Theoretical power density from salinity gradients using reverse electrodialysis

Transcription

1 Available online at Energy Procedia 0 (01 ) Tecnoport EC esearc 01 Teoretical power density from salinity gradients using reverse electrodialysis David A. Vermaas a,b*, Enver Guler a,b, Micel Saakes b, Kitty Nijmeijer a a Membrane Science & Tecnology, University of Twente, MESA Institute for Nanotecnology, P.O. Box 17, 7500 AE Enscede, Te Neterlands b Wetsus, Centre of Excellence for Sustainable Water Tecnology, P.O. Box 1113, 8900 CC, Leeuwarden, Te Neterlands Abstract everse electrodialysis (ED) is a tecnology to generate power from mixing waters wit different salinity. Te net power density (i.e. power per membrane area) is determined by 1) te membrane potential, ) te omic resistance, 3) te resistance due to canging bulk concentrations, 4) te boundary layer resistance and 5) te power required to pump te feed water. Previous power density estimations often neglected te latter tree terms. Tis paper provides a set of analytical equations to estimate te net power density obtainable from ED stacks wit spacers and ED stacks wit profiled membranes. Wit te current tecnology, te obtained maximum net power density is calculated at.7 W/m. Higer power densities could be obtained by canging te cell design, in particular te membrane resistance and te cell lengt. Canging tese parameters one and two orders of magnitude respectively, te calculated net power density is close to 0 W/m. 01 Publised by by Elsevier Ltd. Ltd. Selection Selection and/or and peer-review under under responsibility of te of Centre Tecnoport for and te enewable Centre for Energy. enewable Open Energy access under CC BY-NC-ND license. Keywords: ion excange membranes; boundary layer; profiled membranes; spacers, reverse electrodialysis; salinity gradient energy 1. Introduction everse electrodialysis (ED) is a tecnology to generate electricity from te salinity difference between two solutions, e.g. seawater and river water. Te principle of ED is illustrated in Fig. 1. A ED system is composed of ion excange membranes and compartments for seawater and river water (in alternating order). Te ion excange membranes are selective for eiter cations or anions. Te salinity difference * Corresponding autor. Tel.: ; Fax: address: david.vermaas@wetsus.nl Publised by Elsevier Ltd. Selection and/or peer-review under responsibility of te Centre for enewable Energy. Open access under CC BY-NC-ND license. doi: /j.egypro

2 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) between seawater on one side and river water on te oter side of te membrane creates a potential difference. Multiple cells, eac comprising a cation excange membrane (CEM), a seawater compartment, an anion excange membrane (AEM) and a river water compartment, can be piled up to increase te voltage. Electrodes at bot ends of te pile facilitate a redox reaction, wic generates an electrical current to power an external device. Fres water Salt water e - 4- Fe(CN) 6 3- Fe(CN) 6 Na Cl - Na Cl - Na Fe(CN) 6 4- Fe(CN) 6 3- e - Figure 1. Principle of reverse electrodialysis (ED) Brackis water Te global potential for salinity gradient power is large. Eac cubic meter of river water can generate 1.4 MJ of energy wen mixed wit equal amounts of seawater, and over MJ wen mixed wit an excess of seawater [1]. Te global runoff of river water into te sea as a potential to generate more tan te prospected global electricity demand for 01 []. Moreover, te power output from ED could be controlled by regulating te water flow, especially wen a lake is available for fres water storage. As suc, salinity gradient energy can be stored and used wen te power production from sun and wind is at a low level. ecent developments improved te experimentally obtained power density (i.e. power per membrane area) for representative seawater and river water, to a maximum value of. W/m. Wen taking into account te energy spent for pumping te water, a maximum net power density of 1. W/m was found []. Te increase in practical net power output in ED to a value of 1. W/m was obtained by optimizing te intermembrane distance, imposed by spacers. Tinner spacers improve te power output, but also increase te power consumption for pumping te feed waters troug te tin compartments between te []. Te non-conductive spacers obstruct te transport of feed water and reduce te ion transport and consequently te power output. To solve tis issue, we proposed a spacer-free design tat uses profiled membranes, supplied wit straigt ion conductive ridges, to integrate te membrane and spacer functionality. Wit tese profiled membranes, te pumping losses were reduced by a factor of 4 and te absence of te non-conductive spacers reduced te omic resistance significantly [3]. On te oter and, te boundary layer resistance increased wen using profiled membranes. Neverteless, te net power density was approximately 10% iger tan wen a stack wit spacers was used [3]. A design wit profiled membranes not only increases te maximum value of te net power density, but also sifts te maximum to iger flow rates [3] and enables lower intermembrane distances. Te present work aims to estimate te optimum intermembrane distance and flow rate to reac te maximum net power density obtainable in ED, for designs wit spacers and designs wit profiled

3 17 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) membranes. Te power is estimated using teoretical equations for te produced stack voltage, stack resistance and pumping power. Previous attempts [4-6] to estimate te maximum power density did not include estimations for te boundary layer resistance. However, experiments indicate tat te maximum net power density can be found for relatively small intermembrane distances and using profiled membranes [, 3]. Under tese conditions, te boundary layer resistance cannot be neglected. Tis researc demonstrates ow te boundary layer resistance can be estimated based on te practical parameters residence time and intermembrane distance. Te remaining of tis paper will describe te individual components (electromotive force, omic resistance, boundary layer resistance and pumping power) tat are required to calculate te net power density. Te calculated boundary layer resistance is calibrated using several data sets from previous researc [, 3]. Using tese components, te optimum conditions for a maximized net power density and te sensitivity of te individual design parameters are sown. Nomenclature b widt between profiled ridges (m) c concentration of feed water (mol/liter) d E F ydraulic diameter (m) electromotive force (V) faraday constant (96485 C/mol) intermembrane distance (m) j current density (A/m ) N m number of membranes (-) p pressure difference over feed water compartment (Pa) P net net power density (W/m ) universal gas constant (8.31 J/(mol K)) omic BL o b area resistance due to bulk concen ) ) ) S sp /V sp ratio between te surface and volume of te spacer filaments (1/m) T temperature (K) t res v residence time (s) velocity (m/s) z valence of ions (-) membrane permselectivity (-) mask factor (-) activity coefficient (-) porosity (-) (non-omic) overpotential feed water conductivity (S/m) viscosity of water (Pa s)

4 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) Teory.1. Voltage Te salinity difference over eac membrane creates a potential difference wic is given by te Nernst equation. Te electromotive force over a series of N m membranes, eac wit an apparent permselectivity, is given by: T sea csea E N m ln (1) z F c river river In wic E is te electromotive force (V), is te universal gas constant (8.31 J/(mol K)), T is te absolute temperature (K), z is te valence of te ions (-), F is te Faraday constant (96485 C/mol), is te activity coefficient (-) and c is te concentration at te membrane-solution interface (mol/liter). Te subscripts sea and river indicate te solution on eiter side of te membrane. Te produced voltage drives an electrical current wen an external circuit is connected. Due to te omic resistance of te stack itself, te voltage over te electrodes will decrease. At a current density j (A/m ), te voltage U (V) is given by: U E omic j () In wic omic is te omic area resistance ). Wen no current is applied, te electromotive force E can be estimated using te inflow concentrations of te feed waters in eq. 1. Tis voltage is referred to as te open circuit voltage E OCV. Wen a current is applied, ions are transported from te salt water side troug te membranes to te fres water side, and te concentration witin eac compartment canges. Te concentration difference at te membrane-solution interfaces will be smaller tan te concentration difference between te seawater and river water at te inflow. As a consequence, te electromotive force will be lower tan E OCV. Tis decrease in potential can be subdivided into a contribution due to te concentration cange in te boundary layers, BL, and a contribution due to te concentration cange in te bulk of te solution, C. In fact, BL considers te concentration gradient perpendicular to te membrane surface witin eac compartment (assuming developed boundary layers), wile C considers te concentration gradient parallel to te membranes. Including tese two potential losses, te voltage over te stack is given by: U EOCV C BL omic j (3) In wic E OCV, BL and C are in Volt. Te losses due to boundary layer effects and concentration canges in te bulk can be compared to te omic loss wen BL and C are divided by te current density, i.e. interpreting bot as a (non-omic) resistance: U E j OCV omic C BL (4)

5 174 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) Te next part gives a matematical description on ow to estimate te contribution of eac of te individual resistance factors omic, C and BL... esistance Wen spacer effects are neglected, te omic resistance is determined by te membrane resistance, te water conductivity and te intermembrane distance [7, 8]. However, te non-conductive spacer does ave a significant effect on te omic resistance because it blocks part of te membrane area (spacer sadow effect) [9] and imposes a tortuous ionic flow in te water compartments [1, 10]. A more accurate way to estimate omic is to include te porosity, and a mask fraction tat accounts for te spacer sadow effect [1]. Including tese effects, te omic resistance can be estimated by [1]: omic N m 1 AEM 1 CEM sea sea river river electrodes In wic AEM and CEM are te area ), respectively, is te intermembrane distance (m), is te electrolyte conductivity (S/m) and electrodes is te (omic) resistance of bot electrodes and teir ). Te spacer porosity, and te mask fraction are dimensionless. Teir values vary between 0 and 1; a completely open compartment would give = 1 and = 0, wereas a solid spacer would be represented by = 0 and = 1. Te porosity is squared in eq. 5, because two effects play a role: 1) te spacer filaments block a certain fraction of te compartment, so te current density is intensified in te pores and ) te spacer filaments force a longer, tortuous pat for te electrical current. Te geometry of te spacer filaments influences te exact relation between te electrical resistance and te porosity. As a first approximation, is squared in eq. 5, in accordance wit previous researc [1]. C can be estimated from te concentration cange due to carge transport. Assuming a linear decrease of te electromotive force between feed water inlet and outlet, and neglecting canges in activity coefficients due to ion excange, C can be estimated from []: (5) C N m T ln z F j A A river sea (6) j tres j tres In wic Ariver 1 and Asea 1, in wic t res is te residence time F river criver F sea csea of te feed water in te stack (s). Fig. sows te calculated C versus t res / using te combined experimental data of Vermaas et al. [, 3]. Bot data sets were obtained from a stack wit 5 ED cells, wit an electrode dimension of 10 cm by 10 cm and using artificial seawater (0.510 M) and river water (0.017M). Te first data set contained 4 different intermembrane using spacers [], wereas te oter data set compared te use of profiled membranes and spacers, bot wit an intermembr [3]. For all data, te current density was cosen suc tat te power density was maximized.

6 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) Figure. C as function of te residence time of te feed water in a ED stack (t res) divided by te intermembrane distance. Data adopted from [, 3] led membranes. Fig. sows tat te data from different stacks are close to a unified line wen scaled to t res /. Te sligt deviations are due to differences in current density, wic are a combined effect of te electromotive force and te omic resistance. Even witout eq. 6, te dependency on t res / could be expected. Te cumulative ion transport from a volume of seawater to a volume of river water increases wit te residence time, wile te effect on te concentration is inversely proportional to te water volume, tus to te intermembrane distance. Te experimental data in Fig. sow a linear fit wit = Tis linearity cannot be derived from eq. 6 a priori, due to te fractions and te logaritm. Apparently, instead of eq. 6, a linear approac would estimate C closely. Tis work uses te more complex, but more pysical, formulation from eq. 6. Te boundary layer resistance BL is dependent on te cange in concentration at te middle of a compartment and te concentration at te membrane-solution interface [7]. BL was not estimated teoretically before for applications in ED using input parameters only. Previous researc sowed tat BL reduces wen te velocity of te feed water increases, since iger velocities improve te mixing rate [, 3, 8, 9]. amon et al. [5] suggested a relation wit te eynolds number, Scmidt number, diffusion coefficient and ydraulic diameter. However, wen te experimental data [, 3] are combined, tese do not correlate well ( <0.5), neiter wit te feed water velocity, nor wit te flow rate, eynolds number, Serwood number or te suggested relation of amon et al. [5]. A new, pysically based approac is proposed in tis researc. Te mixing in te boundary layers can be assumed proportional to te momentum excange toward te membrane, wic is proportional to te velocity sear at te membranesolution interface [11] (i.e. te velocity gradient perpendicular to te membrane). Terefore, BL can be expected to be inversely proportional to te velocity sear at te membrane-solution interface: 1 dv BL (7) dy membr. sol. interface

7 176 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) In wic v is te local velocity magnitude (m/s) and y is te coordinate perpendicular to te membrane (m). For laminar uniform flow (Poiseuille flow), tis yields [11]: BL v average t res L (8) In wic v average is te average velocity (m/s) and L is te cell lengt (m), i.e. te average pat lengt of te feed water in eac compartment. Experimental data from [, 3] are used to sow te relation between BL and t res /L. For simplicity, te compartments wit spacers are considered as straigt flow cannels, disregarding te volume of te spacers. Fig. 3 sows te calculated values for BL for a) stacks wit several spacer ticknesses and b) stacks wit profiled membranes. Figure 3. BL as function of t res /L for ED stacks wit a) different intermembrane spacer ticknesses and b) profiled membranes [, 3]. Altoug te data start to deviate from te linear fit for larger values of t res /L, most values for BL are on a reasonable linear line, especially considering tat te difference between te tinnest and tickest spacer is a factor 8. Scattering is explained by non-ideal uniform flow (near profiled ridges and spacer filaments) and te relatively large error of BL in te measurements. BL is derived from te difference ( total omic C ), eac contribution wit a certain error. Te values for total and C are largest for ig t res, so te error in BL increases wen t res /L increases. In addition, te different spacers ave minor canges in spacer mes size, mes angle and porosity, wic may also influence te mixing rate [1]. Fig. 3 also sows tat BL is clearly iger wen profiled membranes are used compared to a design wit spacers. For spacers, BL can be approximated by: N m BL 0.6t res 0.05 (9) L

8 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) wile for profiled membranes te data best fit: N m BL 0.96t res 0.35 (10) L Tese equations sow tat te linear fit for te stack wit profiled membranes does not intersect te origin, wereas te trendline for te stack wit spacers does approac te origin. Tis unexpected beavior for profiled membranes migt be caused by preferential flow pats. Small irregularities on a profiled membrane may prevent flow troug tat complete cannel, wereas in te case of spacers water can flow around suc an obstruction..3. Pumping losses A part of te obtained power is required to pump te feed waters troug te stacks. Tis pumping power can be calculated from te pressure drop over te inlet and outlet of te feed waters and te flow rate of te feed waters. In te most ideal case, for a laminar, fully developed flow in an infinite wide uniform cannel, te pressure drop can be estimated using te Darcy-Weisbac equation [11]: 1 L v 1 L p (11) t res 1 4 d In wic d is te ydraulic diameter of te cannel (m). In te case of an infinite wide cannel tis ydraulic diameter equals [13]. Te experimental pressure drops are significantly iger tan tis idealized case. Te experimentally determined pressure drop in a stack wit profiled membranes was approximately 0 times iger tan te idealized equivalent values, wereas te spacers sowed pumping losses of more tan 80 times te values calculated from eq. 11. Te excess in pressure drop for profiled membranes is partly due to te finite widt of te cannels and partly due to a non-optimal design. Te flow was non-uniform especially at inflow and outflow, were te flow was forced to make sarp corners. In te case of spacers, te pumping power is additionally increased due to te spacer filaments tat obstruct te flow. Te spacer filaments make te effective ydraulic diameter smaller tan tat of a non-filled cannel. To anticipate on tat effect, te ydraulic diameter for spacer filled cannels can be derived from [13, 14]: d 1 4 S sp V sp (1) In wic S sp /V sp is te ratio between te surface and volume of te spacer filaments. For profiled membranes, te ydraulic diameter can be derived from [13]: 4b d b (13)

9 178 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) In wic b is te widt of eac cannel between te profiled ridges (m). Assuming bot compartments to be equally tick, te pumping power P pump (W/m ), for bot feed waters togeter can be calculated from [3]: res p 1 L P pump (14) A t 1 4 d In wic is te volumetric flow rate (m 3 /s) and A is te total membrane area (m ). Tis pumping power sould be representative for a large scale operation. Small scale experiments still sow a iger pressure drop [-4, 15] due to relatively ig losses at te in- and outlet of te feed water or parameters as te spacer mes angle. A more complex approac to calculate te pressure drop in spacers is available [14], but is beyond te scope of tis paper..4. Net power density Te gross power density generated wit a ED stack can be calculated by multiplying te stack voltage U (eq. 4) by te current density j. To calculate te net power density, te power spent on pumping (eq. 14) needs to be subtracted from tis generated power. Tis yields for te net power density of a ED stack: P net E OCV j omic N m C BL j P pump (15) Combined wit te set of previous equations for E OCV, omic, C, BL and d (eq. 1, 5-14), te net power density can be estimated using design parameters only as input. 3. esults and discussion Te parameters tat determine te net power density are membrane and spacer properties, electrode resistance, feed water concentrations, temperature, cell dimensions and residence time. Most parameters cannot be tuned in a wide range. For example, te feed water concentrations are limited to te availability. Tree parameters tat can be tuned in a wide range and are expected (deduced from previous experiments) to ave a major impact on te net power density are te residence time, te intermembrane distance, te current density and te cell lengt. Te cell lengt as no (finite) optimum. A smaller cell lengt reduces te pumping power significantly, as indicated by eq. 14. A reduced pumping power allows smaller intermembrane distances and smaller residence times, wic would reduce BL and omic, and consequently a smaller cell lengt would always lead to a iger net power density. Te benefit of small cell lengt was already recognized in previous researc [4]. Practical limitations determine te cell lengt. As a first estimate, a value of 0.1m is cosen. Te intermembrane distance, te residence time and te current density can be varied to find te optimum net power output. Te residence time and intermembrane distance of te seawater was set equal to tat for river water. Table 1 sows representative values for te oter relevant parameters for a large scale operation tat serve as input parameters for te calculations to estimate te maximum net power

10 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) output obtainable in ED. Altoug stacks wit tese specifications ave not been tested experimentally, a combination of previous researc indicates tat suc stacks can be manufactured wit te current tecnology [, 3, 16, 17].

11 180 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) Table 1. Typical specifications for a ED stack using spacers and a ED stack using profiled membranes. Parameter Spacers Profiled membranes (= river = sea) Varied between 1 Varied between 1 t res (= t res, river = t res, sea) Varied between s Varied between s j Varied between A/m Varied between A/m L 0.1 m 0.1 m AEM = CEM electrodes a a 0.97 b 0.97 a N m c sea M NaCl M NaCl c river M NaCl M NaCl T 98 K 98 K 0.50 c 0.1 d 0.70 b 0.9 c b - 9 c S sp/v sp 8/ e - Te net power density, as estimated using te equations presented in tis work and by caracteristic values summarized in Table 1, is sown in Fig. 4 as function of t res and, for a) stacks wit spacers and b) stacks wit profiled membranes. Te current density j is cosen for eac value of t res and suc tat te net power is maximized. b Based on Fumatec FKS / FAS membranes [] c Based on open area and porosity of Sefar woven spacers [] d Assuming 10% of te membrane area occupied by profiled ridges and neglecting ion-conduction troug te profiled ridges. If tis ion-conduction is not neglected, is even lower. e Based on 4/d filament [14]

12 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) Figure 4. Net power density for stacks wit spacers (a) and stacks wit profiled membranes (b), as function of te intermembrane distance and residence time. Te residence time is plotted on a logaritmic scale. Fig. 4b sows tat te maximum net power density obtainable is.7 W/m, using a stack wit profiled membranes, an intermembrane distance of 5.4 s. Te net power density for a stack wit spacers is only 1.34 W/m, for an intermembrane distance of 70 residence time of 7. s (Fig. 4a). Tis is close to te experimentally derived maximum of 1. W/m, obtain 8 sec. Fig. 4 also sows tat te optimum residence time is rater independent of te intermembrane distance for ; te igest net power densit residence time of approximately.5 sec. Te larger residence time for stacks wit spacers (approximately 7 sec) compared to stacks wit profiled membranes is caused by te larger contribution of te pumping power loss in te case of stacks wit spacers. To improve te net power density, different values of te parameters listed in Table 1 can be considered. A sensitivity analysis is performed to investigate wat parameter as te largest influence on te net power density. Te temperature and feed water concentrations are left out of consideration, because tese parameters can not be influenced. Te sensitivity analysis was done by canging eac of te variables to a 1% lower or iger value and calculating te maximum net power density, not necessarily at te same t res, and j. For every run, te optimum values for t res, and j were determined. Te result of tis sensitivity analysis is sown in Table.

13 18 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) Table. Sensitivity analysis for parameters determining te net power density. Positive values indicate tat a iger parameter value would imply an increase in net power density and vice versa elative increase in P net per relative increase in parameter value (-) Parameter Spacers Profiled membranes AEM = CEM electrode N m L b S sp/v sp Table sows tat te net power density is most sensitive for te permselectivity ( ) and te porosity ( ). Tese parameters can be improved only to a limited extend, wic would sligtly increase te net power density. Te membrane resistance and cell lengt ave a smaller influence on te net power density, but ave relatively muc larger possibilities for improvement. Teoretically, tese parameters ave no minimum value, wereas te permselectivity is limited to a value of 100%. Terefore, reducing te membrane resistance and cell lengt are promising for improving te net power density tan improving te membrane permselectivity. Fig. 5 sows te net power density as a function of te cell lengt, for different membrane resistances. Figure 5. Net power density as function of te cell lengt, for membrane resistances of 0.1, 0.3, 0.5 and 1.0 spacers (a) and stacks wit profiled membranes (b). Te cell lengt is plotted on a logaritmic scale., for stacks wit

14 D.A. Vermaas et al. / Energy Procedia 0 ( 01 ) Fig. 5 sows tat te net power density increases rapidly as te cell lengt decreases, reacing a value of almost 0 W/m for profiled membranes wit a cell lengt of 0.001m and a membrane resistance of 0.1. Naturally, a 1 mm cell lengt and suc a low membrane resistance are not realistic at te present state of tecnology. Moreover, te optimum current density to obtain 0 W/m at tese conditions can get up to 500 A/m, wic requires attention to suit te electrode system [18]. Neverteless, te tremendous increase in net power density for small cell lengts empasizes te sensitivity of te net power density on te cell lengt. Te straigt or even convex saped graps using logaritmic x-axes in Fig. 5 suggest an asymptotic increase to an infinite net power density as te cell lengt approaces zero. However, te finite membrane resistance will prevent an infinite net power density wen te cell lengt approaces zero. Fig. 5 also sows tat decreasing te membrane resistance is more effective wen a small cell lengt is cosen. For example, reducing te membrane resistance from 1 to 0.5 leads to a 19% increase in net power density for a cell lengt of 0.1m, wereas te same reduction leads to a 47% increase in net power density for a cell lengt of 0.001m. educing te cell lengt is accompanied wit decreasing optimum intermembrane distances, and terefore a larger influence of te membrane resistance. A design wit very sort cell lengts requires an intelligent feed water distribution system for an operation at large scale. An example is given by Veerman et al. [4], proposing a fractal design for distributing feed waters. Suc a design involves profiled membranes wit (deep) cannels carved out to supply te feed water to (sallow) cells wit a cell lengt in te order of 1 mm. A ED-design wit suc small cell lengts was not tested experimentally before, but can be manufactured wit te current tecnology. Tis calculation sows tat te net power density can be improved significantly in tis way. 4. Conclusions Te power density obtained from reverse electrodialysis can be estimated based on a set of analytical equations. Tis estimation of te net power density better reflects te reality in comparison to previous attempts, were te boundary layer resistances and pumping power were often left out of consideration. Tis researc sows tat te boundary layer resistance can be estimated based on input parameters, in tis case t res /L. Te igest net power density, using parameters tat are typical for te current state of tecnology, is.7 W/m. Tis value is predicted for a stack wit profiled membranes, wit an intermembrane distance of 5.4 s. Higer net power densities can be obtained by improving te membrane properties (permselectivity, resistance), increasing te (spacer) porosity and using sorter cell lengts. Te combination of decreasing cell lengt and decreasing membrane resistance is an effective strategy to improve te net power density. A net power density close to 0 W/m using a cell lengt of 1 mm. A design wit suc a small cell lengt is not tested yet and suc a small membrane resistance is not obtained yet. Tis researc demonstrates tat te strategy to reduce bot te cell lengt and membrane resistance is very effective to improve te net power density in reverse electrodialysis. Acknowledgements Tis researc is performed at Wetsus, Tecnological Top Institute for Water tecnology. Wetsus is funded by te Dutc Ministry of Economic Affairs, te European Union egional Development Fund, te Noord- Landustrie, Magneto Special Anodes, MAST Carbon and A. Hak.

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