoir geology nd production schemes of the middle prt of the sixth Oilfield in Xing Shugng, three mechnism models of multi-lyer heterogeneous reservoir ere constructed to simulte the lenstrtified ter injection. The influences of different segments numbers, modes of combintion in segment lyer nd rhythm chrcteristics of remining oil reserves nd distribution re evluted. Keyords Len-strtified ter injection Well model Numericl reservoir simultion Remining oil evlution Interctive lo-permebility reservoir & Dpeng Go godpeng009@163.com 1 3 Institute of Mechnics, Chinese Acdemy of Sciences, Beijing , Chin PetroChin Reserch Institute of Petroleum Explortion nd Development, Beijing , Chin School of Erth nd Spce Science, Peking University, Beijing , Chin Introduction Len-strtified ter injection (LSWI) is kind of lyer trgeted ter injection to enhnce terflooding recovery of multi-lyer reservoirs, hich divides ellbore into five or more segments, nd every segment injects ter for less thn six lyers. This technology cn improve terflood verticl seep efficiency, nd hs been idely used in mny multilyer sndstone reservoirs ith high ter content (He et l. 013), such s Chinese Dqing Oilfield ith higher thn 40 % terflood recovery. Furthermore, it is required to mtch the development dynmic history for every oil lyer in the process of reservoir numericl simultion during secondry development, for the ske of incresing the prediction precision for remining oil in ech snd body, especilly in min snd body (Dkung 010). The ter injection rte enters ech oil lyer cnnot follo the mobility llocted principle set in conventionl simultion model. This defect leds to inccurcy for mtching the remining oil distribution nd injected ter rte in reservoir numericl simultion. Reservoir numericl simultion methods considering LSWI contin injected ter dedupliction by mny injection ells nd coupled simultion for ter chokes, injection ell nd reservoir. The former is suitble for reservoir possessed enough injectivity test dt, nd the ter injection rte cn be clculted by rel-time monitoring test dt, nd these vlues cn be used s inner boundry condition in model (Dumku et l. 01; Villnuev-Trin et l. 013; Stone et l. 1989; Ding 011), prcticlly, injectivity test dt re very fe, so the complete injection process cnnot be represented by them (Go et l. 015). The ltter needs enough dt of injection ell devices, such s dimeters of ter chokes, hich should be used to clculte the pressure loss coupled ith ell bottom pressure (BHP) nd 13

2 70 J Petrol Explor Prod Technol (016) 6: reservoir pressure (Zho et l. 01; Lin et l. 011), nd this results in quit complex clcultion. In this pper, e propose simple method of modeling LSWI considering inner ellbore constrint condition, nd this method cn be used to simulte the development effect nd remining oil distribution in reservoir ith extreme high ter content, s relible evidence ill be provided for reservoir history mtching nd project design. Well model considering LSWI ¼ P n XM ly¼ 1, X M 6 4 os ðlyþ op oðlyþ 3 S n1 ðlyþ S n ðlyþ 7 o ðlyþ P n 5 o ðlyþ ð3þ A ne ell model considering LSWI should be constructed s the inner boundry condition for numericl reservoir simultion, nd the folloing ssumptions re mde. 1. Injection ell is divided into N segments verticlly, nd every segment contins M oil lyers.. The totl injected ter rte is knon, nd mintins constnt. 3. Every segment is seprted by pckers in tubingcsing nnulus, so there is no fluid floing through beteen them. 4. Only oil nd ter phses re considered in the model, nd the cpillry is neglected. The totl injected ter rte is expressed s: Q ¼ XN seg ¼ 1 Q ðsegþ ¼ XN X M q ðsegþðlyþ seg ¼ 1 ð1þ Every injection rte of ech segment of ellbore is solved by liner implicit method to enhnce the stbility of numericl equtions. Tking ter sturtion, injection pressure nd oil phse pressure s unknon prmeters, the injection rte cn be expressed by Tylor-formul t to continuous time steps s Eq.. Q n1 ðsegþ Q n ðsegþ XM 6 4 os ðlyþ op oðlyþ 3 S n1 ðlyþ S n ðlyþ o ðlyþ P n o ðsegþðlyþ 7 P n 5 ðþ Although injected ter rte of every oil lyer vries during these to continuous time steps, the totl injected ter rte of every segment is constnt (Q n1 ðsegþ ¼ Q n ðsegþ ) under the ssumption bove, nd then the ell model considering LSWI is deduced from Eq.. here Q is the totl injected rte; seg is the lbel for segment; ly is the lbel for lyer; n is the lbel for time step; N is the totl segment number for LSWI ell; M is the totl number of lyers; q is the injected ter rte for every oil lyer; s is the ter sturtion; P o is oil pressure; P f is injected pressure djusted by ter chokes. Coupled numericl model Assuming tht the pressure grdient in tubing-csing nnulus is constnt t different time steps, nd then the injected pressure fter ter chokes nd connected reservoir grid flo rte nd pressure re given by: Wellbore pressure model: f ¼ Pf n1 n H H ðsegþ ðsegþ ð4þ Flo model of reservoir grid (Yn et l. 008): q n1 ¼ q n1 ðsegþðlyþ ¼ WI f k L ð5þ Oil ter to phse flo models re discretized, nd pressure nd sturtion re solved implicitly, residul equtions of the reservoir grid ith producer or injector contin source nd sink terms. Oil phse residul eqution: R o R ¼ V Dt Xb " /ð1 S Þ n1 /ð1 S # n Þ B o B o i¼1 ½T oi ðdp c o DZÞ n1 q n1 Wter phse residul eqution: " ¼ V /S n1 /S # n Dt B B Xb i¼1 ½T i ðdp c DZÞ n1 q n1 ð6þ ð7þ 13

3 J Petrol Explor Prod Technol (016) 6: Oil phse residul equtions of reservoir grid ithout producer nd injector re conventionl s hevy oil model, injected pressure needs to be considered only for these grids ith producer nd injector, nd these terms re functions of ter sturtion nd oil pressure s represented in Eq. 3, so the unknon prmeters re ter sturtion nd oil pressure hen solving the nonliner eqution set consists of these residul equtions of every grids. Coupled ith ell model, ellbore pressure model nd reservoir grid flo model, ter phse residul eqution for reservoir grids ith injector is expressed s: 8 or n o Po n1 op P n or n >< S n1 o os S n ¼ R o or n op P o n1 P n or n >: o os Sn1 S n ¼ R ð9þ Every element in the coefficient mtrix cn be simplified A o P s 9 submtrix: o A o S, A P o A S R " ¼ V /S n1 /S # n Dt B B WI 8 >< >: XM 6 4 Xb i¼1 ½T i ðdp c DZÞ n1 P n n ðh H ðsegþ Þ oq n 3 S n1 os S n, X M oq n 7 op P n 5 o oq k L 9 >= >; ð8þ here n is ter pressure grdient in ell segment; is the lbel of center grid; H is depth; i is the djcent grid; k is threshold pressure grdient; L is the distnce beteen ell nd grid boundry; R o is the oil phse residul for center grid; R is the ter phse residul for center grid; b is the totl number of djcent grids; T o, T re the oil nd ter trnsmissibility beteen grids; B o, B re the oil nd ter volume fctors; q o, q re the injected nd produced oil/ter rte in grid; WI is ell index; c o, c re oil/ter grvity; / is the porosity. All of the oil ter residul equtions of reservoir grids re combined s huge liner eqution set (Eq. 9), hich cn lso be ritten s the mtrix formts ith seven digonl sprse coefficient mtrix, nd its structure is s sme s the coefficient mtrix of conventionl reservoir numericl simultion model ithout LSWI (Jigen et l. 007). A P o ¼ or ¼ V op o Dt 8 owi op o n1 o /S B op o o Pb i¼1 ½T i ðdpc DZÞ op o n1 P n n H H ðsegþ P n1 k L 9 oq n 3 P M os S n1 S n >< >= 6 oq n 7 4 o op P n 5 o P M n >: >; WI 1 oq op o oq ", X M n # oq ð10þ 13

4 7 J Petrol Explor Prod Technol (016) 6: A S ¼ or ¼ V o Pb ½T i ðdp c DZÞ n1 / i¼1 os DtB os 8 P n n H H ðsegþ P n1 k L 9 oq n 3 S owi P M n1 os S n >< >= os 6 oq n 7 4 o op P n 5 o P M n >: >;, oq n X M WI os oq oq ð11þ The coefficient of the grid ith LSWI becomes more complex s indicted in Eqs. 10 nd 11, so every submtrix cn be regrded s n integrl term hen the overll numericl model is solved by block pretretment of generlized miniml residul lgorithm (Bohu et l. 013). Model vlidtion The model proposed in this pper is vlidted by the test dt from LSWI ell (X6-3-31) locted in the middle prt of the sixth Oilfield in Xing Shugng, nd the results of injected ter rtio clculted by the model re compred to tht of injectivity test dt nd conventionl hevy oil model ithout LSWI, s shon in Fig. 1. Figure 1 is the comprtive results in 00, hen the LSWI ell is divided into four segments by three pckers, nd Fig. 1b is the comprtive results in 010, hen the ell is divided into six segments by five pckers. It is obviously tht conventionl hevy oil model cnnot simulte the effect of LSWI, but the LSWI model cquires more ccurte injected ter rtio close to the injectivity test dt in these yers. Cse study Geologicl mechnism model Considering the specific sitution of LSWI ells, reservoir geology nd production schemes of the middle prt of the sixth Oilfield in Xing Shugng, three mechnism models of multi-lyer heterogeneous reservoir ere constructed to simulte the LSWI. Ech of the models hs dimensions of 80 ft 9 80 ft 9 88 ft, nd is discretized eqully by grids horizontlly nd 54 grids verticlly, so it hs 135,000 regulr grids totlly. Generlly, there re to kinds of oil lyers in the model, nd they re high-permebility ( md) nd interctive lo-permebility (5 10 md) oil lyers, hich hve oil lyers totlly. One of them is thick high-permebility oil lyer (3.8 ft), nd 1 of them re interctive lo-permebility oil lyers, hich contin lo-permebility oil lyers connected ith high permebility prts. As shon in Fig., there re four kinds of interctive lo-permebility oil lyers in this model from top to bottom: continuous delt front sheet snd oil lyers (Fig. : continuous 1 7), prtil delt front sheet snd oil lyers (Fig. b: prtil 1 6), delt sheet snd edge oil lyers (Fig. c: sheet 1 5) nd overflo chnnel snd oil lyers (Fig. d: overflo 1 3). Especilly, sheet 3, continuous 7 nd overflo 13 re three independent lo-permebility oil lyers. Recovery nd verticl seep efficiency Six LSWI projects re designed for the three geologicl mechnism models, nd they re totlly developed for 0 yers ith the sme injection ter rte. In the initil 5 yers of production, five-spot terflood ell pttern is used for the development, nd the injector ith 30 m 3 /dy injection ter rte is locted t the center of the model. Afterrds, the injector is divided into four segments for terflooding. 5 yers lter, it is subdivided into 5 10 segments ith LSWI by subdivision nd restructuring of originl segments, nd four producers re dded into this terflood ell pttern to enhnce the. The injection ter rte (100 m 3 /dy) nd bottom ellbore pressure of producer keep constnt during the 10 yers development yers ith LSWI. Figures 3, 4 shos the ultimte recovery nd verticl seep efficiency of interctive lo-permebility oil lyers vrying ith segment numbers under different modes nd rhythm chrcteristics fter developing 0 yers. Hoever, it is very difficult to find the regulrity beteen the ultimte recovery nd segment numbers, becuse there re too mny fctors influencing the ultimte recovery, hich include geologicl models, production schemes nd so on. There is no point tnlyse the optimum number of intervls under specil model nd production scheme. For exmple, the ultimte recovery under seven segments is higher thn tht under 8 segments, even the ellbore nd oil lyers hve been subdivided to be much lener. Presently, some possible instructions cn be drn by us s follos in broder sense. The ultimte recovery of model ith different rhythms increses t first, nd then become smooth, hoever, the 13

5 J Petrol Explor Prod Technol (016) 6: Fig. 1 The comprtive results of injectivity test dt, LSWI model nd conventionl hevy oil model verticl seep efficiency increses grdully. When segments number of LSWI increses under subdivision of originl segments, ultimte recovery nd verticl seep efficiency both increses ith strong fluctution. Hoever, ultimte recovery increses ith smller fluctution under segmenttion nd restructuring, nd the verticl seep efficiency increses grdully. It illustrtes tht more segments nd more complete restructuring of segments my not be effected, so the modes of segmenttion nd segment numbers need to be optimized. The vrition tendency of recovery nd verticl seep efficiency re the sme, nd high ultimte recovery ill be obtined ith high verticl seep efficiency of interctive lo-permebility oil lyers, so the key of enhncing production lies in incresing verticl seep efficiency. 13

6 74 J Petrol Explor Prod Technol (016) 6: Interctive lo-permebility oil lyer extended connected ith high-permebility oil lyer Independent lo-permebility oil lyer Horizontl section: 1Continuous 1- nd 5-6 Continuous 3-4 3Continuous 7 Verticl section: 1 Continuous 1- nd 5-6 Continuous 3-4 Continuous delt front sheet snd oil lyer Lenticel lo-permebility oil lyer Horizontl section: 1Prtil 1- Prtil 3-4 3Prtil 5-6 Verticl section: 1Prtil 1- Prtil 3-6 b Prtil delt front sheet snd oil lyer Interctive lo-permebility oil lyer extended connected ith high-permebility oil lyer Independent lo-permebility oil lyer Independent lo-permebility oil lyer Horizontl section: 1Overflo 1 Thick high-permebility oil lyer 3Overflo 4Overflo 4 Verticl section: Overflo 1-3 nd Thick high-permebility oil lyer c Overflo chnnel snd oil lyer Independent lo-permebility oil lyer Independent lo-permebility oil lyer Horizontl section: 1Sheet 1- Sheet 3 3Sheet 4-5 Verticl section: 1Sheet 1-3 Sheet 4-5 d Edge delt stble sheet snd oil lyer Fig. Initil oil sturtion of four types of model ith interctive lo-permebility reservoirs nd high-permebility reservoirs Rhythm chrcteristics of high-permebility oil lyers hve little influence for ultimte recovery of interctive lo-permebility oil lyers, but segmenttion modes hve more obvious influence. Hoever, verticl seep efficiency re lmost equl for models ith reverse rhythm nd composite rhythm, nd both higher thn positive rhythm model. Distribution regulrity of remining oil Remining oil cused by incomplete terflood ell pttern cnnot be sept effectively. Tke the overflo to oil lyer shon in Fig. 5 s n exmple, only one injector is locted in the center of the interctive oil lyer, nd its lopermebility prt connects ith high-permebility prts t both sides, so there is no producer corresponded ith the injector in lo-permebility prts. Consequently, most remining oil concentrtes in I nd II prts. Besides, lthough there is no injector corresponded ith producer in these to high permebility edge prts, ter injected for lo-permebility prts flos to these prts, so remining oil is only trpped in top nd bottom corners of these prts. Becuse of the verticl heterogeneity of the multi-lyer reservoir models, the injected ter minly flo into the thick high-permebility oil lyers rpidly, though these lyers hve reched extreme high ter content, so the 13

7 J Petrol Explor Prod Technol (016) 6: Fig. 3 The ultimte recovery vrying ith segment numbers under different modes Fig. 4 Verticl seep efficiency vrying ith segment numbers under different modes djcent lo-permebility oil lyers hve not been sept effectively. As Fig. 6 shos, overflo 1 nd, hich re the upper nd loer oil lyers of the thick high-permebility oil lyer, hve not been sept hen the LSWI ell re divided into five segments. Tht is becuse bottom ellbore pressure of injector is less thn threshold pressure, so ter cnnot be injected in these lo-permebility oil lyers. Independent lo-permebility oil lyers hve poor physicl properties, so they re difficult to be sept even by LSWI. As shon in Fig. 7, sheet 3 is independent lo-permebility oil lyer, hich cnnot be sept hen the injector is divided into five segments by LSWI. After subdividing into ten segments, the oil lyer cn be sept finlly. Hoever, the terflood production isn t entirely effective, so more stimulting 13

8 76 J Petrol Explor Prod Technol (016) 6: I Interctive lo-permebility oil lyer High-permebility oil lyer II High-permebility oil lyer (Top) (Middle) (Bottom) Fig. 5 Oil sturtion distribution of overflo oil lyer fter developing 0 yers ith ten segments Overflo 1 High-permebility oil lyer Thick high-permebility oil lyer Interctive lo-permebility oil lyer *Complete non-sept *Full strong seep *Totl non-sept Overflo (Overflo 1) (Thick high-permebility oil lyer) (Overflo ) (Verticl section of 3 oil lyers before) Fig. 6 Oil sturtion distribution of overflo 1, nd high permebility oil lyers fter developing 0 yers ith five segments Fig. 7 Oil sturtion distribution of Sheet 3 oil lyer fter developing 0 yers ith five nd ten segments *Complete non-sept (5 segments) (10 segments) mesures re necessry, such s hydrulic frcturing nd gs injection. Conclusions Injection pressure djusted by ter chokes, ell grid pressure nd fluid sturtion re mde s three unknon prmeters, nd the source terms of injector ellbore re solved implicitly, nd then ell model of LSWI is estblished, hich coupled ith oil ter to phses model to form the finl numericl models. It cn lso be represented s close liner system ith seven digonl sprse coefficient mtrix, nd solved by block pretretment of generlized miniml residul lgorithm. According to the theory of LSWI, the numericl model proposed, reservoir strtum distribution nd injector segments chrcterized in the Chinese Dqing Oilfield, three multi-lyer reservoir 13

9 J Petrol Explor Prod Technol (016) 6: mechnism models re estblished ith positive rhythm, negtive rhythm nd composite rhythm, respectively in high-permebility oil lyers. Lo-permebility oil lyers re primry potentil for multi-lyer reservoirs ith extreme high ter content, nd LSWI ill help them to get higher recovery. More segments is not the gol of LSWI, the structure of ellbore segments need to correspond ith distribution of remining oil, nd verticl heterogeneity should be ekened. The key of enhncing recovery is to increse verticl seep efficiency, the remining oil cused by verticl heterogeneity nd poor physicl properties cn be terflooded by djusting structure of segmenttion. Hoever, some other stimulting mesures re necessry to be used for developing the remining oil cused by bd connectivity beteen injectors nd producers. Acknoledgments This study hs been crried out under the frmeork of the ntionl meg project of science reserch (011ZX ) finnced by Chinese government, nd hs been prtilly supported by Petro-chin. Open Access This rticle is distributed under the terms of the Cretive Commons Attribution 4.0 Interntionl License ( cretivecommons.org/licenses/by/4.0/), hich permits unrestricted use, distribution, nd reproduction in ny medium, provided you give pproprite credit to the originl uthor(s) nd the source, provide link to the Cretive Commons license, nd indicte if chnges ere mde. Dkung H (010) Discussions on concepts, countermesures nd technicl routes for the redevelopment of high ter-cut oilfields. Pet Explor Dev 37(5): Ding DY (011) Coupled simultion of ner-ellbore nd reservoir models. J Pet Sci Eng 76:1 36 Dumku FA et l (01) Revie of ell models nd ssessment of their impcts on numericl reservoir simultion performnce. J Pet Sci Eng 15: Go D, Ye J, Hu Y et l (015) Numericl reservoir simultion constrined to fine seprted lyer ter injection. Chin J Comput Phys 3(3):38 44 He L, Xiogung P, Ki L (013) Current sttus nd trend of seprted lyer ter flooding in Chin. Pet Explor Dev 40(6): Jigen Y, Xinghong W, Yixing Z et l (007) Study on computer ssisted history-mtching method in corner point grids. Act Petrolei Sinic 8():83 86 Lin CY, Hung LH, Li DL et l (011) The coupling study of throttle nd reservoir seepge of ter injection in development of oil field. Chin J Comput Mech 8(4): Stone TW et l (1989) A comprehensive ellbore/reservoir simultor. SPE Villnuev-Trin B et l (013) Rigorous simultion of production from commingled multilyer reservoirs under vrious crossflo nd boundry conditions. SPE Yn Z, Xie J, Yng W et l (008) Method for improving history mtching precision of reservoir numericl simultion. Pet Explor Dev 35():5 7 Zho G, Sun W, He X (01) Reservoir simultion model bsed on strtified ter injection nd its ppliction. J Northest Pet Univ 36(6):8 87 References Bohu W, Shuhong W, Dkung H et l (013) Block compressed storge nd computtion in lrge-scle reservoir simultion. Pet Explor Dev 40(4):