Kinetics and Mass Transfer Within Microbial Fuel Cells

C H A P T E R

15 Kinetics and Mass Transfer Within Microbial Fuel Cells V^ ania B. Oliveira, Joana Vilas Boas, Alexandra M.F.R. Pinto University of Porto, Porto, Portugal

Nomenclature AC

anode chamber

AE AP As B C C226 CC CCC CE CP CO2,ref D Deff Ecell F fx Gr g hmass Icell 2 IO 0, ref k K226 KA Kdec L

anode electrode anode acrylic plate surface area of the membrane, m2 biofilm concentration, mol/m3 concentration at the interfaces, mol/m3 cathode chamber current copper plate cathode electrode cathode acrylic plate reference concentration of oxygen, mol/m3 diffusion coefficient, m2/h effective diffusion coefficient, m2/h thermodynamic equilibrium potential, V Faraday´s constant, 96500 C/mol reciprocal of wash-out fraction Grashof number gravitational acceleration, 9.8
36002 m/h2 mass transfer coefficient, m/h cell current density, A/m2 exchange current density of oxygen, A/m2 constant in the rate expression, mol/(m3 h) partition coefficients half velocity rate constant for acetate, mol/m3 decay rate, h1 anode chamber length, m

Progress and Recent Trends in Microbial Fuel Cells https://doi.org/10.1016/B978-0-444-64017-8.00015-4

313

# 2018 Elsevier B.V. All rights reserved.

314 M N n P q R Ra Rcell Sc Sh T YX/A V Vcell x

15. KINETICS AND MASS TRANSFER WITHIN MICROBIAL FUEL CELLS

membrane molar flux, mol/(m2 h) number of electrons of the anodic and cathodic reactions pressure of air in cathode, atm flow rate, m3/h gas constant, 8.314 J/(molK) Rayleigh number internal resistance of the MFC, m2/S Schmidt number Sherwood number temperature, K bacterial yield volume, m3 cell voltage, V coordinate direction normal to the anode, m

Greek Δ αa αc δ ε ηactivation ηa ηconcentration ηc ηohmic κ μmax v

variation anodic transfer coefficient cathodic transfer coefficient thickness, m porosity activation overpotential, V anode overpotential, V concentration overpotential, V cathode overpotential, V ohmic overpotential, V ionic conductivity of the membrane, S/m maximum specific growth rate, h1 kinematic viscosity, m2/h

Subscripts A O2 X

acetate oxygen biomass

Superscripts 0 AC AE AF B CC CCC CE CF M

feed conditions anode compartment anode electrode anode flow biofilm cathode compartment current copper collector cathode electrode cathode flow membrane

15.2 MODELING APPROACHES FOR MFCs

315

15.1 INTRODUCTION An MFC is a complex system because it involves different phenomena that occur simultaneously in an operating cell, such as mass, charge, energy and heat transfer, anode and cathode electrochemical reactions, microbial metabolism and electron transfer. It is required to have a multidisciplinary knowledge of electrochemistry, fluid mechanics, microbiology, and engineering to clearly understand these systems. Considering this complexity, early stage research in this field was focused on experimental investigation of the effect of different parameters on cell performance toward an understanding of their influence on system efficiency. However, experimental research is expensive, time consuming, and some phenomena and specific parameters are difficult or cannot be measured by experimental techniques [1]. In order to address these limitations, the development of mathematical models can give considerable contribution. Modeling can be a handful tool to understand MFC working phenomena, because it allows for the simulation of different processes, predicting its effects on MFC performance. Some common steps can be adopted to develop a mathematical model [2]. First, it is essential to identify all the variables and processes of the MFC system that will be included in the model. Second, mathematical equations and laws need to be chosen or developed to mathematically translate these processes. Third, define the interaction between them and how they may be related. All parameters used on the model equations must be experimentally obtained or if not possible, carefully selected from literature or assumed to solve the equations and validate the model. Modeling can include different steps of complexity according to the processes that the model considers [3,4]. The ideal model should be robust and can predict performance accurately in a short period of time [4]. To be robust means that it can predict performance in a wide range of operating conditions. The accuracy of the model strongly depends on the equations, parameters, and assumptions adopted that will influence the trend of the simulation results and its fitting with the experimental results [4]. In literature, different modeling approaches for MFCs can be found, however, the research field of modeling MFC systems is relatively new. Although the first modeling work was reported more than 20 years ago [5], the number of published papers regarding the mathematical modeling of MFCs has only significantly increased in the last decade [1,6–28].

15.2 MODELING APPROACHES FOR MFCs Models being developed to describe MFC systems are one, two, or three dimensional, being categorized, respectively, as 1D, 2D, and 3D models. Additionally, they can be classified in two groups according to cell domain, namely full domain models, and specific models [3]. Full domain models help to understand the behavior of this type of fuel cell as a unit, and focus on the MFCs’ overall performance, whereas specific models help to understand a specific process or component/side. The majority of models are focused only on the anode side, neglecting the cathode side. There are only a few models that attempt a complete approach of the entire MFC system [1,13]. A very common categorization of fuel cell models is to divide the models into basic models (analytical and semiempirical models) and mechanistic models. The basic models are a useful

316

15. KINETICS AND MASS TRANSFER WITHIN MICROBIAL FUEL CELLS

tool to predict MFC performance using rapid calculations [1,7,13,15]. The analytical models are generally 1D models, whose main goal is to predict the cell or current voltage output, and the effect of the different parameters on them. They do not require a very robust computational software to solve the equations. The semiempirical models are the simplest ones due to the use of simple empirical equations and rely on empirical assumptions and correlations with the experimental data for different operating and design conditions. The main drawback of these models are the limitations on their accuracy for operation and design conditions that are different from the ones used on model development. As previously mentioned, basic models can help to understand MFC behavior according to specific conditions. However, because the MFC is a complex system, it requires more complex models to further understand the influence of mass transfer and bioelectrochemical processes occurring in an operating cell. Mechanistic models can achieve this because they are complex multidimensional numerical models and are developed based on complex governing equations. They clearly describe all the phenomena inside an MFC and predict cell performance with a higher accuracy. However, these models require extensive calculations to solve equations, which are performed by specific and very robust computational software (CFD), and require a long time to reach to model outputs [6,9]. Despite different approaches used to model an MFC system, the most common modeling equations to describe the phenomena and reactions in these systems are: (a) Monod equation: to describe the substrate consumption and bacterial growth; (b) Fick’s law: to describe the diffusion and mass transfer phenomena, through the concentration gradient in each cell component; (c) Tafel equation: to describe anode and cathode kinetics, commonly combined with Monod equation; (d) Butler-Volmer equation: to calculate the electric current density, through the cell potential of both anode and cathode; (e) Ohm’s law: to calculate current or voltage output from the MFC system; and (f) Nernst equation: to describe the electrochemical reactions. The anode reaction is usually related to the oxidation of acetate, which is the carbon source [1,6–8,13,16,20–22] because it is the simplest one that can be used by microorganisms to produce electricity. However, some models attempt to describe more complex substrates, such as wastewater streams, as this is more in line with MFC technology in applications such as wastewater treatment [6,10,19,23,25,28–30]. Some models assume that the anode electron transfer mechanism occurs using mediators [6,9,11,12,14,24]. Nevertheless, direct electron transfer has recently been preferred because of the mediatorless MFC operation through the use of electricigen species [1,7,13,22,23,25,26].

15.3 CASE STUDY—1D ANALYTICAL MODEL FOR CONTINUOUS OPERATION Having in mind the advantages of the basic models, a steady-state, one-dimensional and analytical model, coupling the biological, energy and mass transfer effects along with the

15.3 CASE STUDY—1D ANALYTICAL MODEL FOR CONTINUOUS OPERATION

317

electrochemical reactions on both anode and cathode sides is here presented. This model aims to accurately describe the main processes within the operation of an MFC. The cell voltage, Vcell, is described by the theoretical voltage at thermodynamic equilibrium potential, Ecell, subtracting the losses originated from: (a) activation overpotential: related to the rates of electrode reactions, ηactivation; (b) ohmic overpotential: related to the resistance to the flow of ions in the electrolyte and electrons through the external electrical circuit, ηohmic; and (c) concentration overpotential: related to mass transfer limitations of the different species transported to or from the electrode, ηconcentration. The cell voltage can then be estimated by: Vcell ¼ Ecell  ηactivation  ηconcentration  ηohmic

(15.1)

Both ηactivation and ηconcentration consider the losses that occur at the anode and cathode sides, therefore Eq. (15.1) can be rewritten as: Vcell ¼ Ecell  ηa  ηc  Icell Rcell

(15.2)

where, ηa and ηc are the anode and cathode overpotentials and the ηohmic is the ohmic losses calculated through the Ohm’s Law: ηohmic ¼ Icell Rcell

(15.3)

where, Icell is the cell current density (A/m2) and Rcell the internal resistance of the MFC (m2/S), given by: Rcell ¼

δM κ

(15.4)

where, δM is the membrane thickness (m) and κ is the ionic conductivity of the membrane (S/m).

15.3.1 Model Structure and Flux Balance The model is based on a dual-chambered MFC, constituted by an anode chamber with an electrode, a proton exchange membrane, which separates both compartments and a cathode chamber with an electrode. Moreover, the cell is divided in layers, being the anodic part constituted by an anode acrylic plate (AP), an anode chamber (AC), a biofilm (B), and an anode electrode (AE), a membrane (M) dividing the chambers, and at the cathodic side, it was considered a cathode electrode (CE), a cathode chamber (CC), and a cathode acrylic plate (CP). The schematic representation can be found in Fig. 15.1. In other fuel cells, such as direct methanol fuel cells, it is common to divide the electrode layer in diffusion layer and catalyst layer. In the present model, the two layers are modeled in one single homogeneous layer, the electrode layer. The anode chamber is supplied with substrate in a constant and known flow rate and a single culture of microorganisms is considered. The anodic reaction is the oxidation of acetate ((CH2O)2), which is the substrate, by the catalytic activity of microorganisms to release carbon

318

FIG. 15.1

15. KINETICS AND MASS TRANSFER WITHIN MICROBIAL FUEL CELLS

Schematic representation of a dual chamber MFC.

dioxide (CO2), electrons and protons. The electrons and protons are transferred to the cathode by, respectively, an external electrical circuit and a polymer electrolyte membrane (PEM). As cathodic reaction, the reduction of oxygen (O2) to form water (H2O) is considered. The anodic and cathodic reactions are: Anodic reaction: ðCH2 OÞ2 + 2H2 O ! 2CO2 + 8H + + 8e

(15.5)

O2 + 4H + + 4e ! 2H2 O

(15.6)

Cathodic reaction:

Based on a common assumption in fuel cells, all the fluxes are equal and can be related to the current density by the following equation: N¼

Icell nF

(15.7)

where, n is the number of electrons from the corresponding reaction, F is the Faraday’s constant (96,500 C/mol) and N the molar flux (mol/(m2 h)).

15.3.2 Model Assumptions To reduce the complexity of the MFC system, and to simplify the model, since it is intended to develop an analytical model, some assumptions were adopted: (a) Operation at steady-state conditions; (b) Only the x-direction is considered, 1D (Fig. 15.1); (c) The mass transfer through the electrode layers and biofilm is predominantly performed by diffusion, so the mass transfer by convection is neglected; (d) Fick models are used to describe the mass transfer in the electrodes and biofilm; (e) Constant pressure and temperature across the cell is considered; (f) At the anodic chamber, only the liquid phase is considered; (g) Local equilibrium at interfaces is represented by partition functions; (h) The electrodes are assumed to be a macro-homogeneous porous layer so the reactions are modeled as a homogeneous reaction being the overpotential constant through these layers;

15.3 CASE STUDY—1D ANALYTICAL MODEL FOR CONTINUOUS OPERATION

319

Anode kinetic is described by Tafel and Monod equations; Cathode kinetic is described by Tafel equation; The anode and cathode chambers are treated as a continuous stirred tank reactor (CSTR); The anodic mass balances take into account the rates of reaction in the anodic chamber, biofilm and on the electrode; (m) CO2, (CH2O)2 and O2 do not diffuse into the membrane; and (n) A steady-state biofilm is maintained through the equilibrium between the overall rate of microbial growth through the substrate utilization and the overall rate of biomass losses. (i) (j) (k) (l)

15.3.3 Governing Equation and Boundary Conditions The crucial part on the development of a mathematical model is to set the equations that will describe the phenomena inside the cell, because they will dictate the model behavior. It is intended that the model allow estimating the substrate and biomass concentration profiles across the layers, the biofilm thickness as well as, the anode and cathode overpotentials. The major goal of the model is to predict the cell performance for different operating and design conditions. This can be achieved through Eq. (15.2) and after estimation the anode and cathode overpotential for each condition. 15.3.3.1 Mass Transfer The mass transfer effects will be described here as molar fluxes and for the different processes occurring in all the MFC layers along the x-direction (Fig. 15.1). Anode: The anode chamber is treated as CSTR, so the mass balance for acetate and biomass are described, respectively, by:  qAF
0 CA  CAC A s A

(15.8)

 V AC Kdec CX qAF
0  s CX  CX S A YX=A A fx YX=A

(15.9)

NA ¼ NA ¼

where, NA is the molar flux of acetate (mol/(m2 h)), qAF the anode flow rate (m3/h), As the active area, corresponding to the surface area of the membrane (m2), VAC is the volume of the anode chamber (m3), Kdec is decay rate (h1), YX/A is the bacterial yield and fx is the reciprocal of wash-out fraction. The C0A is the initial acetate concentration and the CAC A the acetate concentration at the anode chamber layer. The C0X and the CX are the concentrations of acetate in the biomass at initial and steady-state conditions. All concentrations are presented in mol/m3. The decay/inactivation process is included on the current model once it is common in almost any biofilm models and expresses the biomass losses [31,32]. The acetate flux in the biofilm is assumed to be performed by diffusion, so the flux can be described by Fickian diffusion: NA ¼ Deff,B A

dCBA dx

(15.10)

320

15. KINETICS AND MASS TRANSFER WITHIN MICROBIAL FUEL CELLS

B where, Deff, is the effective diffusion coefficient of acetate trough biofilm (m2/h) and CBA is A the acetate concentration through the biofilm layer (mol/m3). In this model, the spatial distribution of microorganisms in the biofilm is assumed to be homogeneous. Furthermore, the biofilm is at its steady-state growth, so an equilibrium exists between biomass detachment by decay and microbial growth. Based on these considerations, the biofilm thickness can be related to the biomass concentration:

NA ¼ Kdec CX δB

(15.11)

where, δ is the biofilm thickness (m). In the anode electrode, the acetate flux is also considered to be a diffusion flux, being also described by Fickian diffusion: B

NA ¼ Deff,AE A

dCAE A dx

(15.12)

AE where, Deff, is the corresponding effective diffusivity of acetate through anode electrode A 2 3 (m /h) and CAE A is the concentration of acetate though the anode electrode layer (mol/m ). As already referred, partition coefficients (K26) were considered at the different layers interfaces, assuming an equilibrium between them. Based on that, the boundary conditions at the AC/B and B/AE interfaces are given by:

At x ¼ x2 : CB2, A ¼ K2 CAC A

(15.13)

where, CB2, A is the acetate concentration at the AC/B interface, in the biofilm layer (mol/m3). B At x ¼ x3 : CAE 3,A ¼ K3 C3, A

(15.14)

B where, CAE 3, A and C3, A are the acetate concentrations at the B/AE interface, in the biofilm and anode electrode layers, respectively (mol/m3). Membrane: At the interface AE/M (x ¼ x4), once it is assumed that no acetate passes through the membrane, the concentration, CM A is equal to zero. A similar assumption is made for the oxygen concentration in CE/M interface.

AE At x ¼ x4 : CM A ¼ K4 C4,A ¼ 0

CM A

(15.15) CAE 4, A 3

is the acetate concentration at the membrane layer, and is the acetate concenwhere, tration of the anode electrode layer at the AE/M interface (mol/m ). CE At x ¼ x5 : CM O2 ¼ K5 C5,O2 ¼ 0

(15.16)

CE where, CM O2 is the oxygen concentration at the membrane, and C5,O2 is the oxygen concentration of the cathode electrode layer at the CE/M interface (mol/m3). Cathode: Like at the anode side, the cathode chamber is treated as a CSTR, so the oxygen flux is described by:  qCF  (15.17) NO2 ¼ s C0O2  CCC O2 A

where, NO2 is the molar flux of oxygen (mol/(m2 h)), qCFis the cathode flow rate (m3/h) and C0O2 3 and CCC O2 the oxygen concentrations of the air and cathode chamber, respectively (mol/m ).

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15.3 CASE STUDY—1D ANALYTICAL MODEL FOR CONTINUOUS OPERATION

At the cathode electrode, the oxygen flux can be calculated by Fickian equation and based on the concentration gradient of oxygen in this layer, as: NO2 ¼ Deff,CE O2

dCCE O2 dx

(15.18)

where, Deff,CE is the corresponding effective diffusivity of oxygen through cathode electrode O2 3 (m2/h) and CCE O2 , the oxygen concentration of the cathode electrode (mol/m ). The boundary conditions of Eq. (15.18) are: CC At x ¼ x6 : CCE 6,O2 ¼ K6 CO2

(15.19)

where, CCE 6,O2 is the oxygen concentration of the cathode electrode at CE/CC interface (mol/m3). 15.3.3.2 Kinetics—Anode and Cathode Anode: As explained in Eq. (15.7), all the fluxes on the anode side can be given by: NA ¼

Icell 8F

(15.20)

where, 8 is the number of electrons of the anodic reaction, the acetate oxidation (Eq. 15.5). The reaction at the anode includes the biological degradation of acetate by microbial activity, therefore the Monod-Tafel equation is used, assuming direct electron transfer by both microorganisms in the biofilm and suspended microorganisms:     CAC αa ηa F αa ηa F CAB A A C + k exp CX (15.21) NA ¼ k exp X AC RT KA + CA RT KA + CAB A where, k is a constant mol/(m3 h), αa is the anodic transfer coefficient, KA is the half velocity rate constant for acetate (mol/m3), R is the gas constant (8.314 J/(mol K) and T is the temperature of operation (303 K). The first term describes the electrons production on the anode chamber and the second the electrons production on the biofilm. Cathode: At the cathode, the oxygen flux, NO2, is equal to: NO2 ¼

Icell 4F

(15.22)

where, 4 is the number of electrons from the cathodic reaction (Eq. 15.6). The cathode overpotential is obtained using the Tafel equation to represent the oxygen reduction reaction:   CCE αc ηc F O2 O2 exp NO2 ¼ I0, ref CE (15.23) RT CO2 , ref 2 CE 2 where, IO 0, ref is the exchange current density of oxygen (A/m ), CO2 , ref is the reference con3 centration of oxygen (mol/m ) and αc the cathodic transfer coefficient. All the parameters used in the model should be as realistic as possible and adequate for the cell operating and design conditions. For this model, the parameter values were selected base on previous modeling works and can be found in the Table 15.1.

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15. KINETICS AND MASS TRANSFER WITHIN MICROBIAL FUEL CELLS

TABLE 15.1 and Units Parameter

Value

Reference 5

2.25
10

AF

q

V

Parameters Used in the Model and Its Corresponding Values

AC

,V

CC

C0A

5

5.5
10

3

m /h

[13]

3

m

[13]

3

1.56 mol/m

[13] 3

k

0.207 mol/(m h)

[13]

αa

0.051

[13]

T

303 K

assumed 3

KA

0.592 mol/m

[13]

fX

10

[13]

C0X

0 mol/m

YX/A

0.05

3

8.33
10 4

5
10

S

AE Deff, A B Deff, A

,ε

ε

[8] 4

Kdec A

AE

[13]

CE

AE2.5

ε

h

1

[13]

2

m

[13] 9

(1.1
10


3600) m /h 2

9

0.8
(1.1
10

[11]


3600) m /h 2

[8]

0.86

[33]

0.000023 m

assumed

K26

0.8

assumed

δAE, L

0.1 m  1:75  2:5
5:8
104 εCE T 27:772
P
3600
104 m2/h

assumed

δ

,δ

AE

eff, DO 2

CE

CE

CE CO 2

0:21
P RT

COCE 2, ref

0:21
P RT

mol/m3

4:222
102 exp

P

1 atm 1.11
10

αc

0.44

Ecell

0.77 V

κ

3

m /h

1 353  T

A/m2

[33]

[13]

[13] [33]

3.6 S/m

δ

R

 1

assumed

2

M

[33] 73200


assumed 3

q

CF

assumed

mol/m3

2 IO 0, ref

[33]

4

1.778
10

m

[33]

15.4 ADAPTATION FOR BATCH OPERATION

323

15.4 ADAPTATION FOR BATCH OPERATION In this subsection the one-dimensional, steady-state an analytical model developed for continuous operation will be adapted to describe once again the biological, energy and mass transfer effects but now for a cell operated in batch mode. Because the system under study is the same and only diverge on its operation mode the model domain is the same as the one presented in Fig. 15.1, the mass transfer equations for the anode biofilm, anode and cathode electrode and membrane and its corresponding boundary conditions are the same for both systems. Moreover, the kinetic equations are, also, described by the same equations of the continuous operation (Eqs. 15.5, 15.6). The main difference for the mass transfer phenomena between for operating modes are for the anode compartment, which in this case cannot be described as a CSTR. The governing equation and boundary conditions for mass transfer are: Anode: In order to describe the batch operation mode, it is assumed that the acetate flux on the anode chamber is governed by natural convection:
0  AC (15.24) NA ¼ hAC mass,A CA  CA where, the hAC mass, A is the mass is the mass transfer coefficient of acetate in water (m/h) and can be estimated by the Sherwood number, Sh, using the following equation [34]: 2 32 6 6 hAC mass,A L 6 Sh ¼ 60:825 + D 6 4

7 7 0:387 Ra1=6 7 7 ! 8=27  9=16 7 0:492 5 1+ Sc

(15.25)

where, L is the length of active area (m), D the diffusion coefficient (m2/h), Ra the Rayleigh number and the Sc the Schmidt number. The Ra is obtained by: Ra ¼ Gr Sc

(15.26)

where, Gr is the Grashof number, which is calculated by: g ΔC L3 (15.27) C v2 where, v is the kinematic viscosity (m2/h), g the gravitational acceleration (m/h2) and C is the molar concentration (mol/m3). The Sc is given by: v (15.28) Sc ¼ D The biomass concentration on the anodic chamber can be related to its initial concentration and its growth and decay rate through equation: Gr ¼

Cx ¼ C0x +

NA AS Yx=A NA AS Yx=A  AC V AC μmax V Kdec

where, μmax is the maximum specific growth rate (h1).

(15.29)

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15. KINETICS AND MASS TRANSFER WITHIN MICROBIAL FUEL CELLS

15.5 MODIFICATIONS FOR A SINGLE CHAMBER CONFIGURATION A single chamber MFC comprises an anode chamber with an electrode, a proton exchange membrane and a cathode electrode with an electron collector. In contrast to the dual chamber layout, the single one does not have a cathode chamber and the cathode is an air-breathing one, so it is opened to the air. Therefore, in this configuration, the cathode end plate (CP) is removed and a current collector (CCC) is used instead. The current collector has holes to provide the oxygen supply to the cathode layer (CE) and the products removal. It is important to notice that in a single chamber MFC, the active area should be the open area of the cathode current collector, the total area of the holes, since this is the region where the oxygen is fed to the cathode electrode. Toward the development of a mathematical model for this configuration the assumptions, equations and boundary conditions for the anode side are equal to the ones presented for the dual chamber configuration and the only differences are for the cathode side. In this case, the cathode works in a passive mode, all the transport phenomena are governed by natural convection and diffusion. A schematic representation of a SCMFC is provided in Fig. 15.2. As already mentioned, the mass transfer equations for the anode side and the kinetics ones are, the same for the two configurations. Regarding the mass transfer equations for the cathode side, the only difference is on the equation for the cathode compartment that is replaced by Eq. (15.30). For this configuration, the oxygen transport from the surroundings to the CCC is due to natural convection. Therefore, the oxygen flux is described by:   0 CCC C  C (15.30) NO2 ¼ hCCC mass, O2 O2 O2 where, hCCC mass, O2 is the oxygen mass transfer coefficient in the air (m/h), estimated through 3 Eq. (15.25) and CCCC O2 is the concentration of oxygen at the current copper collector (mol/m ). The equation used to describe the oxygen flux in the cathode electrode in a dual chamber configuration can, also, be used in this case and the corresponding boundary condition is: CCC At x ¼ x6 : CCE 6,O2 ¼ K6 CO2

(15.31)

where, CCE 6,O2 is the concentration of oxygen at the cathode electrode at CE/CCC interface (mol/m3).

FIG. 15.2

Schematic representation of a single chamber MFC.

REFERENCES

325

15.6 SUMMARY Recently, the use of mathematical models to describe and predict the MFC behavior and performance has gained acceptation by the MFC research community. However, most of the models are, only, focused on the biofilm formation and its phenomena and only a few number has been developed to describe all phenomena occurring in a working cell. Despite its simulation times and complexity, mechanistic models are needed since they provide a detailed knowledge on the effect of various operating and design parameters on the cell performance. Toward a rapid prevision of the fuel cell behavior, high accurate analytical models, such as the one proposed on this chapter, can be used as a more user-friendly tool. Despite the modeling approach used, mathematical models provide a better knowledge of the different phenomena and interactions within the cell, so there is no doubt that modeling will accompanied the MFC development thru its commercialization. Based on that the main goal of the present chapter was to develop an analytical and one-dimensional model coupling the mass and charge transfer with the biological and electrochemical processes that occur in a working MFC, that can be used to predict its performance under different operating and design conditions. Besides that, the model, also, allows to predict the concentration profiles of the different species on the different fuel cell layers, as well as to estimate the biofilm thickness. Regarding the applicability of the model developed for a dual chamber MFC and continuous operation, it was shown that with simple and few modifications, it can be applied to different operation conditions (continuous and batch operation) and designs (dual and single chamber). This demonstrates that despite the basic models’ limitations, they can be a resourceful instrument to predict the behavior of different MFC systems. Considering the MFCs applications, such as the wastewater treatment, it is mandatory to develop simpler models than can describe with accuracy more complex MFC systems, such as the ones fed with complex substrates and different microorganism.

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