Salinity Gradient Energy at River Mouths - ACS Publications

Letter pubs.acs.org/journal/estlcu

Salinity Gradient Energy at River Mouths Oscar Alvarez-Silva,*,† Christian Winter,‡ and Andres F. Osorio† †

OCEANICOS-Research Group in Oceanography and Coastal Engineering, Universidad Nacional de Colombia, Carrera 80 # 65-223, 050041 Medellín, Colombia ‡ MARUM-Center for Marine Environmental Sciences, University of Bremen, Leobener Strasse, 28359 Bremen, Germany ABSTRACT: River mouths are potentially abundant locations for the exploitation of the clean and renewable salinity gradient energy (SGE) as here perpetually fresh water mixes with saline seawater. However, the practical yield of SGE depends on the spatiotemporal variability of the salinity structure. Here we show this relationship for exemplary river mouths. Depending on characteristics of the salinity structure, SGE resources can be reduced to only 0.2% of the theoretical potential. We derive a descriptor for a quick general assessment of the site specific potential and propose a classification of river mouths according to their suitability for SGE generation. It is shown that the tidal range is the most limiting factor for the harnessing of SGE at river mouths. Systems with a tidal range greater than 1.2 m seem not to be suitable locations.

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introduced concept of a site specific potential (SSP)12,13 and show how the theoretical SGE resources in river mouths are reduced to a practical yield depending on the local salinity structure of river mouths and energy losses.

INTRODUCTION Salinity gradient energy (SGE) can be gained from the controlled mixing of two solutions with different salt concentrations, taking advantage of the chemical potential difference.1 Two technologies for harvesting SGE are in latter stages of development: pressure-retarded osmosis (PRO)2 and reverse electrodialysis (RED).3 Additionally, capacitive mixing (CapMix) is another emerging technology that has recently developed quickly.4 River mouths (estuaries and deltas) are manifest locations for SGE exploitation with a global availability of adjacent water resources of different salt concentrations. Most recent assessments of the maximal theoretical power potential of river mouths systems range from 1.724 to 3.158 TW (equivalent to 15102 and 27664 TWh per year, respectively),5,6 which is on the same order of magnitude as worldwide electricity consumption in 2011 of 20407 TWh.7 Available global, regional, and local estimates are based on average salinity differences between the fresh water of rivers and the nearby ocean;5,6,8−10 however, for more realistic estimations of the potential, the site specific spatiotemporal variability of the salinity in river mouths must be taken into account.11−13 River mouths with extensive salt and fresh water mixing zones must be discarded because larger distances between the intake points of diluted and concentrated solutions imply greater energy losses for the transport of water toward the power plants.6 Extensive mixing zones occur in weakly stratified to well-mixed river mouths, associated with moderate to strong tidal forcing and weak to moderate river discharge.14 On the other hand, narrow mixing zones occur in strongly stratified and salt−wedge river mouths, associated with weak to moderate tidal forcing and moderate to large river discharge.14 The salinity gradients may also change temporally as the mixing zone migrates on seasonal time scales because of the variability of the river discharge.15 Here we further develop the recently © 2014 American Chemical Society

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METHODS The necessity of a site specific potential analysis taking into account environmental forcing at river mouths where SGE projects are proposed was first discussed by Ortega et al.12 and later defined as the theoretical net energy density (energy per unit volume of the diluted solution) considering the temporal variability of the salinity at the intake locations of diluted and concentrated solutions.13 As mentioned before, the most important effect of the salinity structure’s behavior at river mouths in terms of SGE harnessing, apart from the variability of the theoretical potential, is the relation between the extension of the brackish zone and the energy losses. Accordingly, the concept of SSP is extended here to the net energy density considering the temporal variability of the salinity and the energy losses caused by the transport of water toward the power plant. It can be expressed as SSP(L , t ) = G(L , t ) − H(L)

(1)

where G (joules per cubic meter) is the theoretical SGE potential or Gibbs free energy of mixing per unit volume, H (joules per cubic meter) is the longitudinal energy losses for water transport, L (meters) is the distance between intake points of diluted and concentrated solutions [Pd and Pc, respectively (Figure 1)], and t is the temporal variability of the Received: Revised: Accepted: Published: 410

August 1, 2014 August 29, 2014 September 2, 2014 September 3, 2014 dx.doi.org/10.1021/ez500239n | Environ. Sci. Technol. Lett. 2014, 1, 410−415

Environmental Science & Technology Letters

Letter

river discharge scenarios averaged over a neap-spring tidal cycle are known: Chesapeake (United States),17 Huangmaohai (China), 24 Magdalena (Colombia), 13 Pamlico (United States),25 Pearl (China),18,19 Sepik (Papua New Guinea),26 and Weser (Germany). Temperature structures were used where there are known and average values otherwise. The relation between SSP and the theoretical SGE potential may be quantified with a dimensionless energy potential number

Figure 1. Longitudinal transect of a river mouth system. Dashed lines represent the isohalines. The figure shows the intake points of diluted and concentrated water (Pd and Pc, respectively), the distance L between them, and the location of L = 0. Pd is located close to the surface and Pc close to the bottom to maximize the difference in salinity between solutions.

E = SSPmax /Gmax

in which SSPmax (joules per cubic meter) is the average of the maximal SSP for high- and low-river discharge scenarios: SSPmax = [SSPmax (thd) + SSPmax (tld)]/2

(2)

where c and d indicate the concentrated and diluted solutions, respectively, and b indicates the brackish solution after mixing. For ideal dilute solutions, the Gibbs free energy (Gi) of each electrolyte solution (i = c, d, or b) is given by Gi = Tm i i R[x i ln(x i) + yi ln(yi )]

(3)

where Ti (kelvin) is the absolute temperature of each solution, mi is the total number of moles per cubic meter, R is the universal gas constant (8.314 J mol−1 K−1), and x and y are the molar fractions of ions (Na+ and Cl−) and water, respectively. Meanwhile, the energy losses are calculated from the energy conservation equation in pipes22 as

H = 8fQ 2ρL /(π 2D5)

(4)

for a unitary flow Q = 1 m /s, density ρ = 1000 kg/m for both solutions, friction factor f is estimated with the Colebrook− White equation using a roughness height of 3.5 × 10−5 m (characteristic of the pipes used in desalination plants23), and pipe diameter D = 0.71 m (28 in.) optimized to minimize the friction factor. In river mouths with a mixing zone of fresh water and seawater, the usable salinity difference of the solutions depends on where along the estuary the water intake points Pd and Pc can be located (Figure 1). According to eq 1, the optimal distance between intake points (L) is a trade-off between the maximal expected salinity difference and thus the theoretical potential G and energy losses H. An optimal location for L = 0 in stratified estuaries is the point at which the time-averaged vertical salinity difference ΔS z (grams per liter) is maximal (Figure 1), as at zero longitudinal distance, the average salinity difference between the surface and the bottom is maximal (and hence the theoretical energy potential), with minimal energy losses. The salinity structure of river mouths can be highly variable on seasonal time scales depending on the river discharge;15,16 the energy potential of two extreme steady states is considered to represent the temporal variability of the salinity structure: the high- and low-river discharge scenarios (thd and tld, respectively) (usually associated with dry and wet seasons17−19 or winter and summer20,21). Then the timeaveraged vertical salinity difference is defined as 3

ΔSz(x) = [ΔSz(x , thd) + ΔSz(x , tld)]/2

(7)

where SSPmax(t) = max{SSP(L,t)}L and Gmax (2.55 MJ/m3) is the maximal theoretical energy density of the ocean, calculated assuming the salinity of the concentrated solution is the maximum for the ocean (0.72 mol/L = 42 g/L),27 the salinity of the diluted solution is the average for the rivers (0.0022 mol/ L = 0.13 g/L),28 the volumetric ratio is 1:1, and the temperature of both solutions is the maximum of the ocean (40 °C).27 The spatiotemporal variability of SSP depends on the characteristics of the stratification of river mouths, and this in turn depends on the physical forcings acting on the river mouths. Estuarine stratification characteristics commonly are quantified by descriptors like the Richardson number,32 the Canter−Cremers number,32 the Ippen−Harleman number,33 or the stratification level number,33 among others. As these require detailed information about river mouth density structure and turbulent quantities, we here introduce a simple dimensionless stratification number for which input data for several other systems are accessible, to relate the dimensionless energy potential E with the degree of stratification:

salinity structure represented by temporal scenarios as explained below. G is expressed as8 G = Gc + Gd − G b

(6)

3

M = Q̅ h ̅ /(ΔQ̅ A̅ )

(8)

where Q̅ (cubic meters per second) is the mean discharge of the river, h̅ (meters) is the mean depth of the river mouth, ΔQ̅ (cubic meters per second) is the difference between the monthly maximal discharge (Q̅ max) and the monthly minimal discharge (Q̅ min), and A̅ (meters) is the mean tidal range. Greater values in the numerator imply stronger stratification,16 while greater values in the denominator imply higher variability of the mixing zone (with greater ΔQ̅ ) or weaker stratification (with greater A̅ ).

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RESULTS AND DISCUSSION The site specific potential of all the studied river mouth systems is higher during the high-river discharge scenario, and different ranges of variability are observed (Figure 2): the Magdalena system features the highest SSP values (up to 2.06 MJ/m3) with low temporal variability, while the Weser system presents the lower SSP (up to 0.01 MJ/m3) also with low variability. The other systems range between these extremes. A higher variability of SSP is related to the higher variability of the salinity structure. This is the case for the Chesapeake, Huangmaohai, and Pamlico systems that change from stratified or partially mixed conditions during high river discharge to partially mixed or well-mixed conditions during low river discharge.17,24,25 In terms of the spatial behavior of SSP, all systems show maximal values for L < 2000 m. When comparing SSP with theoretical SGE potential using the energy potential

(5)

The SSP here is estimated for seven exemplary river mouths for which the longitudinal salinity structures for high- and low411

dx.doi.org/10.1021/ez500239n | Environ. Sci. Technol. Lett. 2014, 1, 410−415


Letter

Figure 2. Site specific potential as a function of the distance between the intake points of diluted and concentrated solutions for high-river discharge () and low-river discharge (---) conditions. Negative values are not plotted. Gmax is shown. Figure 3. Sigmoid function relating stratification number and energy potential number in river mouths. Black dots represent the seven exemplary studied systems used for the fitting. Dashed lines show the confidence interval with a significance level of 95%. Gray dots are estimations for 20 river mouths. Green, orange, and red areas show the intervals of suitable, partially suitable, and nonsuitable systems for SGE exploitation, respectively. The standard error50 of the fit is 0.060.

number E, we found reductions in the practical yield of up to 99.8% (Table 1). Observed stronger and more stable salinity stratification in the river mouths (i.e., higher M values) results in a higher SSP (Table 1). For the seven river mouth systems, a significant dependency between M and E can be identified. The sigmoid function: E = Emax /[1 + e

−a(M − b)

]

(M < 4.5), like Pearl and Weser, where there is low SSP under both flow conditions. Interestingly, the river discharge is not the main influencing factor of SGE suitability; rivers with mean discharge from tens of cubic meters per second to tens of thousands can be found in all categories. The same applies for the average depth, where similar values can be found for all categories. However, all river mouths that are classified as suitable and partially suitable are microtidal systems, with mean tidal ranges A̅ ≤ 1.1 m. Other river mouths like those of the Delaware, Cape Fear, and Godavari rivers, with mean tidal range A̅ ≥ 1.3 m, are classified as nonsuitable systems. We thus conclude that the tide is the most restrictive driving force in terms of suitability of SGE exploitation in river mouths and that a threshold in the mean tidal range around 1.2 m may be suggested as a limit beyond which harnessing this renewable energy may not be suitable. It has to be mentioned that deep river mouth systems with less impact of tidal mixing, e.g., fjords, are an exception to this conclusion because here tidal mixing may not influence the stratification.33 An additional factor possibly restricting the technical feasibility of particular river mouths is the water quality, as pretreatment of the water (to reduce fouling and clogging) must be considered. Energy consumption of RED plants has been estimated to be 50 KJ/m3,5 approximately half of which corresponds to water pretreatment.51 Alternative less energy

(9)

describes the relation between both dimensionless numbers with a coefficient of correlation of 0.96, where a = 0.22 and b = 17.7 are fit parameters representing the growing rate and the inflection point of the function, respectively (Figure 3). The sake of this formulation lies in the easy application to various river mouth systems for an assessment of SSP, yet the confidence interval of the function is broad, because of the limited number of reference studies describing the spatiotemporal variability of the salinity structure of river mouths with the required resolution (averaged structure over a spring-neap tidal cycle under high- and low-river flow conditions). As more studies are conducted and included in the fit, the confidence interval will be narrower. The function was used to predict the average maximal SSP for 20 systems worldwide, where relevant parameters could be obtained from the literature (Table 2). These river mouth systems may be classified according to the technical suitability of SGE exploitation into “suitable systems” (M > 12), like Magdalena and Sepik, that feature high SSPs during high- and low-flow conditions; “partially suitable systems” (4.5 < M < 12), like Chesapeake, Pamlico, and Huangmaohai, where there is high to medium SSP under high-flow conditions but low potential under low-flow conditions; and “nonsuitable systems”

Table 1. Mean, Maximal, and Minimal Monthly Discharges, Mean Tidal Ranges, Mean Depths, Stratification Numbers (M), and Energy Numbers (E) for the Studied River Mouthsa

a

river mouth

Q̅ (m3/s)

Q̅ max (m3/s)

Q̅ min (m3/s)

A̅ (m)

h̅ (m)

M

E

Magdalena Sepik Chesapeake Huangmaohai Pamlico Pearl Weser

7200 3700 2262 1500 90 5150 323

10287 4700 4162 2800 400 10500 527

4068 2600 922.6 650 20 1800 172

0.5 0.8 0.46 1.34 0.15 1 3.6

11 6 6.8 10 3 7 9

25.5 13.2 10.3 5.2 4.7 4.1 2.3

0.797 0.376 0.098 0.038 0.035 0.018 0.002

Main references for data: 18−20, 25, 26, and 29−31. 412



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Table 2. Stratification Numbers and Average Maximal SSPs for 20 Representative River Mouthsa Q̅ (m3/s)

Q̅ max (m3/s)

Congo La Plata Nile Rhone Ebro Niger

42000 22000 1254 1693 424 1044

75500 22496 1741 2050 662 1424

Mississippi Brazos Po Strymon

15360 222 1511 60

57900 331 2102 122

Delaware Ems Cape Fear Gironde estuary Tweed Godavari Seine Selangor Mekong Tamar

341 86 161 1000 78 3038 450 53 14904 34

629 154 730 1800 140 11568 650 122 40000 290

river mouth

a

Q̅ min (m3/s)

A̅ (m)

Suitable Systems (M > 12) 24700 1.1 20714 1 1034 0.2 1150 0.4 135 0.2 750 0.8 Partially Suitable Systems (4.5 < M < 12) 2830 0.3 82 0.5 936 0.5 18 0.3 Nonsuitable Systems (M < 4.5) 178 1.7 34 2.3 15 1.3 400 3.3 30 3.3 87 1.5 200 5 23 2.7 2000 2.9 3 3.5

h̅ (m)

M

SSPmax (MJ/m3)

400 20 6.5 9 5 7.7

301 247 57.7 42.3 25.1 14.9

2.55 2.55 2.55 2.54 2.12 0.89

12 6 4 3

11.2 10.7 10.4 6.2

0.49 0.45 0.43 0.19

3.1 2.8 2.0 1.7 1.5 1.2 1.2 1.2 0.8 0.8

0.10 0.10 0.08 0.08 0.07 0.07 0.07 0.07 0.06 0.06

7 9 11.6 8 7 7 6 6 6.3 24

Main references for data: 21 and 34−49.

expensive antifouling techniques related to flow switching or disturbance in the energy generation devices have shown significant reductions in the level of fouling on experimental scales.52 However, this parameter still needs to be investigated further for large scale SGE power plants. For potential future implementation of large scale SGE plants in river mouths, the environmental impact must be taken into account. The extraction of large amounts of fresh water and seawater may potentially produce imbalances in the mixing and circulation patterns, water quality, ecological systems, sediment balance, and other uses of the river mouths.6,12,51 Therefore, detailed studies of the environmental flows and maximal water extraction factors for SGE purposes should be conducted to determine the exploitation thresholds that ensure ecosystem functions and the balance between energy production and environmental sustainability. Recently, it has been stated that up to 20% of the mean river discharge may still be considered tolerable;12 however, more research along this line is necessary. SGE generation does not produce harmful effluents; nevertheless, attention must be paid to how the effluent brackish water is discharged into the environment.12 Additionally, if chemicals are used for cleaning or antifouling purposes, precautions are required to prevent leakage to the environment. River mouths with valuable ecosystems or river mouths very sensitive to salinity changes might not be suitable for the harnessing of SGE from environmental and social points of view. Additional environmental considerations are discussed in ref 10. Approximately 30% of the coastal zones of the world have a mean tidal range of >1.2 m,53 including coasts with relevant river mouths like the Gulf of Alaska, Hudson Bay, North Brazil, United Kingdom, Bay of Biscay, North Sea, Norwegian Sea, Mozambique Channel, east Bay of Bengal, Yellow Sea, Timor Sea, and New Zeeland, among others. Thus, the estimations of global and regional potential conducted under the assumption

that all river mouths can be exploited for SGE generation should be re-evaluated; it will lead to smaller but more accurate quantification of the global amount of this valuable energy source.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +57 301 4253034. Fax: +574 4255103. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank COLCIENCIAS (Departamento Administrativo de Ciencia Tecnologiá e Innovación de Colombia), CEMarinCenter of Excellence in Marine Sciences, Kellner & StollFoundation for Climate and Environment, and MARUMCenter for Marine Environmental Sciences for the funding of this research. Data for the Weser River have been provided by the German Federal Waterways Engineering and Research Institute (BAW).

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NOTE ADDED AFTER ASAP PUBLICATION There was an error in the density value noted below equation 4 in the version of this article published September 5, 2014. The corrected version published September 10, 2014.

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