Download Full cell simulation and the evaluation of the buffer system on air

Journal of Power Sources 347 (2017) 159e169
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Journal of Power Sources
journal homepage: www.elsevier.com/locate/jpowsour
Full cell simulation and the evaluation of the buffer system on
air-cathode microbial fuel cell
Shiqi Ou a, *, Hiroyuki Kashima b, Douglas S. Aaron c, John M. Regan b,
Matthew M. Mench c
a
b
c
National Transportation Research Center, Oak Ridge National Laboratory, Knoxville, TN, 37932, USA
Department of Civil & Environmental Engineering, The Pennsylvania State University, University Park, PA, 16801, USA
Department of Mechanical, Aerospace and Biomedical Engineering, The University of Tennessee, Knoxville, TN, 37996, USA
h i g h l i g h t s
The full cell model provides a macro/micro perspective of the MFC interrelation.
Study of the effects of mass transport drivers (diffusion and electric migration).
Analysis of the Hþ/OH- transport and pH change in the whole cell system.
Overall impacts of various buffers on the whole reactor are compared.
Quantitative delineation of overpotentials at both anode and cathode in MFC.
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 13 October 2016
Received in revised form
19 January 2017
Accepted 10 February 2017
This paper presents a computational model of a single chamber, air-cathode MFC. The model considers
losses due to mass transport, as well as biological and electrochemical reactions, in both the anode and
cathode half-cells. Computational fluid dynamics and Monod-Nernst analysis are incorporated into the
reactions for the anode biofilm and cathode Pt catalyst and biofilm. The integrated model provides a
macro-perspective of the interrelation between the anode and cathode during power production, while
incorporating microscale contributions of mass transport within the anode and cathode layers. Model
considerations include the effects of pH (Hþ/OH transport) and electric field-driven migration on
concentration overpotential, effects of various buffers and various amounts of buffer on the pH in the
whole reactor, and overall impacts on the power output of the MFC. The simulation results fit the
experimental polarization and power density curves well. Further, this model provides insight regarding
mass transport at varying current density regimes and quantitative delineation of overpotentials at the
anode and cathode. Overall, this comprehensive simulation is designed to accurately predict MFC performance based on fundamental fluid and kinetic relations and guide optimization of the MFC system.
© 2017 Elsevier B.V. All rights reserved.
Keywords:
Microbial fuel cell
Computational simulation
Mass transport
Buffer system
pH
Concentration overpotential
1. Introduction
Microbial fuel cells (MFCs) have been the subject of years of
research; despite much effort, the performance of MFCs has not
improved to the point that they are economically viable as power
sources. Part of this slow development is due to the need for greater
* Corresponding author. National Transportation Research Center, Energy and
Transportation Sciences Division, Oak Ridge National Laboratory, Knoxville, TN
37932, USA.
E-mail address: [email protected] (S. Ou).
http://dx.doi.org/10.1016/j.jpowsour.2017.02.031
0378-7753/© 2017 Elsevier B.V. All rights reserved.
fundamental understanding of how these devices convert wastewater streams into electricity e bioelectricity generation from
biomass by using organic substrates [1]. In the MFC system, the
microorganisms on the anode generate electrons by consuming
organic matter; electrons then flow to the anode via self-produced
mediators or nanowires [2]. The electrons are conducted through
an outer circuit to the cathode, permitting reduction reactions to
occur, typically on a cathodic catalyst. In certain MFC reactors (e.g.,
two-chamber design), a membrane (e.g., cationic, anionic, or ultrafiltration membrane) is placed between the anode and cathode
to prevent electrical shortage and minimize oxygen infiltration to
the anode-respiring bacteria (ARB). However, this design increases
160
S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
the internal resistance and reduces the power output [1], increasing
the system cost [3]. A single chamber air-cathode reactor uses air
passively supplied to the cathode and avoids the cost of a membrane; in this design, the cathode environment shares bulk liquid
with the anode electrode [3].
Historically, most MFC development has been experimentbased. Recent efforts at simulation allow multiple controlling
phenomena to be considered, which can guide system optimization
[4]. Building off the MFC models have been refined and expanded to
become useful tools for MFC behavior analysis. The initial focus for
most MFC models was regional analysis of the anode and electron
generation: Picioreanu et al. described transient anodic biofilm
growth model from 1D to 3D [5]; Strycharz-Glaven et al. presented
a mathematical model focused on anode biofilm conductivity [6].
Although MFC model development has progressed, few models
focus on cathode performance, and even fewer couple the anode
and cathode into a comprehensive, whole-cell model [7].
In the single chamber MFC reactor, protons (Hþ) are produced
during microbial respiration while electrons are transported to the
anode. The protons accumulate near the anode and then diffuse via
concentration gradient through the bulk liquid to the cathode. The
anode pH is typically below 7 as protons accumulate and develop a
concentration gradient; experiments have shown that acidic pH
results in a significant decrease in voltage efficiency, current density, and resultant power output by negatively affecting ARB
metabolism via Le Chatlier's principle [8,9]; this effect is illustrated
by the half reaction for acetate oxidation in the anode, shown in
Eqn. (1).
contributes to inhibited power output. In a single-chamber MFC
reactor, cathode pH spans a range from 7.0 to 13.0, according to
multiple studies [15,17]. Considering pH effects in both the anode
and cathode regions, pH regulation and Hþ/OH mass transport
mechanisms are important topics for MFC development. In this
modeling work, electric migration and the effects of pH on
concentration-driven diffusion were included in mass transport
calculations for varying buffer systems.
2. Methods
2.1. Experiments and set up
A single-chamber MFC that has been used in earlier work [18]
was employed in the series of buffer studies described here.
There was no convection present in the system because no stirring
or flow was implemented. Anode materials consisted of carbon
paper, as indicated in the discussion. Effluent from a mature MFC
reactor was used as inoculum, and enriched in batch mode with a
growth medium including 50 mM phosphate buffer solution (PBS)
and 1.0 g/L sodium acetate as the electron donor. Polarization
analysis was conducted by varying external resistance; data points
were collected with 20-min time steps while measuring cell
voltage and both electrode potentials against an Ag/AgCl reference
electrode [19]. Since cell voltage was measured for varying resistors
(from 10 M-ohm down to 130 U) connecting the anode and cathode, current was calculated using Ohm's law.
2.2. Model formation
1
3
1
1
þ
CH COO þ H2 O/ CO2 þ HCO
3 þH þe
8 3
8
8
8
(1)
Electrochemically, lower pH also contributes to increased concentration overpotential for substrate oxidation [9], increasing
potential loss for the whole MFC. Because of the numerous impacts
of pH, pH regulation is an important consideration for improvement of MFC performance. Several works have detected, via multiple experimental techniques, that the anode biofilm pH is
normally in the range of 5e7 [4,10,11]. As a result of these insights,
buffer systems have been introduced to stabilize pH, supporting
biological growth and decreased anode concentration overpotential [9].
In addition to the kinetic losses associated with microbial
respiration, mass transport losses also contribute to cell overvoltage. Such losses are the result of concentration gradient-driven
diffusion and migration flux in the MFC when no bulk liquid flow
occurs. Convection also affects performance, but is often ignored in
experimental single-chamber MFCs. Diffusion is proportional to a
concentration gradient while migration is proportional to the bulk
liquid electric field and ionic concentration. Prior work has indicated that migration is minor compared to diffusion flux in single
chamber MFCs [6,9]. Thus, most MFC modeling efforts only
consider diffusion as a mass transport mechanism [5,12-14].
At the cathode, it is increasingly accepted that high pH is due to
the generation of OH instead of the consumption of Hþ [15e17].
This reaction, an alternative to typical oxygen reduction to water as
in a hydrogen fuel cell, is shown in Eqn. (2).
1
1
O þ e þ H2 O/OH
4 2
2
(2)
The bulk liquid separating the anode and cathode thus exhibits a
pH gradient from acidic to basic [15]. Accumulation of OH at the
cathode affects MFC performance in a manner analogous to Hþ
accumulation at the anode: higher pH decreases biomass metabolism efficiency, increases cathode concentration loss, and
The steady-state nature of this model assumes constant biomass
due to equal detachment and attachment rates in the biofilms and
that the substrates and biomass reach a dynamic balance [12]. In
the MFC system, the biofilms will mature regardless of substrate
abundance in the reactor [5,18]. Therefore, the thickness and
biomass density of the biofilms in MFC reactor are assumed to be
unchanged in this steady state model, shown in Table 1. The model
discussed herein is based on a single chamber air-cathode MFC, an
exploded-view schematic of which is shown in Fig. 1 a). The bulk
liquid fills a cylindrical space separating the anode and cathode. In
the model reactor, the anode electrode is carbon paper instead of
the better-performing carbon brush [1]. The carbon paper design
simplifies model formulation and optimizes simulation speed, but
results in poorer MFC power output. ARB adhere to the carbon
paper, forming a relatively thin anodic biofilm. The layered cathode
was arranged from the interior to the outside in contact with air as:
Pt/C catalyst, hydrophilic carbon cloth, and hydrophobic PTFE. The
structural properties of the MFC are included in Table 1, along with
other model parameters. Similar to the anodic biofilm, the aerobic
cathode microorganisms form a relatively thick biofilm on the Pt/
Carbon catalyst layer.
2.2.1. Mass balance for substrate transport
Mass transport relations are formulated for all domains in the
MFC, separated based on the physical properties of the materials in
each layer. From cathode to anode, they include the PTFE layer,
carbon cloth, Pt/C catalyst layer, cathodic biofilm, bulk liquid,
anodic biofilm and carbon paper; this structure is shown in Fig. 1b).
along with initial and boundary conditions for pH and acetate
concentration. Most layers were assumed to be fully saturated with
growth medium; however, the cathode carbon cloth was studied by
Ou et al. [18] and found to possibly contain a small, ca. 3% by volume, quantity of gas. Additionally, the PTFE layers were assumed to
have no liquid present due to their strong hydrophobicity. In the full
cell model, the PTFE layer was neglected to simplify calculations
S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
161
Table 1
Model parameters for full cell model.
Name
Description
Values
Unit
cAc,0
cO2,g
cO2,ref
DAc,liq
DCO3,liq
DHCO3,liq
DH2CO3,liq
DHPO4,liq
DH2PO4,liq
DH3PO3,liq
DNH3,liq
DNH4,liq
DOH,liq
DO2-N2
DO2,liq
E0C
F
HO2
KAcH
KO2
KO2A
KO2H
Lbio
Lbl
Lbdl
Lcc
Lcl
Lpdl
pH0
P0
qmax.AcH
qmax.Acsus
qmax.AcA
R
Scathode
T
Xabio
Xcbio
Xsus
εbio
εcc
εcl
εpdl
Initial Concentration, sodium acetatea
Boundary concentration, gaseous oxygena
Reference concentration in reactor, oxygen
Diffusion coefficient in liquid, acetateb
Diffusion coefficient in liquid, CO2-c
3
Diffusion coefficient in liquid, HCO2-c
3
Diffusion coefficient in liquid, H2COc3
Diffusion coefficient in liquid, HPO2-c
4
Diffusion coefficient in liquid, H2POc
4
Diffusion coefficient in liquid, H3POc4
c
Diffusion coefficient in liquid, NH3
Diffusion coefficient in liquid, NHþc
4
Diffusion coefficient in liquid, hydroxidec
MS diffusivity, O2eN2 componentb
Diffusion coefficient in liquid, oxygenb
Cathode equilibrium voltageb (v.s. SHE)
Faraday constantb
Henry constant, oxygene
Half-max-rate acetate concentration, heterotrophic biomass
Half-max-rate oxygen concentration in cathode
Half-max-rate oxygen concentration, autotrophic biomass
Half-max-rate oxygen concentration, heterotrophic biomass
Length, cathode biofilm
Length, bulk liquidb
Length, boundary diffusion layerb
Length, carbon clothb
Length, Pt/C catalyst layerb
Length, PTFE diffusion layerb
pH in bulk liquid
Gas pressureb
Maximum specific rate of acetate utilization, heterotrophic biomass
Maximum specific rate of acetate utilization, suspended biomass
Maximum specific rate of oxygen utilization, autotrophic biomass
Gas constant
Cathode cross sectional area in MFCb
Temperature
Biomass concentration in anodic biofilm
Biomass concentration in cathodic biofilm
Suspended biomass concentration in liquid
Porosity, biofilm
Porosity, carbon clothb
Porosity, Pt/C catalyst layerb
Porosity, PTFE diffusion layers
Cathode half-max overpotential
Density, bulk liquidb
Density, biomass
Mass fraction of HAB in biofilm
Conductivity, anode biofilm
Conductivity, bulk liquidb
Conductivity, Pt/C catalyst layer
Conductivity, carbon cloth
Conductivity, Pt/C catalyst layer
800
237.66
3.79
1.21 109
8.00 1010
1.09 109
1.09 109
7.60 1010
8.80 1010
1.00 109
1.64 109
1.97 109
4.59 109
2.30 105
2.10 109
552
96485
7.79 104
150
0.128
1.28
1.28
1.0
39.0
0.5
0.18
0.032
0.032
7.08
1.01 105
1.00 104
1.00 104
2.00 105
8.314
7.07 104
303.15
24.0
25.0
0.05
0.95
0.75
0.30
0.10
240.028
1.05
1.54
0.85
0.02
0.755
0.05
1.00 105
1.00 103
mg/L
mg/L
mg/L
m2/s
m2/s
m2/s
m2/s
m2/s
m2/s
m2/s
m2/s
m2/s
m2/s
m2/s
m2/s
mV
C/mol
J/mol
mg/L
mg/L
mg/L
mg/L
mm
mm
mm
mm
mm
mm
\
Pa
(mg Ac)/(mg HAB s)
(mg Ac)/(mg SUS s)
(mg O2)/(mg AAB s)
J/mol K
m2
K
g/L
g/L
g/L
\
\
\
\
mV
g/cm3
g/cm3
\
S/m
S/m
S/m
S/m
S/m
hK
rbl
rbio
s
sabio
sbl
scbio
scc
scl
e
Values for other model parameters were assumed based on common practical experience.
a is from experimental data.
b is from Ref. [28].
c is from Ref. [29].
d is from Ref. [30].
e is from Ref. [23].
f is from Ref. [31].
and because gas transport in a porous medium is well-known. The
amount of dissolved oxygen was calculated according to Henry's
law in equilibrium with air. To improve computational accuracy,
two boundary diffusion layers were added into the model. These
boundary diffusion layers serve as transition regions between the
electrodes and bulk liquid [20].
The NernstePlanck equation describes electric field-affected
mass transport for each compound and is shown in Eqn. (3).
vci
¼ V Fdiff þ Fmig þ ri
vt
(3)
where Fdiff is the diffusion flux:
Fdiff ¼ Di
vci
vx
and Fmig is the electric migration flux [9]:
(4)
162
S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
Fig. 1. a) Structure of the single chamber air-cathode MFC reactor; b) Schematic diagram for the domains and initial conditions addressed in this model.
Fmig ¼ zi F vV
D
RT i vx
(5)
In these relationships, i is for each species, ci is concentration
(mg/L), Di is effective diffusion coefficient (m2/s), zi is ionic charge
(C), V is the local electric potential (mV), and ri is the reaction rate
(mg/L s). The reaction rate is characterized by the bioelectrochemical reaction in the anode and cathode biofilms, as
well as Pt-catalyzed oxygen reduction in the cathode. It is assumed
that ARB respiration is the only operationally-relevant reaction in
the anode biofilm, where the ARB transfer electrons from acetate to
the anode. Electronic conduction in the anode causes local potential
gradients over the anodic biofilm. In addition to the effects of local
electronic potential, acetate concentration affects ARB metabolism.
The ARB reaction rate is thus related to the local overpotential and
local electron source (acetate); the Monod-Nernst equation includes these considerations for ARB metabolism [14]. Eqn. (6)
shows this relationship and has been validated by kinetic experiments [21].
cAc
rAc;ARB ¼ qAc;ARBmax XARB
cAc þ KAc
1
0
1
A
@
Fh
F
1 þ exp RT
act;A þ RThK;A
(6)
where rAc,ARB is ARB acetate reaction rate (mg/L s), qAc,ARBmax is ARB
maximum specific rate of acetate consumption (mg Ac/mg ARB s),
XARB is ARB concentration (mg/L), cAc is local acetate concentration
(mg/L), hact,A is anodic activation overpotential (V), hK,A is halfmaximum activation overpotential (V) [14], F is the Faraday constant (C/mol), T is temperature (K), and R is the ideal gas constant (J/
mol K).
Oxygen reduction occurs at both the Pt/C catalyst layer and in
the cathodic biofilm. In the catalyst layer, oxygen is the electron
acceptor and OH is generated, as shown in Eqn. (2). While the
cathode biofilm is comprised of a consortium of microbes, this
study simplifies the cathodic biofilm microbial species into two
groups based on their electron sources: autotrophic aerobic
biomass (AAB), and heterotrophic aerobic biomass (HAB) [18].
Electrons from the anode are consumed in both the Pt/C layer and
S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
in the biofilm [19]. The porous cathode catalyst structure is the
same as in conventional PEM fuel cells; the reaction rate calculation
in the catalyst layer is described by a simplified Butler-Volmer
expression in Eqn. (7) [22].
"
#
1
c
bF
ic;0 O2
MO2 dcl
rO2 ;cl ¼ exp
h
4F
RT act;C
cO2
(7)
where rO2,cl is oxygen reaction rate in the catalyst layer (mg/L s), ic,0
is the cathode exchange current density (A/m2), c*O2 is the saturation concentration of oxygen (g/L), b is the symmetry factor of the
reaction, MO2 is oxygen molecular mass (mg/mol), and dcl is the
catalyst specific area (m2/m3). In the cathode biofilm, the MonodNernst equation for reaction rates is used. Eqn. (8) is the AAB reaction rate, and Eqn. (9) is the HAB reaction rate in the cathode
biofilm [18].where rO2,AAB is AAB oxygen reaction rate (mg/L s),
rO2 ;AAB ¼ qO2 ; AABmax XAAB
163
anode voltage, E0A, is 500.46 mV. The experimental cell voltage is
calculated based on the attached external resistance and the
measured current as shown in Eqn. (14). The model has been
constructed to use external resistance as the defining input, with all
other parameters responding appropriately.
Vcell ¼ IRext
(14)
The biofilms in both electrodes are assumed to be electronically
conductive, described by an electron balance and Ohm's law [14],
shown in Eqn. (15). This relationship is also used for the metallic
catalyst in the cathode.
0¼s
v2 hact
þ Fgr
vx2
(15)
where s is conductivity (S/m); hact is local activation overpotential
cO2
1
F
KO2 ;AAB þ cO2 1 þ exp F h
RT act;C þ RThK;C
(8)
cO2
cAc
1
F
KO2 ;HAB þ cO2 KAc;HAB þ cAc 1 þ exp F h
RT act;C þ RThK;C
(9)
rAc;HAB ¼ qAc; HABmax XHAB
qO2,AABmax is maximum specific rate of oxygen consumption (mg
O2/mg AAB s) for AAB, XAAB is the AAB concentration (mg/L), KO2,AAB
is the half-max-rate oxygen concentration (mg/L), hact is the
cathodic activation overpotential (V), hK,C is the cathodic half-max
overpotential (V), rAc,HAB is HAB acetate reaction rate (mg/L s),
qAc,HABmax is maximum specific rate of acetate consumption (mg
Ac/mg HAB s) for HAB, XHAB is HAB concentration (mg/L).
2.2.2. Current generation
Generally, overpotential analysis in MFCs is similar to that in
PEMFCs [23]. The overpotential is divided into three sources: activation overpotential hact, ohmic overpotential hohm, and concentration overpotential hcon; all are relevant in both the cathode and
anode [23]. The total overpotential htotal is shown in Eqn. (10). The
overpotential balance is shown in Eqn. (11).
htotal ¼ hact þ hcon þ hohm
(10)
Vcell ¼ E0C hC;act hC;con E0A þ hA;act þ hA;con jhohm j
(11)
It is assumed that the internal resistance is comprised of the
anodic resistance RA, cathodic resistance RC, and electrolyte resistance in bulk liquid RBL, as shown in Eqn. (12) and Eqn. (13).
jhohm j ¼ hA;ohm þ hC;ohm þ hBL;ohm (12)
jhohm j ¼ IRA þ IRC þ IRBL
(13)
The open circuit voltages (v.s. Ag/AgCl) for the anode and
cathode in this model have been measured experimentally: the
equilibrium cathode voltage, E0c , is 273.3 mV while the equilibrium
(V); g is electron equivalence (mol e/mol); r is a particular substrate reaction rate (mol/L s): acetate consumption for ARB in the
anode or HAB in the cathode, and oxygen consumption for AAB in
cathodic biofilm, or ORR in cathodic catalyst layer. This steady state
equation is calculated based on two boundary conditions [14],
which are shown in Eqn. (16) and Eqn. (17), respectively.
hact jx¼0 ¼ hele;act
(16)
vhact ¼0
vx x¼L
(17)
where hele,act is local activation overpotential at the electrode. Eqn.
(16) is the condition at the boundaries between conductive electrode materials (anode carbon paper and cathode carbon cloth) and
current collectors shown in Fig. 1 a). Eqn. (17) is the condition at the
boundaries between the boundary diffusion layers and biofilms. In
Eqn. (17), L is the total length of the anode biofilm and carbon paper
in the anode; for the cathode, the relevant L is the length of the
cathodic biofilm, Pt/C layer, and carbon cloth, shown in Fig. 1 b).
2.2.3. Buffer system
This work includes the effects of several common buffers,
including: NH4Cl, NaHCO3, and PBS (phosphate buffered system).
The relationship between pH and ARB metabolism or ARB growth is
difficult to experimentally analyze [13], thus this study only
considered the effects of buffers on overpotentials that respond to
pH. Eqn. (18) shows the concentration overpotential (hcon,pH)
related to pH values.
hcon;pH
cHþ =OH
RT
ln 0
¼
nF
cHþ =OH
!
(18)
where the anode concentration overpotential is dependent upon
164
S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
Table 2
Buffer chemical reactions in simulation.
Buffer name
Equation
pKa
H2O
NH4Cl
NaHCO3
H2O 4 OH þ Hþ
þ
NHþ
4 4 NH3 þ H
þ
H2CO3 4 HCO
3 þ H
þ
2HCO
3 4 CO3 þ H
þ
H3PO4 4 H2PO
4 þ H
þ
2H2PO
4 4 HPO4 þ H
þ
3HPO24 4 PO4 þ H
14
9.25 [32]
6.37 [33]
10.3 [33]
2.12 [34]
7.21 [34]
12.32 [34]
PBS
Hþ concentration, while the cathode depends on OH concentration. Local pH in the bulk liquid is assumed to be influenced by
proton transport from the anode and hydroxide transport from the
cathode; cHþ/OH- is local Hþ or OH concentration and c0Hþ/OH- is
initial Hþ or OH concentration in the bulk liquid. The initial pH is
set to be 7.08, based on experimental measurement. Table 2 lists the
buffer chemical dissociation equations adopted in the model.
An algorithm has been established for calculating the buffer
equilibria and other reactions in all MFC domains. The algorithm
with related equations is shown as a flow diagram in Fig. 2. Via
Eqns. (6)e(9), rAc, rO2 and rH are obtained in every domain. Eqn. (3)
gives the mass transport calculations for each species; concentrations (including pH) are updated for each iteration until the residuals between adjacent iterations are smaller than the tolerances.
These reactions and mass transport affect pH, thus chemical and
electrochemical reactions must be rebalanced. The buffers obey
typical dissociation behavior, shown in Eqns. (19) and (20).
Fig. 3. Influence of electric migration inclusion on simulation of MFC power
production.
ðc ÞðcHþ Þ
Ka ¼ B
cBH
(19)
BH4B þ Hþ
(20)
Ka is the dissociation constant, while cBH and cB- represent the
concentrations of undissociated and deprotonated buffer in the
equilibrium, respectively. This model assumes that the dissociation
Fig. 2. Flow diagram of the algorithm for buffer chemical reactions and pH in MFC
system modeling.
Fig. 4. Polarization and power density curves for an experimental MFC with 50 mM
buffer and simulations of unbuffered, 50 mM buffered, and an ideal scenario in which
pH effects are neglected.
S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
reaction rates (Eqn. (20)) are much faster than the timescale of
mass transport [13]. Thus, updated local concentrations of B and
BH are defined by Eqn. (19). Stepping through the algorithm, results
from mass transport calculations update in each control volume, a
new balance is established, and new pH values are obtained based
on Eqn. (19), as shown in Fig. 2. The residual of the pH values in
adjacent iterations is calculated and compared to a tolerance to
decide the next computational step.
Picioreanu et al. [13] also presented a method for simulating the
pH of a buffer in a MFC half-cell, which included dissociation rate.
This work defined the dissociation equilibrium reaction rate as
shown in Eqn. (21):
c c þ
ra;BH ¼ kBH cBH B H
Ka
(21)
where, kBH is the rate constant for the dissociation equilibrium
(s1). In this study, both the proposed buffer algorithm shown
above and the Picioreanu et al. algorithm (with kBH assumed to be
1010 s1) were compared in the full cell model for calculating the
pH values as well as the buffer concentrations. Modeling results for
these two algorithms were compared and the maximum
disagreement between these two algorithms was less than 0.8%.
165
3. Results and discussion
Three cases were discussed in the study: 1) Baseline experimental results simulation with concentration overpotential impact
analysis; 2) MFC performance comparison for multiple buffer solutions; 3) comparison of varying buffer concentrations. In the
steady state model, the external resistance was decreased from
4000 U to 50 U. The electrochemical results (e.g., polarization
curves, power density, overpotentials), species distributions (e.g.,
oxygen, acetate, buffer chemicals), and pH profiles in the full cell
were simulated and evaluated.
3.1. Numerical evaluation for electric migration in the mass
transport
Mass transport in the microbial fuel cell can be influenced by
convection, diffusion and electric migration. Convection was
neglected in the model because there was no stirring in or flow
through the reactor. The relative influences of diffusion and electric
migration were compared by assessing two mass transport scenarios against relevant experimental data: once with only diffusion
and once with both drivers of transport. In Eqn. (22), the two
Fig. 5. a) pH distribution across the MFC at varying current densities for the 50 mM buffer simulation; b) Maximum cathode pH and minimum anode pH responses to current
density for unbuffered and 50 mM buffered MFCs.
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S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
scenarios were with or without the second diffusion term in parentheses [19]:
vci
v
¼
vx
vt
Deff
i
vci zi F eff vE
Di
þ ri
vx
vx RT
(22)
where i is for each species, ci is concentration, Deff
i is the effective
diffusion coefficient, zi is charge of any ion, E is local electric potential, and ri is reaction rate. We note that, in this assessment, the
model was first compared to the experimental data and obtained
very good fit, as shown in Fig. 3. After obtaining all model parameters for diffusion-only mass transport, the model was modified to
include electric migration and refit to the experimental data while
retaining the values obtained in the diffusion-only case; this analysis allowed the illustration of the impact of electric migration by
slightly overestimating MFC output.
As shown in Fig. 3, inclusion of electric migration flux in mass
transport for all three major regions of the MFC resulted in over
prediction of the maximum power output by 7.4% compared to the
scenario in which electric migration is neglected, as well as the
experimental results. Because the impact of migration is small
under these conditions, it is neglected in some modeling work
[9,24,25]. For the comparison of multiple buffer concentrations in
Section 3.4, electric migration was included in the model because
buffer concentration affects the conductivity of the bulk liquid.
However, the purpose of this study was to compare the performances between different buffer solutions. Thus, the experimental
results serve as a reference for calibration and comparison in the
study.
3.2. Simulation of buffer impact
As seen in Fig. 4, the model fit the experimental results very well
when a 50 mM buffer was included and electric migration was
neglected. The simulated buffer consisted of 50 mM phosphate
buffer (17.77 mM NaH2PO4/H2O and 32.23 mM Na2HPO4) along
with 1.74 mM KCl and 5.79 mM NH4Cl. The next comparison
removed the influence of a buffer and the effects of pH from all
reactions. These two scenarios represent a relatively poor case
(uncontrolled pH) and an ideal case (where Hþ and OH concentrations do not affect concentration overpotential), respectively.
Aside from buffer behavior, all parameters used in this section are
as described in Table 1. These three scenarios are shown, along with
the experimental data, in Fig. 4.
Shown in Fig. 4, simulated MFC power output in the absence of
any buffer (but with pH effects on concentration overpotential)
averaged ~9.80% less than the 50 mM buffer case. The lower output
from the unbuffered simulation is primarily due to increased
overpotential on the cathode; the anode overpotential also
increased slightly compared with the buffered scenario. When pH
effects on concentration overpotential were neglected (the ideal
case), the MFC produced ~21.9% higher power than the 50 mM
buffer scenario. The overpotentials in both the anode and cathode
sides were obviously smaller in this ideal simulation.
The pH distribution across the entire cell was also analyzed.
Fig. 5 a) shows the calculated distribution of pH across the MFC for
varying current densities. The cathodic pH is defined by the production of OH, while the anodic pH is due to Hþ production. The
bulk liquid initial pH was set to an experimentally-measured 7.08;
Fig. 5 a) shows that pH < 7.08 over most of the bulk liquid while
Fig. 6. a) Polarization and power density curves; and b) pH profiles for different buffer solutions.
S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
167
pH > 7.08 is true for the entire cathode. This asymmetry arises
because the Hþ diffusion coefficient is much larger than that of
OH, facilitating faster proton diffusion in the bulk liquid, and a
resultant slightly acidic bulk liquid.
Fig. 5 b) shows the maximum pH in the cathode and minimum
pH in the anode over a range of current density for both unbuffered
and 50 mM buffered scenarios. Since the “Ideal” simulation ignored
pH influence, this profile is not included in Fig. 5 b). It is apparent
that the 50 mM buffer moderates the changes in pH for both halves
of the MFC, especially in the anode.
According to Eqn. (18), Hþ/OH concentration affects MFC mass
transport overpotential. Since the buffer solution moderately
changes in pH, the concentration overpotential is less severe,
leading to increased power production. However, it is apparent
from the simulation results that the 50 mM buffer solution has
limited capacity to accommodate changes in pH. If the “Ideal”
simulation is the best-case scenario in which the pH influence by
the concentration overpotential is completely eliminated, 50 mM
buffer mitigates approximately 31% of the pH influence on MFC
performance. Because buffer compounds cannot instantly move
throughout the electrodes, it is expected that pH effects on concentration overpotential cannot be completely circumvented. Any
activity in the anode or cathode will cause pH to deviate from ~7,
even if the bulk liquid pH may be close to neutral.
3.3. Comparison of multiple buffer solutions
To assess the effect of buffer type, with attendant differences in
buffer mass transport, two other buffers were considered. In this
section, 50 mM PBS, 50 mM NaHCO3, and 50 mM NH4Cl were
considered in the model with dissociation behavior as outlined in
Table 2.
In Fig. 6 a), simulation results for polarization and power density
curves are presented. The type of buffer did not greatly affect MFC
output in the steady-state model. The 50 mM PBS yielded the best
performance, though the anode was barely affected, indicating that
the cathode responded relatively sensitively to the buffer type.
Overall, the peak power for the PBS simulation was only 5% greater
than the peak power output for the NH4Cl system. Fig. 6 b) shows
trends in maximum cathode pH and minimum anode pH for
increasing current density for the three buffer systems. It is
apparent that any buffer solution was able to mitigate pH changes
for both the anode and cathode compared to a MFC with no buffer.
Of the buffers considered, 50 mM PBS buffer was most effective in
the anode. pH regulation capability of the PBS buffer was less superior in the cathode when the current density neared the
maximum. This superior performance is likely due to the properties
shown in Table 2: there are three equilibrium reactions for phosphate species, allowing more Hþ to be buffered. However, phosphate has a smaller diffusion coefficient, limiting PBS mass
transport; this effect becomes more pronounced at high current in
the thick electrode, leading to the tighter spread of pH between
buffers at high current. In the cathode layers, porosity exacerbates
buffer mass transport limitations by limiting Hþ transport from the
anode to participate in pH neutralization. In this model, the diffusion coefficient of PO34 is an order of magnitude smaller than that
for both NHþ
4 and HCO3 , shown in Table 2.
The model in this study can yield microscale insights regarding
concentration potential losses. Fig. 7 a) shows the total concentration overpotentials in the whole cell MFC (including both cathode and anode) for multiple buffer liquids. As expected,
concentration overpotential increases with current density, but this
increase in overpotential is mitigated in the presence of any buffer.
It appears as though, under these conditions, each of the buffer
systems is similarly effective, with 50 mM PBS slightly
Fig. 7. a) Concentration overpotentials at varying external resistance for all buffer
systems considered; b) Cathode concentration overpotential; c) Anode concentration
overpotential.
outperforming the others. However, concentration overpotential is
typically a relatively minor contributor to total MFC overpotential;
this observation is evident here, as well, since the buffers show
little variability between themselves [19].
Having compared the total MFC concentration overpotential,
the model also allows investigation of concentration overpotential
in the anode and cathode. Fig. 7b) and c) respectively show the
anode and cathode overpotentials with the four buffer scenarios. It
is confirmed in Fig. 7 b) that PBS most effectively reduces concentration overpotential losses in the anode side, followed by NaHCO3
and then NH4Cl. This same trend occurs for the total concentration
overpotential losses shown in Fig. 7 a). In Fig. 7 c), the PBS buffer
actually performs worst at small external resistance (at high current density), though the difference is small. This agrees with the
PBS simulation results in Fig. 6. Since phosphate is a relatively large
molecule, with a correspondingly smaller diffusion coefficient
compared with HCO
3 and NH3, its mass transport through electrode layers is slower. This is most evident in the cathode at higher
current density.
168
S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
Fig. 8. Polarization curves and pH for different PBS concentration solutions.
3.4. Effect of PBS concentration
4. Conclusions
The bulk liquid conductivity was kept constant in previous
simulations since the buffer concentrations were identical. However, bulk liquid conductivity variations strongly influence MFC
power production by affecting ohmic overpotential. To assess this
effect, changes in the phosphate buffer concentration were simulated for the full cell system.
The polarization and power density curves for 50 mM,
100 mM and 200 mM PBS are shown in Fig. 8. The conductivity of
bulk liquid with 50 mM PBS has been measured at 5.9 mS/cm
[26], with 100 mM PBS it is 10.2 mS/cm [26], and with 200 mM
PBS it is 22.0 mS/cm [27]. As expected for the increase in bulk
liquid conductivity, greater PBS concentration yielded decreased
internal resistance and a more neutral pH environment, thus
enabling greater power output. While PBS yields the best performance, it is also the most expensive buffer considered here;
this provides an optimization point to balance increased system
cost against improved power density. It is evident that the pH
change from 50 mM to 100 mM PBS is larger than the pH changes
from the 100 mM and 200 mM curve shown in Fig. 8 b). Due to
the dissociation equilibria of PBS, its pH buffering performance
does not linearly improve with the amount of PBS present.
The buffer liquid has two major roles in the MFC system: 1.
create a pH-friendly environment for biomass growth (biological
influence); 2. balance ionic concentration/pH for mass transport
and electrochemical reactions (electrochemical influence). The
simulation results shown in Fig. 8 reflect the impacts of the electrochemical influence in this analysis, therefore the differences of
the power outputs shown in Fig. 8 a) are not as great as expected
from experimental results elsewhere [26], however the pH curves
showed large differences for different amounts of PBS buffers in
Fig. 8b).
Mass transport of Hþ/OH strongly influences MFC power
output due to impacts on microbial metabolism. A model for a
single chamber MFC system, including the anode, bulk liquid, and
cathode, was used here to analyze mass transport drivers (diffusion
and electric migration), as well as biological and electrochemical
reactions in the whole system. A numerical method was devised for
combinations of anode and cathode subsystems, two relatively
independent components of the model, and then used for a steady
state simulation at each external resistance. Electric migration was
found to have a minor influence on current generation in the single
chamber MFC.
The effects of three buffer solutions (PBS, NaHCO3, NH4Cl) were
simulated in the steady state full cell model, with the PBS buffer
solution proving most capable of pH neutralization. However, the
large diffusion coefficient for PBS inhibited its performance at high
current density. When multiple concentrations of PBS were
compared, maximum power output occurred for the highest PBS
concentration. This model quantitatively described the mass
transport and electrochemical reactions by mathematical algorithm optimization, and provided scenario analysis for full cell MFC
system with various buffer solutions, which are difficult to be
accomplished experimentally. However, this work captured impacts of pH on multiple overpotentials, while neglecting pH influence on suspended biomass growth in the bulk liquid, which could
introduce minor inaccuracy in power outputs. Therefore, more
work is needed to quantitatively consider the pH effect on the
biomass growth in both anodic and cathodic sides.
Acknowledgments
This research was supported by the US Army Research Office,
contract number: W911NF-11-1-0531.
S. Ou et al. / Journal of Power Sources 347 (2017) 159e169
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