Staged Microbial Fuel Cells with Periodic Connection of External Resistance

11th IFAC Symposium on Dynamics and Control of Process Process Systems, Systems, including including Biosystems Biosystems 11th Symposium on Dynamics and Control of JuneIFAC 6-8, 2016. 2016. NTNU, Trondheim, Trondheim, Norway 11th IFAC Symposium on Dynamics and Controlonline of June 6-8, NTNU, Norway Available at www.sciencedirect.com Process Process Systems, Systems, including including Biosystems Biosystems June 6-8, 2016. NTNU, Trondheim, Norway June 6-8, 2016. NTNU, Trondheim, Norway

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IFAC-PapersOnLine 49-7 (2016) 091–096 Staged Microbial Microbial Fuel Fuel Cells Cells with Periodic Periodic Connection of of External External Resistance Resistance Staged with Connection Staged with Periodic Connection of22 External Staged Microbial Microbial Fuel Fuel Cells Cells with Periodic External Resistance Resistance 1,2 Connection of Dídac Dídac Recio-Garrido Recio-Garrido1,2,, Boris Boris Tartakovsky Tartakovsky

1 1 Michel Perrier 2 Michel 1,2 Perrier 1,2 Dídac ,, Boris Dídac Recio-Garrido Recio-Garrido1,2 Boris Tartakovsky Tartakovsky22 1 1 Michel Michel Perrier Perrier1 1 1 Department of of Chemical Chemical Engineering, Engineering, École École Polytechnique Polytechnique de de Montréal, Montréal, C.P.6079 C.P.6079 Succ., Succ., Centre-Ville Centre-Ville Montréal, Montréal, QC, QC, Canada Canada Department H3C 3A7 (Tel: +1-514-340-4711 ext. 4130; e-mail: [email protected]). 1 H3C 3A7 (Tel: +1-514-340-4711 ext. 4130; e-mail: [email protected]). 1Department of Engineering, École de C.P.6079 Succ., Centre-Ville Montréal, QC, 1 2 Department of Chemical Chemical Engineering, École Polytechnique Polytechnique de Montréal, Montréal, C.P.6079 Succ.,H4P Centre-Ville QC, Canada Canada 2National Research Council of Canada,6100 Royalmount Ave., Montréal, QC, 2R2 (Tel:Montréal, +1-514-496-2664; National Research Council Canada,6100 Royalmount QC, Canada Canada H4P 2R2 (Tel: +1-514-496-2664; H3C 3A7of(Tel: (Tel: +1-514-340-4711 ext. Ave., 4130;Montréal, e-mail: [email protected]). [email protected]). H3C 3A7 +1-514-340-4711 ext. 4130; e-mail: e-mail: [email protected]) 2 e-mail: [email protected]) 2 2National National Research Research Council Council of of Canada,6100 Canada,6100 Royalmount Royalmount Ave., Ave., Montréal, Montréal, QC, QC, Canada Canada H4P H4P 2R2 2R2 (Tel: (Tel: +1-514-496-2664; +1-514-496-2664; e-mail: e-mail: [email protected]) [email protected]) Abstract: Reactor staging staging is is widely widely used used in in wastewater wastewater treatment treatment where where treatment treatment norms norms are are achieved achieved by by Abstract: Reactor connecting two or more reactors in series. The first reactor operates at high carbon source loads and the connectingReactor two or staging more reactors in series.inThe first reactor operates at high carbonnorms source loads and the Abstract: is wastewater treatment where by Abstract: Reactor staging is widely widely used used inMicrobial wastewater treatment(MFCs) where treatment treatment norms are are achieved achieved by last performs the final Fuel are bioelectrochemical devices last reactor reactor two performs thereactors final polishing. polishing. Microbial Fuel Cells Cells (MFCs) arecarbon bioelectrochemical devices connecting or more in series. The first reactor operates at high source loads and the connecting two or more reactors in series. The first reactor operates at high carbon source loads and the designed for direct production organic matter. of designed forperforms direct electricity electricity production from from organic matter. Periodic Periodic connection connection of the the MFC MFC external external last reactor the final Microbial Fuel are devices last reactor performswas the demonstrated final polishing. polishing. Microbialperformance. Fuel Cells Cells (MFCs) (MFCs) are bioelectrochemical bioelectrochemical devices electrical resistance was demonstrated to increase increase An engineering tool to understand this electrical resistance to performance. An engineering tool to understand this designed for direct electricity production from organic matter. Periodic connection of the MFC external designed for direct electricity production from organic matter. Periodic connection of the MFC external periodic mode of operation is developed. Effluent quality control can be ensured by developing control periodic mode of operation is developed. Effluent quality control can be ensured by developing control electrical resistance was demonstrated to increase performance. An engineering tool understand electrical resistance wasvariability demonstrated increase performance. An tracking engineering tool to to understand this this strategies able reject in concentration while aa desired set-point. strategies able to to reject variability in the thetoinfluent influent concentration while tracking desired set-point. periodic mode of operation is developed. Effluent quality control can be ensured by developing periodic mode of operation is developed. Effluent quality control can be ensured by developing control control Keywords: Microbial cell; dynamic modelling; reactors in intermittent effluent strategies able to variability in concentration while tracking aa Ltd. desired set-point. © 2016, IFAC (International Federation Automatic Control) Hosting by Elsevier Alloperation; rights reserved. Keywords: Microbial fuel cell; dynamic modelling; reactors in series; series; intermittent operation; effluent strategies able to reject rejectfuel variability in the theofinfluent influent concentration while tracking desired set-point. quality control; PID. quality control; PID. Keywords: Microbial Keywords: Microbial fuel fuel cell; cell; dynamic dynamic modelling; modelling; reactors reactors in in series; series; intermittent intermittent operation; operation; effluent effluent quality quality control; control; PID. PID. intermittent intermittent connection connection counteracts counteracts considerable considerable losses losses in in 1. INTRODUCTION INTRODUCTION 1. power output as compared to MFC operation with fixed power outputconnection as compared to MFCconsiderable operation with fixed intermittent counteracts losses in intermittent connection counteracts considerable losses in 1.(MFCs) INTRODUCTION resistance (Grondin et 2012), particularly when Microbial are INTRODUCTION externaloutput resistance (Grondin to et al. al. 2012), particularly when Microbial Fuel Fuel Cells Cells1. (MFCs) are bioelectrochemical bioelectrochemical devices devices external power as compared MFC operation with fixed power output as compared to MFC operation with fixed operating at at values values of of the the external external resistance resistance which which were were designed for electricity production operating designed Fuel for direct direct electricity production from from organic organic external resistance resistance (Grondin et al. al. 2012), 2012), particularly particularly when when Microbial Cells (MFCs) (MFCs) are bioelectrochemical bioelectrochemical devices external (Grondin et Microbial Fuel to Cells below the the internal internal resistance. resistance. While previous works works study study the the matter. Similar Similar conventionalare fuel cells, cells, they they consist consistdevices of two two below While previous matter. to conventional fuel of operating at at values values of of the the external external resistance resistance which which were were designed for for direct direct electricity electricity production production from from organic organic operating designed of time connection and switching frequency electrodes connected connected by by an an external external electrical electrical circuit. circuit. The The effect effect of time connection and switching frequency electrodes below the the internal internal resistance. resistance. While While previous previous works works study study the the matter. Similar Similar to to conventional conventional fuel fuel cells, cells, they they consist consist of of two two below matter. experimentally (Gardel et Grondin et al. MFC anodic compartment benefits from the biocatalytic experimentally (Gardel et al. al. 2012, 2012, Grondin et frequency al. 2012, 2012, MFC anodic compartment benefits from the circuit. biocatalytic effect of time connection and switching electrodes connected by an external electrical The effect of time connection and switching frequency electrodes connected by anbacteria, externalwhich electrical circuit. The et 2013a), is still of activity of externally release Coronado et al. al. (Gardel 2013a), there there still aa lack lack of an anetengineering engineering activity of exoelectricigenic exoelectricigenic release Coronado experimentally et al. al.is 2012, 2012, Grondin al. 2012, 2012, MFC anodic anodic compartment bacteria, benefitswhich from externally the biocatalytic biocatalytic experimentally (Gardel et Grondin ettheal. MFC compartment benefits from the tool useful to further extend the understanding of periodic electrons from the oxidation of organic matter. The released tool useful to further extend the understanding of the periodic electrons from the oxidation of organic matter. The released Coronado et al. 2013a), there is still a lack of an engineering activity of of exoelectricigenic exoelectricigenic bacteria, bacteria, which which externally externally release release Coronado et al. 2013a), there is still a lack of an engineering activity effect on performance. Very studies have electrons flow through the electrical circuit while operation on MFC MFC performance. Very few few have electrons from flow the through the external external electrical while operation tool usefuleffect to further further extend the understanding understanding of studies the periodic periodic electrons oxidation of organic organic matter. circuit The released released tool useful to extend the of the electrons from the oxidation of matter. The considered the effect of the connection time and switching protons migrate to the cathode to reduce oxygen and form consideredeffect the effect of performance. the connection timefew and switching protons migrate to the cathode to reduce oxygen and while form operation on MFC Very studies have electrons flow through the external electrical circuit MFCperformance performance. Very few studies have electrons flow2008). through the external electrical circuit while operation frequency effect in the theonMFC MFC and microbial structure. water frequency in performance and microbial structure. water (Logan (Logan 2008). considered the effect of the connection time and switching protons migrate to the cathode to reduce oxygen and form effect of themodelling connection timeshed and some switching protons migrate to the cathode to reduce oxygen and form considered In this this way, way,the MFC dynamic could light In dynamic modellingand could shed some light frequency in MFC the MFC MFC performance microbial structure. water (Logan 2008). Microbial fuel cells in the performance and microbial structure. water (Logan Microbial fuel2008). cells are are able able to to treat treat low low strength strength wastewater. wastewater. frequency in the subject and be used for developing MFC-based in the subject and be used for developing MFC-based In this this way, way, MFC MFC dynamic dynamic modelling modelling could could shed shed some some light light Their for energy recovery provides an to Their ability ability energy recovery provides an opportunity opportunity to In treatment systems with volumetric power Microbial fuelfor cells are able able to treat treat low strength strength wastewater. treatment systemsand withbehigh high volumetric power output. output. Microbial fuel cells are to low wastewater. in the subject used for developing MFC-based develop a novel wastewater treatment technology (Du et al. in the subject and be used for developing MFC-based develop a novel wastewater treatment technology (Du et al. Their ability for energy energy recovery provides an opportunity opportunity to Their ability for recovery provides an to treatment systems with high high volumetric power output. The significant significant charge storage capacitypower of electrochemically electrochemically 2007). context, reactor staging is where treatment systems with volumetric output. The charge storage capacity of 2007). In Ina such such context, reactor staging technology is widely widely used used where develop novel wastewater treatment (Du et al. develop novel wastewater treatment technology al. active active biofilms biofilms (Schrott (Schrott et et al. al. 2011) 2011) results results in in aa complex complex nonnontreatmenta norms norms are achieved achieved by connecting connecting two(Du or et more treatment are by two or more The significant significant charge charge storage storage capacity capacity of of electrochemically electrochemically 2007). In such context, reactor staging is used where The 2007). context, staging is widely widely usedat behavior during intermittent connection of the external reactorsInin insuch series with reactor the first first reactor operating atwhere high linear linear behavior during intermittent connection of the external reactors series with the reactor operating high active biofilms biofilms (Schrott (Schrott et et al. al. 2011) 2011) results results in in aa complex complex nonnontreatment norms are achieved by connecting two or active treatment norms areand achieved by connecting two the or more more resistance in This results aa combination of fast, carbon source loads the reactor performing final resistance in MFCs. MFCs. This results in in connection combination of external fast, i.e. i.e. carbon source loads and the last last reactor performing the final linear behavior during intermittent of the reactors in series with the first reactor operating at high linear behavior during intermittent connection of the external reactors inStaging series increases with the treatment first reactor operating (Pinto at high time constants in the order of milliseconds, charge/discharge polishing. performance et time constants in the order of milliseconds, charge/discharge polishing. Staging increases treatment performance (Pinto et resistance in in MFCs. MFCs. This This results results in in aa combination combination of of fast, fast, i.e. i.e. carbon source loads last reactor the resistance carbon source loads and and the the last flow reactor performing performing the final final dynamics with slower of biofilm al. 2010a) as aa plug An in dynamics with inmuch much slowerof dynamics dynamics of microbial microbial biofilm al. 2010a) Staging as it it resembles resembles plug flow reactor. reactor. An increase increase in time constants the order order milliseconds, charge/discharge polishing. increases treatment performance (Pinto et time constants in the of milliseconds, charge/discharge polishing. Staging increases treatment performance (Pinto et growth decay, i.e. time in the order to the reactor volume results of power density growth and andwith decay, i.e. slower time constants constants in of themicrobial order of of hours hours to the 2010a) reactor as volume results ain in aa decrease decrease of the the An power density dynamics much dynamics biofilm al. reactor. increase in with much slower dynamics of microbial biofilm al. 2010a) as it it resembles resembles a plug plug flow flow reactor.with An the increase in dynamics days. Such behavior has not been described by previous due to an increase of the internal resistance volume days. Such behavior has not been described byof previous due reactor to an increase of the internal resistance with the volume growth and decay, i.e. time constants in the order hours to the volume results in a decrease of the power density and decay, i.e. time constants in the order of that hoursinto to the reactor volume resultset a decrease of the power smaller density growth MFC models models (Recio-Garrido et al. al. 2016a). 2016a). Taking of reactor (Clauwaert 2008). Thus, stacking MFC (Recio-Garrido et Taking that into of the the reactor (Clauwaert etinal. al. 2008). Thus, stacking smaller days. Such behavior has not been described by previous due to an increase of the internal resistance with the volume Such has not been described by previous due to in an series increase the internal resistance with voltage the volume account, thisbehavior study presents presents a combined combined bioelectrochemicalMFCs in series andofparallel parallel is aa way way to increase increase voltage and days. account, this study bioelectrochemicalMFCs and is to and MFC models models (Recio-Garridoa et et al. al. 2016a). 2016a). Taking that that into into of the reactor (Clauwaert et al. 2008). Thus, stacking smaller MFC (Recio-Garrido Taking of the reactor (Clauwaert et al. 2008). Thus, stacking smaller current densities. densities. electrical (CBE) (CBE) model model of of an an MFC MFC obtained obtained by by combining combining current electrical account, this study presents a combined bioelectrochemicalMFCs in series and parallel is a way to increase voltage and this equations study presents combined bioelectrochemicalMFCs in series and parallel is a way to increase voltage and account, fundamental baseda on mass and balances fundamental equations mass and electron electron balances current electrical (CBE) (CBE) modelbased of an an on MFC obtained by combining combining As other model of MFC obtained by As any any densities. other electrical electrical voltage voltage source, source, the the electrical electrical power power electrical current densities. with equations describing an equivalent electrical circuit. with equations describing an equivalent electrical circuit. fundamental equations equations based based on on mass mass and and electron electron balances balances produced by MFCs suffers dramatic losses when the produced by the the MFCsvoltage sufferssource, dramatic losses when the fundamental Accordingly, the presented CBE model describes both fast As any other electrical the electrical power Accordingly, the presented CBE model describes both fast As any other electrical voltage source, the electrical power with equations equations describing describing an an equivalent equivalent electrical electrical circuit. circuit. external resistance resistance does does not not match match the the value value of of the the internal internal with external (milliseconds) and slow (hours and days) MFC dynamics and produced by the MFCs suffers dramatic losses when the (milliseconds) and slow (hours and days) MFC dynamics and produced by the MFCs suffers dramatic losses when the Accordingly, the presented CBE model describes both fast resistance of of the the reactor. reactor. For For this this reason, reason, research research has has been been Accordingly, the presented CBE model describes both fast resistance external resistance does not match the value of the internal is the behavior of two MFCs is used used to to describe describe the behavior of MFC two staged staged MFCs external resistance does not match the value of the internal (milliseconds) and slow (hours and days) dynamics and devoted to tracking internal resistance in MFCs by adjusting (milliseconds) slow connection (hours and days) MFC dynamics and devoted to of tracking internal resistance in MFCs by adjusting resistance the For research has operated underand periodic of the external resistance. operated periodicthe connection the two external resistance. resistance ofresistance the reactor. reactor. For this this reason, reason, research has been been is used under to describe describe behaviorof of of staged MFCs the external (Woodward et al. 2010). However, the is used to the behavior two staged MFCs the external resistance (Woodward et al. 2010). However, the devoted tracking resistance in Steady-state values values are are used to to study study the the effect effect of of connection connection devoted to toresistance tracking internal internal resistancechanged in MFCs MFCsinby by adjusting adjusting Steady-state operated under under periodic periodicused connection of the the external resistance. external cannot operated of resistance. external resistance cannot be be et changed in practical practical the external resistance (Woodward al. 2010). However, the time ratio ratio and and switching switching connection frequency on on MFCexternal performance. the external resistance (Woodward et al. 2010). However, the time frequency MFC performance. Steady-state values are used to study the effect of connection applications. Recent works have demonstrated that applications. Recent works behave demonstrated that Steady-state values are used to study the effect of connection external external resistance resistance cannot cannot be changed changed in in practical practical time ratio and switching frequency on MFC performance. time ratio and switching frequency on MFC performance. applications. Recent works have demonstrated applications. Recent works have demonstrated that that

Copyright © 2016 91 Copyright © 2016, 2016 IFAC IFAC 91 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Peer review under responsibility of International Federation of Automatic Control. Copyright © © 2016 2016 IFAC IFAC 91 Copyright 91 10.1016/j.ifacol.2016.07.222

IFAC DYCOPS-CAB, 2016 92 Dídac Recio-Garrido et al. / IFAC-PapersOnLine 49-7 (2016) 091–096 June 6-8, 2016. NTNU, Trondheim, Norway

𝑑𝑑𝑋𝑋𝑚𝑚

2. MATERIALS AND METHODS

𝑑𝑑𝑑𝑑

= (𝜇𝜇𝑚𝑚 − 𝐾𝐾𝑑𝑑,𝑚𝑚 − 𝛼𝛼𝑚𝑚 𝐷𝐷)𝑋𝑋𝑚𝑚 ,

2.1 MFC Design and Operation

𝑑𝑑𝑀𝑀𝑜𝑜𝑜𝑜

Experiments were conducted in two membraneless aircathode MFCs with an anodic compartment volume of 50 mL. The two MFCs were connected in series, i.e. the effluent of the first reactor was the influent of the second reactor. MFC design and operating conditions are provided elsewhere (Coronado et al. 2013a).

Where S is the substrate (acetate) concentration consumed by the electricigenic bacteria Xe, capable of producing electricity by means of an intracellular mediator Mox, or by the methanogenic archaea Xm that produce methane. Sin is the input substrate concentration, 𝐷𝐷 = 𝐹𝐹𝐹𝐹𝐹𝐹 ⁄𝑉𝑉 is the dilution rate with the input flow rate Fin and the volume of the anodic compartment V. Kd is the microbial decay rate, Y is the yield of oxidized mediator, γ is the mediator molar mass, m is the number or electrons transferred, F is the Faraday constant and Icell is the current produced by the MFC. The corresponding microbial growth rates μ and substrate consumption rates q are defined using multiplicative Monod kinetics as follows:

𝑑𝑑𝑑𝑑

Throughout the tests, the two MFCs were operated using intermittent connection or pulse-width modulated connection of the external resistor (R-PWM mode). Each MFC was electrically independent. Such operation involved connecting the external resistor (Rext) to MFC terminals with a low resistance (<0.4 Ω) electronic switch (ADG801, Analog Devices Inc.). The switch was computer-controlled using a Labjack U3-LV data acquisition board (LabJack Corp., Lakewood, CO, USA). The data acquisition board was used to record MFC voltage at a maximum rate of 22,500 scans s-1. More details are provided in Coronado et al. (2013a).

= −𝑌𝑌𝑞𝑞𝑒𝑒 + 𝛾𝛾

𝐼𝐼𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐

(4)

𝑚𝑚𝑚𝑚𝑚𝑚𝑋𝑋𝑒𝑒

𝜇𝜇𝑒𝑒 = 𝜇𝜇𝑚𝑚𝑚𝑚𝑚𝑚,𝑒𝑒 (

𝑆𝑆

)(

𝑞𝑞𝑒𝑒 = 𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚,𝑒𝑒 (

𝑆𝑆

)(

𝐾𝐾𝑠𝑠,𝑒𝑒 +𝑆𝑆

𝐾𝐾𝑠𝑠,𝑒𝑒 +𝑆𝑆

2.2 Numerical Methods and Calculations

𝜇𝜇𝑚𝑚 = 𝜇𝜇𝑚𝑚𝑚𝑚𝑚𝑚,𝑚𝑚 (

Matlab R2014a (Mathworks, Natick, MA, USA) was used for all calculations. Parameter estimation was performed using the fmincon subroutine of the Matlab Optimization ToolboxTM and the model equations were solved using a variable order integration method for stiff differential equations (ode15s). Additional information can be found elsewhere (Recio-Garrido et al. 2016b, Pinto et al. 2010b). On-line estimations of the equivalent circuit model parameters were carried out using the algorithm described by Coronado et al. (2013b).

𝑞𝑞𝑚𝑚 = 𝑞𝑞𝑚𝑚𝑚𝑚𝑚𝑚,𝑚𝑚 (

,

(5)

𝑀𝑀𝑜𝑜𝑜𝑜

),

(6)

𝑀𝑀𝑜𝑜𝑜𝑜

),

(7)

𝐾𝐾𝑀𝑀 +𝑀𝑀𝑜𝑜𝑜𝑜

𝐾𝐾𝑀𝑀 +𝑀𝑀𝑜𝑜𝑜𝑜

𝑆𝑆

),

(8)

𝑆𝑆

),

(9)

𝐾𝐾𝑠𝑠,𝑚𝑚 +𝑆𝑆

𝐾𝐾𝑠𝑠,𝑚𝑚 +𝑆𝑆

with KS and KM the Monod half rates for the substrate and oxidized mediator terms, respectively.

3. RESULTS AND DISCUSSION 3.1 Model Formulation and Structure The CBE model structure (Fig. 1) was obtained by combining equations describing microbial, carbon source and electron balances of the bioelectrochemical model developed by Pinto et al. (2010b) with equations describing the equivalent electrical circuit (EEC) of a MFC presented by Coronado et al. (2013a). The EEC model only accounts for the internal capacitance and resistance of the anode thus lacking biomass and carbon source material balances. CBE model assumptions are inherited from Pinto et al (2010). Similar to the EEC model, internal resistance R1 represents the electrolyte ohmic resistance, while a resistor/capacitor circuit is included to describe the internal capacitance C and the activation losses R2. Accordingly, MFC internal resistance Rint is defined as 𝑅𝑅𝑖𝑖𝑖𝑖𝑖𝑖 = 𝑅𝑅1 + 𝑅𝑅2.

(1)

MFC mass balances are given by the following equations: 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑

= −𝑞𝑞𝑒𝑒 𝑋𝑋𝑒𝑒 − 𝑞𝑞𝑚𝑚 𝑋𝑋𝑚𝑚 + 𝐷𝐷(𝑆𝑆𝑖𝑖𝑖𝑖 − 𝑆𝑆),

𝑑𝑑𝑋𝑋𝑒𝑒 𝑑𝑑𝑑𝑑

= (𝜇𝜇𝑒𝑒 − 𝐾𝐾𝑑𝑑,𝑒𝑒 − 𝛼𝛼𝑒𝑒 𝐷𝐷)𝑋𝑋𝑒𝑒 ,

(2) (3)

Fig. 1. Schematic diagram of the CBE model for MFCs presented in Recio-Garrido et al. (2016b). 92

IFAC DYCOPS-CAB, 2016 June 6-8, 2016. NTNU, Trondheim, Norway Dídac Recio-Garrido et al. / IFAC-PapersOnLine 49-7 (2016) 091–096

The CBE model (1-21) describes fast and slow MFC dynamics in both MFCs. State variables, inputs and outputs of the model are summarized in Table 1. A more detailed description of the bioelectrochemical model can be found in Pinto et al. (2010b) and Recio-Garrido et al. (2016b).

The biomass retention parameter α used to represent the limiting effect of the biofilm in the microorganisms concentration is defined by the empirical expression 1

𝛼𝛼 = [1 + 𝑡𝑡𝑡𝑡𝑡𝑡ℎ[𝐾𝐾𝑥𝑥 (𝑋𝑋𝑒𝑒 + 𝑋𝑋𝑚𝑚 − 𝑋𝑋𝑚𝑚𝑚𝑚𝑚𝑚 )]],

(10)

2

93

where Kx is a steepness factor and Xmax is the maximum microbial concentration in the biofilm.

Table 1. State variables, inputs, outputs and estimated parameters for the CBE model.

The electrochemical balance is given by

Description State variables Substrate Exoelectricigenic Methanogenic Oxidized mediator Capacitor voltage Inputs Flow rate Input substrate External resistance Outputs Substrate Voltage Methane production Estimated parameters Yield in (5) Consumption rate Steepness in (15-18) Monod half rate (16-18)

𝐼𝐼𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =

𝐸𝐸𝑜𝑜𝑜𝑜 −𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 −𝑉𝑉𝑐𝑐 𝑅𝑅𝑒𝑒𝑒𝑒𝑒𝑒 +𝑅𝑅1

(

𝑀𝑀𝑟𝑟𝑟𝑟𝑟𝑟

𝜀𝜀+𝑀𝑀𝑟𝑟𝑟𝑟𝑟𝑟

),

(11)

Where Eoc is the open circuit voltage, Vc is the voltage at the capacitor, Rext is the external resistance applied to the MFC, Mred is the reduced oxidized mediator concentration and ε is the parameter for the Monod-like term which limits calculated MFC current at low values of Mred. The concentration losses ηconc are defined as 𝜂𝜂𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 =

𝑅𝑅𝑅𝑅

𝑙𝑙𝑙𝑙 (

𝑀𝑀𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

),

(12)

𝑀𝑀𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 = 𝑀𝑀𝑜𝑜𝑜𝑜 + 𝑀𝑀𝑟𝑟𝑟𝑟𝑟𝑟 .

(13)

𝑚𝑚𝑚𝑚

𝑀𝑀𝑟𝑟𝑟𝑟𝑟𝑟

with R the ideal gas constant, T the temperature of the MFC and Mtotal the total concentration of intracellular mediator. Also, the following dynamic equation is used to describe the voltage at the internal capacitor: 𝑑𝑑𝑉𝑉𝑐𝑐 𝑑𝑑𝑑𝑑

1

= (𝐼𝐼𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 − 𝐶𝐶

𝑉𝑉𝑉𝑉

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅,2

).

(14)

The following empirical expressions were derived based on previously obtained experimental results (Pinto et al. 2010, Grondin et al. 2012, Coronado et al. 2013a) and are used to describe the dependence of the internal resistances R1 and R2, the internal capacitance C, and the open circuit voltage Eoc on the anodic biofilm: 𝑅𝑅1 = 𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚1 + (𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚1 − 𝑅𝑅𝑚𝑚𝑎𝑎𝑎𝑎 )𝑒𝑒 −𝐾𝐾𝑟𝑟 𝑋𝑋𝑒𝑒 , 𝑅𝑅2 = 𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚2 + (𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚2 − 𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚 )𝑒𝑒

𝐸𝐸𝑜𝑜𝑜𝑜 = 𝐸𝐸𝑜𝑜𝑜𝑜,𝑚𝑚𝑚𝑚𝑚𝑚 + (𝐸𝐸𝑜𝑜𝑜𝑜,𝑚𝑚𝑚𝑚𝑚𝑚 − 𝐸𝐸𝑜𝑜𝑜𝑜,𝑚𝑚𝑚𝑚𝑚𝑚 )𝑒𝑒 𝐶𝐶 = 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 + (𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 − 𝐶𝐶𝑚𝑚𝑚𝑚𝑚𝑚 )𝑒𝑒

, 𝑆𝑆 ) 𝜉𝜉+𝑆𝑆

(16) ,

(17)

−1

𝐾𝐾𝑟𝑟 𝑋𝑋𝑒𝑒 (

𝑆𝑆 ) 𝜉𝜉+𝑆𝑆

,

Output electrical voltage and power are given by the following expressions: 𝑃𝑃𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑅𝑅𝑒𝑒𝑒𝑒𝑒𝑒 .

(19) (20)

Fin Sin Rext

L d-1 mg-S L-1 Ω

S Vcell Q

mg-S L-1 V mL d-1

Y qmax,e Kr ξ

mg-M mg-S-1 mg-S mg-X-1 d-1 L mg-X-1 mg-S L-1

Because of the limited number of measurable variables, the confidence intervals obtained from the Fisher information matrix were used to select parameters that can be estimated with an acceptable accuracy (Recio-Garrido et al. 2016b). The selected parameters for estimation were Y, qmax,e, Kr and ξ. It should be mentioned that no methane production was observed during the experiments due to the operational

Finally, the rate of methane production, Q, by methanogenic microorganisms is assumed to be proportional, with yield YCH4, to the substrate consumption rate by this trophic group 𝑄𝑄 = 𝑌𝑌𝐶𝐶𝐻𝐻4 𝑞𝑞𝑚𝑚 𝑋𝑋𝑚𝑚 𝑉𝑉.

mg-S L-1 mg-X L-1 mg-X L-1 mg-M L-1 V

Experimentally, the input flow rate was maintained so that the total hydraulic retention time (HRT) within the two staged MFCs was about 6 h and the input substrate concentration was subjected to step-wise changes (Fig. 2 A). Also, the external resistance was set to 5 Ω for the first MFC and 10 Ω for the second MFC and controlled using the intermittent model of operation (R-PWM) at 100 Hz of switching frequency and a 90 % connection time ratio. The connection time ratio (also called duty cycle) represents the ratio between the time when the circuit is connected with respect to the total cycle time.

(18)

where Kr is a steepness factor, min and max indicate the minimum and maximum values for the variables and ξ is the parameter for the Monod-like term which links the EEC electrical variables to the substrate concentration.

𝑉𝑉𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = 𝐼𝐼𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 𝑅𝑅𝑒𝑒𝑒𝑒𝑒𝑒 ,

S Xe Xm Mox Vc

To estimate model parameters, the difference between model simulations and the corresponding experimentally measured values was minimized. Thus, experimental values for the effluent concentration S and voltage produced Vcell were used for parameter estimation (Fig. 2). Additionally, on-line estimations using the EEC model (Coronado et al. 2013b) provided values for the open circuit voltage EOC and internal resistance R2 (data not shown) that were also used during the optimization problem. A set of experimental data was used for parameter estimation and another set for model validation.

−1

𝐾𝐾𝑟𝑟 𝑋𝑋𝑒𝑒 (

Units

3.2 Parameter Estimation

(15)

𝑆𝑆 −𝐾𝐾𝑟𝑟 𝑋𝑋𝑒𝑒 ( ) 𝜉𝜉+𝑆𝑆

Symbol

(21)

93

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conditions favoring growth of the electricigenic bacteria (Kaur et al. 2014). Accordingly, equation (4) was not considered for parameter estimation and all the parameters related to the methanogenic population were taken from previous experiments where methane production was measurable (Pinto et al. 2010b). Any other parameters remaining were not considered because either they presented negligible magnitude effects on the outputs or their values could be assumed (e.g. physical constants) or experimentally measured and did not need to be re-estimated. The estimated values of Y in mg-M mg-S-1, qmax,e in mg-S mg-X-1 d-1, Kr in L mg-X-1, and ξ in mg-S L-1 for the models representing the two staged MFCs are 24.7, 16.87, 0.0198, and 14.85, respectively for the first MFC and 73.8, 15.0, 0.027, and 1.9, respectively, for the second MFC (units are indicated in Table 1). To evaluate the estimation accuracy, the confidence intervals were calculated. Assuming a 95% confidence level, the intervals of confidence were 3.7 %, 3.8 %, 0.039 % and 6.8 % for Y, qmax,e, Kr, and ξ, respectively for the first MFC and 8.5 %, 0.4 %, 0.1 % and 3.7 %, respectively for the second MFC. Such values are acceptable considering the complex microbial dynamics and the relatively small number of estimated model parameters. On the other hand, parameters included in the empirical equations (15–18) were manually selected based on the results of the on-line estimation procedure (results not shown). Accordingly, parameters Rmax, Rmin1 and Rmin2 in (15) and (16) were set to 1,000 Ω, 0.97 Ω and 3.01 Ω for the first MFC and to 1,000 Ω, 2.27 Ω and 8.64 Ω for the second MFC, respectively. Also, parameters Emax and Emin in Eq. (17) were set to 0.26 V and 0.01 V for the first MFC and 0.35 V and 0.01 V for the second MFC, respectively. Finally, parameters Cmax and Cmin in Eq. (18) were set to 0.61 F and 0.01 F for the first MFC and 0.49 F and 0.01 F for the second MFC, respectively, based on the estimated capacitance values obtained during MFC startup and operation. Other parameters were taken from Pinto et al. (2010b).

Fig. 2. Comparison of effluent concentration (A) and MFC voltage (B) experimental values with the calculated profiles obtained using the CBE model (Recio-Garrido et al. 2016b). Fast-changing voltage profile is shown for day 13 in the validation data set (C). 3.3 Effect of Connection Time Ratio and Switching Frequency on MFC Performance A few recent publications show experimental results obtained from operating MFCs in an intermittent connection of the external resistance (Gardel et al. 2012, Grondin et al. 2012, Coronado et al. 2013a). Interestingly, in Gardel et al. (2012) microbial communities were found to be unaffected by such periodic operation in a broad range of switching frequencies. At the same time, MFC operation at different values of fixed external resistances was observed to result in different microbial populations (Lyon et al. 2010). However, the effect of the connection time ratio and switching frequency on the MFC performance still needs a deeper understanding. In this work, the CBE model is used to qualitatively study the effect of those two variables in the microbial distribution and substrate consumption as well as in the electrical performance of MFCs. All the parameter values are the same ones as used for the first MFC in section 3.2 and the minimum value of the applied external resistance is 5 Ω.

Figure 2 compares model simulations with the corresponding measurements. The first part of experimental results corresponding to days 0 to 9 of operation was used for parameter estimation and the remaining set of data for model validation. Effluent acetate concentrations were well described by the model at all influent concentrations (Fig. 2 A). MFC output voltage was observed to depend on the influent acetate concentration (organic load) with voltage drops during low load operation (days 7 to 10, Fig. 2B). Effluent concentrations and voltage trends were correctly described with MSE values of 0.59 and 48.1 for the first MFC and 3.1 and 10.6 for second MFC, respectively for the effluent concentration and the output voltage experimental profiles, considering the two data sets. Concerning the microbial population, the profile of the concentration for the electricigenic bacteria showed a population decrease during the low influent concentration while attaining a plateau during substrate-replete conditions. This effect was especially notable in the case of the second MFC. Additionally, the model provided an adequate description of the intermittent output voltage during pulse-width modulated connection of Rext. Fig. 2 C shows a zoom at the end of the 13th day.

Figure 3 shows the average steady-state values of the effluent, electricigenic and methanogenic concentrations as a function of the connection time ratio and for two different switching frequencies. Additionally, the upper x-axis represents the apparent external resistance seen by the MFC as if it were operated in a continuous mode. Exoelectricigenic bacteria demonstrate highest concentration at low values of the apparent external resistance (high connection time ratio) 94

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while methanogenic bacteria proliferate in the regions where the external resistance is at its highest value (low connection time ratio). It can be observed that the effluent substrate concentration presents a maximum (lowest substrate consumption by the microorganisms) at around 30% duty cycle, the coexistence region between the two microbial populations. This result was already shown for the continuous operation mode in Pinto et al. (2010a). The increase of the switching frequency shifts all the profiles toward the left (or always disconnected region), thus expanding the range favorable to the electricigenic bacteria.

95

ratio (close to always connected state) the average power output presents the maximum value while average voltage and current values remain similar to their values obtained in the fixed connection. Maximum power extends toward lower duty cycles (around 90%) when increasing the switching frequency. This result corroborates the positive effect of the intermittent operation of the external resistance on the electricity production even during mismatch with the internal resistance value, experimentally observed in previous works (Grondin et al. 2012, Coronado et al. 2013a). On the other hand, maximum voltage corresponding to the open circuit voltage can be observed at low duty cycles in the region where there still are electricigenic bacteria present in the microbial community. Once methanogenic microorganisms are the only ones populating the biofilm, voltage and current drop as observed near the 20 % connection time ratio. 3.4 Simulation Example: Effluent Quality Control for two Staged MFCs In parallel to investigating MFC staging, control strategies need to be developed in order for the process to counteract the unpredictable fluctuations in the environment that can directly affect its performance (Oh et al. 2010). Current control strategies only deal with the control of the electrical component in MFCs (Recio-Garrido et al. 2016a) while completely disregarding the treatment performance of MFCs. Their application to staged MFCs could result in failure of the process due to downstream MFC starvation. Control strategies dealing with the electrical and treatment performance of staged MFCs are expected to ensure a more stable operation.

Fig. 3. Effect of the connection time ratio and switching frequency on the effluent, electricigenic and methanogenic microbial concentrations.

This work presents a very simple control strategy (Fig. 5) to ensure the effluent quality control in two staged MFCs consisting on: (i) A PID controller that manipulates the treatment flow, and (ii) an ON/OFF controller that manipulates the connection time ratio in MFC 1 by switching from connected at a 90 % duty cycle to fully disconnected. Both controllers consider the error with respect to the desired effluent concentration.

Fig. 4. Effect of the connection time ratio and switching frequency on the electrical performance: average voltage, current and power produced by the MFC. Densities are expressed per volume of anodic compartment. The average steady-state values of the output voltage, current and power produced by the MFC under intermittent operation are shown in Figure 4. At high values of connection time

Fig. 5. Simple effluent quality control strategy for staged MFCs in wastewater treatment applications. Each MFC is represented using the CBE model. 95

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The operational conditions and the parameters presented in section 3.2 are used for the simulation. Under no other ground than to speed the simulation, a switching frequency of 0.1 Hz is used. The two controllers are discretized with sampling periods of 5 min for the ON/OFF controller and 10 min for the PID controller. The PID controller is used in discrete incremental form tuned at 2.5 mL d-1, 240 min and 0 min for Kc, τI and τD, respectively. The treatment flow presents lower and upper boundaries set at 0.1 L d-1 and 0.5 L d-1, respectively. Remark that the ON/OFF controller only acts when the error in the desired effluent is positive. Otherwise the effect of the ON/OFF controller would contribute to increase the error because an electrical disconnection of the first MFC results in a greater amount of substrate going into the second MFC.

REFERENCES Clauwaert, P., Aelterman, P., Pham, T., Schamphelaire, L., Carballa, M., Rabaey, K., Verstraete, W (2008). Minimizing losses in bioelectrochemical systems: the road to applications. Appl. Microbiol. Biotechnol., 79, 901-913. Coronado, J., Perrier, M., Tartakovsky, B. (2013a). Pulsewidth modulated external resistance increases the microbial fuel cell power output. Biores. Technol., 147, 65-70. Coronado, J., Perrier, M., Tartakovsky, B. (2013b). Online monitoring and parameter estimation of a microbial fuel cell operated with intermittent connection of the external resistor. 12th IFAC Symposium on Comput. Appl. in Biotechnol., 233-237. Du, Z., Li, H. and Gu, T. (2007). A state of the art review on microbial fuel cells: A promising technology for wastewater treatment and bioenergy. Biotechnol. Adv., 25, 464-482. Gardel, E.J., Nielsen, M.E., Grisdela, Jr.P.T., Girguis, P.R. (2012). Duty cycling influences current generation in multi-anode environmental microbial fuel cells. Environ Sci. Technol. 46, 5222-5229. Grondin, F., Perrier, M. and Tartakovsky, B. (2012). Microbial fuel cell operation with intermittent connection of the electrical load. J. Power Sources, 208, 18-23. Kaur, A., Boghani, H.C., Michie, I., Dinsdale, R.M., Guwy A.J., Premier, G.C. (2014). Inhibition of methane production in microbial fuel cells: Operating strategies which select electrogens over methanogens. Biores. Technol., 173, 75-81. Lyon, D.Y., Buret, F., Vogel, T.M., Monier, J.M. (2010). Is resistance futile? Changing external resistance does not improve microbial fuel cell performance. Bioelectrochem., 78, 2-7. Logan, B.E. (2008) Microbial fuel cells. John Wiley & Sons, Hoboken, New Jersey. Oh, S.T., Kim, J.R., Premier, G.C., Lee, T.H., Kim, C., Sloan, W.T. (2010). Sustainable wastewater treatment: how might microbial fuel cells contribute. Biotechnol. Adv., 28, 871-881. Pinto, R.P., Tartakovsky, B., Perrier, M., Srinivasan, B. (2010a). Optimizing treatment performance of microbial fuel cells by reactor staging. Ind. Eng. Chem. Res., 49, 9222-9229. Pinto, R.P., Srinivasan, B., Manuel, M.-F., Tartakovsky, B. (2010b). A two-population bioelectrochemical model of a microbial fuel cell. Biores. Technol. 101, 5256-5265. Recio-Garrido, D., Perrier, M., Tartakovsky, B. (2016a). Modeling, optimization and control of bioelectrochemical systems. Chem. Eng. J., 289, 180-190. Recio-Garrido, D., Perrier, M., Tartakovsky, B. (2016b). Combined bioelectrochemical–electrical model of a microbial fuel cell. Bioproc. Biosyst. Eng., 39(2), 267-276. Schrott, G.D., Bonanni, P.S., Robuschi, L., Esteve-Nuñez A., Busalmen, J.P. (2011). Electrochemical insight into the mechanism of electron transport in biofilms of Geobacter sulfurreducens. Electrochim. Acta, 56 (28) 10791-10795. Woodward, L., Perrier, M., Srinivasan, B., Pinto, R.P., Tartakovsky, B. (2010). Comparison of real-time methods for maximizing power output in microbial fuel cells. AIChE J., 56, (10) 2742-2750.

Figure 6 shows a simulation of the performance of such control strategy after a sudden decrease of 33% in the influent concentration followed by an increase of 100% of the effluent desired concentration (set-point). It can be observed that the effect of the ON/OFF controller introduces oscillations in the effluent concentration with respect to the set point (lower than a 5 % variation) but improves dramatically the disturbance rejection capability (5-25 h) and increases the response speed during regulation (at 30 h). Additionally, the treatment flow remains more stable around the initial value which can be desirable in wastewater treatment applications.

Fig. 6. Comparison of the effluent quality control performance on two staged MFCs using a PID to manipulate the treatment flow alone (blue) or with the help of an ON/OFF controller to manipulate the connection time in MFC 1 (red). 4. CONCLUSIONS The CBE model adequately describes MFC dynamics under periodic connection/disconnection of the external resistance and represents a useful tool for simulation of staged MFCs. Such an engineering tool can be used for the study of the effect of connection time and switching frequency on MFC performance. The apparent external resistance obtained by changing the time of connection and the switching frequency has been found to affect the distribution of the effluent and microbial populations as well as the electrical performance of MFCs. 96