Deep-Subsea OTEC. Vicente Fachina 1. Correspondence: Vicente Fachina, Petrobras, Brazil.

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1 Deep-Subsea OTEC Mechancal Engneerng Research; Vol. 7 No. 1; 2017 ISSN E-ISSN Publshed by Canadan Center of Scence and Educaton 1 Petrobras, Brazl Vcente Fachna 1 Correspondence: Vcente Fachna, Petrobras, Brazl. E-mal: vcentefachna@gmal.com Receved: June 24, 2016 Accepted: July 9, 2016 Onlne Publshed: May 30, 2017 do: /mer.v7n1p1 URL: Abstract A deep-subsea OTEC concept s smulated, and a threefold ncrease n exergy effcency can be acheved as to the topsde one. On the envronmental aspect, a deep-subsea OTEC concept can brng about negatve CO 2 emssons, whch poses a postve envronmental rsk. On the economcs, wth approprate publc fundng, a 100 MW deep-subsea OTEC asset would cost about USD mllon. On the lfe-cost of energy, values between USD 2010 /MWh are predcted. Keywords: ocean CO 2, ocean energy, OTEC, renewable energy, solar energy 1. Introducton Ths paper proposes a concept desgn for a deep-subsea ocean thermal energy converson asset (OTEC) as an alternatve to topsde. Such a concept jons the heat source (tropcal surface ocean water) to the heat snk (deep ocean water) by an nsulated ppe to brng the warm surface ocean water down to the deep-subsea faclty. The key advantages are to elmnate CO 2 upwellng from the deep ocean waters, and to mnmze nvestment and costs for no need of naval structures and human facltes. The physcal prncple of the OTEC energy route s smlar to the geothermal one. Both ones are characterzed by utlzng Rankne-derved thermodynamc power cycles. In the tropcs, heat sources stem from the surface ocean waters, and heat snks from the deep waters below 800 m depth. Snce the sun s the prmary heat source, t s acceptable to qualfy the OTEC energy route as a knd of solar power wth nherent heat storage. Investments on OTEC nclude large equpment needed to convert nto electrcty the low thermal energy densty from the tropcal oceans. Nonetheless, there are two postve expectatons for economc consderaton: 1) 90% operaton capacty (Avery & Wu, 1994), for OTEC should not present the ssues of ntermttent energy supply from drect solar and wnd power, or from ranfall regmes of the hydropower, or from crop seasonalty of bo-fuels; 2) Besdes electrcty, other delverables are possble as desalnated seawater and cold water for ar condtonng or aquculture systems. Cornela and Davs (2012) carred out a comparson study for the renewable ocean energy optons, and the concluson s the OTEC energy route s the best ft for a hgh energy and carbon prces scenaro. These can provde compettve economc performance ndcators n locatons wth no access to hydropower or hgh fuel costs. Ocean slands or tropcal coastal regons may beneft from the OTEC delverables (Fachna, 2016). In case of potental artfcal slands or ocean ctes n a future scenaro, OTEC can be one of the components n a synergc renewable ocean energy portfolo, together wth offshore wnd power, solar power, and others such as currents, tdes and waves. In terms of planetary techncal energy resource, ocean thermal gradents account for about 7 TW (Rajagopalan & Nhous, 2013). 2. Concept Desgn of a Deep-Subsea OTEC Asset Equaton (1) s an exergy model (exergy per unt mass) (Callen, 1985), whch stems from the complete Legendre transformaton of energy (Note 1). The functons h (enthalpy) and s (entropy) stem from thermodynamc functons of workng fluds. If there are chemcal, nuclear reactons n the power cycle, energy potentals (μ), together wth varaton n mol, atomc numbers (N), shall be consdered. The gravty force depends on gravty feld (g) and mass. In case of OTEC, the term wth energy potental does not apply for there are no chemcal, nuclear reactons n the power cycle, only heat transfers. The deep ocean water (DOW) s the heat snk, for whch there must have reference values for the temperature, enthalpy and entropy. The surface ocean water (SOW) s the heat source. Also, any flud 1

2 column (L) above the water lne becomes mportant, and undesrable, f the water pumps are not nstalled below the water lne. = h (1) Fgure (1) shows the thermodynamc power cycle utlzed by the Author for the numerc smulaton. The Equaton set (2) comprses coupled steady-state and energy balance equatons, whch buld the workng model for the smulaton. The Author has utlzed a software tool wth bult-n thermodynamc functons, the ammona-water bnary workng flud ncluded. Equaton (2a) calculates the power cycle overall exergy effcency by solvng for η. Equaton (2b) establshes the overall energy balance n the power cycle, as well as Equaton (2c) for electrcty only. Equaton (2d) establshes the energy balances for every system depcted n Fgure 1. On the workng flud, research and development actvtes snce the 1980 s have leaded to the utlzaton of the ammona-water mxture on the OTEC power cycles for ts larger enthalpy gap between the lqud and the vapor phases than wth ammona only (Kalna, 1982). = (2a) Q W = 0 (2b) + gross W = 0 (2c) ( ) + ( ) =0 (2d) T5 5 OH- 11 λ NH4+ 6 SEPARATOR 1-λ 7 yλ TG-1 8 W (1-y)λ TG-2 9 W NET POWER Q 4 10 U ABSORBER EVAPORATOR REGENERATOR 3 NH4 + OH - NH4 + OH - 1 CONDENSER T2 Q C 2 Fgure 1: The Uehara s power cycle Table 1 shows three numerc smulatons: the Vega s (Vega & Mchaels, 2010), the Ouch s (Ouch, Jtsuhara, & Watanabe, 2011), and the Author s. The mssng data n Table 1 are not avalable. The performance metrcs consder electrcty as the only output. The Ouch s paper does consder desalnated seawater as an output besdes electrcty; nevertheless, electrcty has to be used for actually makng desalnated seawater and pumpng t to onshore or offloadng t to a tanker shp. The more desalnated seawater to make and pump, the less delverable electrcty becomes avalable and vce-versa. 2

3 Table 1. Numerc smulatons Desgn attrbute Vega s Ouch s Author s Concept desgn Topsde Topsde Deep-subsea Power cycle type NH 3 -Rankne Uehara Uehara Gross power 80 MW 5 MW 5 MW Net power 53 MW 3 MW 3 MW Ancllary electrc consumpton Not avalable Not avalable 5% gross power SOW temperature 299 K 298 K 299 K DOW temperature 278 K 278 K 279 K SOW flow m 3 /s 14.5 m 3 /s 4.7 m 3 /s Heat exchanger (HX) effectveness Not avalable Not avalable 75% Turbo generator effcency Not avalable Not avalable 80% Pumpng effcency Not avalable Not avalable 75% HX nlet-outlet temperature gap 3 K 3 K 3 K HX pressure loss NA NA 1.5 bar Seawater flow velocty 2.0 m/s 2.0 m/s 2.0 m/s Ppng nternal wall roughness NA NA 50 μm Performance metrcs Overall exergy effcency 6% 7% 22% Energy content (as to SOW) 0.20 MJ/m MJ/m MJ/m 3 Note: Uehara (Noda, Ikegam, & Uehara, 2002). From the performance metrc results, the deep-subsea OTEC concept presents values about three tmes larger as to the topsde ones. The former s top advantages are lower seawater flows per unt power, for there s no nternal consumpton of desalnated seawater, less ancllary electrc consumpton, and less-energy ntensve seawater pumpng due to the hgher water densty n the deep sea. Dependng on economc constrants, further mprovements can be acheved by state-of-the-art heat exchangers, whch would rase the nlet-outlet temperature gap, and by lowerng the values of the seawater flow velocty and the ppng nternal wall roughness. Equaton (3) models the CO 2 relatve concentraton n ar-to-water nterfaces (R, the Revelle Factor) (Wess, 1974). Such a concentraton vares between 8 and 15, dependng on the CO 2 temperature and concentraton at the sea level atmosphere. As a base case, the Author assumes that to be 10. R = Δ Δ[ CO2] /[ CO ] ar 2 ar [ CO2] /[ CO2 ] 醙 ua 醙 ua The concentraton gradent of dssolved CO 2 n the South Atlantc ncreases vertcally from 2.0 mol CO 2 /t-water at sea level up to 2.2 mol CO 2 /t-water at 1,000 m-depth (Zeebe & Wolf-Gladrow, 2001). Nevertheless, local measurements ought to be made due to vertcal and horzontal ocean current condtons. For the onshore and the offshore topsde assets (wth long DOW ppe), there are CO 2 postve emssons to the atmosphere because DOW (wth hgher CO 2 concentraton) s pumped upwards the sea level (wth lower CO 2 concentraton). For the deep-subsea asset (wth long SOW ppe), there are CO 2 negatve emssons, or capture from the atmosphere, because SOW (wth lower CO 2 concentraton) s pumped downwards to the sea bottom (wth hgher CO 2 concentraton). From Equaton (3) and the concentraton gradent of dssolved CO 2 n the South Atlantc, there would be about 11,700 t CO 2 /yr negatve CO 2 emssons for a 5 MW gross deep-subsea OTEC asset, wth 90% operatonal capacty. Fgure 2 llustrates a concept desgn of a deep-subsea OTEC asset. The SOW ppe has to be robustly nsulated for a 1 K maxmum temperature decrease (whch s a symmetrc desgn requrement for a DOW ppe n case of a topsde faclty). The SOW s pumped downwards the evaporator ntake n the deep sea, and then upwards enough for safely dschargng t away from the DOW ntake (Fry, Adams, & Jrka, 1977). The DOW has to be pumped through the condenser, and then upwards enough for safely dschargng t away from ts ntake (Fry, Adams, & Jrka, 1977). (3) 3

4 Sea level 299 K SOW ntake -20 m (Ref) -700 m -800 m SOW dscharge DOW dscharge Moorng cables Subsea DOW ntake 279 K Fgure 2. Concept desgn of a deep-subsea OTEC asset (not to scale) 3. Economcs of a Deep-Subsea OTEC Asset On the nvestment (I), Equaton (4) stems from the Vega s model (Vega, 2010) for estmatng the nvestment on frstgeneraton topsde OTEC assets, wth 2010-based USD values. Specfcally for a deep-subsea OTEC asset, nvestments are expected to be about 30% less than for topsde (Note 2) (Osmundsen, 2011). In the Equaton (4), the 0-subscrpt means the currency values shall be converted to the same tme base, usually the producton start-up as tme zero. Table 2 compares normalzed nvestments between the topsde and the deep-subsea concepts. Techncal servces comprse busness case and ntal engneerng studes, whch are assumed to cost the same for both concepts. The other actvty blocks dffer substantally for the nherent deployment nature of the deep-subsea concept as to the topsde one: no need for floatng naval structures and related crew needs. Specfcally for the deep-subsea equpment, ther hgher costs should be offset by even hgher ones for the floatng naval structures and human HSE systems n the topsde concept. Table 2. Normalzed nvestments Actvty block Top Deep Dfferences Deep as to Top (base case) Techncal servces Onshore assembles No floatng and human HSE systems Offshore assembles Less workmanshp and related HSE systems Commssonng No human HSE systems to commsson Grand totals Fgure 3 dsplays Equaton (4), wth 10 MW 100 MW (red lne). More accurate values should come up wth the frst commercal assets. Equaton (5) models the lfe-cost of energy (LCOE) as a functon of the operatonal cost ndex ( ), and the net power ( ). The assumptons for Equaton (5) are: constant 10%/yr dscount rate (j), 90% operaton capacty (α) (1), and 25 years for the asset lfe tme (n). Fgure 3 dsplays Equaton (5), wth 2% ξ 10%, and 10 MW W 100 MW. I =kw (4) LCOE = (1+ x ) (5) t = 8,760αn x 1+j 0<ξ<1 0 4

5 On the operatonal cost ndex ( ), t depends on the asset sze and technology, and t s modeled as a fracton of the total nvestment at each tme perod. For smplfcaton, t s set constant n all tme perods. Such a factor shall get smaller f an effectve carbon market actually comes true. Publc fundng becomes fundamental due to hgher rsks nvolved before market maturty; nevertheless, the partcpaton of prvate fundng s necessary n order to promote better busness effcency under proper publc regulaton frameworks. LCOE [USD/MWh] 160 ξ 2% 4% 6% 8% 10% I 0 [USD x 10 6 ] j=10%/year n=25 years Net power [MW] Fgure 3. LCOE and 2010 nvestment estmates for frst-generaton deep-subsea OTEC 4. Conclusons The OTEC energy route taps nto the solar heat storage n the tropcal oceans. An overall advantage of the OTEC route as to other renewable routes s the 90% expected operaton capacty, whch s far greater than drect solar or wnd power. Out of the several OTEC confguratons, the deep-subsea one offers advantages as to the topsde ones. On the techncal aspect, a deep-subsea OTEC concept can have exergy effcences about threefold hgher as to the topsde ones. On the envronmental aspect, the deep-subsea OTEC concept can brng about negatve CO 2 emssons, for t has to pump surface ocean water downwards the deep sea, whch poses a postve envronmental rsk. On the economcal aspect, the deep-subsea OTEC concept can cost about 30% less than a topsde one. An economc model for a 100 MW asset yelds USD mllon nvestments, and USD 2010 /MWh LCOE. Acknowledgement The Author thanks Petrobras for ther receptvty to the OTEC energy route. Glossary DOW: Deep Ocean Water; g: gravty feld; : specfc enthalpy; HSE: Health, Safety and Envronment; HX: heat exchanger; I: nvestment amount; L: flud column; LCOE: Levelzed Cost Of Energy; : ether DOW, SOW or workng flud mass; : ether mol or atomc number; OTEC: Ocean Thermal Energy Converson; P: absolute pressure; Q: ether gross, net or nternal heat; s: specfc entropy; SOW: Surface Ocean Water; T: absolute temperature; : ether gross, net or nternal work; : operatonal factor; η: ether energy or exergy effcency; : ether chemcal or nuclear potental; : specfc exergy (exergy per unt mass). References Avery, W. H., & Wu, C. (1994). Renewable energy from the ocean: a gude to OTEC. Oxford Unversty Press. 5

6 Callen, H. B. (1985). Thermodynamcs and an Introducton to Thermostatstcs. s.l.: John Wley & Sons, Inc. Fachna, V. (2016). Sustanable freshwater from the tropcal oceans. Journal of the Brazlan Socety of Mechancal Scences and Engneerng, 38(4), Fry, D. J., Adams, E. E., & Jrka, G. H. (1977). Evaluaton of mxng and recrculaton n generc OTEC dscharge desgns (No. COO ). Massachusetts Inst. of Tech., Cambrdge (USA); Cornell Unv., Ithaca, NY (USA). Kalna, A. I. (1982). U.S. Patent No. 4,346,561. Washngton, DC: U.S. Patent and Trademark Offce. Noda, N., Ikegam, Y., & Uehara, H. (2002, January). Extracton condton of OTEC usng the Uehara cycle. In The Twelfth Internatonal Offshore and Polar Engneerng Conference. Internatonal Socety of Offshore and Polar Engneers. Noel, C., & Davs, R. (2012, Aprl). Renewables, Ready or Not?. In Offshore Technology Conference. Offshore Technology Conference. Osmundsen, P. (2011). Choce of development concept-platform or subsea soluton? Implcatons for the recovery factor. s.l. : Unversty of Stavanger, Norway. Ouch, K., Jtsuhara, S., & Watanabe, T. (2011, January). Concept desgn for offshore DOW platform as nfra-structure of solated sland. In ASME th Internatonal Conference on Ocean, Offshore and Arctc Engneerng (pp. 9-13). Amercan Socety of Mechancal Engneers. Rajagopalan, K., & Nhous, G. C. (2013). Estmates of global Ocean Thermal Energy Converson (OTEC) resources usng an ocean general crculaton model. Renewable Energy, 50, Vega, L. A. (2010, January). Economcs of ocean thermal energy converson (OTEC): an update. In Offshore Technology Conference. Offshore Technology Conference. Vega, L. A., & Mchaels, D. (2010, January). Frst generaton 50 MW OTEC plantshp for the producton of electrcty and desalnated water. In Offshore Technology Conference. Offshore Technology Conference. Wess, R. (1974). Carbon doxde n water and seawater: the solublty of a non-deal gas. Marne chemstry, 2(3), Zeebe, R. E., & Wolf-Gladrow, D. A. (2001). CO2 n seawater: equlbrum, knetcs, sotopes (No. 65). Gulf Professonal Publshng. Notes Note 1. A Legendre transformaton substtutes functon s frst dervatves for the functon tself. The complete Legendre transformaton of energy s = ( ), where φ s exergy, u s energy, and x represents energy ndependent varables. The Ensten s summaton conventon over s appled for the u partal dervatves to x. Such a conventon s appled n all models for replacng the Σ symbol. Note 2. The k-factor value n the Equaton (4) s 53 x 10 6 [USD/MW], whch should be multpled by 0.7 n order to account for the lower expected nvestment for the deep-subsea OTEC asset. The value of λ s 0.6. Copyrghts Copyrght for ths artcle s retaned by the author(s), wth frst publcaton rghts granted to the journal. Ths s an open-access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton lcense ( 6