Mathematical modelling, design, and optimization of electrochemical capacitor cells
Date
2017
Authors
Ike, Innocent Sunday
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The effects of self-discharge on the performance of symmetric electric double layer capacitors
(EDLCs) and active electrolyte enhanced supercapacitors (AEESCs) were examined by
incorporating self-discharge into electrochemical capacitor (EC) models during charging and
discharging. The effects of self-discharge on the performance of asymmetric ECs were also
studied by including applicable self-discharge mechanisms into mass transfer and charge
conservation equations during charging and discharging. Sources of self-discharge in capacitors
are several impurities, side-reactions, redox reactions and electric double layer's (EDLs)
instability. Incorporation of self-discharge into symmetric and asymmetric EC models, created a
platform to reduce the number of experiments to determine the minimum allowable amount of
impurities and redox species in components of the device for maximum performance. It was
observed that key self-discharge parameters to be tuned in order to suppress the EC self
discharge rate are concentration of shuttle impurities, concentration of redox species, and
thickness of the separator. Tuning key self-discharge parameters of a symmetric device with both
side-reactions/redox reactions and EDLs instability self-discharges, improved first and second
charge-discharge cycle efficiency 1 E
and 2 E
. These charge-discharge cycle efficiencies ( 1 E
and
2E
) were enhanced from 38.13% and 38.14% to 80.54% and 81.56% respectively, compared
with 84.24% and 84.25%, respectively in similar capacitor without self-discharge. The tuning
process also improved energy efficiencies 1 E
and 2 E
of the asymmetric device with both side
reactions/redox reactions and EDL's instability self-discharges from 67.21% and 75.00% to
87.21% and 88.70% respectively, compared with 90.72% and 90.82%, respectively in a similar
capacitor without self-discharge. Energy loss by self-discharge in the symmetric capacitor with
tuned key self-discharge parameters was reduced from 28.38Wh in untuned to 5.60Wh, while
that of the asymmetric capacitor with tuned key self-discharge parameters was reduced from
59.53Wh in untuned to 7.43Wh. Fast charging and discharging of the EC greatly reduced the
self-discharge rate, compared with slow charging and discharging. In symmetric and asymmetric
capacitors, both EDL's instability and side-reactions and/or reactions self-discharges occurs in
significant measure but side-reactions or reactions contributed to the majority of the self
discharges. It was shown that models that incorporated self-discharge give more practical
evaluation of voltage decay and energy dissipation during self-discharge.
The influence of different charging current densities, charging times and several structural
designs on symmetric EC performance such as capacitance, energy density and power density
was investigated through modelling and simulation. The effects of different charging current
densities, charging times and several structural designs on asymmetric EC performance via
modelling and simulation can be investigated, and the results would be similar. The difference
between symmetric and asymmetric ECs is that symmetric use the same type of electrode
while asymmetric use different types of electrodes. Clear understanding of the effects of
different structural design variables and operating conditions on capacitors’ performance will
guide in optimal design and fabrication of high performance ECs. The operating conditions
and design configurations examined are charging current density, charging times, electrode
and electrolyte effective conductivity, electrode thickness and electrode porosity. It was
revealed that ECs with low electrode and electrolyte effective conductivities can only be
effectively charged at a low current density for extended periods of time. ECs with high
concentrations of impurity ions and redox species exhibit high self-discharge rates, which
result in voltage decay after charging. Reduction of charging time by charging the EC fast,
greatly reduced the rate of self-discharge compared with the slow charging process. The
simulation showed that the typical electrode length scale over which the liquid potential drop
occurs and electrode utilization can be used as a design parameter to optimize electrode
thickness (effective thickness) of the EC which should function within a specific current
density range. This is also a guideline that can be used to determine the optimum electrodes
thickness (100% electrodes utilization), optimum charging current density and optimum
charging time for cells of a given voltage, electrode's thickness, and electrodes and
electrolyte’s effective conductivities. The energy density of the capacitor with specific
electrodes and electrolyte effective conductivities was increased 2.125, 4.750 and 10.75 folds
by reducing the electrode's thickness 1.33, 2.00, and 4.00 folds, respectively. The power
density of the capacitor, with specific electrodes thickness, and given electrode and electrolyte
effective conductivities charged at a specific current density, increased by a factor of 10, 100
and 1000, when the charging rate was increased 10, 100 and 1000, times respectively. The
power density of the capacitor with specific electrodes thickness, and a given electrodes and
electrolyte effective conductivities, also increased approximately eleven-fold when the
electrode's thickness was reduced four-fold under a given charging conditions. The ragone
plots generated for different electrode sizes via modeling and simulation, can be used to select
optimum electrode dimensions to attain certain energy and power densities specifications.
Theoretical expressions for performance parameters of different ECs were optimized by
writing MATLAB scripts to solve them and also via the MATLAB R2014a optimization tool
box. Performances of different kinds of ECs at given circumstances were compared through
theoretical equations and simulation of various models, subject to the conditions of device
components using optimal BMopt K and Eopt K , as well as the symmetric EDLC experimental data.
The storable energy Ech, maximum energy density EDmax and power density PDmax of
symmetric and asymmetric EC using suitable electrode mass, operating potential range ratios
and proper organic electrolyte (optimum BMopt K and Eopt K ) were 562.78Wh, 382.42Wh/kg &
76.29W/kg and 1304.30Wh, 837.00Wh/kg & 167W/kg, respectively. Estimations of
performance parameters were feasible and achievable once details of electrodes mass ratio,
operating potential range ratio and specific capacitance of electrolyte are known.
Performances of asymmetric EC with suitable electrode mass and operating potential range
ratios using aqueous electrolytes, and that with suitable electrode mass, operating potential
range ratios and organic electrolyte with appropriate operating potential range and specific
capacitance were 2.20 and 5.56 folds, respectively, greater than those of symmetric EDLC and
asymmetric EC using the same aqueous electrolyte. This enhancement came together with
reduction in cell mass and volume. Storable and deliverable energies of the asymmetric EC
with suitable electrode mass and operating potential range ratios using proper organic
electrolyte were also a factor of 12.9 greater than those of symmetric EDLCs using aqueous
electrolyte reduction in cell mass and volume by a factor. Storable energy, energy density and
power density of asymmetric EDLCs with suitable electrode mass and operating potential
range ratios, using proper organic electrolyte, were a factor of 5.56 higher than those of
similar symmetric EDLCs using aqueous electrolyte reduction in cell mass and volume by a
factor 1.77. These results can obviously reduce the number of experiments needed to
determine the optimum manufacturing state of ECs. They also demonstrated that introduction
of an asymmetric electrode and organic electrolyte was very successful in improving
performance of the EC with reduction in cell mass and volume. Introduction of an asymmetric
EDLC with the same type of electrode, and suitable electrodes mass ratio, working potential
range ratios and proper organic electrolyte, equally enhanced the performance of a
conventional symmetric EDLC using aqueous electrolyte with reduction in cell mass and
volume. These results can be a guideline for design, fabrication and operation of
electrochemical capacitors with outstanding performance in terms of high storable energy,
energy and power densities.
Description
A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering (Chemical Engineering) to the Faculty of Engineering and the Built
Environment, University of the Witwatersrand, Johannesburg, Johannesburg, 2017
Keywords
Citation
Ike, Innocent Sunday (2017) Mathematical modelling, design and optimization of electrochemical capacitor cells, University of the Witwatersrand, Johannesburg, https://hdl.handle.net/10539/24089