Microbial fuel cells: a fast converging dynamic model for ...epubs.surrey.ac.uk/851738/1/Microbial...
Transcript of Microbial fuel cells: a fast converging dynamic model for ...epubs.surrey.ac.uk/851738/1/Microbial...
Microbial fuel cells: a fast converging dynamic model
for assessing system performance based on bioanode
kinetics
Siddharth Gadkaria,b, Mobolaji Shemfeb, Jhuma Sadhukhana,b
aDepartment of Chemical and Process Engineering, University of Surrey, Guildford GU27XH, United Kingdom
bCentre for Environment and Sustainability, University of Surrey, Guildford, SurreyGU2 7XH, United Kingdom
Abstract
In this work, a dynamic computational model is developed for a single
chamber microbial fuel cell (MFC), consisting of a bio-catalyzed anode and
an air-cathode. Electron transfer from the biomass to the anode is assumed
to take place via intracellular mediators as they undergo transformation be-
tween reduced and oxidized forms. A two-population model is used to de-
scribe the biofilm at the anode and the MFC current is calculated based on
charge transfer and Ohm’s law, while assuming a non-limiting cathode reac-
tion rate. The open circuit voltage and the internal resistance of the cell are
expressed as a function of substrate concentration. The effect of operating
parameters such as the initial substrate (COD) concentration and external
resistance, on the Coulombic efficiency, COD removal rate and power den-
sity of the MFC system is studied. Even with the simple formulation, model
predictions were found to be in agreement with observed trends in experi-
∗Corresponding authorEmail address: [email protected] (Siddharth Gadkari)
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mental studies. This model can be used as a convenient tool for performing
detailed parametric analysis of a range of parameters and assist in process
optimization.
Keywords: Microbial fuel cell, Bioelectrochemical system, Mathematical
analysis, Dynamic model, Fast convergence
1. Introduction1
Wastewater treatment consumes large amounts of energy and is a major2
source of greenhouse gas emissions. Moreover, wastewater when discharged3
without treatment causes serious damage to human health and the environ-4
ment [1]. Rising urbanization is leading to increased wastewater generation,5
which further aggravates these challenges, while at the same time using more6
of our planet’s diminishing resources [2]. Thus, recovering energy and re-7
sources from wastewater should be no longer considered a choice, but a key8
opportunity that must be seized for a low carbon future. Wastewater treat-9
ment technologies that can provide energy-neutral operation and help to10
mitigate the multiple challenges of energy efficiency, resource scarcity and11
environmental pollution, can make this process sustainable [3]. In this re-12
gard, microbial fuel cells (MFCs) that use microorganisms as a biocatalyst13
and convert chemical energy from organics in wastewater to (bio)electricity,14
offer a sustainable technological solution [1, 4]. MFCs can transform wastew-15
ater treatment, which is traditionally an energy-consuming process, into an16
energy-neutral and potentially an energy-producing process [3, 5]. This real-17
ization has led to an incremental increase in MFC research in the last 10-1518
years [4–7].19
2
Focused research has helped in improving the power densities with several20
MFC systems reaching close to 1 W m−2 [8, 9]. Few optimized designs have21
managed to obtain even higher power densities up to 3-7 W m−2 [8, 10–13].22
Ren et al. [11] developed a miniaturized MFC with 3D graphene macroporous23
scaffold anode and obtained a record high current density of 15.51 A m−224
(31040 A m−3) and a power density of 5.61 W m−2 (11220 W m−3). Chen25
et al. [12] have reported current densities as high as 390 A m−2 using layered26
corrugated carbon (LCC) as electrodes. However despite this progress, the27
power density of MFCs are still orders of magnitude lower than the chemical28
fuel cells (which are typically > 104 W m−2). This highlights the need for29
further optimization.30
As the electrochemical reactions in an MFC involve biochemical path-31
ways, its performance is not only dependent on operational and design param-32
eters but also on several biological factors [14]. The different processes in an33
MFC with a biocatalysed anode and a chemical cathode, involves a complex34
interplay between electrochemistry, microbiology, material science, transport35
phenomena, and environmental biotechnology [15]. Thus, an in-depth under-36
standing of an MFC system requires a multidisciplinary approach. While the37
advances in MFC design, membrane and electrode materials have certainly38
helped to reduce the cost and increase the power outputs of MFC manifolds,39
a number of challenges still limit the applicability when compared to existing40
technologies [7]. Mathematical models along with experimental studies have41
played an important role in improving MFC performance and facilitating the42
design and system optimization [16–19].Different approaches, ranging from43
the simple formulations describing the bulk bioelectrochemical reactions to44
3
2D/3D formulations accounting for lateral biofilm growth and electrode ge-45
ometries, have been used to model MFC [20, 21].46
Zhang and Halme [22] developed one of the first mathematical models for47
MFC. This was a simple model based on ordinary differential equations, and48
used Monod equation, Faradays law and Nernst equation to calculate the49
MFC current. While the simplistic formulation is based on a lot of assump-50
tions, it served as a good starting point for more advanced analysis. Pinto51
et al. [23] also developed a dynamic model based on ODEs for MFC but they52
used a two population model for representing the microbial population at the53
bioanode, and used the multiplicative Monod kinetics to represent the biofilm54
growth dynamics. They also considered the material balance for substrate55
and mediators and derived the expression for MFC current using Ohms law56
and the voltage over-potentials. While this model was easy to implement and57
allowed fast numerical simulations, the internal resistance and open circuit58
voltage were calculated based on concentration of anodophilic microorgan-59
isms, which is something difficult to measure experimentally, which limits60
the applicability of this approach. Other than the dynamic models based on61
ODEs, more comprehensive mathematical models have also been proposed.62
For e.g. Picioreanu et al. [24] developed a multidimensional mathematical63
model focusing on the anode chamber of MFC considering a mixed culture64
of bacteria. They assumed mediated electron transfer and derived the cell65
voltage using Butler-Volmer equation and Ohms law, while accounting for66
the activation, ohmic and concentration over-potentials at the anode. They67
used the comprehensive model to understand the effect of system parameters68
such as initial substrate and mediator concentrations, mass transfer bound-69
4
ary layer, ratio of suspended to biofilm cells, external load resistance, etc.70
on the power generation capacity and the substrate consumption rate. How-71
ever the added physics, also correspondingly increased the computational72
expense of the simulation, with the full 3D model taking close to 14 h for73
solving about 15 days of MFC operation [24]. More recently Esfandyari et al.74
[25] developed a two chamber batch MFC model consisting of three main do-75
mains, bulk liquid in the anode chamber, biofilm attached to anode and76
bulk liquid in the cathode chamber. They assumed a direct electron transfer77
mechanism and used the Nernst-Monod equation to derive the substrate con-78
sumption rate. The model included the material balance equations for the79
active & inactive bacteria, substrate (lactate), carbon dioxide and protons80
in the biofilm, along with the substrate and CO2 mass balance in the anode81
chamber and oxygen in the cathode chamber. The MFC output voltage was82
calculated by accounting the different overpotential losses. The results from83
the model showed good agreement with the voltage and current observed84
experimentally. While this model was based on ODEs it was relatively more85
comprehensive than Pinto et al. [23]. However on account of improving the86
model rigor and including the various phenomena in the anode & cathode87
chambers and the biofilm, the total number of model equations (total 1088
ODEs and 9 algebraic equations) also correspondingly increase the compu-89
tational expense of the simulation. Additionally, because the model is based90
on lumped formulation, it does not capture the spatial biofilm dynamics even91
with the high computational cost [25].92
Thus, while the more detailed models typically based on partial differen-93
tial equations are expensive in terms of time and computational resources,94
5
the formulations based on ordinary differential equations (ODEs) sometimes95
trivialize the complex process dynamics or are based on parameters that96
are difficult to calculate/measure experimentally. [22–24, 26–28]. The goal97
of this study is to present a simple mathematical formulation that can suffi-98
ciently describe the important processes in an MFC with governing equations99
for mass transfer, bio-electrochemical kinetics, and charge transfer, without100
being computationally intensive. One important distinction of the proposed101
model from the previous approaches is the derivation of concentration over-102
potential, internal resistance and open circuit voltage, which is based here103
on an easily measurable quantity such as the substrate concentration. This104
simplifies the calculation of MFC voltage and provides an easier method for105
assessing system performance and process optimization. In this paper, the106
mathematical model is used to understand the effect of operating parame-107
ters on key performance indicators of MFC such as the, Coulombic efficiency,108
substrate (COD) removal rate and power density of the system.109
2. Model formulation and parameter estimation110
The dynamic model developed in this work is based on the batch operated111
single chamber MFC consisting of a biotic anode and an air-cathode, as112
described in Liu and Logan [29]. The microbial population at the anode113
is represented using a simple two population model, clubbing the bacteria114
into two types, one that consume the substrate (COD) and release electrons115
which are then transferred to the anode via intracellular mediators (primary116
microbial population) and second type that decompose the substrate but do117
not contribute to power generation (secondary microbial population).118
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The important assumptions made in the model are as follows:119
Substrate in the MFC chamber is perfectly mixed.120
Microbial population in the biofilm of the anode is uniformly dis-121
tributed.122
Any gases (CO2, H2, etc.) released during substrate oxidation at the123
anode remain dissolved in the bulk solution.124
MFC is operated in fed-batch mode.125
Changes in pH and temperature are negligible.126
Electrons are transferred from the cells to the anode using intracellu-127
lar mediators, as they undergo transformation between reduced and128
oxidized forms.129
Continuous supply of intracellular mediators is maintained.130
2.1. Mass balance131
The primary microbial population (xp) consumes the substrate (S) and,132
in this process, the oxidized form of the intracellular mediator (Mox) is also133
converted into its reduced form (Mred). This reduced intracellular mediator134
transfers the electron to the anode and also releases a proton as it regains its135
oxidized form. A conceptual schematic of this process is described in figure136
1. Meanwhile, the secondary microbial population (xs) also consumes the137
substrate but does not release any free electrons which can be intercepted by138
the intracellular mediators.139
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Figure 1: Conceptual schematic showing substrate (S) degradation by a primary bacterial
cell (xp) and electron (e−1) transfer to the anode via reduced (Mred) and oxidized (Mox)
intracellular mediators.
Considering a fed-batch operation, the rate of change of substrate and
biomass concentrations can be expressed as follows:
dS
dt= −qpxp − qsxs (1)
dxpdt
= µpxp −Kdpxp (2)
dxsdt
= µsxs −Kdsxs (3)
where S represents the substrate concentration (g-S L−1), x is the microbial140
concentration (g-x L−1), q is the substrate consumption rate (g-S g-x−1 d−1),141
µ is the microbial growth rate (d−1) and Kd is the microbial decay rate (d−1).142
The subscripts ‘p’ and ‘s’ represent the primary and secondary microbial143
populations respectively.144
The intracellular mediator exists in either oxidized (Mox) or reduced form
(Mred), however the total mediator concentration Mtotal remains constant,
8
and can thus be expressed as:
Mtotal = Mox +Mred (4)
The transfer of electrons from intracellular mediator to anode and then
further to cathode, results in current generation. The rate of change of the
oxidized mediator concentration is described as follows:
dMox
dt= −Y qp +
γ
V xp
(IMFC
mF
)(5)
where, Y is the dimensionless mediator yield, IMFC is the MFC current (A),145
m is the number of electrons transferred per mol of mediator, F is the Faraday146
constant (A s mol−1), V is the working volume of the anode chamber, and γ147
is the molar mass of the mediator (g mol−1).148
The substrate consumption rate by the primary microbial population and
the corresponding microbial growth rate are dependent on both the oxidized
mediator concentration and the substrate concentration, and are thus de-
scribed using the multiplicative Monod kinetics. On the other hand, the
substrate consumption rate by the secondary bacteria and the corresponding
microbial growth rate are only limited by the substrate concentration, and
are represented using standard Monod kinetics. The substrate consumption
and growth rates are described as follows:
qp = qmaxp
(S
KSp + S
)(Mox
KM +Mox
)(6)
µp = µmax,p
(S
KSp + S
)(Mox
KM +Mox
)(7)
qs = qmaxs
(S
KSs + S
)(8)
µs = µmax,s
(S
KSs + S
)(9)
9
where, KS and KM are the Monod half saturation coefficients for the sub-149
strate and mediator respectively (g L−1), qmax and µmax represent the max-150
imum substrate consumption rate and maximum growth rate respectively151
(d−1).152
2.2. Ohm’s Law and voltage losses153
The standard electrode potentials determine the maximum theoretical
voltage that can be generated from the MFC. However there are activation,
concentration and ohmic voltage losses in the system. Accounting for these
overpotential losses and the internal & external resistance, the current gen-
erated in the MFC can be expressed using Ohm’s Law as follows [23]:
IMFC =Eocv − ηact − ηconc
Rext +Rint
(10)
where Eocv is the open circuit voltage (V), Rext and Rint are the external154
and internal resistance in the electrochemical cell, ηact and ηconc represent155
the activation and concentration over-potentials (V).156
A constant supply of intracellular electron transfer mediators is assumed,
which undergo transformation between reduced and oxidized forms as they
transfer electrons to the anode. Thus the major limiting factor influencing the
voltage losses at the anode is the substrate concentration. The concentration
overpotential at the anode can therefore be expressed as a function of initial
substrate concentration (Sin) and the dynamic substrate concentration (S),
as follows:
ηconc =RT
mFln
(SinS
)(11)
10
Activation overpotential represents losses due to the slow electrochemical
kinetics, and can be expressed by the following equation:
ηact =RT
βmFsinh−1
(IMFC
Ani0
)(12)
where T is the system temperature (K), R is the universal gas constant (J157
mol−1 K−1), β is the charge transfer coefficient, An is surface area of anode158
(m2), and i0 is the exchange current density (A m2−1).159
It has been shown that increase in organic substrate concentration in-
creases the ionic strength of the anolyte, which helps in improving the open
circuit voltage and reducing the internal resistance of the cell [30–32]. These
correlations can be used to further improve the model efficacy by incorporat-
ing dynamic expressions for open circuit voltage and internal resistance as a
function of substrate concentration:
Eocv = Emin + (Emax − Emin) e−1
Kr1S (13)
Rint = Rmin + (Rmax −Rmin) e1
Kr2S (14)
where, Emin and Emax represent the lowest and the highest observed open160
circuit voltage in the system, Rmin and Rmax represent the lowest and the161
highest observed internal resistance in the system. Kr1 and Kr2 are constants162
[L g−1] which determine the slope of the curve. Similar expressions have been163
previously derived by Pinto et al. [23], considering open circuit voltage and164
internal resistance to be a function of anodophilic microorganisms.165
MFC performance is typically assessed based on the maximum voltage
that can be generated and the substrate or COD removal efficiency. In addi-
tion to these two, Coulombic efficiency (εE) is another important performance
11
indicator and determines the electron recovery of the system. It represents
the ratio of the total number of electrons recovered at the anode and the
maximum number of electrons that could have been recovered if all the con-
sumed substrate contributed to current generation. In the present analysis,
the MFC is assumed to be operating in fed-batch mode and thus εE can be
expressed as [33]:
εE =Mo
∫ t0IMFCdt
FbV∆S(15)
where Mo is the molecular weight of oxygen, b is number of electrons166
exchanged per mole of oxygen and ∆S is the change in substrate (COD)167
concentration over time t.168
2.3. Parameter estimation169
The governing equations described in sections 2.1 and 2.2, can be solved170
in an ODE solver to determine the influence of different parameters on the171
MFC performance. However most of the biological parameters such as the172
maximum substrate consumption rates, maximum microbial growth rates,173
yield coefficient, half saturation constants, etc., are specific to the microbial174
population and the substrate used in the experiment. Thus these parameters175
are estimated using best-fit regression analysis by comparing the numerical176
results with experimental values obtained from Liu and Logan [29].177
12
Figure 2: Predicted values of MFC voltage (black solid line) obtained from curve fitting
using Nelder-Mead Simplex algorithm compared to the corresponding experimental values
red solid circles for 3 days of MFC operation. The experimental data has been adopted
from Liu and Logan [29].
In numerical curve fitting, the objective function (J), which is defined178
as, J =∑t
(yexp(t) − ysim(t)
)2, is minimized to obtain the parameter values.179
Here yexp(t) and ysim(t) represent the values of y obtained from experiment180
and numerical simulation respectively at a particular time t. In this analy-181
sis, the objective function is defined as the difference between theoretical and182
measured MFC voltage. The simplex search method is used for minimizing183
the objective function [34]. Figure 2 shows the experimental and fitted values184
of MFC voltage as a function of time. As can be seen, there is satisfactory185
agreement between the experimental and fitted values, indicating a reason-186
ably good estimate of the parameters. The final parameter values obtained187
from the curve fitting, and other parameters that were directly obtained from188
13
literature are given in Table 1.189
Table 1: Model parameter values
Parameter Value Unit Notes/Reference
qmaxp 0.9 day−1 Estimated
µmaxp 7.1 day−1 Estimated
qmaxs 0.84 day−1 Estimated
µmaxs 0.6 day−1 Estimated
KSs 425 mg L−1 Estimated
KM 0.11 1 Estimated
Rmin 8 Ω Estimated
Rmax 500 Ω Estimated
Kr1 0.5 L mg−1 Estimated
Kr2 0.004 L mg−1 Estimated
i0 0.048 A m−2 Estimated
Y 30.25 1 Estimated
Emin 0.01 V [23]
Emax 0.66 V [23]
Kdp 0.02*µmaxp day−1 [23]
Kds 0.02*µmaxs day−1 [23]
m 2 1 [23]
γ 663.4 g mol−1 [23]
KSp 103 mg L−1 [29]
An 7 cm2 [29]
V 28 cm3 [29]
b 4 1 [33]
F 96,485 A s mol−1 Constant
R 8.314 J K−1 mol−1 Constant
T 298.15 K Assumed
β 0.5 1 Assumed
3. Results and discussion190
The dynamic model is used to study how the operating parameters, in-191
cluding the initial substrate (COD) concentration and the external resistance,192
influence the MFC performance in terms of maximum voltage, COD removal193
14
rate, Coulombic efficiency and power density. While COD removal rate is im-194
portant when discussing MFC as a wastewater treatment technology, power195
density, maximum voltage and Coulombic efficiency values are useful when196
comparing MFC with standard fuel cells or other power generation technolo-197
gies.198
For this analysis, Sin and Rext are assumed to be 1 gL−1 and 1000 Ω re-199
spectively, when not specified separately. To be consistent while comparing200
different initial COD concentrations, it is assumed that the substrate is re-201
plenished when 95 % of the original substrate has been consumed. It should202
be noted that for whole range of parameter values studied in this work, no203
single simulation took more than 3 seconds on a PC with 2.40 GHz dual core204
processor and 8 GB RAM.205
3.1. Effect of initial substrate (COD) concentration206
Figure 3 shows the change in maximum voltage (V), Coulombic efficiency207
(%) and the COD removal rate (g L−1 day−1) of the MFC system as the208
initial COD concentration (Sin) increases from 0.75 gL−1 to 3 gL−1. As209
can be seen from figure 3a, the maximum voltage generated in the MFC in-210
creases with increase in the initial COD concentration. While this increase211
is sharply linear at lower Sin values (< 1.5 g L−1), it begins to plateau with212
further increase in Sin. Such an increase in voltage can be attributed to the213
increased access to the substrate that the primary microbial population has,214
when the initial COD concentration is increased. This results in enhanced215
metabolic activity, thereby providing more electrons that can be transferred216
to the anode, leading to higher voltage generation [35]. However the amount217
of substrate that can be consumed by the microbial populations is also lim-218
15
ited by the maximum consumption rate, and thus the increase in maximum219
voltage slows down at higher values of Sin. The predicted result (figure 3a)220
from the simulation is also fully consistent with that observed in previous221
experimental studies [29, 36–38].222
Figure 3: Predicted values of (A) maximum voltage, (B) Coulombic efficiency, and (C)
COD removal rate as a function of initial COD concentration.
Figure 4 shows the comparison of predicted and experientially observed223
maximum voltage as a function of initial COD concentration. The exper-224
imental data used is adopted from Liu and Logan [29] and refers to the225
experiments where glucose was used as substrate feed at the anode. As can226
be seen from figure 4, there is fairly good agreement between experimen-227
16
tal data and simulation predictions. The percentage difference of maximum228
voltage between predicted and the three experimental values for initial COD229
concentrations of 0.3, 0.6 and 1.2 g/L, is less than 5%. It should be noted230
that plots shown in figure 3, are based on parameters considering wastew-231
ater as the substrate feed. When wastewater is replaced by glucose (as in232
figure 4), the substrate consumption rates are modified and were evaluated233
following the parameter estimation procedure described in section 2.3.234
Figure 4: Predicted values of maximum voltage (black dashed line) obtained from the
simulation compared to the experimental values (red solid circles) as a function of initial
COD concentration. The experimental data is based on glucose concentration (anode
substrate) and has been adopted from Liu and Logan [29].
As can be seen from figure 3b, the initial COD concentration has an235
inverse relation with the Coulombic efficiency. With increase in initial COD236
concentration, Coulombic efficiency decreases in almost a linear fashion. The237
εE values observed here (10-13 %) are in the similar range as that described238
17
for the air-cathode single chamber microbial fuel cell in Liu and Logan [29].239
As the substrate (COD) at the anode is consumed by both primary and240
secondary microbial populations, an increase in substrate concentration also241
leads to increased competition between the two populations. Thus while242
the primary microbial population consumes more substrate and results in243
higher voltage generation as Sin is increased, the corresponding increment in244
substrate consumption by secondary microbial population leads to decrease245
in the Coulombic efficiency of the cell. Several experimental studies that246
have studied the influence of initial COD concentration have also observed a247
similar decreasing trend of Coulombic efficiency with increase in initial COD248
concentration [32, 39, 40].249
However while increase in Sin results in reduced Coulombic efficiency of250
the system, it helps in improving the COD removal rate, as can be seen in251
figure 3c. Similar to the maximum voltage generation, the increase in COD252
removal rate is sharply linear at low Sin values, but slows down and reaches253
a plateau at higher values. In experimental studies, this improvement in254
COD removal rate at higher Sin values is ascribed to the enhanced hydroxyl255
radical (OH) formation, which helps in further oxidative degradation of the256
COD adsorbed on the surface of the electrode [41]. The observed trend from257
numerical results is consistent with that reported in previous experimental258
studies [32, 40, 42].259
As has been shown, while increasing Sin helps in increasing voltage gen-260
eration and COD removal rate, it also reduces the electron recovery of the261
system. In terms of percentage, increasing the initial COD concentration262
from 0.75 to 3 g L−1, results in 10% increase in maximum voltage, 12.5% de-263
18
crease in Coulombic efficiency, and 75% increase in COD removal rate, for the264
MFC system studied in this analysis. Thus depending on the focus of MFC265
end-use, optimum initial COD concentration can be selected by performing266
a parametric analysis using the current model.267
3.2. Effect of external resistance268
Figure 5 shows the influence of external resistance on the MFC perfor-269
mance. As can be seen, the increase in applied external resistance results in270
decrease in maximum current density (mA cm−2), Coulombic efficiency (%)271
and the COD removal rate (g L−1 day−1) of the system.272
Figure 5: Predicted values of (A) maximum current density, (B) Coulombic efficiency, and
(C) COD removal rate as a function of external resistance.
19
Several studies have suggested the strong influence of external resistance273
on biofilm formation, bacterial diversity, intermediate metabolism, internal274
resistance, and anode potential, which thereby affects the electricity gener-275
ation characteristics and COD removal performance [43–45]. Based on the276
current model, current density is expected to decrease with increase in ex-277
ternal resistance as per Ohm’s law. Higher current densities at low external278
resistance drive more effective utilization of the COD, which subsequently279
subsides with increasing Rext. Also, as the current density decreases (with280
increasing external resistance), more substrate becomes available for sec-281
ondary microbial population for purposes other than electricity generation,282
which would lead to decrease in Coulombic efficiency, as observed in the re-283
sults. Overall, increasing Rext from 100 to 2000 Ω, decreases the maximum284
current density by 70 %, Coulombic efficiency by 55 % and the COD re-285
moval rate by 18.5 %. These trends are in agreement with results reported286
in previous experimental studies [29, 32, 39, 40, 46].287
Li and Hua [46] studied the effect of external resistance on a denitrifying288
microbial fuel cell and found that as the external resistance was decreased, it289
increased the COD removal rate, current density and the Coulombic efficiency290
of the system. Similarly Jadhav and Ghangrekar [47] observed that exter-291
nal resistance is inversely proportional to MFC current and COD removal292
rate, however the decrease in COD removal efficiency was only marginal293
with increasing Rext. Katuri et al. [45] also observed that the extent of COD294
removal in MFC only decreased by 6% even after increasing external resis-295
tance manifolds. The results from the current analysis also show a relatively296
small decrease (18.5 %) in COD removal rate even when Rext is increased 20297
20
times. Buitrn and Moreno-Andrade [48] studied the performance of a single-298
chamber microbial fuel cell degrading phenol and found that while increasing299
external resistance resulted in lower current densities, it did not adversely300
affect the substrate degradation rate.301
3.3. Influence of operating parameters on power density302
Figure 6: Predicted values of maximum power density as a function of initial COD con-
centration at different values of external resistance.
Figure 6 shows the effect of initial substrate concentration on the maxi-303
mum power density (mW m−2) of the MFC system for four different external304
resistors. As can be seen, the power density increases with increase in ini-305
tial COD concentration, but decreases as the external resistance is increased.306
The increase in power density is consistent with the increase in maximum307
voltage with increasing Sin as observed in figure 3A. For each resistance, the308
21
power density reaches a maximum value and plateaus after showing a linear309
increasing trend at lower Sin values. Also, high current densities and high310
Coulombic efficiencies at lower external resistance promotes more effective311
utilization of substrate and results in higher power density. Similar rela-312
tionship between power density and initial COD concentration & external313
resistance has been reported in previous works [32, 39, 43, 49, 50].314
For the range of parameter values studied here, maximum power density315
of 730 mW m−2 is obtained for Sin=3 gL−1 and Rext=100 Ω. Experimental316
studies have also pointed out that increased utilization of anode for electrode317
respiration by mixed microbial population at low start-up external resistance318
[43] and increase in ionic strengths due to improved solutions conductivities319
at higher COD considerations [32], could be some of the other possible ra-320
tionales for increase in power densities at lower Rext and higher Sin.321
The current model is applied to MFC studied by Zhang et al. [50] to322
compare the effect of external resistance on power density, as obtained from323
the experiments to that predicted from the simulations. Model parameters324
are first estimated by fitting the current density profile from Zhang et al.325
[50] at external resistance of Rext = 250 Ω. Following this, the model is326
used to calculate power densities at two other external resistances, 50 Ω and327
1000 Ω, which are compared with the experimental values as shown in figure328
7. As can be seen from the figure, there is close agreement between power329
density values obtained from model predictions and those measured in the330
experiment.331
22
Figure 7: Predicted values of power density (black dashed line) obtained from the sim-
ulation compared to the experimental values (red solid circles) as a function of external
resistance. The experimental data has been adopted from Zhang et al. [50].
As seen from figures 3-7, the mathematical model accurately captures the332
trends similar to that observed in vast majority of studies, showing influence333
of external resistance and initial COD concentration on important MFC per-334
formance indices, such as the Coulombic efficiency, COD removal rate, and335
the power density. However some experimental studies that have observed336
either no change or a reverse relationship [48, 50–53]. The factors responsi-337
ble for such variations could be very specific to the design and operational338
conditions of the particular MFC and will need to be studied individually.339
The proposed mathematical model can be easily implemented by exper-340
imentalists and used to run parametric analysis of important operating pa-341
rameters using basic computational resources, to determine the optimum342
range of operation of a given MFC system. The optimum range required343
23
depends on the targeted end-use of the MFC, which can be focused on just344
power generation or wastewater treatment alone, or have a dual goal with im-345
proving the efficiency of both outputs. As seen from figures 3 and 5, increas-346
ing initial substrate concentration increases the maximum voltage and power347
density of the MFC as well as the substrate (COD) removal rate. However348
it also decreases the Coulombic efficiency of the system. Thus even though349
the maximum voltage generated increases initially with increase in substrate350
concentration, the total energy that could be extracted from the substrate is351
getting reduced. Thus it is important to choose the initial substrate concen-352
tration judiciously considering all factors such that the MFC system could353
be operated at optimum efficiency. Similarly the optimum range of operation354
of other important system parameters, like the external resistance, electrode355
surface area, volume of the MFC chamber, choice of substrate and micro-356
bial population (which determine the maximum substrate consumption rate,357
maximum growth rate and half saturation coefficient), can also be studied358
using the proposed modeling framework. The model is not only robust but359
also computationally inexpensive, making it a useful tool for MFC system360
optimization.361
The analysis also suggests that the Achilles’ heel of the microbial based362
electrochemical technology is the potential loss that occurs during transfer363
of electrons from bacteria to the electrode, which along with some other364
factors is one of the major reasons for the poor efficiency of these systems.365
Thus in addition to developing electrodes that can provide better prospect366
for biofilm attachment and growth, as well as increased effective surface area,367
equal or even more focus is needed to be directed towards understanding and368
24
improving the extracellular electron transfer.369
In the current form, the model assumes a non-limiting cathode, however370
including the influence of cathode polarization would enhance the model ac-371
curacy. Similarly in the current model, the presence or influence of any372
ion-exchange membrane between the two electrodes, and dependence of in-373
ternal resistance and open circuit voltage on external load (resistance), has374
not been included. Accounting for these additional factors would further375
increase the applicability of the model to not just two chamber MFC but376
also other bioelectrochemical systems such as microbial electrolysis cell, mi-377
crobial electrosynthesis system, etc. Introducing suitable modifications that378
can improve the model predictions without compromising on the speed of379
convergence, are planned for the near future.380
4. Conclusion381
This study presents a simple, fast converging mathematical model to de-382
scribe a microbial fuel cell system. The model includes governing equations383
for mass transfer of substrate and biomass, bio-electrochemical kinetics and384
charge transfer. The model rigor is further improved by using substrate385
concentration, a simple measurable quantity, to calculate the dynamic open386
circuit voltage and internal resistance of the cell. Model analysis predicts387
a positive influence of increasing initial substrate concentration and lower-388
ing external resistance on the power density and substrate removal rate of389
the system. These predictions are in accordance with previously reported390
experimental studies. The mathematical model is easy to implement and is391
computationally inexpensive, and can thus serve as a good starting point to392
25
determine the operating conditions for fairly optimum system performance,393
before more comprehensive experimental/numerical studies are performed.394
Acknowledgements395
The authors would like to acknowledge the financial support by the Natu-396
ral Environment Research Council (NERC) UK project grant: NE/R013306/1.397
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