Download Salinity gradient energy storage

U.K. Starke
Salinity gradient energy storage
Quantification of the influence of temperature on salinity gradient flow
battery performance.
Salinity gradient energy storage
Quantification of the influence of temperature on salinity gradient flow battery performance.
By
Starke, U.K. (1518232)
in partial fulfilment of the requirements for the degree of
Master of Science
in Mechanical Engineering
at the Delft University of Technology,
to be defended publicly on [To be announced] AM.
Supervisors:
ir J.W. van Egmond (PhD candidate Wageningen University)
Dr. ir D.A. Vermaas
Prof. dr. ir. Thijs J.H. Vlugt
Thesis committee:
This thesis is confidential and cannot be made public.
1
Abstract
The combination of desalination technology (Electrodialysis) and power generation from
salinity gradients (Reverse Electrodialysis) is a novel electrical energy storage system.
The main challenge in the development of this novel energy storage system is to improve the
system performance. The performance of the battery is determined by the efficiency, power
density and energy density. A strategy to increase the performance of the battery is to
increase the temperature of the feed solutions.
The main goal of this thesis is to quantify the influence of temperature on the power density
[W/m2], energy density [Wh/L] and thermodynamic efficiency [%] of a salinity gradient based
energy storage system, charged using electrodialysis and discharged using reverse
electrodialysis.
In chapter 2 a theoretical framework is developed in order to build an understanding of the
fundamental theories that help explain the system characteristics. This is done by studying
the literature. Next, chapter 3 deals with the methodology that will be used in order to obtain
the experimental data that is needed in order to answer the main research question. After
this, the results of the experiments are discussed in chapter 4. In chapter 5 the most
important conclusions are summarized and in chapter 6 there is room for a discussion and
recommendations.
Experimental data showed that:






The total electrical resistance decreases if the temperature increases;
Osmosis and diffusion increases if the temperature increases.
Energy density increases if the operating temperature increases.
Power density increases if the operating temperature increases.
In case of charging the increase of operating temperature increases the systems
thermodynamic efficiency.
In case of discharging the increase of operating temperature increases the systems
thermodynamic efficiency.
In order for the salinity gradient energy storage to be cost competitive the levelized costs
should be at most 0.20 euro/kWh. Pumped hydro storage is the cheapest competitor
available on the energy storage market today with a levelized cost of about 0.10 euro/kWh .
Ways to achieve this competitive price is to decrease the price of the membranes, or
increase the performance of the membranes because the membranes are the most
expensive component of the system. Another approach is to focus on groups of applications
requiring a large capacity to power ratio. The costs of storage capacity of this system are
extremely low making it very suitable for the aforementioned group of applications.
Irreversible water transport of the system has a large impact on the system performance.
Therefore future research should be done in order to decrease this phenomenon. This
means that strategies need to be devised in order to reduce the osmotic pressure difference
between the concentrate and diluate chambers. Furthermore the internal resistance is an
important factor to consider for the overall performance of the system. Currently research is
already being done in order to reduce the internal resistance. Increasing the conductivity of
the diluate chamber is an important strategy. Lastly the self-discharge of the system is also a
parameter to consider and research is also already being done to develop membranes that
have high permselectivity.
2
Acknowledgements
I would like to thank the whole AquaBattery team: Jan-Willem van Egmond who was also my
supervisor at Wetsus, David Vermaas who was my supervisor from the TU Delft, Jan Post,
Emil Goosen, Jiajun Cen and Edoardo Cometti. Thanks Thijs Vlugt for making this whole
collaboration with Wetsus work. Thanks Michel Saakes for the support! Of course my
Spanish Blue Battery teammates at Wetsus deserve a place in this thesis, thanks Cesar and
Laura. I am also very grateful to everyone else at Wetsus for making it possible to work in an
inspiring environment with the best equipment. Finally I would like to thank my family for
supporting me during this thesis and of course the whole period that I studied.
3
Contents
Chapter 1 Introduction ........................................................................................................... 9
Background ....................................................................................................................... 9
Salinity gradient based energy storage .............................................................................. 9
Challenges ........................................................................................................................10
Aim ...................................................................................................................................11
Thesis Outline ...................................................................................................................11
Chapter 2 Theoretical framework .........................................................................................12
Principle of electrodialysis and reversed electrodialysis ....................................................12
System components ......................................................................................................12
Driving force electrodialysis ...........................................................................................13
Driving force reverse electrodialysis ..............................................................................13
Membranes ...................................................................................................................14
Relevant phenomena ........................................................................................................14
Mass transport across the ion-exchange membranes ...................................................15
Electrical characteristics of the system ..........................................................................18
Thermodynamic properties ...............................................................................................22
Activity and osmotic coefficient ......................................................................................22
Density ..........................................................................................................................23
Conductivity...................................................................................................................23
Viscosity ........................................................................................................................23
System performance .........................................................................................................24
Gibbs free energy ..........................................................................................................24
Energy density ..............................................................................................................24
Power density ................................................................................................................25
Thermodynamic efficiency .............................................................................................25
Chapter 3 Materials and methods .........................................................................................26
Methods ............................................................................................................................26
Constant current experiment .........................................................................................26
Single pass experiment .................................................................................................27
Open circuit experiment.................................................................................................28
Materials ...........................................................................................................................30
Stack .............................................................................................................................30
Experimental setup........................................................................................................31
Chapter 4 Results.................................................................................................................33
Introduction .......................................................................................................................33
4
Single pass experiments ...................................................................................................33
Resistance ....................................................................................................................33
Temperature and the boundary layer resistance ...........................................................34
Temperature and the bulk concentration change resistance ..........................................35
Temperature and ohmic resistance ...............................................................................36
Open circuit experiments ..................................................................................................36
Effect of temperature on osmosis and diffusion .............................................................36
Effect of temperature on diffusion ..................................................................................38
Constant current experiments ...........................................................................................39
Optimal current density for charging (ED) ......................................................................39
Optimal current density for discharging (RED) ...............................................................41
Effect of temperature on energy density in ED mode .....................................................43
Effect of temperature on power density in RED mode ...................................................43
Effect of temperature on efficiency in ED mode .............................................................44
Effect of temperature on efficiency in RED mode ..........................................................46
Remarks ...........................................................................................................................47
Experiments done in duplo ............................................................................................47
Chapter 5 Conclusion ...........................................................................................................48
Chapter 6 General discussion and recommendations ..........................................................48
Economics ........................................................................................................................48
Applications ......................................................................................................................49
Recommendations ............................................................................................................50
References
51
Appendix A: Experimental data of constant current ED experiments
53
Appendix B: Experimental data of constant current RED experiments
61
Appendix C: Experimental data of open circuit experiments
67
Appendix D: Experimental data of single pass experiments
70
Appendix E: List of figures
76
Appendix F: List of tables
78
5
Nomenclature
A
Area [m2]
a
activity [-]
c
concentration [kg/m3]
D
Mass transfer coefficient [m2 / s]
d
diameter [m]
F
faraday constant 96486 [C/mol]
g
gravitational constant [m2 / s]
h
intermembrane distance [m]
I
current [A]
j
current density [A/m2]
J
mass flux [kg/(m2∙s)]
kb
Boltzmann constant 1.38064852 ∙10-23 [m2 kg s-2 K-1]
L
length [m]
m
molality [mol/kg]
M
molecular weight [kg/mol]
n
number of moles [mol]
nw
solvent flow rate [kg/s]
Nm
Number of membranes [-]
p
Pressure [bar]
P
Power [W]
PG
Rate of Gibbs free energy [W]
PD
Dissipated Power [W]
Q
volumetric flowrate [m3 / s]
R
universal gas constant 8.31 [J/(mol K)]
Rohmic
ohmic area resistance [Ω ∙ m2]
RBL
boundary layer area resistance [Ω ∙ m2]
RΔc
area resistance due to bulk concentration change [Ω ∙ m2]
r
radius [m]
t
time [s]
T
Temperature [K] or [°C]
6
tw
water transport number [-]
v
stoichiometric coefficient [-]
u
ion mobility [m2 / (s V)]
V
volume [m3]
x
directional coordinate [m]
y
directional coordinate [m]
z
valence [eq mol-1]
Subscripts
a
anion
c
cation
h
hydraulic
i
component
m
membrane
w
water
Greek symbols
α
membrane permselectivity [-]
γ
activity coefficient [-]
ε
porosity [-]
δ
membrane thickness [m]
η
efficiency [-]
θ
viscosity of water [Pa s]
κ
electrolyte conductivity [S/m]
μ
chemical potential of salts [J / mol]
π
osmotic pressure
ρ
density [kg/m3]
τ
dynamic viscosity [Pa s]
φ
electrical potential [V]
ϕ
osmotic coefficient
Π
chemical potential of water [J / mol]
7
Abbreviations
ED
Electrodialysis
RED
Reverse electrodialysis
SOC
State of charge
Don
Donnan
diff
Diffusion
osm
Osmosis
eosm
Electro-osmosis
mig
Migration
dil
Diluate
conc
Concentrate
OCV
open circuit voltage
8
Chapter 1 Introduction
Background
Nowadays more than 80% of the electricity produced worldwide is generated by burning
fossil fuels. The world becomes increasingly aware of the fact that change is needed so
electricity supply from renewable energy technologies is increasing. However, most
renewable resources are inherently intermittent and as a result the electricity supply cannot
easily be matched with the demand. This mismatch can destabilize the electricity grid.
The electrical energy generated by renewables can be stored by using electrical energy
storage systems. Electrochemical batteries or pumped hydropower can be employed to store
the energy when there is an excess, when needed this energy can be released again.
It is however a challenge to store all the excess energy with the current electric energy
storage capacity [1]. The need for a larger energy storage capacity will only grow with the
increasing share of renewable energy. Therefore the current electric energy storage capacity
has to be expanded.
Building an electrochemical battery that has a large capacity is currently not economically
attractive and consequently these batteries are used for short timescales and small
capacities [1]. On the other hand pumped hydropower systems can store large amounts of
energy, however a very large volume of water is needed and these systems are limited to
certain geographical locations [2].
Another option is conversion to hydrogen or syngas; A drawback of this option is that the
process is expensive, explosive and has a relatively low efficiency [3]. Clearly a new
electrical energy storage system is needed which is safe efficient and independent of
location.
Salinity gradient based energy storage
A novel way of storing large quantities of electrical energy is by using a salinity gradient
based energy storage system. By mixing two streams of water with different salinities,
electricity can be generated [4]. The reason for this is that mixing two solutions with different
salinities increases the entropy, thereby releasing energy. There are several ways to capture
this energy; one of those ways is reverse electrodialysis (RED). In RED ion-exchange
membrane pairs are used to selectively allow counter-ion permeation. This gives a net ion
flux which is converted to an electric current for power generation.
Desalination of water is the exact opposite process and is known for a long time. There are
several ways to desalinate water using membranes, for instance electrodialysis (ED). The
combination of desalination technology (ED) and power generation from salinity gradients
(RED) is an electrical energy storage system. (Figure 1)
9
Figure 1: Salinity gradient based energy storage system, charged using electrodialysis (ED) and
discharged using reverse electrodialysis (RED). Figure adopted from David Vermaas, STW proposal
AquaBattery 2015.
Challenges
The main challenge in the development of this novel energy storage system is to improve the
performance. The performance of the battery is determined by the efficiency, power density
and energy density. A working lab-scale salinity gradient based energy storage system was
developed by Kingsbury et al. [5]. Their work consists of two parts, in one part the
performance of the system was determined experimentally and in the other part a
mathematical model was developed in order to describe the performance of the system.
Efficiency
Kingsbury et al [5] showed that the experimental round-trip efficiency ranged from 21.2% to
34% when cycling the system between 33% and 90% state of charge. The state of charge
represents the amount of energy available for discharge.
Power density
The power density was relatively low (0.07-0.44 [W/m2]) compared to the record high
experimentally obtained power densities by Daniilidis et al (6 [W/m2] using river water and 5
[M] brine at 60 [°C] doing RED only). [6] There is a tradeoff between energy efficiency and
power density. [7] Kingsbury made the choice to operate the system at maximum efficiency,
hence a relatively low power density was obtained.
Energy density
The salinity gradient based energy storage system shows similarities with flow batteries.
Flow batteries have energy densities between 16 and 33 [Wh/L]. [8] The energy density that
was obtained in the experiments done by Kingsbury et al [5] was 0.05 [Wh/L] which is
substantially lower than those achieved with other types of flow batteries.
10
Temperature
A strategy to increase the performance of the battery is to increase the temperature of the
feed solutions. Firstly, the increase in temperature will increase the power density. This is
due to the lowered internal resistance [6,23]. Secondly, the increase in temperature allows
for a higher energy density because a higher Gibbs free energy difference can be achieved.
Finally, it is expected that the increase in temperature will increase the thermodynamic
efficiency because of the lowered internal resistance.
Kingsbury et al [5] defined the roundtrip efficiency as the product of a current and voltage
efficiency. The voltage efficiency is associated with the internal resistance and the current
efficiency is associated with self-discharge phenomena (osmosis and diffusion). In order for
the roundtrip efficiency to be a useful quantity the system must return to its initial state of
charge. However, in the experiments done by Kingsbury [5], the system does not return to its
initial state as a result of water transport across the membranes. The usefulness of the
roundtrip efficiency for this specific system is thus questionable. Therefore in this work the
thermodynamic efficiency of each process will be used as primary figure to evaluate
efficiency. The thermodynamic efficiency is defined as the ratio between the excess Gibbs
free energy of mixing and the actual power out/input of the two processes
Increasing temperature is, in principal, a relatively simple way of getting the desired result of
increasing the system performance. An additional advantage of quantifying the system
performance at different temperatures is the fact that a practical battery will be placed at
different locations with varying temperatures. It is therefore desirable to know how this
variation in temperature will affect the battery performance.
Aim
If this technology is to enter the market where existing energy storage technologies already
have a market share, the costs of storing energy must be competitive. The major parameters
influencing the costs are total capital costs and efficiency. The total capital costs are
influenced by the energy density and power density. Energy density determines the size of
the tanks needed while the power density determines the total amount of m2 membranes
needed.
The main goal of this thesis is to quantify the influence of temperature on the power density
[W/m2], energy density [Wh/L] and thermodynamic efficiency [%] of a salinity gradient based
energy storage system, charged using electrodialysis and discharged using reverse
electrodialysis.
Thesis Outline
In chapter 2, a theoretical framework is developed in order to build an understanding of the
fundamental theories that help explain the system characteristics. This is done by studying
the literature. Next, chapter 3 deals with the methodology that will be used in order to obtain
the experimental data that is needed in order to answer the main research question. After
this, the results of the experiments are discussed in chapter 4. In chapter 5, the most
important conclusions are summarized and in chapter 6 there is room for a discussion and
recommendations.
11
Chapter 2 Theoretical framework
The objective of this chapter is to develop a theoretical framework which will form the basis
of this thesis. First, an explanation of the core processes, electrodialysis and reversed
electrodialysis will be given. Secondly, more information is given about the membranes.
Then, a description of the relevant phenomena is given. Next, the effect of temperature on
relevant thermodynamic properties is discussed. Finally, the relation between temperature
and the key performance parameters will be discussed.
Principle of electrodialysis and reversed electrodialysis
Electrodialysis (ED) is an ion-exchange membrane process wherein for instance sodium
chloride can be separated from an electrolyte solution. One practical application of the
technology is desalination of water. In this thesis the electrolyte solution is aqueous sodium
chloride. Reverse electrodialysis is the opposite of electrodialysis. By mixing two streams of
water with different salinities, electricity can be generated.
Electrodialysis and reverse electrodialysis share the same technology. Therefore a
description will be given of the components that build up an ED system. RED can be done
using the same equipment.
In order to desalinate water there needs to be ion transport. This transport of ions is enabled
by a driving force, in the case of electrodialysis this driving force is an electrical potential.
Figure 2 is a schematic diagram illustrating the principle of desalination by electrodialysis.
Figure 2: Schematic diagram illustrating the principle of desalination by electrodialysis in a stack with
cation and anion-exchange membranes in alternating series between two electrodes. Adopted from [9]
System components
An electrodialysis stack, which is the key element of the system, is composed of alternating
series of cell pairs with electrodes on both ends. A single cell consists of a volume between
two adjacent membranes. A cell pair consists of four adjacent elements:
1. a diluate chamber containing diluate in between two adjacent cation- and anionexchange membranes
2. a concentrate chamber containing concentrated solution between two adjacent
cation- and anion-exchange membranes
3. the two adjacent cation and anion membranes enclosing the diluate chamber
Gaskets are used in order to determine if a solution is fed to a cell or not. Spacers are used
to make sure that there is a certain distance between the membranes. Electro-neutrality of
the solutions in both the anode compartment and cathode compartment is maintained
through redox reactions at the electrodes [21, p. 34].
12
As a result electrons can be transferred from anode to cathode via an external electric circuit.
In this thesis the electrode rinse solution is Sodium Sulfate (Na2SO4). Figure 3 shows a
schematic representation of a stack configuration [10].
Figure 3: Schematic representation of a stack configuration consisting of two endplates, gaskets,
spacers, membranes and electrodes. The components enclosed by the accolades form the repeating unit
(cell pairs). Adopted from [10, p. 49]
Driving force electrodialysis
In the case of electrodialysis an electrical potential is applied over the anode and cathode
while an ionic solution, in this case containing sodium chloride, is pumped through the cells.
While the solutions are pumped through the cells ion migration takes place. The positively
charged anions migrate towards the positively charged anode while the negatively charged
cations migrate towards the negatively charged cathode. Both the cation- and anionexchange membranes retain ions of opposite charge. This process results in the depletion of
alternate compartments, while the concentration increases in other compartments. The
depleted and concentrated solutions are referred to as diluate and concentrate respectively.
Driving force reverse electrodialysis
In the case of reverse electrodialysis the driving force is a difference in chemical potential.
This chemical potential results in a potential difference over each membrane, the so called
membrane potential which will be discussed in the section next section. The electric potential
difference between the outer compartments of the membrane stack is the sum of the
potential differences over each membrane. The chemical potential difference causes the
transport of ions through the membranes from the concentrated solution to the diluted
solution. This process results in the depletion of the concentrate while the concentration of
the diluate increases.
13
Membranes
Ion-exchange membranes are the key components of the salinity gradient energy storage
system. Therefore this section is devoted to giving some background information about the
membranes. First, the structure of the membranes will be discussed. Then, some desirable
properties of the membrane will be highlighted and finally some words will be written about
the impact temperature can have on the relevant membrane properties.
There are several ways to classify ion-exchange membranes [9, p.89]. Taking into account
the context of this thesis the membranes will be classified based on their function:


Cation-exchange membranes are permeable to cations and contain negatively
charged fixed ions;
Anion-exchange membranes are permeable to anions and contain positively charged
fixed ions.
Figure 4 shows the structure of a cation-exchange membrane. The fixed negatively charged
anions ions repel the mobile negatively charged ions (co-ions). The mobile positively charged
ions (counter ions) pass through the matrix structure. Anion-exchange membranes have the
opposite structure and only anions will pass through the matrix structure.
Figure 4: Structure of a cation-exchange membrane with fixed anions, a polymer matrix and mobile coand counter-ions.
For proper functioning of ion-exchange membranes a few properties are desired which are
described in [9]. For this thesis the most important properties are the electrical resistance,
which is low in the ideal case, and the permselectivity which should be high in the ideal case.
In the experiments that will be done the membranes will be exposed to higher and lower
temperatures then they normally operate in. Literature [6] shows that permselectivity
decreases when the temperature increases. The electrical resistance of the membrane will
be affected by temperature, it will decrease. This decrease is caused by the increased
mobility of the fixed ions in the membrane. The magnitude of this resistance is considerably
lower than the resistance of the diluate [9, p.121].
Relevant phenomena
This section gives an overview of the phenomena that are relevant in the processes of ED
and RED in the context of the salinity gradient energy storage system. First, the
fundamentals behind the mass transport across the ion-exchange membranes will be
described. Then, the electrical characteristics of the system will be discussed.
14
Mass transport across the ion-exchange membranes
The salinity gradient energy storage system is a closed system. Therefore all mass transfer
will take place through the membranes. Two types of components are being transported:
ions and water.
Transport of ions can be caused by three potential gradients: electric, chemical and pressure
gradients. These three gradients cause the transport of ions through migration, diffusion and
convection respectively. Transport of ions by convection will not be taken into account
because the cell pairs will consist of two geometrically identical compartments which means
that there will be no pressure difference between the two compartments [9]. Water transport
occurs through osmosis, driven by the difference in osmotic pressure, and electro-osmosis
which is driven by the potential gradient.
The direction of the mass flux depends on the mode of operation of the system. Figure 5
gives an overview of the directions while charging and discharging the system.
Mass transfer electrodialysis
(charging)
Concentrate
Diluate
Mass transfer reverse
electrodialysis (discharging)
Concentrate
Diluate
Ji,migration
Ji,migration
Ji,diffusion
Ji,diffusion
Jw,osmosis
Jw,osmosis
Jw,electro-osmosis
Jw,electro-osmosis
Figure 5: Overview of mass transport directions in case of charging(ED) and discharging (RED).
Osmosis occurs from the diluate to the concentrate chambers. Migration and electro-osmosis
occur in equal direction during the respective modes of operation. Diffusion always occurs
from the concentrate to the diluate chambers.
15
Ion transport
The Nernst-Planck equation is used in order to describe the transport of ions [9, p.70]:
z F d 
 dc ( x)
J i   Di  i
 ci ( x) i
RT dx 
 dx
(1)
Ji refers to fluxes of individual components. The two terms describe diffusion (driven by the
concentration gradient) and migration (driven by the potential gradient) respectively. The
Nernst-Planck equation is only valid under a certain set of assumptions of which the most
relevant for this thesis are [9 p. 66]:



Ideal solution, therefore the activity and concentration are equal;
Minimal pressure differences across the membrane;
Completely dissociated salt.
Depending on the position in the cell, transport will be driven by gradients in either electrical
or chemical potential difference.
Migration
The movement of ions due to the electrical potential is caused by the application of a voltage
difference over the two electrodes. The direction of the ion movement depends on the ion
charge. Cations have a positive charge and move towards the negatively charged cathode.
Anions have a negative charge and move towards the positively charged anode.
For strictly permselective membranes and ions with identical valence the salt flux through the
membrane is proportional to the current density and is given by [9 p. 155]:
J i ,migration  J ccm  J aam 

c
j
j

zc F  z a F
(2)
a
Diffusion
A concentration gradient exists in the boundary layer between the cation-exchange
membrane and the bulk solution (concentrate). This gradient is caused by the lower transport
number of ions through the solution compared to the membrane. The concentration of ions
will increase towards the membrane. There will be a net movement of matter from a region of
high concentration to a region of low concentration which is referred to as diffusive mass
transfer.
The mass transport due to diffusion can be described with the following equation [11]
J diff ( x)  2
16
DNaCl
m
[cconcentrate ( x)  cdiluate ( x)]
(3)
Water transport
Osmosis
µd,w
µc,w
pd
pc
Diluate
Concentrate
When two solutions with different concentrations are separated by semi-permeable
membranes, osmotic water transport can occur. In the salinity gradient battery water will flow
from the diluate to the concentrate because the chemical potential of the solvent (water) is
higher in the diluate (Figure 6). It is assumed that the hydrostatic pressure is equal in both
compartments. [9 p. 54]
Jw
Figure 6: Illustration of the principle of osmosis. The concentrate and diluate chambers are separated by
a membrane. Due to the chemical potential difference of the solvent a water flux will occur. This
illustration was adapted from [9, p.54]
This flux can be calculated with:
J osmosis ( x)  2
M

 [cconcentrate ( x)  cdiluate ( x)]   H 2O 
m
  H 2O 
Dw
(4)
Electro-osmosis
Due to coupling with the electric current there is a solvent flux passing through the
membrane. This is caused by applying an electrical potential gradient. The solvent flux is
referred to as the electro-osmosis flux [ 9].
This electro-osmosis flux can be described in terms of a solvent transport number and the
flux of ions passing the membrane through migration. The solvent transport number is
referred to as the water transport number and represents the amount of water that
accompanies an ion across the membrane. The electro-osmosis flux can be calculated
using:
J w, electro  osmosis  tw  J i , migration
(5)
The water transport number can be determined experimentally. [5]
17
Electrical characteristics of the system
This section is devoted first, to introduce the concept of state of charge. Then to describe
how the total voltage of the system can be calculated and which concepts are important for
understanding how this voltage is built up. Lastly, the systems electrical resistances will be
described.
State of charge
The total voltage of the salinity gradient energy storage system is a function of its state of
charge. The state of charge is a measure of the amount of energy that can be extracted out
of the system and is a function of the concentration of the electrolyte solution in the
concentrate and diluate buffer.
The theoretical amount of energy that can be extracted from mixing two solutions with
different salt concentrations is given by the Gibbs free energy of mixing. The state of charge
can be calculated if the salt concentrations are known. Following the definition introduced by
Kingsbury [5], in this thesis the systems state of charge is calculated using:
SOC 
c
c
i concentrate,i
i concentrate,i
  i cdiluate,i
  i cdiluate,i
(6)
Total voltage
When two solutions having a certain concentration are separated by a membrane a potential
is established between these two solutions. This potential is referred to as the membrane
potential. The membrane potential consists out of two parts: the two Donnan potentials
between the membrane and solution and the diffusion potential across the membrane [9, p.
132]:
c
d
m  dif  Don
 Don

The Donnan potential is the potential difference between the membrane and the
adjacent solution. The two Donnan potentials for membrane-concentrate and
membrane-diluate, can be calculated by applying the following formula to the
respective sides:

C
Don
RT  cic 
   
ln  
zi F  cim 
(8)
RT  cid 
ln  
zi F  cim 
(9)
m
c
d
Don
 m d 

(7)
Differences in the transport number of ions in the membrane cause a potential to
arise and this potential is referred to as the diffusion potential. Under the assumption
that the membranes are completely permselective, the diffusion potential is equal to
zero.
Taking into account the assumption of zero diffusion potential gives:
c
d
, which is also referred to as the Nernst equation.
m  Don
 Don
18
By using the Nernst equation one can calculate the electric potential between two solutions,
each having a certain concentration, separated by an ion-exchange membrane:
RT  a c 
m     
ln  
zi F  a d 
c
d
( 10 )
Taking in account the non-ideality of the solution and the fact that many membranes can be
stacked together, the total membrane potential, or electromotive force, can be calculated
using:
RT   c  cc 
  Nm  
ln 
,
zi F   d  c d 
( 11 )
When no current is applied the open circuit voltage can be calculated by using the Nernst
equation with the concentrations equal to the inlet concentrations.
OCV
c

RT   c  cinlet
 Nm  
ln  d d 
zi F    cinlet 
( 12 )
When the system is operated in discharge mode (RED) the total system voltage is calculated
by subtracting the voltage drop due to the systems electrical resistance from the open circuit
voltage [5] (Figure 7):
U [V]
U RED  OCV  IRint ernal
Open
Circuit
voltage
,
( 13 )
Voltage drop
Due to system
resistance
t [s]
Figure 7: When a current is applied to the system a voltage drop will occur due to the systems internal
resistance.
When the system is operated in charge mode (ED) the total system voltage is calculated by
adding the voltage drop due to the systems electrical resistance to the open circuit voltage
[5]:
U ED  OCV  IRint ernal
19
( 14 )
Internal resistances
When a current is applied to the system, the voltage over the electrodes will increase or
decrease (depending on the operating mode) because of the internal resistance of the stack.
This resistance consists of three components [6].
1. Losses due to the ohmic resistance per cell: Rohmic.
2. Losses due to the concentration gradient in vertical direction of the membranes, the
boundary layer resistance: RBL
3. Losses due to the concentration gradient in the horizontal direction of the
membranes, the bulk concentration difference resistance: R∆c
Adding these three factors together gives the total stack resistance, Ri:
Ri  Rohmic  Rc  Rboundary
( 15 )
Ohmic resistance
The membranes, electrodes, diluate and concentrate all contribute to the ohmic resistance.
These contributions can be calculated using the following equation:
Rohmic 

N m  RAEM RCEM
h
h

 2 concentrate  2 diluate   Relectrodes

2  1   1      concentrate    diluate 
( 16 )
Where RAEM and RCEM are the area resistances of the anion and cation-exchange
membranes [Ω m2], h is the intermembrane distance [m], κ Is the electrolyte conductivity
[S/m] and Relectrodes is the (ohmic) resistance of both electrodes and their compartments [Ω
m2]. In order to take into account the effect of the non-conductive spacers, ε the porosity, [-],
and the mask fraction, β [-], are included.[19]
The simplified version of the equation is:
Rohmic  Rmembranes  Rdiluate  Rconcentrate  Relectrodes
( 17 )
Resistance due to the concentration gradient in the bulk
The area resistance caused by the concentration change in the bulk is referred to as R∆c and
can be calculated using [19]:
RC 
20
N m RT  Adiluate 

ln 

2 zFj  Aconcentrate 
( 18 )
This formula is based on the following assumptions:
 linearly decreasing electromotive force between the in- and outlet of the feedwater.
 neglegible changes in activity coefficients due to ion-exchange.
Adiluate and Aconcentrate can be calculated using [19]:
Aconcentrate  1 
Adiluate  1 
j  tres
F    hconcentrate  cconcentrate
j  tres
F    hdiluate  cdiluate .
( 19 )
( 20 )
Boundary layer resistance
The concentration change in the boundary layer causes the boundary layer resistance. In
order to estimate the boundary layer resistance theoretically Vermaas et al proposed an
approach whereby it was assumed that the mixing in the boundary layers was inversely
proportional to the velocity shear the membrane solution interface [19]:
1
 dv 
RBL   
 dy membr.sol.interface
( 21 )
Key to this equation is that it shows that the boundary layer resistance is a function of
velocity and velocity will also be affected by variations in viscosity. This means that
temperature influences the boundary layer resistance through the viscosity.
21
Thermodynamic properties
In order to predict what will happen with the system performance when the temperature is
varied it is important to analyze the influence of temperature on the thermodynamic
properties. Therefore the literature was studied in order to understand how the temperature
influences the activity/osmotic coefficient, density, conductivity and viscosity.
Activity and osmotic coefficient
The activity and osmotic coefficients of the sodium chloride electrolyte solutions at 25 [°C]
will be estimated using the virial equations developed by Pitzer [12]. In his work Pitzer fits
large amounts of experimental data of aqueous electrolytes and then interprets the resulting
parameters in terms of interionic forces.
Pitzer proposes to calculate the activity and osmotic coefficients of the electrolyte solution
using the following equations:
ln   zM z X
  1  zM z X
 2v v
f  m M X
 v

 
2 2  vM v X 
 BMX  m
v

 2v v
f  m M X
 v

3/ 2
 
2 2  vM v X 
 BMX  m
v


CMX
( 22 )
3/ 2

CMX
( 23 )
BMX and CMX are the virial coefficients.
Pitzer also extended the equations above for temperatures other than 25 [℃] by using
temperature dependent coefficients which are given in [13]. The virial equations were
modeled and the results were validated with graphs from [11]. Figure 8 shows a plot of the
activity coefficient at several temperatures. The same plot was made for the osmotic
coefficients and the result is shown in Figure 9. The results of the calculation of the osmotic
coefficients were validated with data from [13].
Figure 8: Activity coefficients calculated using the virial equations of Pitzer. The activity coefficient
decreases when temperature decreases.
22
Figure 9: Osmotic coefficients calculated using the virial equations of Pitzer. The osmotic coefficient
decreases when temperature decreases.
Figure 8 and Figure 9 show that the activity and osmotic coefficient of aqueous sodium
chloride increase when the temperature increases.
Density
The specific volume of the sodium chloride electrolyte solution will be calculated using tables
from Pitzer [14]. The data from these tables can also be calculated using a virial equation.
The data from Pitzer shows that the density of aqueous sodium chloride decreases slightly
when temperature increases.
Conductivity
The conductivity is relevant in order to calculate the resistance of the solution. The resistance
of the electrolyte solutions can be calculated using
Rsolution 
h
 
2
( 24 )
Temperature will tend to increase the conductivity and thus decrease the internal resistance
[9, p. 24]. Experiments to determine the electrical conductance of aqueous sodium chloride
solutions have indeed shown an increase of conductivity for increasing temperature [15].
Viscosity
Viscosity tables from [16] show that the viscosity decreases with increasing temperature. The
Einstein-Stokes expression for ionic diffusivity shows an inverse relation between viscosity
and conductivity [24]:
D
kbT
6 r
( 25 )
With D the diffusion constant, kb the Boltzmann constant, T the temperature, τ the dynamic
viscosity and r the radius of the spherical particle. .
23
System performance
In this section an overview will be given of how power density, energy density and
thermodynamic efficiency are defined in order to predict what the influence of temperature
will be.
Gibbs free energy
The theoretical amount of energy that can be extracted from mixing two solutions with
different salt concentrations is given by the Gibbs free energy of mixing. The formula for
calculating the Gibbs free energy of mixing of a two-component mixture has the following
form [17]:
PG  nsolvent solvent  nsolute solute
( 26 )
Where µsolvent is the chemical potential of water and µsolute is the chemical potentials of sodium
chloride. The chemical potential of water and sodium chloride are a function of temperature,
pressure and their activity and osmotic coefficient respectively. Applying this formula to the
salinity gradient based energy storage system gives the formula to calculate the total Gibbs
free energy of the mixture of water and sodium chloride [18]:
PG = J w  -ΔΠ  +Js  -Δμ s 
`
( 27 )
Where ΔΠw and Δμs are the water and solvent chemical potentials respectively and J w and
J s are the water and salt flux over the membrane respectively. The water and salt flux follow
from the experimental data and the chemical potentials can be calculated using:
Chemical potential difference of salt:
γm 
Δμ s =RTv  ln  c c 
 γd md 
( 28 )
Chemical potential difference of water:
Δw =-RT c mc  d md 
( 29 )
With:

γ c and γ d the concentrate and diluate activity coefficients

c and d the concentrate and diluate osmotic coefficients
Energy density
The energy density can be calculated using:
Energy density 
PG  t
Vd  Vc
( 30 )
Where Vd and Vc are the concentrate and diluate volumes.
From the definition of the Gibbs free energy of mixing it follows that the Gibbs free energy will
increase when the temperature increase. Therefore it is reasonable to expect that the energy
density will increase if the temperature increases.
24
Power density
The net power obtained per m2 membrane is given by [19]:
E
 j (Rohmic  RC  RBL ) j 2
Pnet  OCV
Ppump
Nm
( 31 )
Pumping losses
The pumping power can be calculated from the pressure drop over the inlet and outlet of the
feed waters and the flow rate of the feed water. In the case that both compartments have the
same thickness and the use of spacer filled channels the pumping power Ppump [W/m2] can
be calculated using [19]:
Ppump 
p  Q 12    L2  h  
 2
A
tres  1/ 4  dh2
( 32 )
With Q the volumetric flowrate [m3/s], A the total membrane area [m2], dh the hydraulic
diameter, θ the viscosity of water and L the length of the cell. The other parameters were
already introduced.
When the temperature increases, the pumping losses will decrease because the viscosity
also decreases. The cell resistance also decreases so it is to be expected that the power
density also increases.
Thermodynamic efficiency
In order to cross compare efficiencies of different energy storage technologies, the round-trip
efficiency is often used. The roundtrip efficiency is defined as the ratio of energy released
during discharge to the energy required to charge the battery back to the initial charged
state. However, as stated in the introduction, the usefulness of the roundtrip efficiency in the
context of the salinity gradient based energy storage is questionable. The reason for this is
the fact that in order for the roundtrip efficiency to be useful the system needs to be restored
to its initial state. However, the system does not return to its initial state due to irreversible
water transport.
Therefore the efficiency referred to in this thesis is the thermodynamic efficiency which will
be calculated for both the charge and discharge cycle of the system.
The thermodynamic efficiency for ED and RED can be calculated using:
 ED =
Puseful
Pin

PG
P
 1 D
Psource
Psource
and
 RED =
Puseful
Pin

Pload
P
 1 D
PG
PG
( 33 )
There are three main sources of energy loss in the system [18]: water transport, co-ion
transport due to non-ideality of the membranes and internal resistance. For increasing
temperature water transport increases, the permselectivity of the membrane decreases and
the internal resistance decreases. The expectation is that for increasing temperature the
thermodynamic efficiency of the system will increase while charging and discharging.
25
Chapter 3 Materials and methods
A description of the experiments will be given under methods. First, the constant current
experiments will be described, next the single pass experiments will be described and finally
the open circuit experiments will be described. Figure 13 is a schematic overview of the
experimental setup and Figure 14 is a picture of the actual setup. A description of this setup
will be given in the materials section of this chapter.
Methods
Table 1 gives an overview of the experiments that were done, what was measured and which
parameters are calculated from the experimental data.
Table 1: overview of the experiments
Experiment
Constant current (charge
mode)
Constant current (discharge
mode)
Open circuit
Single pass
Measured values
Current, voltage, mass in
diluate and concentrate buffer,
conductivity
Current, voltage, mass in
diluate and concentrate buffer,
conductivity
Current, voltage, mass in
diluate and concentrate buffer,
conductivity
Current, voltage, conductivity
Calculated from data
Water and salt flux, energy
density,thermodynamic
efficiency
Water and salt flux, power
density,thermodynamic
efficiency
Water flux (osmosis) and
salt flux (diffusion)
Internal resistance
Constant current experiment
Experiment description
U [V]
The purpose of this experiment is to measure the parameters needed to determine the total
mass transfer, power density, energy density and thermodynamic efficiency. In order to fully
charge and discharge the system a constant current is applied while recycling the
concentrate and diluate. The voltage, current, conductivity, pressure and mass in the
concentrate and diluate buffer will be measured. Figure 10 shows the expected response of
the system when applying a constant current.
t [s]
Figure 10: expected response when applying a constant current
The duration of the experiment is coupled to the time it takes until the highest or lowest
possible state of charge is reached, depending on whether the system is charging or
discharging.
26
Current, temperature, concentration and mass
Different currents were tested in order to determine the maximum thermodynamic efficiency
in a certain range of currents. This was done for both charging and discharging. Table 2
show the tested currents.
Table 2: Currents that were used in the constant current eperiments.
Mode of operation
Charging (mA)
Discharging (mA)
150
150
225
225
Current
275
325
300
400
375
The first set of experiments was done at 40 [°C]. After determining the optimal current at 40
[°C] the experiments were repeated at 10 and 25 [°C] using the same current. The
concentrations and mass at the start of the charge and discharge cycles are given in Table 3.
The mass and concentration of the diluate and concentrate at the end of the charge cycle
were used as starting point of the discharge cycle.
Table 3: Concentrations and mass at the start of the constant current experiments.
Fluid
Concentrate
Diluate
Rinse solution
Charge cycle
0.50 [mol/kg] | 250.0 [g]
0.50 [mol/kg] | 250.0 [g]
0.50 [mol/kg] | 500.0 [g]
Discharge cycle
0.85 [mol/kg] | 313.9 [g]
0.025 [mol/kg] | 187.0 [g]
0.50 [mol/kg] | 500.0 [ g]
Single pass experiment
Experiment description
The second type of experiment performed is a single pass experiment. In this case the
electrolyte solutions are not recycled but pass once through the stack. When no current is
applied the voltage equals the open circuit voltage. When a current is applied the voltage
drops due to the systems internal resistance. The purpose of this experiment is to determine
the systems internal resistance at different concentrations pairs. Figure 11 shows the
expected system response for this experiment.
Figure 11: Expected response when doing the single pass experiments. The systems voltage drops when
a current is applied.
27
Currents
For this experiment the system is operated in discharge mode (RED). The current that will be
applied is the optimal current which was determined in the previous set of experiments (150
[mA]).
Temperatures
This experiment will be repeated at three different temperatures: 10, 25 and 40 [°C].
Concentrations
At each temperature different sets of concentrations will be used. The concentrations are
selected by plotting the molality data which was measured in the constant current
experiments against the time. The concentration pairs are selected over the whole range of
the experiment. Table 4, Table 5 and Table 6 show the selected concentration pairs at the
different temperatures. Note that the number of concentration sets differs for the three
different temperatures.
Table 4: Concentration sets for single pass experiments at 10 [°C].
T = 10 [C]
Set 1
Set 2
Set 3
Set 4
Set 5
md [mol/kg]
0,03
0,11
0,18
0,24
0,31
mc [mol/kg]
0,80
0,75
0,70
0,65
0,60
Table 5: Concentration sets for single pass experiments at 25 [°C].
T = 25 [C]
Set 1
Set 2
Set 3
Set 4
Set 5
Set 6
md [mol/kg]
0,03
0,11
0,18
0,25
0,33
0,41
mc [mol/kg]
0,82
0,75
0,70
0,65
0,60
0,55
Table 6: Concentration sets for single pass experiments at 40 [°C].
T = 40 [C]
C1
C2
C3
C4
C5
C6
C7
md [mol/kg]
0,03
0,07
0,13
0,19
0,26
0,34
0,42
mc [mol/kg]
0,84
0,80
0,75
0,70
0,65
0,60
0,55
Open circuit experiment
Experiment description
The third type of experiment which is performed is an open circuit experiment. The
electrolyte solutions are recycled without applying a current. During the experiment the
voltage keeps decreasing because the driving force (concentration difference) also
decreases due to mass transfer by osmosis and diffusion. The purpose of this experiment is
to collect data needed for the calculation of the mass transfer at open circuit condition. This
data can then be used in order to quantify diffusion and osmosis.
Figure 12 shows the expected system response for this type of experiment. The system will
be operated in discharge mode (RED).
28
U [V]
t [s]
Figure 12: Expected response when doing an open circuit experiment
Currents
The system will be operated at open circuit conditions so the current is zero.
Temperatures
These experiments will be repeated for different temperatures: 10, 25 and 40 [°C].
Concentrations
The mass and concentration of the diluate and concentrate at the end of the charge cycle
were used as starting point of the discharge cycle.
Table 7: The fluid concentrations at the start of the charge and discharge cycles.
Fluid
Concentrate
Diluate
Rinse solution
29
Discharge cycle
0.85 [mol/kg] | 313.9 [g]
0.025 [mol/kg] | 187.0 [g]
0.50 [mol/kg] | 500.0 [ g]
Materials
Stack
The stack consists out of the following components:



Three cell pairs
CEM and AEM membranes which will be described next.
Two titanium mesh electrodes coated with Ir/Ru were used (Magneto), with an area of
10 x 10 cm2
Membranes
CMX and AMX membranes were used in the stack. The membranes had the following
properties (specified):


Thickness CMX/AMX: 0.17 [mm] / 0.14 [mm]
Area resistance CMX/AMX: 3 [Ω m2] / 2.4 [Ω m2]
Spacers
The distance between the membranes was fixed using spacers (Sefar) with the following
characteristics:


Thickness: 180 [µm]
open area: 41 %
Feedwater
The feedwaters varied for the different experiment and are specified in the methods section
per experiment. The feedwaters were pumped (Masterflex L/S Easyload II model 77200-60)
through the stack with 35 [mL/min]. The conditions in the concentrate and diluate
compartments were equal. The temperature of the feedwater was contolled using a
temperature bath (Thermo Scientific Haake K10). The mass in the feedwater buffers was
measured using Mettler Toledo PL300 1-S scales. The conductivity of the electrolyte
solutions was measured inline using conductivity probes (Thermo Fischer Scientific) and the
logging device was a Versa Start meter.
Electrode rinse solution
Sodium Sulfate solution 0.5 [mol/kg] was used as electrode rinse solution. The rinse solution
was pumped through the stack with 255 [mL/min].Two reference electrodes, type QM711X
(QIS) were used. The electrodes were placed at the two sides of the stack and made contact
with the electrode rinse solution via a small buffer (Figure 14). The electrochemical
measurements were done using a galvanostat (Ivium Technologies).
30
Experimental setup
Energy Source/Load
Diluate
- Temperature
- Conductivity
Sensor (Out)
Concentrate
- Temperature
- Conductivity
Sensor (Out)
Concentrate
Buffer
ED/RED
Process
Concentrate
Buffer
Scale
Concentrate
- Temperature
- Conductivity
Sensor (In)
Concentrate
Heat
Exchanger
Concentrate Concentrate
Pressure
Pump
Sensor
Figure 13: Schematic overview of the experimental setup.
31
Dilluate
Buffer
Diluate
Buffer
Scale
Diluate
- Temperature
- Conductivity
Sensor (In)
Diluate
Pressure
Sensor
Diluate
Pump
Diluate
Heat
Exchanger
Figure 14: Picture of the actual experimental setup.
32
Chapter 4 Results
Introduction
The objective of this chapter is to report and discuss the most important results from the
three experiments that were done:
1. single pass
2. open circuit
3. constant current (charge and discharge mode)
In the remainder of this chapter first the results from the single pass experiments will be
discussed. Based on the experimental data obtained from those experiments the influence of
temperature on the resistance can be shown. Next, the results from the open circuit
experiments will be discussed; topics are the influence of temperature on osmosis and
diffusion. After this, the basis for the selection of the charge and discharge current will be
explained, including results from the experiments. Then, the water and salt flux will be
discussed for both charge and discharge mode. The final topic will be the influence of
temperature on the system performance (power density, energy density and thermodynamic
efficiency). Plots of the voltage, molality and mass in the buffer are plotted versus time and
can be found in the appendix.
Single pass experiments
Resistance
Experiments were done in order to determine the total area resistance of the system. The
expectation was that the total internal resistance would decrease for increasing operating
temperature. Figure 15 shows a general overview of the results of the experiments. The total
area resistance [Ω∙cm2] is plotted against the state of charge. As expected the total internal
area resistance decreases if the temperature is increased.
Figure 15: Total area resistance per cell plotted against the state of charge for three different
temperatures.
33
The total internal area resistance is the sum of the ohmic area resistance per cell, the
resistance caused by the concentration change in the bulk solution and the area resistance
caused by the concentration change in the boundary layer.
Ri  RBL  R c  Rohmic
( 34 )
Experimental data already confirmed that the total internal area resistance decreases if the
temperature of the electrolyte solution increases. It is however insightful to see how the
separate components are influenced by temperature and to which extent. The components
were calculated based on the data of the single pass experiments. Figure 16, Figure 17 and
Figure 19 show the results of these calculations for the three components respectively.
Temperature and the boundary layer resistance
Figure 16 shows the boundary layer resistance plotted against the state of charge.
Figure 16: Total boundary layer area resistance components plotted against the state of charge for T = 10,
25 and 40 [°C].
The boundary layer resistance is a function of the velocity [19] and the viscosity of the fluid
will decreases if the temperature increases [16].
For laminar flow the boundary layer resistance is proportional to the residence time tres [s],
intermembrane distance, h [m] and cell length, L [m] [19]:
RBL  t res
h
L
( 35 )
In the experiments tres is constant because the volumetric flowrate is held constant. Changes
in the fluid velocity as a result of the change in fluid viscosity are thus compensated by the
pump. The expectation was that the boundary layer resistance would decrease at higher
temperatures. Based on this dataset that hypothesis is not confirmed. An explanation for the
difference in boundary layer resistance could be that the intermembrane distance varies
slightly throughout the different experiments. Overall the boundary layer resistance is not the
dominating factor in the total internal area resistance.
34
Temperature and the bulk concentration change resistance
Figure 17 shows the bulk concentration change resistance plotted against the state of
charge.
Figure 17: Total bulk concentration change resistance components plotted against the state of charge for
T = 10, 25 and 40 [°C].
This resistance depends on the concentration change due to charge transport [19]. It is a
function of temperature directly and through the membrane permselectivity. In order to
understand Figure 17 it is useful to see how temperature influences the permselectivity.
To illustrate that the permselectivity is affected by temperature the data from the single pass
experiments was used and the permselectivity was calculated. Figure 18 shows that
permselectivity indeed decreases at higher temperatures. The decrease in permselectivity
can, in part, be attributed to the fact that the membranes are not specifically designed for
high temperature use.
Figure 18 : Permselectivity versus state of charge, based on dataset of the single pass experiment, for
three different temperatures.
In Figure 17 the bulk concentration change resistance for state of charge higher than 0.75 is
slightly higher for T = 25 [°C] compared to T = 10 [°C]. This is a result of the permselectivity
at T = 10 [°C] being slightly lower than that of T = 25 [°C] for state of charge higher than 0.75.
The bulk concentration change resistance is a function of temperature, however overall
temperature is again not a dominant driver of this resistance component.
35
Temperature and ohmic resistance
Figure 19 shows the ohmic resistance plotted against the state of charge.
Figure 19: Ohmic resistance plotted against the state of charge for T = 40 [°C
The ohmic resistance is clearly the largest component of the total internal area resistance for
the experiments that were done. Figure 19 shows that this resistance increases when the
temperatures decreases. This can be explained by the fact that electrolyte conductivity
increases at higher temperatures.
Open circuit experiments
Effect of temperature on osmosis and diffusion
In Figure 20 the water transport by osmosis is plotted against the state of charge for three
different temperatures: 10, 25 and 40 [°C]. The system was operated in open circuit
(discharge) mode.
Figure 20: Water transport by osmosis for the open circuit experiments done at three different
temperatures.
36
Figure 20 shows that the water transport by osmosis clearly is higher at the highest
temperature of 40 [°C]. This increase is partly caused by the increase in osmotic pressure
difference, which is a function of temperature [9, p. 57]:
 c   d  RT v c  v a  cc  cd  (c  d )
( 36 )
Figure 21 shows that the osmotic pressure difference indeed increases if the temperature
increases. This increase in osmotic pressure difference is a consequence of the increased
water activity (Figure 9).
Figure 21: osmotic pressure difference versus state of charge for experiments done at open circuit
conditions and three different temperatures.
Another driver of the increased water transport is the increase in solvent mobility which is
reflected by a higher water diffusion constant, illustrated in Figure 22.
Figure 22: Water diffusion constant versus the state of charge for experiments done at open circuit
conditions and three different temperatures.
37
Effect of temperature on diffusion
In Figure 23 the salt transport by diffusion is plotted against the state of charge for three
different temperatures: 10, 25 and 40 [°C]. The system was operated in open circuit
(discharge) mode.
Figure 23: Effect of temperature on mass transfer by diffusion. Experiments were done at three different
temperatures.
Mass transfer by diffusion increases when the temperature increases. This increase can be
attributed to the increase in ion mobility and the decrease in permselectivity at higher
temperatures [6]. The influence of temperature on the membrane permselectivity was
already shown in Figure 18.
Figure 24 shows that ion mobility is affected by variations in temperature. Ion mobility is one
of the key drivers of the mass transport. Ion mobility was calculated based on the diffusion
coefficient using:
u
zFD
RT
( 37 )
The increase in ion mobility is an explanation for the increased diffusion coefficient and thus
mass transfer at higher temperatures.
Figure 24: Ion mobility versus state of charge for three different temperatures.
38
Constant current experiments
Optimal current density for charging (ED)
In Figure 25 the thermodynamic efficiency of the system is plotted against the state of charge
for five different currents. The system was operated in ED (charge) mode and the
temperature of the fluids was 40 [°C].
Figure 25: Efficiency of the battery tested at five different currents with temperature held constant at 40
[°C].
For low state of charge water transport is low and will increase as the state of charge
increases. At the start the chemical potential difference of the salt is zero, as a consequence
of the concentrations being equal. This explains why the efficiency is zero at zero state of
charge. As the state of charge increases the efficiency levels out. This leveling out is caused
by the increase of the internal resistance and the increase of the water transport.
Figure 26 shows the efficiency versus the dissipated power for the currents that were tested
in the charge experiments. For increasing current the dissipated power increases.
Figure 26: Efficiency of the system in charge mode versus the dissipated power.
The dissipated power consists of three components, as discussed in the theory. These
components are plotted against the state of charge in Figure 27, Figure 28 and Figure 29.
39
These plots show that the internal resistance losses dominate the total power dissipation.
Furthermore it can be concluded that the most optimal current, based on the chosen set of
currents, is 150 [mA]. However a current density of 325 [mA] was chosen for the charge (ED)
experiments based on the available information at that time.
Figure 27: Dissipated power: water transport losses for five different currents at T = 40 °[C]
Figure 28: Dissipated power: internal resistance losses for five different currents at T = 40 °[C]
Figure 29: Dissipated power: co-ion losses for five different currents at T = 40 °[C]
40
Optimal current density for discharging (RED)
In Figure 30 the efficiency of the system is plotted against the state of charge for four
different currents. The system was operated in RED (discharge) mode and the temperature
of the fluids was 40 [°C].
Figure 30: Efficiency of the system while discharging at different states of charge with temperature held
constant at 40 [C].
For this set of currents 150 mA was selected as optimal current. The remainder of the RED
experiments was done using this current.
Figure 31 shows the efficiency versus the power density for the currents that were tested in
the discharge experiments. Achieving a high power density means that the efficiency will be
lower. Figure 32, Figure 33 and Figure 34 show the dissipated power associated with water
transport, internal resistance and co-ion transport respectively. Figure 33 shows why a higher
power density means that the efficiency will be lower: the associated internal resistance
losses are higher.
Figure 31: Efficiency of the system in discharge mode versus the power density.
The losses associated with water and co-ion transport do not show consistent trends, unlike
those associated with the internal resistance. This is most likely caused by an increased
hydrostatic pressure. The data from the experiments 225 and 300 [mA] experiment show the
expected result: the dissipated power from water losses decreases if the current increases.
41
This result can be expected because osmosis and electro-osmosis work in opposite
directions. Electro-osmosis is coupled to the current, so at the start the water transport by
osmosis is countered by the water transport by electro-osmosis. The dissipated power
associated with the co-ion transport also shows this anomaly. The choice for 150 mA as the
most efficient current was correct because the dissipated power as a result of the internal
resistance was substantially lower compared to the other current densities. .
Figure 32: Dissipated power: water transport losses for four different currents at T = 40 °[C]
Figure 33: Dissipated power: internal resistance losses for four different currents at T = 40 °[C]
Figure 34: Dissipated power: co-ion losses for four different currents at T = 40 °[C]
42
Effect of temperature on energy density in ED mode
Figure 35 is a bar chart of the energy density. Each bar represents the energy density at a
different temperature. The system was operated in discharge (RED) mode at 10, 25 and 40
[°C].
The energy density is defined as the total amount of energy stored per unit volume diluate
and concentrate. The total amount of energy stored is equal to the total excess Gibbs free
energy of mixing. In order to increase the energy density the Gibbs total excess free energy
must be increased. As the temperature increases the excess Gibbs free energy of mixing
also increases [13]:
PG  nw  v  m  R  T  (1    ln  )
( 38 )
The expectation was that the energy density would also increase and Figure 35 shows that
this is indeed case.
Figure 35: Energy density of the system at three different temperatures, based on the excess Gibbs free
energy.
Effect of temperature on power density in RED mode
In Figure 36 the power density is plotted against the state of charge. Each line represents the
power density at a different temperature. The system was operated in discharge (RED) mode
at 10, 25 and 40 [°C].
Figure 36: Power density of the system at different temperatures. Current used was 150 mA.
As expected the power density increases as the temperature increases. This can be
explained by looking at the definition of the power density. The power density is a function of
43
the internal resistance. As the temperature increases the internal resistance decreases.
Hence the net effect is an increase in power density. The power density plotted in Figure 36
is the gross power density.
Effect of temperature on efficiency in ED mode
In Figure 37 the efficiency is plotted against the state of charge. Each line represents the
efficiency at a different temperature. The system was operated in charge (ED) mode at 10,
25 and 40 [°C].
Figure 37: Efficiency of the system while charging. Experiments were done at three different temperatures
using the optimal current density.
The dissipated power is plotted against the state of charge for the three experiments in
Figure 38, Figure 39 and Figure 40. For these experiments the following can be concluded:



For increasing temperature the internal resistance of the battery decreases which has
a positive effect on efficiency;
For increasing temperature the water transport increases (osmosis) which has a
negative effect on efficiency;
For increasing temperature self-discharge (diffusion) increases which has a negative
effect on efficiency;
The net effect is an increase of efficiency for an increase of temperature which can be seen
in Figure 37. The decrease of internal resistance outweighs the other negative effects of the
increase of temperature.
44
Figure 38 Dissipated power of the experiments done at T = 10 °[C] with the system running in charge
mode.
Figure 39 Dissipated power of the experiments done at T = 25 °[C] with the system running in charge
mode.
Figure 40 Dissipated power of the experiments done at T = 40 °[C] with the system running in charge
mode.
45
Effect of temperature on efficiency in RED mode
In Figure 41 the efficiency is plotted against the state of charge. Each line represents the
efficiency at a different temperature. The system was operated in discharge (RED) mode at
10, 25 and 40 [°C].
Figure 41: Efficiency of the system while discharging. The experiments were done at three different
temperatures.
The dissipated power is plotted against the state of charge for the three experiments in
Figure 42 Figure 43 and Figure 44. For these experiments the following can be concluded:



For increasing temperature the internal resistance of the battery decreases which has
a positive effect on efficiency;
For increasing temperature water transport increases (osmosis) which has a negative
effect on efficiency;
For increasing temperature diffusion increases which has a negative effect on
efficiency;
The net effect is an increase of efficiency for an increase of temperature which can be seen
in Figure 41. The decrease of internal resistance again outweighs the other negative effects
of the increase of temperature.
46
Figure 42 Dissipated power of the experiments done at T = 10 °[C] with the system running in discharge
mode.
Figure 43 Dissipated power of the experiments done at T = 25 °[C] with the system running in discharge
mode.
Figure 44 Dissipated power of the experiments done at T = 40 °[C] with the system running in discharge
mode.
Remarks
Experiments done in duplo
One of the major points of improvements of this thesis is the fact that not all experiments
were done in duplo. The data was measured with the following accuracy:



47
Voltage +/- 0.05 mV
Mass +/- 0.05 [g]
Conductivity +/- 0.005 mS/cm
Chapter 5 Conclusion
The main goal of this thesis was to quantify the influence of temperature on the power
density [W/m2], energy density [Wh/L] and efficiency [-] of a salinity gradient based energy
storage system, charged using electrodialysis and discharged using reverse electrodialysis.
Experimental data showed that:






The total electrical resistance decreases if the temperature increases;
Osmosis and diffusion increases if the temperature increases.
Energy density increases if the operating temperature increases.
Power density increases if the operating temperature increases.
In case of charging the increase of operating temperature increases the systems
thermodynamic efficiency.
In case of discharging the increase of operating temperature increases the systems
thermodynamic efficiency.
The figures show to which extent the performance parameters are influenced.
Chapter 6 General discussion and recommendations
In this chapter the economics of this energy storage system will be discussed. Then, the
characteristics of typical applications will be analyzed. Finally, the recommendation will be
given.
Economics
There are two types of cost to consider concerning an electricity storage system:
1. Energy cost: this includes the cost of storage elements, in the case of the salinity
gradient energy storage systems the tanks are a large component of this. The energy
cost is expressed in cost per unit of stored energy: Euro/kWh. Not to be confused with
the conventional cost of purchasing a unit of electricity, which has identical units. The
energy rating of a storage system is the total energy capacity that the system can
store.
2. Power cost: this includes the costs of the power electronics and membranes in the
case of the salinity gradient energy storage system. This power cost is expressed in
cost per unit of power: Euro/kW. The speed of charging and discharging is
determined by the power rating.
The two costs, power and energy, in combination give the total initial capital cost of the
storage system.
A simple method developed by Piyasak Poonpun [22] is used to estimate the economics of
storage units. This method converts the energy, power, installation, operating and
maintenance costs of a storage unit into the cost added to a unit of electricity stored. This
cost, referred to as the levelized cost, is then added to the conventional electricity price to
determine the total price of the stored electricity.
48
Figure 45: Levelized cost per kWh for several energy storage systems. The incumbent technology, a gas
turbine, is indicated by the dotted line. Figure adopted from [1]
Figure 45 shows the levelized cost of a few energy storage technologies in euros/kWh. In
order for the salinity gradient energy storage to be cost competitive the levelized costs
should be at most 0.20 euro/kWh. Pumped hydro storage is the cheapest competitor
available on the energy storage market today with a levelized cost of about 0.10 euro/kWh .
Ways to achieve this competitive price is to decrease the price of the membranes, or
increase the performance of the membranes because the membranes are the most
expensive component of the system. Another approach is to focus on groups of applications
requiring a large capacity to power ratio. The costs of storage capacity of this system are
extremely low making it very suitable for the aforementioned group of applications.
Applications
A way to characterize electricity storage systems is by observing the relation between power
and energy. Based on this relation the salinity gradient based energy storage system can be
positioned in relation to that of other electricity storage systems. Figure 46 is a conceptual
representation of the power/energy relation with the power rating on the horizontal and the
discharge time on the vertical axis. On the one extreme there is pumped hydro with a large
capacity and a discharge time in the order of tens of hours. On the other extreme there are
electrochemical batteries with low power and discharge times in the order of minutes.
Figure 46: Positioning of energy storage technologies based on the power-energy relation. Figure
adopted from [1, p60.]
49
In this context the salinity gradient based electricity storage system can best be compared
with flow batteries. This comparison is justified because just like flow batteries the power
rating is decoupled from the discharge time. Discharge times are expected to be in the order
of hours and power ratings can range from 1 kW to several MW’s. The exact range will
depend on the capital and levelized cost. The salinity gradient energy storage system can
thus best be applied in situations where relatively long discharge time and low power output
are not an issue.
Recommendations
Irreversible water transport of the system has a large impact on the system performance.
Therefore future research should be done in order to decrease this phenomenon. This
means that strategies need to be devised in order to reduce the osmotic pressure difference
between the concentrate and diluate chambers. Furthermore the internal resistance is an
important factor to consider for the overall performance of the system. Currently research is
already being done in order to reduce the internal resistance. Increasing the conductivity of
the diluate chamber is an important strategy. Lastly the self-discharge of the system is also a
parameter to consider and research is also already being done to develop membranes that
have high permselectivity.
50
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from salinity gradients using reverse electrodialysis. Energy Procedia, 20, 170-184.
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52
Appendix A: Experimental data of constant current ED experiments
53
54
55
56
57
58
59
60
Appendix B: Experimental data for constant current RED experiments
61
62
63
64
65
66
Appendix C: Experimental data of open circuit experiments
67
68
69
Appendix D: Experimental data of single pass experiments
T = 10 [°C] series
70
T = 25 [°C] series
71
72
T = 40 [°C] series
73
74
75
Appendix E: List of figures
Figure 1: Salinity gradient based energy storage system, charged using electrodialysis (ED)
and discharged using reverse electrodialysis (RED). Figure adopted from David Vermaas,
STW proposal AquaBattery 2015. ........................................................................................10
Figure 2: Schematic diagram illustrating the principle of desalination by electrodialysis in a
stack with cation and anion-exchange membranes in alternating series between two
electrodes. Adopted from [9].................................................................................................12
Figure 3: schematic representation of a stack configuration consisting of two endplates,
gaskets, spacers, membranes and electrodes. The components enclosed by the accolades
form the repeating unit (cell pairs). Adopted from [10, p. 49].................................................13
Figure 4: Structure of a cation-exchange membrane with fixed anions, a polymer matrix and
mobile co- and counter-ions. ................................................................................................14
Figure 5: Overview of mass transport directions in case of charging(ED) and discharging
(RED). ..................................................................................................................................15
Figure 6: Illustration of the principle of osmosis. The concentrate and diluate chambers are
separated by a membrane. Due to the chemical potential difference of the solvent a water
flux will occur. This illustration was adapted from [9, p.54] ....................................................17
Figure 7: When a current is applied to the system a voltage drop will occur due to the
systems internal resistance. .................................................................................................19
Figure 8: Activity coefficients calculated using the virial equations of Pitzer. The activity
coefficient decreases when temperature decreases. ............................................................22
Figure 9: Osmotic coefficients calculated using the virial equations of Pitzer. The osmotic
coefficient decreases when temperature decreases. ............................................................23
Figure 10: expected response when applying a constant current .........................................26
Figure 11: Expected response when doing the single pass experiments. The systems voltage
drops when a current is applied. ...........................................................................................27
Figure 12: Expected response when doing an open circuit experiment ................................29
Figure 13: Schematic overview of the experimental setup. ...................................................31
Figure 14: Picture of the actual experimental setup. .............................................................32
Figure 15: Total area resistance per cell plotted against the state of charge for three different
temperatures. .......................................................................................................................33
Figure 16: Total boundary layer area resistance components plotted against the state of
charge for T = 10, 25 and 40 [°C]. ........................................................................................34
Figure 17: Total bulk concentration change resistance components plotted against the state
of charge for T = 10, 25 and 40 [°C]. ....................................................................................35
Figure 18 : Permselectivity versus state of charge, based on dataset of the single pass
experiment, for three different temperatures. ........................................................................35
Figure 19: Ohmic resistance plotted against the state of charge for T = 40 [°C.....................36
Figure 20: Water transport by osmosis for the open circuit experiments done at three
different temperatures. .........................................................................................................36
Figure 21: osmotic pressure difference versus state of charge for experiments done at open
circuit conditions and three different temperatures. ..............................................................37
Figure 22: Water diffusion constant versus the state of charge for experiments done at open
circuit conditions and three different temperatures. ..............................................................37
Figure 23: Effect of temperature on mass transfer by diffusion. Experiments were done at
three different temperatures. ................................................................................................38
76
Figure 24: Ion mobility versus state of charge for three different temperatures. ....................38
Figure 25: Efficiency of the battery tested at five different currents with temperature held
constant at 40 [°C]. ...............................................................................................................39
Figure 26: Efficiency of the system in charge mode versus the dissipated power. ................39
Figure 27: Dissipated power: water transport losses for five different currents at T = 40 °[C] 40
Figure 28: Dissipated power: internal resistance losses for five different currents at T = 40
°[C] .......................................................................................................................................40
Figure 29: Dissipated power: co-ion losses for five different currents at T = 40 °[C]..............40
Figure 30: Efficiency of the system while discharging at different states of charge with
temperature held constant at 40 [C]......................................................................................41
Figure 31: Efficiency of the system in discharge mode versus the power density. ................41
Figure 32: Dissipated power: water transport losses for four different currents at T = 40 °[C]
.............................................................................................................................................42
Figure 33: Dissipated power: internal resistance losses for four different currents at T = 40
°[C] .......................................................................................................................................42
Figure 34: Dissipated power: co-ion losses for four different currents at T = 40 °[C] .............42
Figure 35: Energy density of the system at three different temperatures, based on the excess
Gibbs free energy. ................................................................................................................43
Figure 36: Power density of the system at different temperatures. Current used was 150 mA.
.............................................................................................................................................43
Figure 37: Efficiency of the system while charging. Experiments were done at three different
temperatures using the optimal current density. ...................................................................44
Figure 38 Dissipated power of the experiments done at T = 10 °[C] with the system running in
charge mode. .......................................................................................................................45
Figure 39 Dissipated power of the experiments done at T = 25 °[C] with the system running in
charge mode. .......................................................................................................................45
Figure 40 Dissipated power of the experiments done at T = 40 °[C] with the system running in
charge mode. .......................................................................................................................45
Figure 41: Efficiency of the system while discharging. The experiments were done at three
different temperatures. .........................................................................................................46
Figure 42 Dissipated power of the experiments done at T = 10 °[C] with the system running in
discharge mode. ...................................................................................................................47
Figure 43 Dissipated power of the experiments done at T = 25 °[C] with the system running in
discharge mode. ...................................................................................................................47
Figure 44 Dissipated power of the experiments done at T = 40 °[C] with the system running in
discharge mode. ...................................................................................................................47
Figure 45: Levelized cost per kWh for several energy storage systems. The incumbent
technology, a gas turbine, is indicated by the dotted line. Figure adopted from [1] ...............49
Figure 46: Positioning of energy storage technologies based on the power-energy relation.
Figure adopted from [1, p60.] ...............................................................................................49
77
Appendix F: List of tables
Table 1: overview of the experiments ...................................................................................26
Table 2: Currents that were used in the constant current eperiments. ..................................27
Table 3: Concentrations and mass at the start of the constant current experiments. ............27
Table 4: Concentration sets for single pass experiments at 10 [°C]. .....................................28
Table 5: Concentration sets for single pass experiments at 25 [°C]. .....................................28
Table 6: Concentration sets for single pass experiments at 40 [°C]. .....................................28
Table 7: The fluid concentrations at the start of the charge and discharge cycles. ................29
78