Hydrogen Production Automatic Control in Continuous Microbial

Electrolytic Cells Reactors used in Wastewater Treatment V. Alcaraz-Gonzalez (1), G. Rodríguez-Valenzuela (1), G. Dotto(2), R.A. Flores-Estrella(3)

(1)(2) University of Guadalajara-CUCEI,. M. García Barragán 1451, 44430, Guadalajara, Mexico +(52) 33 1378 5900, victor.alcaraz@cucei.udg.mx

(2) Universidade Federal de Santa Maria, Av. Roraima, nº 1000, Santa Maria, RS, Brazil.(3) ITESO, Periférico Sur M. Gómez Morín 8585, 45604 Tlaquepaque, México.

1. Introduction –Nowadays, the current energy needs worldwide have been increasing with a velocity without precedents. It iswell known that demand for hydrocarbons; which are the mostly energy source used today, exceeds thereserves forecast for the next decades, as well as that those will not last long [1]. Furthermore, theenvironmental impact that their utilization has caused is responsible for Global Warming, destruction of theOzone Layer and disappearance of ecological systems as well as animal and plant species in what some callthe sixth massive extinction [2]. Thus, whole world is searching for alternative environmentally friendlyenergy sources able to satisfy the current energy demand, and, at the same time, to restrain the environmentaldeterioration or at least to slow it down. Solar energy, wind energy and combustible biogas obtained fromorganic waste and wastewater (e.g., methane by Anaerobic Digestion, bio-hydrogen by Dark Fermentation),to name just a few, are alternatives that have had a great trajectory of research and application since themiddle of the last century and which are certainly highly promising [3,4,5]. Certainly hydrogen, the mostlyabundant element in the universe is also one of them. Furthermore, as fuel, it has the greatest energy potentialin nature. It has been already applied with success in many fields, mainly through Fuel Cells Technology.However, his current industrial production still depends upon hydrocarbons by natural gas steam reforming[6]. Thus, in the last two decades, its production has been proposed by using microbial ways instead of thecurrent fossil fuels-based ones [5,7,8]. In particular, the Microbial Electrolytic Cells (MEC) is a verypromising new technology in which a small voltage (0.1 – 0.4 V) applied externally in a circuit allows itsproduction from agro-industrial wastewaters [9,12]. However, like other biological biogas productionmethods, MEC suffers from some drawbacks, mainly for control, and thus, efficiency purposes. The mainreasons for this are its highly nonlinear dynamic behavior and the presence of major disturbances that affectthis same behavior. The mathematical models that have tried to represent it are still in development andtherefore they are highly uncertain, which suggest the use of adaptive-robust type control approaches [10,11].In this work we present the automatic control of a continuous MEC reactor using the dilution rate as controlinput for regulating the production of Bio-hydrogen. Thus, this work presents the automatic control of acontinuous Microbial Electrolytic Cell for hydrogen production. Both. the dilution rate and the appliedpotential are used as a control input variable with the objective to regulate the production of Bio-hydrogen ina MEC system. The control law approaches are nonlinear adaptive-robust type and they were tested usingnumerical simulations. Results show the high efficiency of these control laws to regulate the production ofBioH2 at a desired optimum point.

2. Methodology2.1 Model2.1.1 Electrode reactions: The model presented in this work has been adapted from the proposed originally by[13], and after modified by [12] and [14].The resulting model represents a continuous system in which itpossible to use the dilution rate or the applied potential as input control variable. The mathematical modelrepresents the competition of three microorganism population in the MEC. The model considers thecompetition between anodophilic and methanogenic microorganisms for the carbon source. According with

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[7] the main substrate model carbon source has been considered as acetic acid Thus, the reactions in the anodeand cathode are described then as follows:Anode

𝐶!𝐻!𝑂! + 2𝐻!𝑂 + 4 𝑀!" ⟶ 4𝑀!"# + 2𝐶𝑂! (𝑎)

4𝑀!"# ⟶ 4 𝑀!" + 8𝑒! + 8𝐻! (𝑏)

𝐶𝑂! + 𝐻𝐶𝑂!! + 8𝑒! + 8𝐻! ⟶ 𝐶𝐻!𝐶𝑂𝑂! (𝑐)

Cathode 𝐶!𝐻!𝑂! ⟶ 4𝐶𝐻! + 𝐶𝑂! (𝑑)

𝐶𝑂! + 4𝐻! ⟶ 𝐶𝐻! + 2𝐻! (𝑒)

2𝐻!𝑂 + 2𝑒! ⟶ 2𝑂𝐻! + 𝐻! (𝑓)

The overall reaction of acetic acid at the anode and cathode is described as:

𝐶𝐻!𝐶𝑂𝑂! + 3𝐻!𝑂 ⟶ 𝐻𝐶𝑂!! + 4𝐻! (𝑔)

𝑀!" and 𝑀!"# are the reduced and oxidized forms of the intracellular mediator [12]. The mathematical model represents de competition for a substrate (acetic acid) of three microbial populations: anodophilic, methanogenic acetoclastic and methanogenic hydrogenotrophic. The nomenclature used in the equations (1) - (17) is known for people that work the area, and it can be found in the cited literature.

2.1.2 Mass balances for the MEC: From the mass balance in a continuous MEC reactor, the model may be represented by the following equations [12,13,15]:

𝑑𝑆𝑑𝑡

= 𝐷(𝑆! − 𝑆) − 𝑞!𝑋! − 𝑞!𝑋! (1) 𝑑𝑋!𝑑𝑡

= 𝜇!𝑋! − 𝐾!,!𝑋! − 𝛼!𝐷𝑋! (2) 𝑑𝑋!𝑑𝑡

= 𝜇!𝑋! − 𝐾!,!𝑋! − 𝛼!𝐷𝑋! (3) 𝑑𝑋!𝑑𝑡

= 𝜇!𝑋! − 𝐾!,!𝑋! − 𝛼!𝐷𝑋! (4)

where 𝑆, is the substrate concentration and 𝑋!, 𝑋! and 𝑋!, are the anodophilic, methanogenic acetoclastic and methanogenic hydrogenotrophic microbial population respectively. The rate of hydrogen production is described as follows:

𝑄!! = 𝑌!!𝐼!"#𝑚𝐹!

𝑅𝑇𝑃− 𝑌!𝜇!𝑋!𝑉! (5)

2.1.3 Intracellular mass balances: The following balanced equations may be written for each electrogenic microorganism [13]:

𝑀!"#$% = 𝑀!"# +𝑀!" (6)

𝑑𝑀!"

𝑑𝑡=

𝛾𝑉!𝑋!

𝐼!"#𝑚𝐹!

− 𝑌!𝑞! (7)

2.1.4 Kinect equations: The following expressions for the microbial growth are obtained by using multiplicative Monod kinetic as follows [13]:

𝜇! = 𝜇!á!,!𝑆

𝐾!,! + 𝑆𝑀!"

𝐾! +𝑀!"

(8)

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𝜇! = 𝜇!á!,!𝑆

𝐾!,! + 𝑆(9)

𝜇! = 𝜇!á!,!𝐻!

𝐾! + 𝐻!(10)

𝑞! = 𝑞!á!,!𝑆

𝐾!,! + 𝑆𝑀!"

𝐾! +𝑀!"

(11)

𝑞! = 𝑞!á!,!𝑆

𝐾!,! + 𝑆(12)

2.1.5 Electrochemical equations: The voltage in a MEC is calculated using theoretical values of electrode potential, Ohmic resistance, activation and concentration losses. Therefore, the electrochemical equilibrium is obtained as follows [13]:

𝐸!""#$%& = 𝐸!"# − 𝜂!!! − 𝜂!"#! − 𝜂!"# (13)

Losses in the anode are calculated by the Nerst equation [2]:

𝜂!"#!,! =𝑅!𝑇𝑚𝐹

𝑙𝑛𝑀!"#$%

𝑀!"# (14)

Cathodic activation losses are calculated by an approximation of the Butler-Volmer equation as [2]:

𝜂!"# =𝑅!𝑇𝛽𝑚𝐹

𝑠𝑖𝑛ℎ!!𝐼!"#

𝐴!"#,!𝑖! (15)

Therefore, the MEC current is calculated by combining equation 13-15 [2]:

𝐼!"# =𝐸!"# + 𝐸!""#$%& − 𝑅!𝑇 𝑙𝑛 𝑀!"#$%

𝑀!"#+ 1𝛽 𝑠𝑖𝑛ℎ

!! 𝐼!"#𝐴!"#,!𝑖!

𝑅!"# (16)

To improve the model accuracy, it is proposed that 𝑅!"# values be linked to the concentration of electrogenic microorganisms as follows:

𝑅!"# = 𝑅!"# + 𝑅!"# − 𝑅!"# 𝑒!!!!! (17)

It is important to notice that the oxidative mediator concentration Mox is a very important variable in this process, whose dynamical behavior with respect to time could be nevertheless neglected with respect to other state variables. For control purposes it has been already proposed in [11]. However, without loss of generality it is still preserved in this work.

2.2 Control Approaches Dilution rate: The proposed control law is adaptive linearizing type. From equation (2), it is desirable that the output 𝑋! → 𝑋!,! following the trajectory 𝑋! such that:

𝑑𝑋!𝑑𝑡

= 𝑘! 𝑦! − 𝑦 (18)

The main objective is that the concentration of 𝑋! take a reference value, because this state variable is strongly linked with the electrical current (Eq., 16), which at his time is related with the produced hydrogen (Eq 5). Higher is 𝑋! concentration; higher is as well the hydrogen production. From (2) and (18), and after some algebraic manipulations the following control law is obtained:

𝐷 =𝜇!𝑋! − 𝐾!,!𝑋! − 𝑘!𝑒

𝛼!𝑋! (19)

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Applied potential: From equation (7), it is desirable that the output 𝑀!" → 𝑀!",! follows the trajectory 𝑀!",! such that:

𝑑𝑀!",! 𝑑𝑡

= 𝑘! 𝑦! − 𝑦 (20) The main objective is that the concentration of 𝑀!" take a reference value because this state variable is linked with the electrical current (16), which at his time is related with the produced hydrogen (5). Thus, the applied potential may be used as manipulable variable (i.e., control input). Then from (7) and (20), and after some algebraic manipulations the following control law is obtained:

𝐸!"" = 𝑅!"#𝜁 𝑘!𝑒 + 𝑌!𝑞! +𝑅!𝑇𝑚𝐹

𝑙𝑛𝑀!"#$%

𝑀!"! +

1𝛽𝑠𝑖𝑛ℎ!! 𝜁∗ 𝑘!𝑒 + 𝑌!𝑞! (21)

The control laws (19, 21) were simulated in MATLAB-SIMULINK® for evaluating the capability that this law for controlling the system. The results of the control laws are shown and discussed in the following section.

3. Results and Discussion

Numerical simulations in closed loop were developed for the control variable 𝐷. Two set-point changes were introduced as 𝑋!= [450, 600] (𝑚𝑔 𝑋 ∙ 𝐿!!) at days 0 and 25 respectively In addition, input disturbances introduced as 𝑆!" = [2000, 3000] ( 𝑚𝑔 𝑆 ∙ 𝐿!!) at days 0 and 50 respectively. Figure 1 illustrates the dynamic behavior of the output variable 𝑋! . It can be seen that the control law is able to achieve the anodophilic microorganism concentration reference 𝑦! = 450 (𝑚𝑔 𝑋 ∙ 𝐿!!) and then 600. Moreover, this is law is able to reject the referred disturbances as well. Figure 2 shows the hydrogen produced and the current generated by the MEC system. Notice that, as expected by of the model, there is dependence between the hydrogen produced and the current generated. These results are consistent with those reported by [12] this figure also show that a bio-hydrogen flow is produced.

Figure 1. Behavior of anodophilic microorganisms Xa

Numerical simulations in closed loop were also developed for the control variable 𝐸!"" , a reference change was introduced as 𝑀!" = [800, 950] (𝑚𝑔 𝑋 ∙ 𝐿!!) at days 0 and 30 and also a input disturbances introduced as 𝑆!" = [2000, 3500] (𝑚𝑔 𝑋 ∙ 𝐿!!) at days 0 and 25. Figure 3 illustrates the dynamic behavior of the output variable 𝑀!" . It can be seen that this control law is able to achieve the mediator concentration reference 𝑦! = 800 (𝑚𝑔 𝑋 ∙ 𝐿!!) and then 950, and this is law is able to reject the disturbances as the numerical simulations shown. The Figure 4 shows the hydrogen produced and the current generated by the MEC system. Notice that

Time [d]0 50 100 150

Xa

[mg=L

]

0

100

200

300

400

500

600Xa

First Reference

Second Reference

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in this case if we compared both control laws the current generated when we used 𝐸!"" as a control variable is higher and therefore a great flow hydrogen is awaited as the figure 4 shows.

Figure 2. Produced hydrogen an electrical current.

Figure 3. Mediator behavior Mox.

Figure 4. Produced hydrogen an electrical current.

Time [d]0 50 100 150

QH

2[L

=d]

0

0.2

0.4

0.6

0.8

1

I ME

C[A

]

0

0.02

0.04

0.06

0.08

0.1QH2

IMEC

Time [d]0 10 20 30 40 50 60 70 80 90 100

Mox

[mgM

=mgX

]

0

100

200

300

400

500

600

700

800

900

1000Mox

First Reference

Second Reference

Time [d]0 10 20 30 40 50 60 70 80 90 100

QH

2[L

=d]

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QH2

IMEC

I ME

C[A

]

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0.2

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4. ConclusionsThe field of study of MEC systems is undoubtedly still at an early stage, especially with respective modelsreported in the literature. Although the interest of the scientific community has increased in the last twodecades, it is necessary to emphasize that there is still a lot of work to be done in this research area in order tofully exploit this technology.This work has proposed and simulated two simple control laws for a MEC type system using the dilution rate𝐷 as well as applied potential as control variable. Simulations show that it is possible to control this systemunder simple by useful linearizing adaptive-robust control schemes. For this work step changes wereintroduced into the substrate fed to the reactor as well as reference changes, the simulations show that it ispossible to control the system and bring the concentration of anodophilic microorganisms 𝑋! to the desiredreference value in order to regulate at his time the MEC Bio-hydrogen production.

Acknowledgements. Authors acknowledge to CONACYT for the scholarship granted to G.R.V., during his Postgraduate studies, for the support provided to R.A.F.E. during his Postdoctoral project SENER-CONACYT Energy Sustainability and for the support provided to V.A.G., during his sabbatical stay in 2018. R.A.F.E. also wants to thank the ITESO Fund for Research Support 2018.

5. References[1] R. Schaeffer, A. Salem, A. Frossard, P. D. Lucena, B. Soares, M. Cesar, L. Pinheiro, P. Nogueira, F.Pereira, A. Troccoli, M. Harrison, M. Sadeck. A review. Energy, 38(1), (2012), p. 1-12.[2] M. J. Ring, D. Lindner, E. F. Cross, M. E. Schlesinger. Scientific Research, 2(4), (2012), p. 401-415.[3] R. Salazar Peña, V. Alcaraz González, V. González Álvarez, R. Snell Castro, H. O. Méndez Acosta.Bioprocess Biosyst Eng. 37(6), (2014), p. 1031-1042.[4] J. Jimenez, E. Latrille, F. Daniel, G. Christian, W. Francis, O. Bernard, O. Hugo, A. G. Victor, D.Zitomer, D. Totzke, H. Spanjers, F. Jacobi, A. Guwy, R. Dinsdale, G. Premier, S. Mazhegrane. Environ SciBiotechnol, 14(4), (2016), p. 615-648[5] J.P. Steyer, X. M. Guo, E. Trably, E. Latrille. International Journal of Hydrogen Energy, 35(19), (2010)p. 10673-10673.[6] A. F. Felix, M. G. Simoes, (2006), Integration of Alternative Sources of Energy, Canada, Jhon Wiley andSons. Inc.[7] A. Marone, O. R. Ayala-Campos, E. Trably, A. A. Carmona-Martinez, R. Moscoviz, E. Latrille, et al.International Journal of Hydrogen Energy, 42(3), (2017), p. 1609-1621.[8] G. S. Rodolfo, R. I. Roberto, G. M. Guadalupe, A. G. Enrique, et. al. International Journal of HydrogenEnergy, 43(33), (2018), p. 15857-15869.[9] H. Wang, Z. J. Ren, Biotechnology Advances, 31(8), (2013), p. 1796-1807.[10] F. E. René Alejandro, G. R. Uriel de Jesús, H, Andreas, A. G. Victor, Processes, 7(4), (2019), p. 183.[11] F. E. René Alejandro, R. V. Guillermo, R. L. Jonathan Rafael, A. G. Victor, G. A. Victor. ChemicalEngineering Comunications. (2019), p. 1563-5201.[12] A.M. Yahya, M.A. Hussain, A.K. Abdul Wahab. Int. J. Energ. Res., 39(4), (2015), p. 557-572.[13] R.P. Pinto, B. Srinivasan, A. Escapa, B. Tartakovsky. Int. Environ. J. Sci. Tech., 45(11), (2011) p. 5039-5046.[14] R. P. Pinto, B. Srinivasan, M. F. Manuel, B. Tartakovsky. Bioresource Technology, 101(14), (2010), p.5256-5265.[15] R.P. Pinto, B. Srinivasan, A. Escapa, B. Tartakovsky. IFAC World Congress (2011) p. 5046-5051.

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