Rise and Dissolution Modeling of CO 2 Droplet in the Ocean

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1 Kyuhu Unverty Global COE Program Journal of Novel Carbon Reource Scence Vol. 7 pp Feb. 013 Re and Doluton Modelng of CO Droplet n the Ocean Changhong Hu *1* Makoto Sueyoh *1* Fe Jang *3 Kmnor Shtahma * Tetuo Yanag *1* *1 Reearch Inttute for Appled Mechanc Kyuhu Unverty * Internatonal Inttute for Carbon-Neutral Energy Reearch (WPI- ICNER) Kyuhu Unverty *3 Interdcplnary Graduate School of Engneerng Scence Kyuhu Unverty (Receved October 6 01; accepted December 1 01) A numercal approach propoed to tudy the behavor of a natural carbon doxde (CO ) droplet leaked from the eafloor. Moton and deformaton of the droplet at the ntal tage are mulated by a lattce Boltzmann mult-phae method to obtan the termnal velocty. The whole proce of droplet re and doluton modeled by a mplfed analytcal method. The n-tu experment cae on a natural CO droplet at the Oknawa Trough (Shtahma et al. 1) ) tuded by ung the propoed numercal model. Numercal experment how trong dependency between the termnal velocty and the droplet denty. The phenomena obtaned n the on-ea obervaton are dcued by the preent numercal tudy. 1. Introducton The ocean baed carbon capture and torage (CCS) technology condered a a hopeful method to mtgate the global warmng. Among everal type of the ocean CCS the ocean geologcal CCS n whch the CO tored beneath the eabed wll be the mot practcable approach n the near future. However due to unpredctable reaon uch a earthquake there tll a rk of CO leakage from the torage reervor. It neceary to nvetgate the behavor of rng CO droplet for elucdaton of the mpact on marne ecoytem and for degnng an effcent montorng ytem. One approach to tudy CO droplet n the deep ea the natural analogue. Large amount of natural CO ooze from the eabed around under-ea volcanoe. Obervaton of th knd of CO droplet provde an opportunty for undertandng the behavor of CO n the ocean. Shtahma et al. 1) carred out a ere of ntu experment on rng hydrothermal CO droplet from 1430 m deep eafloor at the Oknawa Trough. They tracked the CO droplet emtted from the eafloor by a remotely operated vehcle (ROV) for everal hundred meter. In-tu data of temperature alnty ph and partal preure of CO (pco ) near the CO droplet were meaured and the change n droplet ze and re rate were alo calculated from the vdeo record. For droplet wth about 7 mm dameter the average re rate about 0 cm/. On the other hand P. G. Brewer et al. ) performed a real ea n-tu experment n 800 m deep Monterey Bay Calforna. They releaed pure CO droplet by a ppe and tracked them by a ROV. However the mean acent rate meaured n the experment 1.8 cm/ for the droplet wth the mlar ze of Shtahma experment. The motvaton of the preent reearch to fnd out the reaon of th dcrepancy. Snce n-tu experment n the deep ocean uually encounter dffculte uch a rkne and hgh cot the numercal mulaton condered a an effcent method whch can provde much more detaled nformaton. Recently a novel lattce Boltzmann method (LBM or LB method) ha been developed by Jang and Hu 3) for th purpoe. LBM ha everal advantage over the conventonal Naver-Stoke olver epecally n dealng wth complex boundare ncorporatng of mcrocopc nteracton and parallelzaton of the algorthm. The lqud CO and eawater ytem a typcal mmcble mult-phae flow problem and can be treated by the LBM wth the Rothman-Keller/ Guntenen (RK) twophae model. The ntal tage of a CO droplet rng.e. the droplet move from quecence to teady tate at the termnal velocty mulated by the LBM. Deformaton of the droplet an mportant factor of th tage. Smulaton of the whole proce of the droplet rng untl t fully dolved n the eawater wll cot too much CPU tme by LBM. Therefore a mplfed analytcal method alo propoed n th paper to model the whole proce of the droplet re wth the conderaton of doluton. Th paper organzed a follow. In ecton the RK mult-phae LBM model are brefly ntroduced wth valdaton. In ecton 3 the mplfed analytcal model propoed. In ecton 4 Shtahma n-tu experment cae tuded by the propoed numercal model. Fnally a concluon of th tudy decrbed.. Lattce Boltzmann two-phae model In th ecton the lattce Boltzmann two-phae RK model outlned. A D3Q19 (nneteen velocty vector n 3D) lattce model adopted n th tudy. Th method nclude two LB cheme: a LB flow olver wth the multrelaxaton tme (MRT) collon operator 4) ncorporatng the effect of urface tenon and a LB cheme for the phae feld 5)

2 Journal of Novel Carbon Reource Scence Vol.7 Feb Lattce Boltzmann cheme for flow feld The lattce Boltzmann uaton to decrbe flud flow can be a f ( x + c δ t t + δt ) = f ( x t) + Ω = (1) In the uaton f ( t) x the partcle dtrbuton functon whch repreent the probablty of fndng a partcle at the node x and the tme t wth velocty c. δ t the tme tep relatng to the grd pacng through h = c δt. The collon operator of the MRT model gven by ( ) Ω 1 = M S Mf m () where M the tranformaton matrx 6). Th matrx contructed from the orthogonal ba vector 7) whch tranform the dtrbuton nto moment pace. The ulbrum vector m compoed of ulbrum moment 7). Durng the collon the moment { m k k = } are alway conerved leadng to ma and momentum conervaton of th algorthm. The matrx S a dagonal collon matrx ndcatng the relaxaton rate. The collon parameter S (the egenvalue of the collon matrx) contan zero part and non-zero part. The non-zero part are = e = ξ = 6 6 = 8 8 = q = = = = = = π = = =. m = The relaxaton rate ν can be calculated from the knematc vcoty ν by ν (3) 1 ν 1 = 3 +. (4) ν c δt The parameter e ξ q π and m have to be choen n the range [0] and are ued to mprove numercal accuracy and tablty 8). The macrocopc properte of denty varaton velocty and preure varaton are defned n term of partcle dtrbuton functon by δρ δρ = f u = f c δp =. (5) ρ 3 = 0 0 = 0 phae feld ψ where eparated LB uaton: ψ = ρ or ρ done wth a g ( t + t x + e t) = g ( ψ ( t x) u( t x) ). (6) where g are dmenonle denty dtrbuton. The ulbrum dtrbuton functon gven by 3 g ( ψ u) = wψ 1+ e u. (7) c The velocty u computed by the flow olver decrbed above. The weght coeffcent are 1 3 = 0 w = 1 18 = 1 6. (8) 1 36 = 7 18 An order parameter φ then defned a φ ρ ρ r b =. (9) ρr + ρb Here φ = 1 mean the red phae and φ = 1 mean the blue phae. The value of φ contant n the bulk of each phae and vare n the range [-11] at the dffuve nterface. Then the gradent of the phae feld C defned and can be calculated ung th order parameter: 3 C ( t x) = w eφ( t x + e t). (10) c t The normalzed gradent whch defne the orentaton of the nterface obtaned by Cα n α =. (11) C The color gradent C ntroduced n the phae feld olver ued to calculate addtonal term whch are ncorporated nto the ulbrum dtrbuton functon of the moment pace. Thee term are appled to generate urface tenon through a perturbaton baed on the gradent of the phae feld. Th LB cheme for the phae feld reult n an advecton dffuon uaton olver 10). The dffuon coeffcent α = ( 1 / 6) c δt whch underable for mmcble flud and a recolorng algorthm 9) appled to cancel out the dffuon effect. By th recolorng tep we can acheve a phae eparaton. The recolorng tep redtrbute the ma dtrbuton of phae ρ r and ρb o that the nner product of the gradent C and the momentum of phae ρ maxmzed. r r b. Lattce Boltzmann cheme for phae feld The advecton of the phae feld alo done n the LB framework and a recolorng approach 9) mplemented to keep the nterface harp. For the phae feld we ntroduce bnary mmcble red and blue flud wth flud denty ρ and ρ repectvely. The advecton of thee calar r b.3 Valdaton of LBM The above decrbed LBM valdated agant the expermental data by Ozak 11). In the experment a nozzle wa ued to generate varou ze of lqud CO droplet n a large hgh-preure tank and the termnal velocty of the droplet wa meaured. The experment

3 Re and Doluton Modelng of CO Droplet n the Ocean were executed under the condton wth the preure of 00 atm and the temperature of 5 C whch correpond to the tuaton of 000 m deep ocean. The phycal properte of the lqud CO /ea water ytem uch a denty vcoty and urface tenon at thee condton are lted n Table 1. The proce of CO droplet wth dfferent dameter (.0 mm mm) rng from quecence to a teady tate mulated by ung the above parameter. The termnal velocty of the rng droplet calculated from the mulaton reult. A comparon between the numercal reult and Ozak experment data hown n Fg. 1. The mulaton reult are n an excellent agreement wth the expermental data epecally for mall droplet. For the droplet wth dameter below 8 mm the phercal hape mantaned. Obvou deformaton tart to be oberved when the droplet dameter exceed 1 mm. A nonlnear relatonhp between droplet ze and rng velocty found when the droplet ze larger than 10 mm. The hape of the droplet wth dameter 14 mm at dfferent tme (t = and 1.40) durng rng proce are hown n Fg.. It can be found that the droplet begn to deform oon after releang and become ellptcal fnally. About one econd rured for thee droplet to reach ther termnal rng tate. The vertcal computaton doman about one meter for th ntal tage and the LBM mulaton eem effcent and accurate. For the whole rng proce whch may cover everal hundred meter vertcal dtance the analytcal model can be ued. Table 1 Phycal properte of the lqud CO /ea water ytem at 5 C 00 atm Property Sea Water Lqud CO Denty [kg/m 3 ] Vcoty [kg/(m)] 1.6* *10-3 Interfacal tenon [N/m] 7.0*10 - Termnal velocty [cm/] Ozak' Experment LBM mulaton Dameter [mm] Fg. 1 Correlaton between termnal velocty and droplet ze. Fg. Deformaton of a CO droplet wth dameter of 14 mm. 3. Modelng droplet re and doluton In th ecton a mplfed analytcal model to mulate whole the rng proce of the CO droplet wth the conderaton of doluton decrbed. The moton of uaton of a droplet wrtten a d dz m = Fd + Fb Fg (1) dt dt where m the ma of droplet z the poton F d drag F b buoyancy and F g gravty force. Th moton of uaton numercally calculated from the ntal poton to the fully dolved poton explctly. The drag force F d calculated by 1 Fd = Cd ρ AU U (13) where C d ρ A and U are the drag coeffcent the denty of ea water the reference area of droplet and the re rate at the poton z repectvely. The buoyancy force F b calculated by F b = ρ Vg (14) where V the volume of droplet and g the gravty acceleraton. The gravty force F g expreed by F g = ρ Vg (15) d where ρ d the denty of droplet. At each tme tep the

4 Journal of Novel Carbon Reource Scence Vol.7 Feb. 013 ma of droplet decreaed by doluton to the ea water. Varaton of ma due to doluton gven by dm = KS (16) dt where K the doluton rate and S the urface area of droplet. In th model the hape of droplet regarded a a phere. Wth the droplet denty at the poton z the ma of droplet m determned by ung the reference area A and the urface area S of droplet a follow: 1 m 3 3 V = r = V A = π r S = 4A. (17) ρd 4π When the denty of poton z gven the uaton (1) ealy computed n tme doman uentally from the releae poton and other ntal condton. Fg. 3 how the dagram of the numercal computaton. tart Gve ntal condton(m z) Compute envronmental condton(pt) Compute droplet condton(ρ CO ) Compute droplet hape(asv) Compute drag(f d ) Compute buoyancy and gravty(f b F g ) Compute uaton of moton(u) Update droplet poton(z) Compute doluton of droplet(m) Check lmt ze of droplet End Fg. 3 Suence dagram of numercal mulaton for droplet rng by ung analytcal model. 4. On the n-tu experment cae In th ecton we tudy an n-tu experment cae 1) by the above propoed model. In the experment re of hydrothermal CO droplet wa oberved and meaured. Fg. 4 how varaton of the ze (projected area) and the rng rate of a CO droplet n the deep ea for two cae. Obervaton wa carred out from the eafloor at the Oknawa Trough of 1430 m depth. In general the re rate decreaed wth the ncreae of droplet acent dtance. It condered that the tart velocty n Fg. 4 approxmately ual to the termnal velocty. The decreae of the rng velocty due to the reducton n the droplet ze caued by the CO doluton. The tart velocty.e. the termnal velocty near 0 cm/ n the meaurement. In another n-tu experment ) by ung pure lqud CO droplet n the deep ea wth the depth of 800 m a mean acent rate of 1.8 cm/ wa obtaned for the mlar ze droplet. We conder that the dfferent depth not the only reaon whch caue uch large dcrepancy between the two experment. Other factor that affect the droplet rng rate need to nvetgate. Here we ue the propoed numercal model to tudy th problem and try to fnd an anwer. Depth (m) Re rate (cm/) Droplet ze (mm ) dve 005 dve 004 Fg. 4 Vertcal change n droplet ze and re rate of CO droplet. 4.1 Termnal velocty obtaned by LBM At frt we check the termnal velocty at the experment condton by numercal mulaton. The LB method propoed n Secton ued. Phycal properte of the lqud CO vary wth the preure and temperature. Hgh preure and low temperature are the vtal condton that nfluence not only the denty dfference between ea water and lqud CO but alo the extence of the hydrate flm on the urface of the droplet and conuently nfluence the buoyance and the urface tenon. In the LB method thee condton are adjuted by changng the urface tenon coeffcent parameter σ and the dente of lqud CO and eawater. Numercal mulaton on the two n-tu experment cae Shtahma experment 1) and Brewer experment ) are carred out. The parameter ued n the computaton are lted n Table and Table 3 repectvely. Sngle phere droplet wth dameter of 9 mm mulated from quecence to teady rng tatu. The termnal velocty of the droplet computed when the droplet reache a teady tate for the above two expermental cae. For Brewer cae the termnal velocty of 1.3 cm/ obtaned whch very cloe to the experment. Snce n the experment pure lqud

5 Re and Doluton Modelng of CO Droplet n the Ocean Table Phycal properte of the lqud CO /ea water ytem at 3.9 C 140 atm Property Sea Water Lqud CO Denty [kg/m 3 ] Vcoty [kg/(m)] 1.6* *10-3 Interfacal tenon [N/m] 7.0*10 - Rng rate Table 3 Phycal properte of the lqud CO /ea water ytem at 4.4 C 80 atm Property Sea Water Lqud CO 0 0% 5% 10% 15% 0% 5% 30% 35% Impurty ga percentage Denty[kg/m 3 ] Vcoty[kg/(m)] 1.6* *10-3 Interfacal tenon[n/m] 7.0*10 - Fg. 5 Relatonhp between ga percentage and rng rate for a CO droplet wth dameter 7 mm. CO droplet ued and the envronment condton are relatvely deal comparon between the numercal reult and the expermental reult atfactory. On the other hand for Shtahma cae the calculated termnal rng rate 9.7 cm/ whch very below the expermental reult of 0 cm/. Several reaon can be condered for th dcrepancy. Frt the CO droplet emtted from the eafloor near under-ea volcanoe uually contan other ga pece uch a methane and helum. Thee ga pece reduce the overall denty of droplet. Therefore uch large denty dfference can caue hgher rng rate due to the larger buoyancy. In the paper 1) t reported that the natural CO droplet cont of about 5% mpurte. However a th value obtaned accordng to the meaurement on the ground the ga component n the droplet may be underetmated due to the envronment change. The exact component of the natural CO droplet n the deep ocean mpoble to meaure n tu. Therefore n th tudy we ue numercal mulaton method to nvetgate the effect of the purty of the CO droplet on the rng velocty. The upwellng current n the deep ocean condered a another reaon whch can accelerate the droplet rng rate. Snce the ntenty of upwellng current very dffcult to meaure n the experment and t effect on the rng velocty condered le mportant than the prevou reaon quanttatve aement of the upwellng current effect left for the future reearch. Therefore n order to nvetgate the effect of purty on rng rate we carred out everal mulaton wth varou dente of CO droplet. Aume that f the amount of contaned ga pece 10% n volume the CO droplet denty mply multpled by weght 0.9 n our mulaton nce the ma of ga can be neglected by comparng to that of lqud CO. The range of the volume percentage of the mpurty ga from 0% to 35%. Correlaton between th ga percentage and computed termnal velocty hown n Fg. 5. The hgh rng rate 0 cm/ obtaned n the experment correpondent to the ga percentage larger than 30%. It alo found that for cae that the ga percentage lower than 15% the termnal velocty ncreae wth the ga percentage lnearly. It condered that n th regon ntead of the buoyancy the urface tenon condered a the domnant force. A the mpurty ncreae further the buoyancy become much more mportant. The droplet tart to deform becaue the urface tenon cannot balance the flow preure due to hgh buoyancy. Th deformaton ncreae the drag coeffcent and reult n a non-lnear behavor of the rng rate. The vdeo captured n the experment 1) ndeed how large deformaton of the droplet. Therefore we can preumably conclude that to acheve the 0 cm/ rng rate the contaned ga percentage n the nonlnear regon and mut be over 30% n volume. 4. Smulaton of whole rng proce The whole rng proce untl the dappearance of the droplet can be mulated by the analytcal method decrbed n Secton 3. The doluton the mot mportant factor n th tage. Snce th a long term mulaton t not reaonable to apply LBM whch rure large memory ze and long CPU tme for mulaton. Some numercal mulaton by ung the analytcal model are carred out. Fg. 6 how the mulated rng rate and droplet ze wth varou properte. In thee mulated cae 3 μmol/cm / ued a the doluton rate and the ntal dameter of droplet 7.0 mm. Two extreme tuaton are tuded. One aumng ame doluton rate to both lqud CO and mpurty ga but wthout conderng compreblty of the ga. Fgure 6 how that f we do not conder ga expanon the predcted droplet rng rate gettng maller wth the decreae of depth more quckly than that n the experment

6 Journal of Novel Carbon Reource Scence Vol.7 Feb. 013 Depth (m) Re rate (cm/) Droplet ze (mm ) pure CO lqud 10% mpurty ga 0% mpurty ga 30% mpurty ga 30% expanonary ga 10% expanonary ga dve 005 dve 004 Fg. 6 Comparon of vertcal change n droplet ze and re rate of CO droplet between experment and analytcal model. In the cae of pure CO lqud the ntal rng rate maller than 10 cm/ whch mlar to the above LBM reult. In the cae of 30 percent contaned ga the LBM predcted ntal rng rate about 0 cm/. The preent analytcal method gve a reult of 5 cm/ whch cloe to the expermental meaurement. The hgher predcted termnal reult than the LBM predcton due to the neglect of droplet deformaton reultng n a maller drag coeffcent Cd. In the experment a typcal feature that the rng rate appear to keep contant from the depth of 1400 m to 850 m. However numercal reult wth the conderaton of the doluton rate cannot keep the rng rate a a contant. Another factor that hould be condered the effect of ga compreblty. Here we conder an extreme tet tuaton. The mpurty ga undolved n the ea water and obey the ga law. The reaon for uch treatment that the doluton rate of the ga unknown. Two cae wth 10 and 30 percentage n volume of expanonary ga are calculated. The ga compreble. The volume of the droplet then calculated by m V = + V (18) g ρd where V g the ga volume of the droplet that obtaned by the ga law. V g become larger wth the decreae of the water depth. Wth th expanonary ga model the reult how obvouly dfferent curve wth a wndng pont whch ndcate that the lqud CO ha fully dolved and only ga bubble remaned. The expermental data of re rate ext n the area between the cae of 30 percent mpurty ga and 30 percent expanonary ga lne. In a real phycal proce the ga can alo be dolved n the eawater. Th mple that uch mple analytcal model ha the capablty to mulate the expermental data when the contaned ga doluton rate to ea water gven utably. A another future work the accuracy of the model wll be mproved by ung the utable drag coeffcent ncludng the effect of deformaton of droplet. 5. Concluon In th paper a numercal approach propoed to tudy the behavor of a natural CO droplet leaked from the eafloor. Moton and deformaton of the droplet at the ntal tage are mulated by a LB mult-phae method to obtan the termnal velocty. The LB method accurate and effcent for hort term problem. The whole proce of droplet re modeled by a mplfed analytcal method n whch the CO doluton and mpurty ga compreblty are condered. The propoed numercal model are appled to tudy of the phenomena raed n the n-tu experment on a natural CO droplet at the Oknawa Trough. From the numercal reult t found that hgh rng rate meaured n the experment can be explaned by the mpurty ga n the ntal droplet. More that 30 percent n volume of the mpurty ga rured to obtan the termnal velocty meaured n the experment. From the numercal reult by the analytcal method the expermental phenomena of the contant rng velocty from the depth of 1400 m to 850 m cannot be explaned by only conderng the doluton. The effect of ga expanon hould be ncluded. Acknowledgement: Th work wa upported n part by World Premer Internatonal Reearch Center Intatve (WPI) MEXT Japan. Reference 1) K. Shtahma Y. Maeda Y. Koke and T. Ohum Int. J. Greenhoue Ga Control (1) 95 (008). ) P. G. Brewer E. T. Peltzer G. Frederch and G. Rehder Envron. Sc. Technol. 36(4) 5441 (00). 3) F. Jang and C. Hu Journal of Novel Carbon Reource Scence 5 10 (01). 4) D. d Humère n Rarefed Ga Dynamc: Theory and Smulaton Progre n Atronautc and Aeronautc ed. by B. D. Shzgal and D. P. Weaver Vol. 159 Amercan Inttute of Aeronautc and Atronautc Wahngton DC p. 450 (199). 5) A. K. Guntenen D. H. Rothman S. Zalek and G. Zanett Phycal Revew A (1991). 6) B. Ahrenholz Ph. D. The Technche Unvertät Braunchweg Braunchweg Germany (009). 7) J. Tölke S. Freudger and M. Krafczyk Computer & Flud 35(8-9) 80 (006). 8) P. Lallemand L. Luo Phycal Revew E 61(6) 6546 (000). 9) J. Tölke M. Krafczyk M. Schulz and E. Rank Phloophcal Tranacton: Mathematcal Phycal and Engneerng Scence 360(179) 535 (00). 10) D. Kehrwald Ph. D. The Unverty of Kaerlautern Kaerlautern Germany (003). 11) M. Ozak J. Mnamura Y. Ktajma S. Mzokam K. Takeuch K. Hatakenaka Journal of Marne Scence and Technology 6() 51 (001)

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