Estimating the practical potential for deep ocean water extraction in the Caribbean

Journal Pre-proof Estimating the practical potential for Deep ocean water extraction in the Caribbean Jessica Arias-Gaviria, Andres F. Osorio, Santiago Arango-Aramburo PII:

S0960-1481(19)31955-X

DOI:

https://doi.org/10.1016/j.renene.2019.12.083

Reference:

RENE 12792

To appear in:

Renewable Energy

Received Date: 1 February 2019 Revised Date:

17 December 2019

Accepted Date: 18 December 2019

Please cite this article as: Arias-Gaviria J, Osorio AF, Arango-Aramburo S, Estimating the practical potential for Deep ocean water extraction in the Caribbean, Renewable Energy (2020), doi: https:// doi.org/10.1016/j.renene.2019.12.083. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

Jessica Arias-Gaviria: Conceptualization, Methodology, Data curation, Formal analysis, Visualization, Writing-Original draft preparation Andrés F. Osorio: Conceptualization, Methodology Validation, Supervision, Writing Review & Editing Santiago Arango-Aramburo: Validation, Supervision, Writing - Review & Editing

1

Estimating the Practical Potential for Deep Ocean Water Extraction in the Caribbean Jessica Arias-Gaviria1*, Andres F. Osorio2, Santiago Arango-Aramburo1 1

Decision Sciences Group, Facultad de Minas, Universidad Nacional de Colombia, Medellin. OCEANICOS Research Group, Facultad de Minas, Universidad Nacional de Colombia, Medellin.

2

* Corresponding author: [email protected] Carrera 80 No 65-223 office M8A 403, Robledo, Medellin, Colombia.

1 2 3

Estimating the Practical Potential for Deep Ocean Water Extraction in the Caribbean

4 5

Abstract

6

Deep ocean water (DOW) is a renewable alternative to the many sustainability challenges

7

that the Caribbean faces today. DOW can provide seawater air conditioning (SWAC) for

8

buildings and greenhouses, provide electricity through an ocean thermal energy conversion

9

plant (OTEC), and provide nutrients for aquaculture and cosmetic industries. However,

10

today the implementation of DOW technologies in the Caribbean is inexistent, and studies

11

about DOW potential in the Caribbean are limited. We present a methodology for

12

estimating the practical potential of a city while considering constraints in ocean currents,

13

temperature, and salinity. We applied the methodology to five cities in the Caribbean and

14

found that the average potential is about 50 m3/s per city, enough to supply more than

15

100% of a city’s demand for air conditioning and 60% of its demand for electricity. We

16

also estimated the monthly availability of DOW resource, with maximum extraction

17

potentials between December to March, and minimum values between August to October.

18

These estimations serve as input for future feasibility and design studies on DOW

19

technologies in the Caribbean. Given the assumptions, the found potential may be

20

underestimated; thus, the results of this study can be considered as a minimum reference

21

value, complementary to the maximum theoretical potential found in previous studies.

22

Keywords: Deep Ocean Water; Energy Potential; Ocean Ecopark; Ocean Energy; Ocean

23

Thermal Energy Conversion; Seawater Air Conditioning

24 25 26 27

Abbreviations and Nomenclature

28 29 30 31 32

DOW LCOE OTEC SIDS SWAC

Acronyms Deep ocean water Levelized cost of energy Ocean Thermal Energy Conversion Small islands development states Seawater air conditioning

1

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69

Symbols

ℎ

Heat capacity (J/K) Return factor Enthalpy (J) Height (m) OTEC potential (MW) Volumetric flow (m3/s) Salinity (g/l) Temperature (°C) Ocean current velocity (m/s) Volume (m3)

Greek symbols Δ Δ Δ Δ Δ Δ

Ratio between warm water and cold water Temperature gradient (°C) Design temperature gradient (°C) Historical temperature variation of the system (°C) Historical salinity variation of the system (g/l) Length of influence volume in dimension (m) Length of influence volume in dimension (m) Efficiency of the OTEC generator Density (kg/m3)

Subscripts

! !"# $ % &

Cold water Deep water mixed layer Minimum value Return currents Surface water Discharge Warm water Northward Direction of remaining currents Eastward

2

70

1. Introduction

71

Caribbean islands currently face major challenges to attaining sustainable development.

72

Most Caribbean islands are net energy importers, have vulnerable and inefficient energy

73

systems, and are highly dependent on fossil-fuels [1]. These energy issues are barriers to

74

economic development. Deep ocean water (DOW) technologies are an alternative to not

75

only supply energy, but also raw material for innovative industries that could support the

76

economic development of the Caribbean [2]. Given the novelty of these technologies, the

77

potential for DOW extraction in the Caribbean is unknown. This paper presents a

78

methodology for estimating practical DOW extraction potential and applies it to calculate

79

the DOW extraction potential of five cities in the Caribbean.

80

The ocean can provide many forms of energy, such as tidal, wave, thermal and osmotic

81

energy [3,4], which has a combined theoretical energy potential of more than 20,000

82

TWh/yr, enough to supply electricity to the entire planet [3]. Despite its vast potential,

83

ocean energies have had minor deployment compared to other renewables, accounting for

84

less than 0.06% of the global renewable capacity [5]. Most ocean technologies are still in

85

development or demonstration phases and several challenges must be overcome before they

86

can advance on to commercial stages: information is lacking on ocean energy reliability, its

87

levelized cost of energy (LCOE) is high compared to other renewables, and there is a lack

88

of studies about realistic potential estimations [6,7].

89

DOW is the cold water located below the ocean’s surface layer (and below the

90

thermocline). Its typical stable temperatures are about 5°C and it usually has higher

91

concentrations of nutrients than shallow waters [8]. The physicochemical conditions of

92

DOW make it an exploitable resource with several applications. For instance, its low

93

temperatures can power a cooling system, such as a seawater air conditioning (SWAC)

94

district [9]. It can also produce electricity and desalinized water using the temperature

95

gradient with surface water through ocean thermal energy conversion (OTEC) [10]. DOW

96

nutrients can also serve as resources for mariculture [11], cosmetic and pharmaceutical

97

industries, and seawater greenhouses, among others. A previous study proposed that ocean

98

science and technology Ecoparks should be established in the Caribbean for the research

99

and development of DOW technologies [2]. An Ecopark could contribute to an island’s 3

100

sustainable development by providing renewable energy alternatives, technologies for

101

improving food security, and by providing support for research and development of

102

nutrient-based industries.

103

In order to materialize the Ecoparks concept in the Caribbean, the Caribbean’s practical

104

potential must be quantified. Previous studies have focused on estimating theoretical OTEC

105

potential, only taking the temperature gradient between DOW and surface waters into

106

consideration [12], and studies on practical DOW extraction potential throughout the world

107

are unknown to our knowledge. Experience has shown that less than 5% of the world’s

108

theoretical ocean potential is located in feasible areas [13,14]. Studies on practical potential

109

are needed in order to continue developing the technology of renewable energy [15].

110

Furthermore, there are only two studies that are available to the public about practical

111

DOW potential in the Caribbean [16,17], but these exclude natural limitations such as water

112

resources, temperature and salinity alterations.

113

This paper presents a methodology for estimating practical DOW potential, based on a

114

steady state model, and calculates the average potential of five cities in the Caribbean.

115

Section 2 provides an overview of thermal energy and DOW potential, sections 3 and 4

116

explain the proposed methodology and provide the results on the five Caribbean cities, and

117

conclusions are discussed in section 5. This study constitutes a starting point for a more

118

realistic estimation of DOW potential, however some of the model’s assumptions should be

119

addressed before using the methodology in a real application. Given such assumptions, our

120

results may be underestimated.

121 122

2. Background of ocean thermal energy and DOW potential

123

Renewable energy potential can be classified as: theoretical, geographical, technical, or

124

economic [15]. Theoretical potential is the maximum energy flux that can be extracted from

125

a renewable resource; geographical potential is the energy flux that can be extracted from

126

suitable areas, excluding areas that do not meet minimum requirements (e.g. minimum

127

wind speed for wind energy, minimum radiation for solar energy, and minimum thermal

128

gradient for SWAC and OTEC); technical potential is the geographical potential after 4

129

conversion losses, site-specific restrictions and environmental constraints; and economic

130

potential is the technical potential that is cost competitive compared to a locally relevant

131

alternative [15,18].

132

The theoretical potential of a renewable energy source is the starting point for a potential

133

assessment, but it is not practical for decision-making and planning [15]. Geographical,

134

environmental, social and economic restrictions can significantly decrease theoretical

135

potential, even by two orders of magnitude [19]; therefore, rather than theoretical values,

136

these reduced and realistic potentials should be considered for renewable energy planning.

137

Several studies have evaluated the technical and limited potential for different renewables

138

such as solar, wind, and tidal energy (see e.g. [20–22]). However, studies on ocean energy

139

are mostly focused on theoretical potential [7], with some developments made on tidal

140

energy [13] and salinity gradient energy [14,23].

141

Studies on DOW systems have focused on global OTEC theoretical potential and market

142

assessments. In regards to the theoretical potential, Vega (2010) [24] states that a potential

143

location for OTEC should meet the following conditions: (i) the thermal gradient of its first

144

kilometer of water should be greater than 20°C all year round; (ii) it should have a steep

145

bathymetry; (iii) there should be dependence on fossil fuels for the energy supply; and (iv)

146

the availability of other forms of energy should be low. Under such conditions, existing

147

studies have identified tropical waters as potential regions [25], with a global theoretical

148

potential of about 12 – 15 TW (5 TW in the Atlantic ocean) and including 98 countries and

149

territories [26], 38 of which are located in the Americas. Almost all these nations are

150

located in the Caribbean, except for Brazil, French Guiana, Guyana and Suriname.

151

In regards to market assessments, Vega (2012, 2010) [24,27] classified market potential

152

into small islands development states (SIDS) that need power and fresh water and could

153

implement plants with capacities between 1 – 20 MW; and mainland industrialized

154

countries that need large power plants. The Development Bank of Latin America (CAF)

155

prioritized ten cities that meet market and socioeconomic conditions for SWAC and OTEC

156

in the Caribbean, such as high energy and air conditioning demand, high energy prices, and

157

locations near a DOW source [28]. In a parallel study that is currently under development,

5

158

we classified all the islands in the Caribbean into three clusters with respect to their market

159

potential: high, medium and low.

160

Studies about the realistic or practical potential1 of DOW applications in the Caribbean are

161

limited; to our knowledge, there are only two studies available to the public that have

162

evaluated DOW or OTEC resources in the Caribbean. Devis-Morales et al (2014) evaluated

163

Colombia’s ocean thermal resources and found the island of San Andres to be the most

164

suitable place for them [16]. They also studied variations in the energy that a 10 MW

165

OTEC plant would provide considering annual variations in the thermal gradient of San

166

Andres, assuming flow rates for both cold and warm water were constant. CAF presented a

167

pre-feasibility assessment and the conceptual designs for two SWAC systems, one in

168

Montego Bay, Jamaica, and the other in Puerto Plata in the Dominican Republic [17].

169

While studies about practical ocean potential have increased in recent years, they have

170

mostly focused on mature ocean technologies such as tidal energy [13], and salinity

171

gradient energy [14,23]. These studies have found that less than 5% of their theoretical

172

potential are located in suitable areas. Research on practical –and more realistic– potential

173

is one of the main barriers to improving the design of DOW technologies, and to achieving

174

a competitive LCOE at larger scales [6]. This study was motivated by the need to have

175

estimations of practical potential, not only for OTEC but for all DOW technologies.

176 177

3. A methodology for estimating DOW practical potential

178

As previously described, most studies on DOW and OTEC potential have been focused on

179

the availability of a thermal gradient and the maximum OTEC power that can be obtained

180

from this gradient. Since the intention of Ocean Ecoparks is to implement different DOW

181

technologies [2], this study proposes a methodology for estimating the DOW practical

182

potential of the maximum water flows that can be extracted from –and returned to– the

183

ocean, based on mass and energy balances, taking factors such as the market, technology

184

and the environment into account. First, we assumed that the resource is what determines

1

“Practical potential” can be defined as the maximum extractable resource, considering the geographical and environmental constraints identified in section 3.

6

185

the theoretical DOW potential, which in this case, is the ocean water. Second, we

186

considered three constraints in order to determine the limits of extraction potential:

187

(i) Market and socioeconomic conditions: The Caribbean’s potential is limited to cities

188

that best meet the characteristics for DOW applications. Here, we considered the cities

189

prioritized by CAF [28].

190

(ii) Technology conditions: In following the Ecoparks Concept [2], the Caribbean’s

191

potential depends on the different intended uses of DOW. This study assumes the main

192

uses to be a SWAC district and an OTEC plant for each site, given that the DOW flow

193

requirements of these two technologies are higher than other DOW technologies.

194

Moreover, a fraction of water must return to the ocean after utilization, and the

195

parameters of the return current also influence the maximum DOW flow to be

196

extracted.

197

(iii) Social and environmental conditions: One of the main concerns related to ocean

198

energy is the potential environmental impact on ocean ecosystems and human activities

199

[6]. Social and environmental conditions have been identified as one of the main

200

limitations to renewable energy around the world [15], and the Caribbean is not an

201

exception [29]. Since these conditions are site-specific, and because this study aims to

202

develop a general methodology, this study considers that intake and discharge activities

203

should not be located in protected areas. It also considers that intake and discharge

204

flows should only minimally alter the ocean’s natural conditions of temperature,

205

currents, and salinity, both on the surface and in the deep ocean.

206 207

3.1 Delimiting and modeling the system

208

Figure 1 shows a system where cold water flow is pumped from deep water for several

209

uses, such as SWAC and OTEC, and warm water is also pumped from the surface in order

210

for OTEC to operate. After using both the cold and warm water, it is returned to the ocean’s

211

surface in a unified discharge flow. Both the extraction and discharge flows change the

212

water’s temperature, salinity and ocean currents; the aim is to minimize this. We defined a

213

control volume for the cold water intake (deep control volume) and a control volume for

214

the warm water intake and discharge (surface control volume). These volumes are assumed 7

215

to be constant and to have stirred tank conditions.2 After these volumes were determined,

216

we developed the mass and energy balances for each volume in order to calculate

217

maximum cold water and warm water flows, subject to the previously described

218

constraints.

219

220 221

Figure 1 – System delimitation for DOW potential estimation

222 223

Deep control volume

224

The deep control volume represents the deep water located around the DOW intake, a depth

225

of about 800 – 1000 m with temperatures typically at about 5°C. The control volume is

226

determined by an influence area (Δ

Δ ) and an influence height (ℎ ). The tank has two

2

Stirred tank conditions are assumed given that the influence areas considered in this study are less than 1km2 and that the available data has a spatial resolution of 1/12° (~8.75km).

8

227

inflows (

228

'

and

) that correspond to the eastward and northward currents (

respectively) and two outflows. The first outflow is the cold water intake (

'

and

( ),

and

229

the second is the combined flow that corresponds to the remaining currents3 (

230

exclude the vertical flows due to data limitations, and assuming that horizontal flows

231

account for 70-90% of the currents. However, future work should evaluate the pertinence to

232

include such vertical components. The density of all four flows is assumed to be the same;

233

and therefore, the mass balance in the constant deep control volume is determined by

234

equations (1) and (2). Since water is not discharged into the deep control volume, the

235

dynamics of extracting DOW do not affect the temperature and salinity of the tank

236

(equation 3). The temperature and salinity of the four flows are therefore equal to deep

237

ocean conditions (

238

normal ocean variations.

and

'

). We

) and could only vary naturally with seasonality and other

239 240

(1)

241

(2)

242

(3)



' '



,-

+

=

= 0,

=

'

(

+

Δ ℎ ; 0-

'

=

Δ

ℎ

=0

243 244

Surface control volume

245

We considered a surface control volume, which was determined by a surface influence area

246

(Δ

Δ ) and surface height, in this case, equivalent to the mixed layer height (ℎ1 )4. Three

247

inflows influence this volume: eastward surface currents, northward surface currents (

248

and

249

similar to the deep control volume, the flow (

) and the discharge flow (

2 ).

The two outflows are warm water intake ( '

(( )

'

and,

) corresponding to the remaining

3

includes the flow of both eastward and northward currents, modified after the extraction of the DOW. ' Both currents are considered as one flow since this variable is not relevant for the purpose of this research and because the extraction flow is expected to be too small to change the direction of the currents. The same assumption has been applied to ' . 4 The mixed layer is the upper portion of the ocean where air-sea exchanges generate turbulence, causing the water to mix and become vertically uniform in temperature, salinity and density [44].

9

250

eastward and northward surface currents5. As a first modelling approach, we considered

251

that the discharge flow is located in the surface volume. However, a more realistic model

252

should consider a third control volume, with a unified discharge located between 100 – 200

253

m deep.

254

In order to obtain a first approach, we here assumed equal densities; however, density

255

changes due to temperature cannot be neglected in real applications, because it is a crucial

256

property in the discharge flume evolution. . The total mass balance is therefore determined

257

by equations (4) and (5).

258 259

(4)

'

260

(5)

'

+

=

+

'

2

=

((

Δ ℎ1 ,

+

'

=

Δ

ℎ1

261 262

Variations in salinity were observed with the salinity balance of equation (6.a), where

263

changes in the salinity of the surface control volume (

264

salinity of incoming surface currents ( ) and on the salinity of the discharge ( 2 ). Because

265

stirred tank conditions are assumed to be present, both outflows have the same salinity as

266

the surface control volume (

267

reaches a continuous operation state, changes in surface salinity over time are expected to

268

be negligible (

,33

(( ).

(( )

over time depends on the

Under steady state conditions, i.e., when the Ecopark

= 0), as shown in equation (6).

269 270

(6.a)

271

(6)

,33

((

=

=

4

'

+

5+

2

2

−

(( ( '

+

(( )

,9 4:;9 <:=9 5<,> :> :33 <:;=9

272 273

Similar to salinity, an energy balance was used to estimate changes in the surface

274

temperature (

(( ).

Since volume and pressure were assumed to be constant, the system’s

10

275

energy will vary only depending on the enthalpy of the flows (equation 7). Under constant

276

volume conditions, enthalpy depends on the water heat capacity and the difference between

277

the system’s temperature and a reference point. By assuming that surface temperature ( )

278

is a reference for enthalpy and that the density and heat capacity of all currents are

279

approximately the same, the expression for determining temperature variation is presented

280

in equation (8.a). Finally, under steady state conditions, the temperature of the surface

281

control volume is determined by equation (8).

282 283

(7)

284

(8.a)

285

(8)

?

=

@ ((

4

'

+ 09

5

033

−

=@

(:;9 <:=9 )B9 CD9

A=@

+

2 2

:> B> CD>

B33 CD33

:33 B33 CD33

A(

A(

−

2

(( 4 ((

−

2

−

2)

+

)−4

+

'

+

'

5

((

(( 5( ((

−

)

2

286 287

Water uses

288

Last, the parameters of the discharge flow depend on the use of both cold and warm water;

289

here we assumed that DOW can be used simultaneously for OTEC and SWAC, however,

290

this assumption and the parameter’s values will depend on the specific case under study.

291

Additionally, DOW is not used to directly supply in the cooling district or the electricity

292

production; instead it can be used to feed a cooling station to cold down a second fluid that

293

would latter supply the cooling district, and to operate the thermal cycle for electricity

294

production. Since the details about the DOW uses are not in the scope of this paper, we

295

assume that the two extracted currents are assumed to mix into one discharge flow after

296

utilization (equation 9); however, a detailed modelling of an application case should

297

consider separated flows, and separated properties for discharges.

298

Both cold and warm currents could be used for other applications; therefore, return factors

299

were included (

300

respectively, to be discharged back into the ocean. Since the use of warm water is only

301

being considered for OTEC, this flow is assumed as a dependent variable of the cold water,

(

and

(( )

to indicate the amounts of cold water and warm water,

11

302

according to the

303

in equation (10). Finally, the salinity of the discharge (

304

to be returned (equation 11).

design parameter which is typically between 1.5–2 [30], as represented

305 306

(9)

2

307

(10)

((

308

(11)

2

=

=

=

(

E

:>

(

+

((

2)

will depend on the two fractions

((

(

(

(

(

+

(( (( )

((

309 310

The cold DOW water return temperature (

311

higher than the intake temperature (usually about 5°C); and the salinity of the deep currents

312

( , ) is also assumed to be the same, since neither SWAC nor OTEC affect the salinity of

313

the cold current. The temperature of the warm current is expected to be lower than the

314

ocean temperature after it is used for OTEC. Therefore, after a steady state energy balance,

315

the temperature of the discharge current can be calculated as shown in equation (12).

316 317

(12)

2

G

:

B33 CD33

= @ 33 :33B

> > CD>

A4

(,F )

((,F

−

is assumed to be between 12–15 °C [17],

(,F 5

+

(,F

318 319

We used Nihous’ expression (equation 13) to estimate OTEC potential [30]. This equation

320

calculates net OTEC power through

321

((

−

, the ocean temperature gradient (Δ =

(,

), the efficiency of the generator (

), deep water pumping losses, and pipeline

322

losses. These last two depend on the design temperature gradient (Δ

323

real gradient. In this study, we used fixed values of

324

more detailed optimization model could include

325

specific conditions. Additionally, the chosen OTEC configuration (land-based or floating

326

plant, unified or separate discharge) will affect the net power potential, depending on the

327

height to be overcome by the pumps. Thus, in a real application these elements should be

328

considered in the potential optimization.

and

), rather than the

reported in [30]; however, a

as a parameter to find, considering site-

329 12

330 331 332

=

(13)

:H3 B I JKL OP N Δ Q M033 Q(ERP)

− 0.18Δ

Q

P Q.WX

− 0.12 @ A Q

Δ

Q

Y

Additional constraints

333

As mentioned before, in this study, we defined DOW potential as the maximum cold DOW

334

flow (

335

identified, as well as their temperatures and salinities, cold water flow can be calculated

336

using the previous equations, while accounting for the following constraints.

337

First, the magnitude of the remaining currents after both warm and cold water extraction

338

should be greater or equal to the minimum currents that the system can support. The

339

remaining current was calculated as a ratio between the remaining outflows and the

340

were

()

that can be extracted from the ocean. If deep and surface currents have been

respective cross-sectional area. To simplify this, the dimensions of Δ

and Δ

341

assumed to be equal, therefore, only Δ and the height of the volume were used to calculate

342

the area. Since data reports minimum currents in two directions (x and y), the minimum

343

total current can be estimated as the magnitude of the resulting vector, as shown in the right

344

side of equations (14) and (15).

345 :;=-

≥^

' ,1



:;=9

≥^

' ,1



346

(14)

Z[- \-

347

(15)

Z[9 \_

348 349

Q

+

,1

Q

+

,1

Q

Q

Second, the variations in temperature and salinity of the surface control volume should be

350

lower than the natural, historical variations (Δ

351

assuming that these are the maximum changes that the ecosystems can support.

352 353

(16)

354

(17)

| |

(( ((

−

−

and Δ

in equations 16 and 17),

|≤Δ

|≤Δ

355 13

356

3.2 Estimation methodology

357

Figure 2 presents the flow diagram for the proposed methodology of the DOW potential

358

estimation. This methodology starts by first identifying a city that has market potential and

359

the necessary technical conditions such as: high energy and air conditioning consumption,

360

an acceptable level of energy prices, its location and distance must have access to a DOW

361

source, and it must have a steep bathymetry. We performed steps 1 through 8 for each

362

selected city, as explained below.

363

364 365

Figure 2 – Methodology for DOW potential estimation

14

366 367

First, based on information about the temperature profile, we identified the depth at which

368

the desired temperature (~ 5°C) is reached, which is typically around 1,000 m. Then, with

369

the bathymetric profiles, we selected the coordinates for cold water intake, in order to reach

370

the desired temperature at a distance that was close to the shoreline, both for the warm

371

water intake and discharge. In order to keep the intake and discharge at an allowable

372

distance, our recommendation is to check if there are protected and vulnerable areas or

373

activities prohibitions.

374

In the second step, we used the available historical information on temperature, salinity and

375

ocean currents for both the surface and deep points. According to the available data, we

376

selected the time resolution for the analysis was defined in order to capture seasonal

377

variations from throughout the year, as this can affect the availability of cold water. We

378

performed a monthly analysis for this study, followed by tests on the sensitivity of results

379

with daily variations; however, this time resolution will be affected by the availability of

380

data.

381

In the third step, for each timespan of the analysis, we selected the constraint parameters for

382

the estimation of the DOW flow. We identified ocean currents for both surface and deep

383

control volumes. With these currents and the control volume parameters, we defined the

384

inflows in the system (

385 386

,1

,

' ,1

,

,1

'b , ).

b,

'

,

) and minimum historical currents (

' ,1

,

We used historical data to identify average temperature and

salinity as well as the maximum deviations from these averages that the system had

387

supported in the past (Δ

and Δ

388

The discharge parameters in step four depend on the uses of both DOW and warm water. In

389

this study, we used the parameters mentioned in the previous section, assuming two

390

applications for them: SWAC and OTEC. In step five, the dimensions of the control

391

volumes must be defined before performing a potential estimation. Here we recommend

392

selecting the maximum values based on the mixed layer height, the distance to the shore,

393

and the distance to protected areas.

).

15

394

The model described in the previous section has 13 unknown variables to estimate and 16

395

equations (12 steady state balances and four constraints). Therefore, we used an

396

optimization method in step six to solve the nonlinear problem: Maximize

397

equations (1) through (12) (excluding 6.a and 8.a), and constraints (14) to (17). We

398

performed The optimization for each timespan selected; therefore, the maximum potential

399

will vary throughout the year (e.g., monthly), according to seasonality, and we estimated

400

The OTEC potential with the output of the optimization model by using equation (13) .

401

After finding the DOW potential and its inter-annual variations, we performed a sensitivity

402

analysis on time resolution, control volume dimensions, and intake and discharge

403

parameters. If the available data allows, sensitivity to coordinates can also be tested.

404

Finally, this model also allows the dynamic behavior of the system to be tested by

405

simulating the temperature changes and salinity in the surface with dynamic equations (6.a)

406

and (8.a), and by using historically available data and estimated DOW flows as

407

perturbations to the system. This analysis helps observe whether the system can support

408

continuous DOW extraction and how the system would respond under extreme events, such

409

as zero currents, cold currents, or a sudden loss in demand, etc.

(

subject to

410 411

3.3 Reference Case and Sensitivity Analysis

412

Accounting for the parameters in Table 1, we established a generic reference case, with

413

typical annual average values in the Caribbean, in order to test the robustness of the model

414

and to identify its most sensitive parameters. We performed the nonlinear optimization of

415

the model developed in the previous section using the interior-point method with the

416

“fmincon” default function in Matlab 2014b.

417

16

418

Table 1 – Reference parameters for DOW potential estimation

Parameter Deep water parameters Influence area (Δ Δ ) Influence height (ℎ ) Total average inflows ( ' +

)

Total minimum historical current c^

Salinity ( ) Temperature ( ) Surface water parameters Influence area (Δ Δ ) Mixed layer height (ℎ1 ) Total average inflows 4 ' +



5

Total minimum historical current c^

419

' ,1

Salinity ( ) Temperature ( ) Salinity variation (Δ ) Temperature variation (Δ ) Water use parameters Warm water return fraction ( (( ) Temperature of cold water return ( DOW return fraction ( ( )

' ,1

(,F )



Q

Q

+

+

,1

,1

Q

Q

d

d

Units

Reference Value

Ha m m3/s m/s

1 100 400 0.009

g/l °C

34.8 5

Ha m m3/s

1 40 960

m/s

0.03

kg/m3 °C kg/m3 °C

35.75 28 0.4 0.8

°C

1 12 1

420

Table 2 shows the results for the reference case with a DOW extraction potential of 41.5

421

m3/s. Such potential could supply a cooling SWAC district of 280 kton of refrigeration, and

422

an OTEC plant of 18 MW. In this case, the remaining ocean currents, both surface and

423

deep, are higher than the restriction values, which indicates that water availability is not a

424

limitation. Similarly, the salinity of the surface remains within allowed limits, indicating

425

that the changes in salinity are not a limitation. The dominant constraint, in this case, is the

426

variation in temperature, since the discharge temperature is lower than the ocean’s surface

427

temperature. Under a steady state operation, the temperature of the surface control volume

428

would decrease from 28°C to 27.2°C, reaching the minimum allowed temperature. If the

17

429

DOW flow were to increase to over 41.5 m3/s, then the discharge flow would also increase,

430

and the surface temperature would decrease below natural limits.

431 432

Table 2 – DOW constraint results for the reference case

Variable DOW potential Remaining deep current Remaining surface current Salinity in surface control volume Temperature in surface control volume

Units m3/s m/s m/s kg/m3 °C

Value 41.5 0.03 0.25 35.71 27.2

Constraint interval ≥ 0.009 ≥0.03 [35.35 – 36.15] [27.2 – 28.8]

433 434

We tested the sensitivity of the results with different model parameters. Table 3 presents

435

the tested intervals for the parameters with the highest sensitivity and the changes observed

436

in the DOW potential of the reference case. In all the tested cases, the dominant constraint

437

was the limit in the surface temperature. The model proved to be insensitive to changes in

438

deep and surface salinity, and deep temperatures. Moreover, the results are affected by the

439

deep currents only if the velocities have a value close to zero, since relatively small currents

440

(<0.005 m/s) can still provide enough water flow, depending on the size of the control

441

volumes. On the other hand, an increase in the surface currents would allow a faster

442

diffusion of the cold discharge flow and therefore would reduce the effect on the surface

443

temperature. The variations considered in the surface currents can therefore change the

444

DOW potential to about ±70%, in comparison to the reference case.

445

The surface influence area was one of the parameters with the greatest impact on the

446

results. The surface control volume is directly proportional to the influence area; therefore,

447

if the area increases, the volume also increases, assuming the height is constant. If the

448

volume increases, the effect of the discharge on both temperature and salinity decreases,

449

since there is more water to diffuse the discharge’s cold plume. For larger areas, the DOW

450

potential therefore increases as shown in Appendix A. The selection of the influence area is

451

then crucial to identifying the feasible potential. In this study we select a minimum area of

452

1 Ha, guarantying that, in any case, the influence area will remain smaller than the spatial

453

data resolution and that it will be separated from protected areas.

18

454

Finally, the results also proved to be sensitive to the water use parameters, as shown in

455

Appendix A. As expected, if the DOW return fraction decreases, the potential will increase,

456

since the discharge flow depends on the DOW return flow. Moreover, if the discharge

457

temperature increases, the effect on the surface temperature will be smaller, and therefore,

458

more water could be extracted without exceeding the allowed temperature limits.

459 460

Table 3 – Sensitivity to parameters

Parameter

Surface water parameters Salinity Temperature Total average inflows ( ' + Influence area Mixed layer height Water use parameters DOW return fraction DOW return temperature

'

)

Units

Variation interval

Variation in DOW extraction potential m3/s %

kg/m3 °C m3/s Ha m

35.2 – 36.8 26 – 30 400 – 1600 0.01 – 25 20 – 80

41.5 37 – 46 17 – 70 4 – 207 34 – 102

(0%) (±10%) (-60% +67%) (-90% +400%) (-60% +20%)

°C

1–0 8 – 15

41.5 – 230 34 – 53

(+460%) (-18% +28%)

461 462

4. Applied cases in the Caribbean

463

This section first presents the 8-step methodology explained in the previous section with a

464

case study from the Caribbean. We selected Montego Bay in Jamaica given that it has been

465

prioritized by CAF [28]. Additional information from previous studies can also be used as

466

input to validate the methodology’s results [17]. We then applied the methodology to four

467

other prioritized cities in the Caribbean from three market potential clusters [31], and we

468

focused on the results in order to avoid repetition explaining the step-by-step process.

469

19

470

4.1 Data treatment

471 472 473 474 475 476 477 478 479 480 481 482 483

We used the temperature, salinity and current velocities time series from the highresolution Global Analysis and Forecasting System, version 3-release 1 (GPSY4V3R1), developed by Mercator Ocean and available on the Copernicus Marine Environmental Monitoring Service site [32]. This data is updated daily and has a horizontal resolution of 1/12° and 50 vertical depth levels ranging from 0 to 5,500 meters. Data is available for download upon request, with a daily and monthly resolution from 26-12-2006 to date. The application of DOW, OTEC and SWAC and the interaction with sea water column is around 100 m depth and deeper. Therefore, this database (DB) has been used in several cases around the world with high quality standard, although for application in very nearshore (less than 100 m depth). The model has some limitations, however after this depth the DB it has a good performance (see e.g. [33–35]). Given that this is the best DB available we consider that the quality of data is good enough for our purpose. However, results could be improved with primary data from monitoring and measuring programs.

484

We cross-checked Data from Mercator Ocean GPSY4V3R1 with the General Bathymetric

485

Charts of the Oceans (GEBCO-2014) embedded in the NOAA Bathymetric Data Viewer

486

[36]. This helped identify the coordinates and distance to the shoreline at which the desired

487

temperatures are reached. With this information, we identified the coordinates for water

488

intake and discharge. Additionally, we verified the distance of both intake and discharge

489

flows to protected areas or vulnerable ecosystems with the Caribbean Marine Protected

490

Areas database [37], the World Commission on Protected Areas database [38] and the

491

Google Earth Ocean Inventory.

492 493

4.2 Montego Bay

494

Figure 3 shows the average temperature profile of the sea around Montego Bay. From this,

495

we identified that the depth for water intake should be about 1,000 m, where the

496

temperature reaches 5°C. The figure shows that the mixed layer height varies between 20 –

497

80 m during the year; therefore, the warm water intake should be located in the first 20 m to

498

guarantee stability for the temperature and the salinity. The velocity profiles in Figure 4

499

show that ocean currents reach stable values at about 20 m deep; which is why we selected

500

20 m as the intake depth. We used the bathymetry charts from GEBCO to identify the 20

501

coordinates of the cold water intake (77°55'8''W; 18°35'56''N) and the warm water intake

502

and discharge (77°54'25''W; 18°31'33''N), as shown in Figure 5. We also verified that the

503

intake and discharge coordinates meet the restrictions of the protected area, the Montego

504

Bay Marine Park and Fishing Sanctuary.

505 506

(a)

507 508 509 510

(b)

Figure 3 –Temperature profile around Montego Bay (a) Historical monthly profiles for 2007 – 2017 (b) Monthly average profiles+5

Data: Mercator Ocean GPSY4V3R1 [31]

511

512 5

The average temperature for a month m, in a depth of z was calculated using the data from 2007 to 2017,

reported in the MERCATOR database as:

eee( ! f) =

∑2017 2007

!, hi$ (f)

2017−2007

, where

temperature reported by the MERCATOR database in the month m, in a given year

!, hi$ (f)

is the monthly

21

Figure 4 – Monthly average profiles of total currents in Montego Bay+6

513 514

Data: Mercator Ocean GPSY4V3R1 [31]

515

516 517 518

Figure 5 – Selection of intake and discharge coordinates for Montego Bay

Data: GEBCO-14, [34] and Google Earth Ocean Inventory

519 520

Figure 6 shows the input information for estimating the potential in Montego Bay. We

521

used the daily historical values of temperature, salinity and current velocities reported in

522

MERCATOR. Given that we performed a monthly analysis, we calculated the average,

523

maximum and minimum values for each month from the daily average data. The maximum

524

and minimum currents help estimate the maximum and minimum extraction potential of

525

DOW. We used the limits in temperature and salinity variations as constraints in equations

526

(15) and (16). For example, in March, the temperature of the surface control volume can

527 528

vary between 26.5 – 27.7°C (Δ

1 g/l (Δ

= 1l/n).

= 1.2° ), the salinity can vary between 35.5 – 36.5 g/l

529

6

Mercator Ocean database reports the monthly eastward and northward velocities in a depth of z.

The average in a month m for each direction was calculated as: & eeeeee(f) = ',1

eeeeee(f) & ,1 =

∑stuv sttv 2=,_,=opq (r) QwEWRQwwW

Q eeeeeeeeee eeeeeeeeeeQ ^& ',1 (f) + & ,1 (f) .

.

∑stuv sttv 2;,_,=opq (r) QwEWRQwwW

,

Then, the total current for a month was calculated as eeee(f) &1 =

22

530 531 532

Figure 6 – Input data for DOW potential estimation in Montego Bay

Data: Mercator Ocean GPSY4V3R1 [31]

533 534

Figure 7 shows the results of the DOW potential estimation for Montego Bay. We found

535

that its potential has high interannual variability. From December to March Montego Bay

536

has an average extraction potential of about 80 – 100 m3/s; however, the high variability in

537

currents and surface temperature during these months could increase its potential to up to

538

200 m3/s, or reduce it to 21 m3/s. In contrast, the extraction potential between April and 23

539

November is 15-40m3/s, but its variation interval is narrower since temperature and

540

currents are more stable during these months. As was determined by the sensitivity analysis

541

in section 2, the main limitation, in this case, is the restriction on maximum allowed

542

temperature variations; for each month, the temperature of the surface control volume

543

reaches the minimum allowed temperature, while salinity remains almost unaltered (see

544

Figure 8). From April to November, the mixed layer reaches its lowest values. The

545

potential during these months could increase if the discharge was located in colder waters,

546

i.e. below the mixed layer.

547

548 549

Figure 7 – Montego Bay DOW and OTEC potential

550

551 552

Figure 8 – Temperature and salinity of surface volume in steady-state operation

24

553 554

Finally, we used the average values to estimate the monthly availability of DOW and

555

OTEC. From Figure 7, we calculated a total annual average potential of 48 m3/s, which can

556

supply a 21 MW OTEC plant and a 326 kton SWAC cooling district. This SWAC potential

557

could supply the entire city since the air conditioning demand today is estimated at about

558

7.4 ktons [28]. Accounting for monthly variations, estimations for monthly availability are

559

shown in Figure 9. This availability indicates that in October and November the Ecopark

560

should reduce the DOW extraction flow to below 15 m3/s to reduce environmental effects,

561

which in turn will reduce maximum OTEC and SWAC power to 7 MW and 88 ktons,

562

respectively. In contrast, during months such as January and August, the Ecopark could

563

increase the flow up to 50 m3/s without affecting the ocean’s natural conditions. This

564

resource availability constitutes a design parameter to consider in the planning of the

565

Ecopark operations, and it is also comparable with the capacity factor for electric plants.

566

Additionally, it is an indicator of the environmental restrictions that are a necessary part of

567

renewable energy planning [19].

568

569 570

Figure 9 – Resource availability for Montego Bay

571 572

The resource availabilities for DOW and OTEC are similar; however, they differ in some

573

months given the differences in temperature gradients. For example, in July, the DOW 25

574

extraction system could only operate at 60% of its average capacity given the limitations in

575

the ocean’s currents, but the OTEC plant could operate at 72% of its capacity because the

576

thermal gradient is higher in this month than the annual average.

577

We performed dynamic simulations for temperature and salinity with equations (6.a) and

578

(8.a) using ocean data with a daily resolution for a typical year. We assumed an annual

579

average design DOW flow, and limiting the extraction with the monthly availability, in

580

order to evaluate if the system can tolerate a continuous operation. We found that the

581

temperature and salinity will remain between the allowed limits in this case; however, these

582

simulations should be performed with greater detail in real life applications, considering the

583

effect of continuous alterations in nutrients concentration and the ecosystem.

584 585

4.3 Other cities in the Caribbean

586

Table 4 presents the results of DOW potential estimation for five cities in the Caribbean.

587

The cities with the largest market potential [31] (Montego Bay, Puerto Plata, and San

588

Andres) were found to have lower ocean potential compared to other cities, enough for

589

OTEC capacities of between 15 – 20 MW. Resource availability for Puerto Plata and San

590

Andres showed to have lower variability than Montego Bay, with minimum availabilities of

591

about 47%. These results on average potential are consistent with earlier studies [16,17]. As

592

a complement to these studies, extractable water flow was found to be variable throughout

593

the year; this information on monthly resource availability is new and will contribute to

594

future DOW projects in these islands.

595

Barbados, located in the low market potential cluster, has an extraction potential larger than

596

Montego Bay, Puerto Plata, and San Andres, but it has the largest variability of all the cities

597

evaluated. This variability does not pose a limitation for SWAC; however, it is a crucial

598

issue to the evaluation of economic feasibility for OTEC since a 19MW plant would have

599

to operate at less than 50% of its capacity for five months a year.

600

Willemstad, located in the medium market potential cluster, proved to have the largest

601

extraction potential, more than double the average of other islands. Although it has the

26

602

lowest availability of all the cities (15% during October), this minimum value could supply

603

air conditioning for the entire island and produce 10 MW of OTEC power.

27

604 Average potential DOW OTEC SWAC (m3/s) (MW) (kton)

Table 4 – DOW extraction potential and monthly availability in the Caribbean Monthly DOW availability (OTEC in parenthesis) Jan

Feb

49.0

19.3

334

73% (74%)

152% (145%)

47.8

20.5

326

217% (203%)

209% (190%)

41.2

14.8

281.2

159% (149%)

120% (108%)

45.0

18.8

307

200% (186%)

118% (113%)

128

48

878

198% (186%)

176% (165%)

Mar

Apr

May

Jun

Jul

Bridgetown – Barbados 331% 225% 133% 67% 49% (307%) (218%) (136%) (70%) (53%) Montego Bay – Jamaica 216% 55% 43% 41% 60% (196%) (54%) (46%) (47%) (72%) Puerto Plata – The Dominican Republic 238% 76% 71% 87% 63% (201%) (69%) (69%) (91%) (68%) San Andres – Colombia 227% 63% 65% 48% 71% (210%) (63%) (72%) (52%) (75%) Willemstad – Curacao 196% 88% 72% 115% 129% (181%) (86%) (74%) (117%) (130%)

Aug

Sep

Oct

Nov

Dec

37% (43%)

26% (32%)

28% (35%)

34% (40%)

44% (48%)

39% (48%)

31% (39%)

27% (34%)

87% (97%)

174% (174%)

60% (69%)

47% (56%)

68% (86%)

89% (104%)

122% (128%)

72% (80%)

59% (67%)

48% (56%)

86% (92%)

141% (136%)

52% (60%)

26% (33%)

15% (19%)

31% (38%)

102% (110%)

605 606

28

607

Previous studies about thermal potential in the Caribbean suggested there was a theoretical

608

potential of about 5 TW [25], with the temperature gradient considered as the main input.

609

We developed a methodology to include other components, such as water availability and

610

minimum environmental constraints in temperature, salinity and influence area, and with

611

alterations in temperature as the dominant constraint. Studies about practical potential for

612

other forms of renewable energy highlight that instead of this potential being considered as

613

constant parameter, it should be considered as a value that varies with site-specific

614

environmental conditions [19]. Consistent with this, this study found that practical DOW

615

potential may differ between cities in the Caribbean and that its interannual variability is

616

significant.

617

The five cities evaluated here demonstrated having a total potential of 300 m3/s, equivalent

618

to 2,000 kton of SWAC and 120 MW of OTEC. From December to March, extraction

619

flows can reach about 170% of the average flow, only minorly affecting temperature and

620

salinity. This availability decreases to 80% from April to July and falls below 50% from

621

August to November. Even in months with the lower availability, SWAC systems could

622

supply more than 100% of the air conditioning demand in each city. The 120 MW of OTEC

623

can supply more than 1,000 GWh of energy per year, enough to meet about 60% of the

624

annual demand in these five cities. Except for Willemstad, which proved to have a higher

625

potential, these results are consistent with the recommended order-of-magnitude of OTEC

626

plants for small islands, about 20 MW [24,27].

627 628

5. Discussion and Conclusions

629

DOW technologies are still in the preliminary stages of developing their technology; one of

630

the main limitations to reaching commercial stages is the lack of information about the

631

realistic DOW potential of the ocean [7]. Most studies have focused only on theoretical

632

OTEC potential as the maximum energy that can be extracted from the thermal gradient

633

between deep and surface ocean water. This paper develops a general methodology for

634

estimating practical DOW potential as the maximum water flow that can be extracted,

635

accounting for constraints in the influence area, available currents, and in variations in

636

temperature and salinity. We developed a model for an Ecopark operating with SWAC and 29

637

OTEC. The resulting model has the flexibility to include other DOW uses, such as seawater

638

greenhouses and mariculture, as well as account for site-specific environmental constraints.

639

The model developed here proved to be insensitive to changes in deep and surface salinity

640

and in deep temperatures; the variation in surface temperature was found to be the

641

dominant constraint. The DOW extraction potential is inverse to the difference between the

642

discharge temperature and surface temperature.

643

The methodology developed in this study is the first approach to a thanks model for

644

estimating DOW potential. It constitutes a starting point and a guide to future work in this

645

field. However, it has a number of assumptions that must be addressed before using it in

646

real applications. First, changes in density assumed here cannot be neglected because it is

647

determinant in the discharge flume evolution. Second, the water discharge should be

648

managed in a different scheme, and a third influence volume between 100-200m should be

649

considered, instead of assuming a discharge in the surface. Third, due to data limitations we

650

excluded the vertical inflows and outflows that could affect the influence volumes and thus

651

modify the extraction potential. Finally, it is necessary to consider the changes in nutrient’s

652

concentration and its potential effect in primary production. The potential values found in

653

this study may be underestimated given these assumptions; thus, these values should be

654

considered as minimum reference values, rather than realistic ones.

655

Future and ongoing DOW projects and studies should pay special attention to temperature

656

alterations. For example, in order to improve potential estimations, future work should

657

consider conducting a spatial simulation of the discharge plume and evaluating optimal

658

discharge depth to maximize the extraction potential. For instance, if the cold discharge is

659

located below the mixed layer, the impact on the ocean’s natural conditions could be lower,

660

which would allow for a larger DOW extraction.

661

We applied this methodology to five cities in the Caribbean: Bridgetown (Barbados),

662

Montego Bay (Jamaica), Puerto Plata (The Dominican Republic), San Andres (Colombia)

663

and Willemstad (Curacao). Although the practical potential for OTEC was found to be low

664

compared to the Caribbean’s theoretical potential (about 5 TW) [25], it could provide about

665

60% of the demand for electricity in each city; however, our estimations may be

666

underestimated given the mentioned assumptions. In addition, the potential for SWAC 30

667

could supply 100% of the air conditioning demand, not only for one city but for all the five

668

islands.

669

These average values and the monthly availability of DOW potential constitute new

670

valuable information for the financial and technical evaluations of DOW projects in the

671

Caribbean. Moreover, the information on minimum currents, temperature and salinity limits

672

is critical to evaluating environmental impacts and to designing a proper operation of

673

Ecoparks under extreme events. These results contribute to reducing the gap between ocean

674

energy and other renewable energy since estimations of practical potential as well as

675

reliability indicators are necessary parts of achieving mature technology [6,7].

676

The main concerns of DOW uses are related to its environmental impacts [39,40], which

677

have also been one of the main potential limitations for other renewable energies. For

678

industrial-scale OTEC and SWAC, the main impacts are related to nutrients and thermal

679

pollution caused by water exchange, hydrodynamic alterations, and fish impingement and

680

entrainment [41]. The constraints considered in this study address the first two impacts by

681

limiting the variations of temperature and salinity, and by limiting water extraction to the

682

minimum ocean currents supported by the system. However, additional site-specific

683

environmental studies are a necessary complement to this study. For example, equations

684

(14) to (17) could be expanded to include site-specific constraints. Future work should also

685

expand this model to include cumulative effects on ecosystems, since high and permanent

686

perturbations in salinity, temperature or nutrients can damage the surface ecosystem, or

687

introduce new species (e. g. algae contamination) [42,43].

688 689

Acknowledgments

690

This study was financed by the Colombian Administrative Department of Science,

691

Technology and Innovation: Colciencias Doctoral Scholarship (grant 647, 2015). The

692

authors thank the Copernicus Marine Environment Monitoring Service (CMEMS) for

693

providing access to the ocean data, as well as their Service Desk for the technical support in

694

the use of their databases. The authors thank the anonymous reviewers for their valuable

31

695

contributions to improve the manuscript. The opinions expressed in this study are the sole

696

responsibility of the authors.

697

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Highlights • • • • •

Deep Ocean Water (DOW) can contribute to sustainability in the Caribbean There is a large theoretical potential, but the practical potential is unknown We estimated the practical DOW potential for five Caribbean cities DOW can supply 100% of the air conditioning demand in a city DOW can supply up to 60% of the electricity demand in a city

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: