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A Bacteriostatic Control Approach for Mixotrophic Cultures of Microalgae
11th IFAC Symposium on Dynamics and Control of Process including Biosystems 11th IFACSystems, Symposium on Dynamics and Control of Process Systems, including Biosystems June 6-8, 2016. NTNU, Trondheim, Norway 11th IFAC Symposium on Dynamics and Controlonline of Available at www.sciencedirect.com Process including Biosystems June 6-8,Systems, 2016. NTNU, Trondheim, Norway Process including Biosystems June 6-8,Systems, 2016. NTNU, Trondheim, Norway June 6-8, 2016. NTNU, Trondheim, Norway
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IFAC-PapersOnLine 49-7 (2016) 1074–1078 A A Bacteriostatic Bacteriostatic Control Control Approach Approach for for Mixotrophic Mixotrophic Cultures Cultures of of Microalgae Microalgae A Bacteriostatic Control Approach for Mixotrophic Cultures of A Bacteriostatic Control Approach for Mixotrophic Cultures of Microalgae Microalgae Jean-Sébastien Deschênes*
Jean-Sébastien Deschênes* Jean-Sébastien Deschênes* Jean-Sébastien Deschênes* génie, Université du Québec à Rimouski, QC, G5L 3A1 *Département de mathématiques, informatique et *Département de mathématiques, informatique et génie, Université du Québec à Rimouski, QC, G5L 3A1 Canada +1-418-723-1986 Ext. e-mail: [email protected]). *Département de(Tel: mathématiques, informatique et génie, Université du Québec à Rimouski, QC, G5L 3A1 Canada +1-418-723-1986 Ext. 1997; 1997; e-mail: [email protected]). *Département de(Tel: mathématiques, informatique et génie, Université du Québec à Rimouski, QC, G5L 3A1 Canada (Tel: +1-418-723-1986 Ext. 1997; e-mail: [email protected]). Canada (Tel: +1-418-723-1986 Ext. 1997; e-mail: [email protected]). Abstract: Abstract: Mixotrophic Mixotrophic mode mode of of cultivation cultivation is is an an effective effective means means of of producing producing algal algal biomass. biomass. However, However, as it involves growth on an organic carbon source, the risks of bacterial contamination (and takeover) takeover) are Abstract: Mixotrophic mode of cultivation is an effective means of producing algal biomass. However, as it involves growth on an organic carbon source, the risks of bacterial contamination (and are Abstract: Mixotrophic mode of cultivation is industrial an effective means of producing algal biomass. However, higher at large production scales (e.g. pilot or scale) where adequate sterilization is difficult to as it involves growth on an organic carbon source, the risks of bacterial contamination (and takeover) are higher at largegrowth production scales (e.g. pilot source, or industrial scale) where adequate sterilization is difficultare to as it involves on an organic carbon the risks ofasbacterial contamination (andstudy takeover) ensure. This observation also holds for closed systems such photobioreactors. A recent showed higher at large production scales (e.g. pilot or industrial scale) where adequate sterilization is difficult to ensure.atThis observation also holds forpilot closed systems such as where photobioreactors. A recent study showed higher large production scales (e.g. orunder industrial scale) adequate is difficult to that the the This bacterial population can be contained particular constraints on the thesterilization available nutrients in the the ensure. observation alsocan holds for closedunder systems such asconstraints photobioreactors. A recentnutrients study showed that bacterial population be contained particular on available in ensure. This observation alsosimple holds models for closed systems such behavior as photobioreactors. Anutrient recent study showed culture medium. Using very for the dynamic (growth and consumption) that the medium. bacterial Using population be contained particularbehavior constraints on theand available in the culture very can simple models forunder the dynamic (growth nutrientnutrients consumption) that the species bacterialinvolved population can be contained under particular constraints on the available nutrients in the of both both (algae and bacteria), this paper investigates biomass productivity aspects under under culture medium. Using very simple models forthis the paper dynamic behavior biomass (growth productivity and nutrient consumption) of species involved (algae and bacteria), investigates aspects culture medium. Using very simple models for the dynamic behavior (growth and nutrient consumption) such operational constraints as well well as possiblethis approaches for conducting conducting the system. system. of both species involved (algae and as bacteria), paper investigates biomass productivity aspects under such operational constraints as possible approaches for the of both species involved (algae and bacteria), this paper investigates biomass productivity aspects under such operational constraints Federation as well as possible approaches for conducting the system. © 2016, IFAC (International of Automatic Control) Hosting by Elsevier Ltd. limitation. All rights reserved. Keywords: Microalgae, mixotrophy, bacterial contamination, batch control,the nutrient such operational constraints as well as possible approaches for conducting system. Keywords: Microalgae, mixotrophy, bacterial contamination, batch control, nutrient limitation. Keywords: Microalgae, mixotrophy, bacterial contamination, batch control, nutrient limitation. Keywords: Microalgae, mixotrophy, bacterial contamination, batch control, nutrient limitation. model model (Monod, (Monod, 1942) 1942) is is the the accumulation accumulation of of an an intracellular intracellular 1. 1. INTRODUCTION INTRODUCTION quota which governs growth rather than the readily available model (Monod, 1942)growth is the accumulation an intracellular quota which governs rather than theof readily available 1. INTRODUCTION model (Monod, 1942) is the accumulation of an intracellular nutrients from the culture media. Droop kinetics thus allows quota which governs growth ratherDroop than the readily available Mixotrophic for INTRODUCTION from the culture media. kinetics thus allows Mixotrophic mode mode of of1.production production for algal algal biomass biomass has has gained gained nutrients quota which governs growth rather than the readily available to explain a maintained cell growth well after the nutrient has nutrients from the culture media. Droop kinetics thus allows significant attention recently (Wang et al., 2014; Chandra et Mixotrophic mode of production for algal biomass has gained to explain a maintained cell growth well after the nutrient has significant attention recently (Wang et al.,biomass 2014; Chandra et nutrients fromfrom the culture media. Droop kinetics thus allows Mixotrophic mode of production for algal has gained been depleted the media. to explain a maintained cell growth well after the nutrient has al., 2014; Pagnanelli et al., 2014; Wang et al., 2013). In this been depleted from the media. significant attention recently (Wang et al., 2014; Chandra et al., 2014; Pagnanelli et al., 2014; Wang et al., 2013). In this to explain a maintained cell growth well after the nutrient has significant attentionCO recently (Wang et al., 2014; Chandra et been depleted from the media. capture is combined with growth on a mode, autotrophic 2 al., 2014; Wang et al., 2013). In this al., 2014; Pagnanelli is combined with2013). growth mode, autotrophic COet For simplicity, we the depleted from the media. al., 2014; Pagnanelli et2 capture al.,(DOC) 2014; Wang etoften al., Inon thisaa been simplicity, we consider consider the nitrogen nitrogen source source to to be be the the main main dissolved organic carbon source, in is combined withresulting growth on mode, autotrophic CO aa For 2 2 capture dissolved organic carbon (DOC) source, often resulting in limiting nutrient (all other nutrients in excess). A continuous For simplicity, we consider the nitrogen source to be the main capture is combined with growth on mode, autotrophic CO 2 biomass productivity. Another benefit limiting nutrient (all other nutrients in excess). A continuous significant increase of dissolved organic (DOC)productivity. source, often resulting in a supply For simplicity, weprovided considertothethenitrogen source to bethe the main significant increasecarbon of biomass Another benefit is to CO other to nutrients in excess). A continuous dissolved organic carbon (DOC) source, often resulting in a limitingof provided the reactor reactor to regulate regulate the pH pH at at ofnutrient CO22 is (all of this mode is aa reduced dependency on lighting conditions significant increase of biomass productivity. Another benefit supply limiting nutrient (all other nutrients in excess). A continuous of this mode is reduced dependency on lighting conditions a constant value, so carbon is never limiting and the influence is provided to the reactor to regulate the pH at significant increase of biomass productivity. Another benefit supply of CO 2 2 asupply constant value, so carbon is never limiting and the influence (Wang et al., 2014; Chandra et al., 2014; Brennan and of this mode is a reduced dependency on lighting conditions is provided toneglected the reactorintotheregulate the pH at of CO2growth (Wang et al.,is 2014; Chandra et al.,on2014; Brennan and aofconstant pH can model. Lighting value, so carbon never limiting the influence of this mode awhich reduced dependency lighting conditions pH on on cell cell growth can be beis neglected in theand model. Lighting Owende, can be an factor supporting (Wang et2010), al., 2014; Chandra etimportant al., 2014; Brennan and aof constant value, so carbon is never limiting and the influence Owende, 2010), which can be an important factor supporting conditions (available to the cells) are considered constant and of pH on cell growth to can becells) neglected in the model. Lighting (Wang et al., 2014; Chandra et al.,As 2014; Brennanofand conditions (available are considered constant and the scale-up of the production the presence the Owende, 2010), which can be systems. an important factor supporting of pH on cell growth canthe be neglected infurther the model. Lighting the scale-up of the production systems. As the presence of the non-limiting throughout the culture for simplicity. In conditions (available to the cells) are considered constant and Owende, 2010), which can be an important factor supporting non-limiting throughout the culture for further simplicity. In DOC source may to favor bacteria over algae, recent the scale-up of thetend production systems. As thethe presence of the mixotrophic conditions (available to the cells) are considered constant and DOC source may tend to favor bacteria over the algae, recent conditions, the algal growth rate is considered to non-limiting throughout the culture for further simplicity. In the scale-up of the production systems. Asthat theitpresence of the mixotrophic conditions, the algal growth rate is considered to results (Deschênes et al., 2015) showed is possible to DOC source may tend to favor bacteria over the algae, recent non-limiting throughout the culture for further simplicity. In results (Deschênes et al., 2015) showed that it is possible to (on CO ) and the be the sum of the autotrophic growth rate mixotrophic conditions, the algal growth rate is considered to A 2 DOC source may tendpopulation to favor bacteria over the algae, recent be the sum of the autotrophic growth rate A (on CO2) and the contain the bacterial under operational constraints mixotrophic conditions, the algal growth rate isorganic considered to results (Deschênes al., 2015) showed that it is possible to contain the bacterialet population under operational constraints (on the available carbon heterotrophic growth rate (on CO ) and the be the sum of the autotrophic growth rate results (Deschênes et al., 2015) showed that it is possible to H A 2 A 2 carbon imposed on the available nutrients from the culture medium, the available organic heterotrophic growth rate H (on (on CO ) and the be the sum of the autotrophic growth rate contain the bacterial population under operational constraints A 2 imposed on the available nutrients from the culture medium, source), both are subject to kinetics as contain the bacterial population under operational constraints heterotrophic available organic carbon rate HH (on and thus favor in this source), while whilegrowth both processes processes are the subject to Droop Droop kinetics as imposed on the available nutrients growth from the medium, heterotrophic (on the available organic carbon growth rate HCarbon and thus actively actively favor microalgae microalgae in culture this manner. manner. in (Adesanya et al., 2014). proportion in the biomass imposed on the available nutrients growth from the culture medium, source), while both processes are subject to Droop kinetics as in (Adesanya et al., 2014). Carbon proportion in the biomass and thus actively favor microalgae growth in this manner. source), while bothisprocesses areconstant subjectfor to Droop kinetics as (% of dry weight) considered simplicity. This paper further investigates the cell culture behavior under and thus actively favor microalgae growth in this manner. in (Adesanya et al., 2014). Carbon proportion in the biomass of dry weight) is 2014). considered constant for simplicity. This paper further investigates the cell culture behavior under (% et al., Carbon proportion in the biomass in (Adesanya such nutrient limitation constraints using simple simulation This paper further investigates the cell culture behavior under (% of dry weight) is considered constant for simplicity. such nutrient limitation constraints using simple simulation Bacterial biomass composition is considered constant (% of dry weight) is considered constant for simplicity. This paper further investigates the cell culture behavior under models to the challenges difficulties that biomass composition is considered constant (50% (50% C C such nutrient limitation using simple simulation models to show show the main main constraints challenges and and difficulties that arise arise Bacterial and 14% N w/w), from E. coli data (Fagerbakke et al., 1996), such nutrient limitation constraints using simple simulation Bacterial biomass composition is considered constant (50% C in such situations and to begin to define the control problem. and 14% N w/w), from E. coli data (Fagerbakke et al., 1996), models to show the main challenges and difficulties that arise Bacterial biomass composition is considered constant (50%the C in such to situations to begin to define the control that problem. with its growth governed by Monod-type kinetics on both models show theand main challenges andthe difficulties arise and 14% N w/w), from E. coli data (Fagerbakke et al., 1996), The paper is organized as follows: first, model used in the kineticseton both the with its growth governed by Monod-type in such situations and to begin to define the control problem. and 14% N w/w), from E. coli data (Fagerbakke al., 1996), The paper is organized as follows: first, the model used in the nitrogen and the organic carbon sources (Lee et al., 1984). in such situations and to along begin with to define the control The problem. its growth by Monod-type kinetics both the simulations presented its algal nitrogen and thegoverned organic carbon sources (Lee et al.,on 1984). The paper isis organized follows: the model used the with with its growth governed by Monod-type kinetics on both the simulations presentedas withfirst, its parameters. parameters. Thein The paper isisorganized asalong follows: first, the model used inalgal the nitrogen and the organic carbon sources (Lee et al., 1984). growth behavior (alone) is then investigated under different simulations is presented along with its parameters. The algal nitrogen and the organic carbon sources (Lee et al., 1984). growth behavior (alone) is then investigated under different simulations is presented along with its parameters. The algal 2.2 Microalgal growth model feeding approaches, and productivities are growth (alone) is then investigated different 2.2 Microalgal growth model feeding behavior approaches, and biomass biomass productivitiesunder are evaluated. evaluated. growth behavior (alone) is then investigated under different The presence of bacteria is then added to the simulations for feeding approaches, and biomass productivities are evaluated. Microalgal growth model The presence of bacteria is then added to the simulations for aa 2.2 feeding approaches, and biomass productivities are evaluated. 2.2 Microalgal growth model3 better comparison with the practical case. Finally, a very first Microalgal xx (gC/m The presence of bacteria is then added to the simulations for a better comparison with the practical case. Finally, a veryfor firsta Microalgal biomass biomass (gC/m33)) growth growth depends depends on on aa nitrogen nitrogen 3 The presence of bacteria is then added to the simulations 3) growth control problem formulation is proposed for this application. (gN/m is stored in the form of internal source s 3) which better comparison with the practical case. Finally, a very first N depends on an a nitrogen Microalgal biomass x (gC/m 3 control problem formulation is proposed for this application. (gN/m ) which is stored in the form of an internal source s N better comparison with the practical case. Finally, a very first Microalgal ) growth depends on a nitrogen biomass x (gC/m 3 3before quota q (gN/gC) it is effectively used for growth. The control problem formulation is proposed for this application. (gN/m ) which is stored in the form of an internal source s N 3before it is effectively used for growth. N quota q (gN/gC) The control problem formulation is proposed for this application. (gN/mrate ) which is stored in the of form of the an nutrient internal source sNuptake 2. MODELS FOR ALGAL AND BACTERIAL GROWTH (s , q) is a function both nutrient quota q (gN/gC) before it is effectively used for growth. The N 2. MODELS FOR ALGAL AND BACTERIAL GROWTH (s , q) is a function of both the nutrient nutrient uptake rate N quota q (gN/gC) before it is(Michaelis-Menten effectively used fortype growth. The availability in the medium relation) 2. MODELS FOR ALGAL AND BACTERIAL GROWTH (s , q) is a function of both the nutrient nutrient uptake rate N availability in the medium (Michaelis-Menten type relation) N 2. MODELS FOR ALGAL AND BACTERIAL GROWTH (s , q) is a function of both the nutrient nutrient uptake rate N and the of internal quota its availability thethe medium relation) 2.1 and the state statein the internal(Michaelis-Menten quota relative relative to to type its maximum maximum availability in of theal., medium (Michaelis-Menten type relation) 2.1 Generalities Generalities and and hypotheses hypotheses for for the the models models level (Bernard et 2011): and the state of the internal quota relative to its maximum levelthe (Bernard et al., 2.1 Generalities and hypotheses for the models and state of the 2011): internal quota relative to its maximum 2.1 Generalities and hypotheses for the models level (Bernard et al., 2011): The sN The basis basis for for the the model model of of algae algae growth growth is is the the Droop Droop kinetics kinetics level (Bernard et al., 2011): 1 q (1) sN q ss NN ,, qq max (Droop, 1968), which is now widely accepted to describe the (1) The basis1968), for thewhich modelis of algae growth is the Droop kinetics 1 (Droop, now widely accepted to describe the q max K Ns s q N The basis for the model of algae growth is the Droop kinetics N sN max 1 q q dynamic behavior of algae on different nutrients, particularly (1) s K s NN , q max (Droop, 1968), which is now widely accepted to describe the N N N max dynamic behavior of algae on different nutrients, particularly (1) s N , q max (Droop, 1968), which is now widely acceptedwith to describe the s NN 1 q max max K N nitrogen sources. Its fundamental distinction the Monod N max dynamic behavior of algae on different nutrients, particularly K s q nitrogen sources. Its fundamental distinction with the Monod N N max dynamic behavior of algae on different nutrients, particularly nitrogen sources. Its fundamental distinction with the Monod nitrogen sources. Its fundamental distinction with the Monod
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The autotrophic growth rate is described by the Droop model form (Droop, 1968): q min q
A q A max 1
(2) The heterotrophic growth rate is described by the following interaction between Monod kinetics (influence of the organic carbon source) and Droop kinetics for possible occurrence of nitrogen limitation (Adesanya et al., 2014; De la Hoz Siegler et al., 2011):
for this model is summarized in Table 1. Parameter values for the microalgae (specie Scenedesmus obliquus) were obtained either experimentally (Deschênes and Vande Wouwer, 2016) for the autotrophic part of the model, or from the literature for the mixotrophic part. In Girard et al. (2014), shake-flask experiments (using the same strain of Scenedesmus obliquus) showed that the maximum mixotrophic growth rate (posed as the sum of µAmax and µHmax here) was about four (4) times the maximum autotrophic growth rate µAmax. The half-saturation constant KC was obtained by taking the average value from the results of Adesanya et al. (2014) and Yoo et al. (2014).
q (3) 1 min K C sC q In these expressions, KN and KC are half-saturation constants, qmin is the minimum nitrogen quota (below which no growth is possible), max is the maximum nitrogen uptake rate, µAmax and µHmax are the maximum autotrophic and heterotrophic growth rates respectively, and sC is the organic carbon source concentration. In the absence of bacteria, mass balances in the chemostat lead to the following equations set:
H s C , q H max
sC
x x D x q q s N x D s Nin s N s C
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Table 1. Main model parameters Symbol
0.95 h-1 (22.8 d-1)
Symbol KN KC KNB KCB k1 k1B k2B
Value (units) 0.02 gNm-3 4 gGlcm-3 4 gNm-3 4 gGlcm-3 2.5 gGlcgC-1 0.14 gNg-1 1.25 gGlcg-1
(4)
3. BATCH GROWTH AND NUTRIENT BALANCE
Where = A + H is the overall growth rate of the algae, sNin and sCin are the concentrations of nitrogen and organic carbon in the (sterilized) inlet flow and D is the dilution rate. 2.3 Bacterial growth model Bacteria grow heterotrophically on the organic carbon source and the available nitrogen from the culture medium. The following interactive form is used (Lee et al., 1984):
µBmax
max
k 1 H x D s Cin s C
sN (5) K s K s C NB N CB Where µBmax is the maximum (bacterial) growth rate, and KCB and KNB are saturation constants. Values for these parameters are taken from available literature data for Escherichia coli growth on glucose and ammonium ion (Lee et al., 1984).
B s C , s N B max
µAmax µHmax qmax qmin
Value (units) 1.4 gNgC-1d-1 1.5 d-1 4.5 d-1 0.2 gNgC-1 0.02 gNgC-1
sC
To develop a better understanding of the culture behavior, it is natural to first investigate the batch response under varying sets of initial conditions. This section aims to illustrate some of the issues associated with nutrient balance in mixotrophic cultures of microalgae (in particular here, the C:N ratio). A comparison between the autotrophic and mixotrophic growth curves is seen in Fig. 1, with an initial nitrogen concentration (in the medium) of 41 ppm (182 ppm NO3-), as suggested in modified Bold’s basal medium (BBM) formulation for green algae (Stein, 1973). The glucose supply for the mixotrophic culture is 6 gL-1, a moderate concentration compared to other values found in the literature (16.6 gL-1 in Wang et al., 2013; 10 gL-1 in Wang et al., 2014 and up to 30 gL-1 in HerediaArroyo et al., 2010).
2.4 Combined model The combined model for the algae and bacteria consortium in the photobioreactor is thus: x x D x q q x B B x B D x B s N s C
D s Nin s N
D s Cin s C
(6)
x k k x
1B
1
H
B xB k 2B B x B
Here, xB is the bacterial biomass concentration (g/m3) and k1B and k2B are proportionality constants tied to its nitrogen and carbon elementary contents. The complete list of parameters
Fig. 1. Autotrophic and mixotrophic growth curves in batch mode.
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Results show that in both cases (autotrophic and mixotrophic modes), the algae quickly internalize all the nitrogen from the medium, grow until the minimum quota is reached (q = qmin), and reach the same biomass concentration at steady-state. In the mixotrophic culture, this concentration is reached in only one day, versus four for the autotrophic culture. Also, glucose is not fully utilized in this mixotrophic culture: although our model may predict the allowable range of C:N ratios in the biomass (between 5 and 50 as q reaches its boundaries qmax or qmin), the initial conditions in the reactor (2400 gCm-3 in the glucose, q(0) = 0.1 gNgC-1, x(0) = 200 gCm-3 and n(0) = 41 gNm-3) are such that the overall C:N ratio is 42.6. Since part of the carbon intake is related to CO2 in mixotrophic mode, it is difficult to predict (and accordingly adjust) the right C:N balance in the culture medium. A similar result (not shown) is obtained with an initial overall C:N ratio of 39 in the reactor. Using significantly higher initial nitrogen concentrations (e.g. 200 ppm in this case) would lead to an otherwise imbalanced operation: mixotrophic growth would take part for only about the first day, then the algae would grow in autotrophic mode over the rest of the process duration (losing the advantage of the mixotrophic growth approach). Overall, setting the right nutrient balance can be a challenge in mixotrophic cultures.
fed system, additions of nitrate (100 ppm N) and glucose (2 g L-1) were made every two days for the same average. Results show that overall, the two growth curves are similar, and thus there is no necessary loss of productivity due to this mode of nutrition.
Fig. 2. Autotrophic growth followed by different nutrient additions.
4. ALTERNATE FEED OPERATION This section evaluates manners in which an alternate feeding strategy could be implemented and their impacts on biomass productivity. The Droop model predicts that cell growth will cease as their internal (nitrogen) reserves reach a minimum: a successful start-up procedure (for the photobioreactor) should thus provide sufficient amounts of this nutrient before adding glucose. This reasoning is also in accordance with the idea of starting the culture in autotrophic mode until a “minimal” cell concentration (of algae) is obtained to ensure competitiveness over (potentially present) bacteria (Deschênes et al., 2015). The following course of action would thus be to add glucose to the culture and boost the production of algal biomass from this point. However, as shown in Fig. 2, both the timing and magnitude of this glucose addition may need careful planning for good results to be obtained: after an initial (autotrophic) growth phase in normal BBM medium, additions of glucose (4 g L-1 in all) and nitrate (80 ppm N, about twice the amount of normal BBM) are made in different fashions. Here, daily actions (only) are being investigated as a start. Results show that the immediate addition of the complete supply of glucose leads to only a partial intake from the algae. Supplying half the amount first, and then alternating nitrate addition and the other half leads to a complete intake of both nutrients but no significant increase in biomass productivity. Adding nitrate first leads to the best results in this case: it is hence preferable to time these organic carbon additions with a higher state of the internal (nitrogen) quota for more efficiency. To establish the impact of this alternate feeding approach on biomass productivity, a simultaneous feeding approach (with the same amounts of nutrients in total) is compared in Fig. 3. In the simultaneously fed system, daily additions of glucose (1 g L-1) and nitrate (50 ppm N) were made. In the alternately
Fig. 3. Biomass productivity for simultaneous and alternate nutrient additions. 5. SIMULATIONS WITH BACTERIA As seen in Table 1, the bacterial growth rate is a time-scale faster than the algal growth rate (about 15 times faster). Thus, it is clear that if both species are to co-exist in nutrient replete conditions simultaneously, the algae will be outgrown pretty fast. Figs. 4 and 5 show a simulation where an initial bacterial biomass concentration (20 gm-3) is present in the bioreactor, for three different feeding strategies: the same simultaneous and alternate nutrient feedings as in Fig. 3, plus the addition of the entire organic carbon and nitrogen quantities (4 gL-1 glucose and 241 ppm N) at the beginning of the culture. Results show that the best results for algal biomass yield and productivity are obtained with the alternate feeding approach.
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The worst case scenario is when all the nutrients are added at the start, where the bacteria are responsible for consuming most of the glucose. These results also support the instinctive idea of starting the cultures in autotrophic mode, as bacteria could otherwise indeed take over quite easily.
N
t i
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(7)
0
i 1
Where i(t) denotes the concentration of the essential element i (e.g. carbon, nitrogen, phosphorus, sulphur, etc.) supplied in the medium at any given time t. Note that this formulation is flexible, allowing either one of the concentrations to be zero at any given time t. For each of these nutrients, let us allow a possible addition flow Fi(t). From (7), a consistent constraint that could be imposed on these input fluxes could be: M
Fi t 0
(8)
i 1
Where M is the number of input fluxes, and M N accounts for the possible combination of nutrients within a single flow. Each flow would also have its own minimum and maximum limits (0 Fi(t) Fi_max), with constant inlet concentration of nutrient i (i_in). Another important operational constraint in fed-batch mode is the maximum volume of the tank (Vmax): t
f
V0
V max
t 0
Fi t dt
(9)
i
Where V0 is the initial volume of the tank, and tf is the total duration of the operation (which starts at t = 0). Maximizing biomass productivity implies maximizing the final biomass concentration xf over the finite horizon tf :
Fig. 4. Algal growth in the presence of bacteria for different feeding approaches
t
xf
x0
f
x t dt
(10)
t 0
Or the overall biomass production: t
P
f
x t v t dt
(11)
t 0
Fig. 5. Bacterial growth for the different feeding approaches (in relation to Fig. 4). 6. CONTROL PROBLEM DEFINITION The previous results support the idea of an alternate feeding approach for large-scale mixotrophic cultures of microalgae. However, as these results have shown, the decision process for the nutrient additions is not trivial. Also, a daily addition of the nutrients only (manual mode) proves inefficient. This section thus aims to propose a control problem definition for automating the decision process and operation of the system. As this is the very first study of the case, the situation shall be limited to the fed-batch mode, the results of which could be easily extended to the semi-continuous mode (periodic fedbatch operation), being a more realistic solution. The main operational constraint to be imposed on the system is that the product of the element concentrations in the culture medium equals zero (assumption that the bacterial growth rate is indeed an interactive Monod or equivalent form for the nutrients considered). To keep the idea as general as possible, N different elemental species can be considered:
To effectively maintain the system on an optimal trajectory, information on all state variables can be important. Indeed, from the previous results, addition of the organic carbon is most effective when it coincides with a high nitrogen quota value. Also, knowledge of the actual i:j ratio (e.g. C:N) in the reactor, as well as a good estimation (prediction) of the autotrophic carbon intake would be necessary to set the right addition of organic carbon. The addition of the nitrogen (or other) source should also be planned to maximize the results. Biomass measurements can be effected quite efficiently with OD (optical density) sensors (Benavides et al., 2015). Also in some cases, nutrients (such as nitrates) can be measured quite effectively by similar correlations in the UV range. Glucose (and other organic carbon forms) can now be estimated quite effectively by FT-IR analyses (Girard et al., 2013), although the equipment is rather expensive and on-line operation can be somewhat elaborate. As for the intracellular quota, a good approach would be to combine the measurements from the available sensors and model-based information to construct a state observer, which was just proven feasible (Feudjio et al., 2016). Future work will thus imply further study of the intricacies of this system, and the development and application of an effective optimal control strategy for this problem. Also, for a
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more realistic behaviour (and significance of the results), the autotrophic part of the model should account for the photoacclimation and photo-inhibition phenomena (Bernard, 2011; Bernard et al., 2009). This is of particular importance in pilot or large-scale systems where light attenuation is significant, due to the size of the vessels. 7. CONCLUSIONS This paper presented a first study on a possible active control approach to favor microalgae over bacteria in mixotrophic cultures, intended for large scale systems where an adequate sterilization is difficult to ensure. Using a simple model based on the Droop formulation for algae growth and the Monod formulation for bacterial growth, it has been shown possible to exploit the dynamical properties of the consortium to limit bacterial growth with minimal impact on microalgal biomass productivity. The approach is appropriate for microalgae with the ability to internalize nutrients more quickly and in more important amounts than the bacteria present, as is the case for the internalization of nitrate by specie Scenedesmus obliquus used as the basis for this study. The study raised important issues on the elemental (e.g. C:N) ratios in such cultures, and discussed potential solutions to these problems. Finally, a control problem formulation was proposed for the first time for this application. Future work will be devoted to determine an appropriate time window of operation using information from more complex models that take light limitation factors into account (the decisive factor for ending the culture cycle will be the point at which CO2 capture becomes negligible), and obtain the optimal control strategy for this problem. ACKNOWLEDGEMENTS The author would like to thank NSERC for funding (grant # DDG-2016-00008). REFERENCES Adesanya, V.O., Davey, M.P., Scott, S.A. and Smith, A.G. (2014). Kinetic modelling of growth and storage molecule production in microalgae under mixotrophic and autotrophic conditions, Bioresour. Technol., 157, 293-304. Benavides, M., Mailier, J., Hantson, A.L., Muñoz, G., Vargas, A., Van Impe, J. and Vande Wouwer A. (2015). Design and test of a low-cost RGB sensor for online measurement of microalgae concentration within a photo-bioreactor. Sensors, 15, 4766-4780. Bernard, O. (2011). Hurdles and challenges for modelling and control of microalgae for CO2 mitigation and biofuel production. J. Process Control, 21, 1378-1389. Bernard, O., Masci, P. and Sciandra, A. (2009). A photobioreactor model in nitrogen limited conditions. in Proc. 6th Conf. Math. Model., Vienna. Brennan, L. and Owende, P. (2010). Biofuels from microalgae - A review of technologies for production, processing, and extractions of biofuels and co-products, Renew. Sustain. Energy Rev., 14, 557-577. Chandra, R., Rohit, M.V., Swamy, Y.V. and Mohan, S.V. (2014). Regulatory function of organic carbon supplementation on biodiesel production during growth
and nutrient stress phases of mixotrophic microalgae cultivation, Bioresour. Technol., 165, 279-287. De la Hoz Siegler, H., Ben-Zvi, A., Burrell, R.E. and McCaffrey, W.C. (2011). The dynamics of heterotrophic algal cultures, Bioresour. Technol., 102, 5764-5774. Deschênes, J.-S., Boudreau, A. and Tremblay, R. (2015). Mixotrophic production of microalgae in pilot-scale photobioreactors: Practicability and process considerations, Algal Res., 10, 80-86. Deschênes, J-S. and Vande Wouwer, A. (2016). Parameter Identification of a Dynamic Model of Cultures of Microalgae Scenedesmus obliquus – An experimental study (submitted to DYCOPS-CAB 2016). Fagerbakke, K.M., Heldal, M. and Norland S. (1996), Content of carbon, nitrogen, oxygen, sulfur and phosphorus in native aquatic and cultured bacteria, Aquat. Microb. Ecol., 10, 15-27. Feudjio, C., Bogaerts, P., Deschênes, J-S. and Vande Wouwer, A. (2016). Design of a robust Lipschitz observer - Application to monitoring of culture of microalgae Scenesdesmus obliquus (submitted to DYCOPSCAB 2016). Girard, J.M., Deschênes, J-S., Tremblay, R. and Gagnon J. (2013). FT-IR/ATR univariate and multivariate calibration models for in situ monitoring of sugars in complex microalgal culture media. Bioresour. Technol., 144, 664-668. Girard, J.M., Roy, M.L., Hafsa, M.B., Gagnon, J., Faucheux, N., Heitz, M., Tremblay, R. and Deschênes, J.S. (2014), Mixotrophic cultivation of green microalgae Scenedesmus obliquus on cheese whey permeate for biodiesel production, Algal Res., 5, 241-248. Heredia-Arroyo, T., Wei, W. and Hu, B. (2010). Oil accumulation via heterotrophic/mixotrophic Chlorella protothecoides, Appl. Biochem. Biotechnol., 162, 19781995. Lee, A.L., Ataai, M.M. and Shuler, M.L. (1984). Doublesubstrate-limited growth of Escherichia coli, Biotechnol. Bioeng., 26, 1398-1401. Monod, J. (1942). Recherches sur la croissance des cultures bactériennes, Hermann, Paris. Pagnanelli, F., Altimari, P., Trabucco, F. and Toro, L. (2014). Mixotrophic growth of Chlorella vulgaris and Nannochloropsis oculata: interaction between glucose and nitrate, J. Chem. Technol. Biotechnol., 89, 652-661. Stein, J.R. (ED.) (1973). Handbook of phycological methods: culture methods and growth measurements, Cambridge University Press, Cambridge, Great Britain. Wang, J., Yang, H. and Wang, F. (2014). Mixotrophic cultivation of microalgae for biodiesel production: Status and prospects, Appl. Biochem. Biotechnol., 172, 33073329. Wang, Y., Rischer, H., Eriksen, N.T. and Wiebe, M.G. (2013). Mixotrophic continuous flow cultivation of Chlorella protothecoides for lipids, Bioresour. Technol., 144, 608-614. Yoo, S.J., Kim, J.H. and Lee, J.M. (2014). Dynamic modelling of mixotrophic microalgal photobioreactor systems with time-varying yield coefficient for the lipid consumption. Bioresour. Technol., 162, 228-235.
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IFAC-PapersOnLine 49-7 (2016) 1074–1078 A A Bacteriostatic Bacteriostatic Control Control Approach Approach for for Mixotrophic Mixotrophic Cultures Cultures of of Microalgae Microalgae A Bacteriostatic Control Approach for Mixotrophic Cultures of A Bacteriostatic Control Approach for Mixotrophic Cultures of Microalgae Microalgae Jean-Sébastien Deschênes*
Jean-Sébastien Deschênes* Jean-Sébastien Deschênes* Jean-Sébastien Deschênes* génie, Université du Québec à Rimouski, QC, G5L 3A1 *Département de mathématiques, informatique et *Département de mathématiques, informatique et génie, Université du Québec à Rimouski, QC, G5L 3A1 Canada +1-418-723-1986 Ext. e-mail: [email protected]). *Département de(Tel: mathématiques, informatique et génie, Université du Québec à Rimouski, QC, G5L 3A1 Canada +1-418-723-1986 Ext. 1997; 1997; e-mail: [email protected]). *Département de(Tel: mathématiques, informatique et génie, Université du Québec à Rimouski, QC, G5L 3A1 Canada (Tel: +1-418-723-1986 Ext. 1997; e-mail: [email protected]). Canada (Tel: +1-418-723-1986 Ext. 1997; e-mail: [email protected]). Abstract: Abstract: Mixotrophic Mixotrophic mode mode of of cultivation cultivation is is an an effective effective means means of of producing producing algal algal biomass. biomass. However, However, as it involves growth on an organic carbon source, the risks of bacterial contamination (and takeover) takeover) are Abstract: Mixotrophic mode of cultivation is an effective means of producing algal biomass. However, as it involves growth on an organic carbon source, the risks of bacterial contamination (and are Abstract: Mixotrophic mode of cultivation is industrial an effective means of producing algal biomass. However, higher at large production scales (e.g. pilot or scale) where adequate sterilization is difficult to as it involves growth on an organic carbon source, the risks of bacterial contamination (and takeover) are higher at largegrowth production scales (e.g. pilot source, or industrial scale) where adequate sterilization is difficultare to as it involves on an organic carbon the risks ofasbacterial contamination (andstudy takeover) ensure. This observation also holds for closed systems such photobioreactors. A recent showed higher at large production scales (e.g. pilot or industrial scale) where adequate sterilization is difficult to ensure.atThis observation also holds forpilot closed systems such as where photobioreactors. A recent study showed higher large production scales (e.g. orunder industrial scale) adequate is difficult to that the the This bacterial population can be contained particular constraints on the thesterilization available nutrients in the the ensure. observation alsocan holds for closedunder systems such asconstraints photobioreactors. A recentnutrients study showed that bacterial population be contained particular on available in ensure. This observation alsosimple holds models for closed systems such behavior as photobioreactors. Anutrient recent study showed culture medium. Using very for the dynamic (growth and consumption) that the medium. bacterial Using population be contained particularbehavior constraints on theand available in the culture very can simple models forunder the dynamic (growth nutrientnutrients consumption) that the species bacterialinvolved population can be contained under particular constraints on the available nutrients in the of both both (algae and bacteria), this paper investigates biomass productivity aspects under under culture medium. Using very simple models forthis the paper dynamic behavior biomass (growth productivity and nutrient consumption) of species involved (algae and bacteria), investigates aspects culture medium. Using very simple models for the dynamic behavior (growth and nutrient consumption) such operational constraints as well well as possiblethis approaches for conducting conducting the system. system. of both species involved (algae and as bacteria), paper investigates biomass productivity aspects under such operational constraints as possible approaches for the of both species involved (algae and bacteria), this paper investigates biomass productivity aspects under such operational constraints Federation as well as possible approaches for conducting the system. © 2016, IFAC (International of Automatic Control) Hosting by Elsevier Ltd. limitation. All rights reserved. Keywords: Microalgae, mixotrophy, bacterial contamination, batch control,the nutrient such operational constraints as well as possible approaches for conducting system. Keywords: Microalgae, mixotrophy, bacterial contamination, batch control, nutrient limitation. Keywords: Microalgae, mixotrophy, bacterial contamination, batch control, nutrient limitation. Keywords: Microalgae, mixotrophy, bacterial contamination, batch control, nutrient limitation. model model (Monod, (Monod, 1942) 1942) is is the the accumulation accumulation of of an an intracellular intracellular 1. 1. INTRODUCTION INTRODUCTION quota which governs growth rather than the readily available model (Monod, 1942)growth is the accumulation an intracellular quota which governs rather than theof readily available 1. INTRODUCTION model (Monod, 1942) is the accumulation of an intracellular nutrients from the culture media. Droop kinetics thus allows quota which governs growth ratherDroop than the readily available Mixotrophic for INTRODUCTION from the culture media. kinetics thus allows Mixotrophic mode mode of of1.production production for algal algal biomass biomass has has gained gained nutrients quota which governs growth rather than the readily available to explain a maintained cell growth well after the nutrient has nutrients from the culture media. Droop kinetics thus allows significant attention recently (Wang et al., 2014; Chandra et Mixotrophic mode of production for algal biomass has gained to explain a maintained cell growth well after the nutrient has significant attention recently (Wang et al.,biomass 2014; Chandra et nutrients fromfrom the culture media. Droop kinetics thus allows Mixotrophic mode of production for algal has gained been depleted the media. to explain a maintained cell growth well after the nutrient has al., 2014; Pagnanelli et al., 2014; Wang et al., 2013). In this been depleted from the media. significant attention recently (Wang et al., 2014; Chandra et al., 2014; Pagnanelli et al., 2014; Wang et al., 2013). In this to explain a maintained cell growth well after the nutrient has significant attentionCO recently (Wang et al., 2014; Chandra et been depleted from the media. capture is combined with growth on a mode, autotrophic 2 al., 2014; Wang et al., 2013). In this al., 2014; Pagnanelli is combined with2013). growth mode, autotrophic COet For simplicity, we the depleted from the media. al., 2014; Pagnanelli et2 capture al.,(DOC) 2014; Wang etoften al., Inon thisaa been simplicity, we consider consider the nitrogen nitrogen source source to to be be the the main main dissolved organic carbon source, in is combined withresulting growth on mode, autotrophic CO aa For 2 2 capture dissolved organic carbon (DOC) source, often resulting in limiting nutrient (all other nutrients in excess). A continuous For simplicity, we consider the nitrogen source to be the main capture is combined with growth on mode, autotrophic CO 2 biomass productivity. Another benefit limiting nutrient (all other nutrients in excess). A continuous significant increase of dissolved organic (DOC)productivity. source, often resulting in a supply For simplicity, weprovided considertothethenitrogen source to bethe the main significant increasecarbon of biomass Another benefit is to CO other to nutrients in excess). A continuous dissolved organic carbon (DOC) source, often resulting in a limitingof provided the reactor reactor to regulate regulate the pH pH at at ofnutrient CO22 is (all of this mode is aa reduced dependency on lighting conditions significant increase of biomass productivity. Another benefit supply limiting nutrient (all other nutrients in excess). A continuous of this mode is reduced dependency on lighting conditions a constant value, so carbon is never limiting and the influence is provided to the reactor to regulate the pH at significant increase of biomass productivity. Another benefit supply of CO 2 2 asupply constant value, so carbon is never limiting and the influence (Wang et al., 2014; Chandra et al., 2014; Brennan and of this mode is a reduced dependency on lighting conditions is provided toneglected the reactorintotheregulate the pH at of CO2growth (Wang et al.,is 2014; Chandra et al.,on2014; Brennan and aofconstant pH can model. Lighting value, so carbon never limiting the influence of this mode awhich reduced dependency lighting conditions pH on on cell cell growth can be beis neglected in theand model. Lighting Owende, can be an factor supporting (Wang et2010), al., 2014; Chandra etimportant al., 2014; Brennan and aof constant value, so carbon is never limiting and the influence Owende, 2010), which can be an important factor supporting conditions (available to the cells) are considered constant and of pH on cell growth to can becells) neglected in the model. Lighting (Wang et al., 2014; Chandra et al.,As 2014; Brennanofand conditions (available are considered constant and the scale-up of the production the presence the Owende, 2010), which can be systems. an important factor supporting of pH on cell growth canthe be neglected infurther the model. Lighting the scale-up of the production systems. As the presence of the non-limiting throughout the culture for simplicity. In conditions (available to the cells) are considered constant and Owende, 2010), which can be an important factor supporting non-limiting throughout the culture for further simplicity. In DOC source may to favor bacteria over algae, recent the scale-up of thetend production systems. As thethe presence of the mixotrophic conditions (available to the cells) are considered constant and DOC source may tend to favor bacteria over the algae, recent conditions, the algal growth rate is considered to non-limiting throughout the culture for further simplicity. In the scale-up of the production systems. Asthat theitpresence of the mixotrophic conditions, the algal growth rate is considered to results (Deschênes et al., 2015) showed is possible to DOC source may tend to favor bacteria over the algae, recent non-limiting throughout the culture for further simplicity. In results (Deschênes et al., 2015) showed that it is possible to (on CO ) and the be the sum of the autotrophic growth rate mixotrophic conditions, the algal growth rate is considered to A 2 DOC source may tendpopulation to favor bacteria over the algae, recent be the sum of the autotrophic growth rate A (on CO2) and the contain the bacterial under operational constraints mixotrophic conditions, the algal growth rate isorganic considered to results (Deschênes al., 2015) showed that it is possible to contain the bacterialet population under operational constraints (on the available carbon heterotrophic growth rate (on CO ) and the be the sum of the autotrophic growth rate results (Deschênes et al., 2015) showed that it is possible to H A 2 A 2 carbon imposed on the available nutrients from the culture medium, the available organic heterotrophic growth rate H (on (on CO ) and the be the sum of the autotrophic growth rate contain the bacterial population under operational constraints A 2 imposed on the available nutrients from the culture medium, source), both are subject to kinetics as contain the bacterial population under operational constraints heterotrophic available organic carbon rate HH (on and thus favor in this source), while whilegrowth both processes processes are the subject to Droop Droop kinetics as imposed on the available nutrients growth from the medium, heterotrophic (on the available organic carbon growth rate HCarbon and thus actively actively favor microalgae microalgae in culture this manner. manner. in (Adesanya et al., 2014). proportion in the biomass imposed on the available nutrients growth from the culture medium, source), while both processes are subject to Droop kinetics as in (Adesanya et al., 2014). Carbon proportion in the biomass and thus actively favor microalgae growth in this manner. source), while bothisprocesses areconstant subjectfor to Droop kinetics as (% of dry weight) considered simplicity. This paper further investigates the cell culture behavior under and thus actively favor microalgae growth in this manner. in (Adesanya et al., 2014). Carbon proportion in the biomass of dry weight) is 2014). considered constant for simplicity. This paper further investigates the cell culture behavior under (% et al., Carbon proportion in the biomass in (Adesanya such nutrient limitation constraints using simple simulation This paper further investigates the cell culture behavior under (% of dry weight) is considered constant for simplicity. such nutrient limitation constraints using simple simulation Bacterial biomass composition is considered constant (% of dry weight) is considered constant for simplicity. This paper further investigates the cell culture behavior under models to the challenges difficulties that biomass composition is considered constant (50% (50% C C such nutrient limitation using simple simulation models to show show the main main constraints challenges and and difficulties that arise arise Bacterial and 14% N w/w), from E. coli data (Fagerbakke et al., 1996), such nutrient limitation constraints using simple simulation Bacterial biomass composition is considered constant (50% C in such situations and to begin to define the control problem. and 14% N w/w), from E. coli data (Fagerbakke et al., 1996), models to show the main challenges and difficulties that arise Bacterial biomass composition is considered constant (50%the C in such to situations to begin to define the control that problem. with its growth governed by Monod-type kinetics on both models show theand main challenges andthe difficulties arise and 14% N w/w), from E. coli data (Fagerbakke et al., 1996), The paper is organized as follows: first, model used in the kineticseton both the with its growth governed by Monod-type in such situations and to begin to define the control problem. and 14% N w/w), from E. coli data (Fagerbakke al., 1996), The paper is organized as follows: first, the model used in the nitrogen and the organic carbon sources (Lee et al., 1984). in such situations and to along begin with to define the control The problem. its growth by Monod-type kinetics both the simulations presented its algal nitrogen and thegoverned organic carbon sources (Lee et al.,on 1984). The paper isis organized follows: the model used the with with its growth governed by Monod-type kinetics on both the simulations presentedas withfirst, its parameters. parameters. Thein The paper isisorganized asalong follows: first, the model used inalgal the nitrogen and the organic carbon sources (Lee et al., 1984). growth behavior (alone) is then investigated under different simulations is presented along with its parameters. The algal nitrogen and the organic carbon sources (Lee et al., 1984). growth behavior (alone) is then investigated under different simulations is presented along with its parameters. The algal 2.2 Microalgal growth model feeding approaches, and productivities are growth (alone) is then investigated different 2.2 Microalgal growth model feeding behavior approaches, and biomass biomass productivitiesunder are evaluated. evaluated. growth behavior (alone) is then investigated under different The presence of bacteria is then added to the simulations for feeding approaches, and biomass productivities are evaluated. Microalgal growth model The presence of bacteria is then added to the simulations for aa 2.2 feeding approaches, and biomass productivities are evaluated. 2.2 Microalgal growth model3 better comparison with the practical case. Finally, a very first Microalgal xx (gC/m The presence of bacteria is then added to the simulations for a better comparison with the practical case. Finally, a veryfor firsta Microalgal biomass biomass (gC/m33)) growth growth depends depends on on aa nitrogen nitrogen 3 The presence of bacteria is then added to the simulations 3) growth control problem formulation is proposed for this application. (gN/m is stored in the form of internal source s 3) which better comparison with the practical case. Finally, a very first N depends on an a nitrogen Microalgal biomass x (gC/m 3 control problem formulation is proposed for this application. (gN/m ) which is stored in the form of an internal source s N better comparison with the practical case. Finally, a very first Microalgal ) growth depends on a nitrogen biomass x (gC/m 3 3before quota q (gN/gC) it is effectively used for growth. The control problem formulation is proposed for this application. (gN/m ) which is stored in the form of an internal source s N 3before it is effectively used for growth. N quota q (gN/gC) The control problem formulation is proposed for this application. (gN/mrate ) which is stored in the of form of the an nutrient internal source sNuptake 2. MODELS FOR ALGAL AND BACTERIAL GROWTH (s , q) is a function both nutrient quota q (gN/gC) before it is effectively used for growth. The N 2. MODELS FOR ALGAL AND BACTERIAL GROWTH (s , q) is a function of both the nutrient nutrient uptake rate N quota q (gN/gC) before it is(Michaelis-Menten effectively used fortype growth. The availability in the medium relation) 2. MODELS FOR ALGAL AND BACTERIAL GROWTH (s , q) is a function of both the nutrient nutrient uptake rate N availability in the medium (Michaelis-Menten type relation) N 2. MODELS FOR ALGAL AND BACTERIAL GROWTH (s , q) is a function of both the nutrient nutrient uptake rate N and the of internal quota its availability thethe medium relation) 2.1 and the state statein the internal(Michaelis-Menten quota relative relative to to type its maximum maximum availability in of theal., medium (Michaelis-Menten type relation) 2.1 Generalities Generalities and and hypotheses hypotheses for for the the models models level (Bernard et 2011): and the state of the internal quota relative to its maximum levelthe (Bernard et al., 2.1 Generalities and hypotheses for the models and state of the 2011): internal quota relative to its maximum 2.1 Generalities and hypotheses for the models level (Bernard et al., 2011): The sN The basis basis for for the the model model of of algae algae growth growth is is the the Droop Droop kinetics kinetics level (Bernard et al., 2011): 1 q (1) sN q ss NN ,, qq max (Droop, 1968), which is now widely accepted to describe the (1) The basis1968), for thewhich modelis of algae growth is the Droop kinetics 1 (Droop, now widely accepted to describe the q max K Ns s q N The basis for the model of algae growth is the Droop kinetics N sN max 1 q q dynamic behavior of algae on different nutrients, particularly (1) s K s NN , q max (Droop, 1968), which is now widely accepted to describe the N N N max dynamic behavior of algae on different nutrients, particularly (1) s N , q max (Droop, 1968), which is now widely acceptedwith to describe the s NN 1 q max max K N nitrogen sources. Its fundamental distinction the Monod N max dynamic behavior of algae on different nutrients, particularly K s q nitrogen sources. Its fundamental distinction with the Monod N N max dynamic behavior of algae on different nutrients, particularly nitrogen sources. Its fundamental distinction with the Monod nitrogen sources. Its fundamental distinction with the Monod
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The autotrophic growth rate is described by the Droop model form (Droop, 1968): q min q
A q A max 1
(2) The heterotrophic growth rate is described by the following interaction between Monod kinetics (influence of the organic carbon source) and Droop kinetics for possible occurrence of nitrogen limitation (Adesanya et al., 2014; De la Hoz Siegler et al., 2011):
for this model is summarized in Table 1. Parameter values for the microalgae (specie Scenedesmus obliquus) were obtained either experimentally (Deschênes and Vande Wouwer, 2016) for the autotrophic part of the model, or from the literature for the mixotrophic part. In Girard et al. (2014), shake-flask experiments (using the same strain of Scenedesmus obliquus) showed that the maximum mixotrophic growth rate (posed as the sum of µAmax and µHmax here) was about four (4) times the maximum autotrophic growth rate µAmax. The half-saturation constant KC was obtained by taking the average value from the results of Adesanya et al. (2014) and Yoo et al. (2014).
q (3) 1 min K C sC q In these expressions, KN and KC are half-saturation constants, qmin is the minimum nitrogen quota (below which no growth is possible), max is the maximum nitrogen uptake rate, µAmax and µHmax are the maximum autotrophic and heterotrophic growth rates respectively, and sC is the organic carbon source concentration. In the absence of bacteria, mass balances in the chemostat lead to the following equations set:
H s C , q H max
sC
x x D x q q s N x D s Nin s N s C
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Table 1. Main model parameters Symbol
0.95 h-1 (22.8 d-1)
Symbol KN KC KNB KCB k1 k1B k2B
Value (units) 0.02 gNm-3 4 gGlcm-3 4 gNm-3 4 gGlcm-3 2.5 gGlcgC-1 0.14 gNg-1 1.25 gGlcg-1
(4)
3. BATCH GROWTH AND NUTRIENT BALANCE
Where = A + H is the overall growth rate of the algae, sNin and sCin are the concentrations of nitrogen and organic carbon in the (sterilized) inlet flow and D is the dilution rate. 2.3 Bacterial growth model Bacteria grow heterotrophically on the organic carbon source and the available nitrogen from the culture medium. The following interactive form is used (Lee et al., 1984):
µBmax
max
k 1 H x D s Cin s C
sN (5) K s K s C NB N CB Where µBmax is the maximum (bacterial) growth rate, and KCB and KNB are saturation constants. Values for these parameters are taken from available literature data for Escherichia coli growth on glucose and ammonium ion (Lee et al., 1984).
B s C , s N B max
µAmax µHmax qmax qmin
Value (units) 1.4 gNgC-1d-1 1.5 d-1 4.5 d-1 0.2 gNgC-1 0.02 gNgC-1
sC
To develop a better understanding of the culture behavior, it is natural to first investigate the batch response under varying sets of initial conditions. This section aims to illustrate some of the issues associated with nutrient balance in mixotrophic cultures of microalgae (in particular here, the C:N ratio). A comparison between the autotrophic and mixotrophic growth curves is seen in Fig. 1, with an initial nitrogen concentration (in the medium) of 41 ppm (182 ppm NO3-), as suggested in modified Bold’s basal medium (BBM) formulation for green algae (Stein, 1973). The glucose supply for the mixotrophic culture is 6 gL-1, a moderate concentration compared to other values found in the literature (16.6 gL-1 in Wang et al., 2013; 10 gL-1 in Wang et al., 2014 and up to 30 gL-1 in HerediaArroyo et al., 2010).
2.4 Combined model The combined model for the algae and bacteria consortium in the photobioreactor is thus: x x D x q q x B B x B D x B s N s C
D s Nin s N
D s Cin s C
(6)
x k k x
1B
1
H
B xB k 2B B x B
Here, xB is the bacterial biomass concentration (g/m3) and k1B and k2B are proportionality constants tied to its nitrogen and carbon elementary contents. The complete list of parameters
Fig. 1. Autotrophic and mixotrophic growth curves in batch mode.
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Results show that in both cases (autotrophic and mixotrophic modes), the algae quickly internalize all the nitrogen from the medium, grow until the minimum quota is reached (q = qmin), and reach the same biomass concentration at steady-state. In the mixotrophic culture, this concentration is reached in only one day, versus four for the autotrophic culture. Also, glucose is not fully utilized in this mixotrophic culture: although our model may predict the allowable range of C:N ratios in the biomass (between 5 and 50 as q reaches its boundaries qmax or qmin), the initial conditions in the reactor (2400 gCm-3 in the glucose, q(0) = 0.1 gNgC-1, x(0) = 200 gCm-3 and n(0) = 41 gNm-3) are such that the overall C:N ratio is 42.6. Since part of the carbon intake is related to CO2 in mixotrophic mode, it is difficult to predict (and accordingly adjust) the right C:N balance in the culture medium. A similar result (not shown) is obtained with an initial overall C:N ratio of 39 in the reactor. Using significantly higher initial nitrogen concentrations (e.g. 200 ppm in this case) would lead to an otherwise imbalanced operation: mixotrophic growth would take part for only about the first day, then the algae would grow in autotrophic mode over the rest of the process duration (losing the advantage of the mixotrophic growth approach). Overall, setting the right nutrient balance can be a challenge in mixotrophic cultures.
fed system, additions of nitrate (100 ppm N) and glucose (2 g L-1) were made every two days for the same average. Results show that overall, the two growth curves are similar, and thus there is no necessary loss of productivity due to this mode of nutrition.
Fig. 2. Autotrophic growth followed by different nutrient additions.
4. ALTERNATE FEED OPERATION This section evaluates manners in which an alternate feeding strategy could be implemented and their impacts on biomass productivity. The Droop model predicts that cell growth will cease as their internal (nitrogen) reserves reach a minimum: a successful start-up procedure (for the photobioreactor) should thus provide sufficient amounts of this nutrient before adding glucose. This reasoning is also in accordance with the idea of starting the culture in autotrophic mode until a “minimal” cell concentration (of algae) is obtained to ensure competitiveness over (potentially present) bacteria (Deschênes et al., 2015). The following course of action would thus be to add glucose to the culture and boost the production of algal biomass from this point. However, as shown in Fig. 2, both the timing and magnitude of this glucose addition may need careful planning for good results to be obtained: after an initial (autotrophic) growth phase in normal BBM medium, additions of glucose (4 g L-1 in all) and nitrate (80 ppm N, about twice the amount of normal BBM) are made in different fashions. Here, daily actions (only) are being investigated as a start. Results show that the immediate addition of the complete supply of glucose leads to only a partial intake from the algae. Supplying half the amount first, and then alternating nitrate addition and the other half leads to a complete intake of both nutrients but no significant increase in biomass productivity. Adding nitrate first leads to the best results in this case: it is hence preferable to time these organic carbon additions with a higher state of the internal (nitrogen) quota for more efficiency. To establish the impact of this alternate feeding approach on biomass productivity, a simultaneous feeding approach (with the same amounts of nutrients in total) is compared in Fig. 3. In the simultaneously fed system, daily additions of glucose (1 g L-1) and nitrate (50 ppm N) were made. In the alternately
Fig. 3. Biomass productivity for simultaneous and alternate nutrient additions. 5. SIMULATIONS WITH BACTERIA As seen in Table 1, the bacterial growth rate is a time-scale faster than the algal growth rate (about 15 times faster). Thus, it is clear that if both species are to co-exist in nutrient replete conditions simultaneously, the algae will be outgrown pretty fast. Figs. 4 and 5 show a simulation where an initial bacterial biomass concentration (20 gm-3) is present in the bioreactor, for three different feeding strategies: the same simultaneous and alternate nutrient feedings as in Fig. 3, plus the addition of the entire organic carbon and nitrogen quantities (4 gL-1 glucose and 241 ppm N) at the beginning of the culture. Results show that the best results for algal biomass yield and productivity are obtained with the alternate feeding approach.
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The worst case scenario is when all the nutrients are added at the start, where the bacteria are responsible for consuming most of the glucose. These results also support the instinctive idea of starting the cultures in autotrophic mode, as bacteria could otherwise indeed take over quite easily.
N
t i
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(7)
0
i 1
Where i(t) denotes the concentration of the essential element i (e.g. carbon, nitrogen, phosphorus, sulphur, etc.) supplied in the medium at any given time t. Note that this formulation is flexible, allowing either one of the concentrations to be zero at any given time t. For each of these nutrients, let us allow a possible addition flow Fi(t). From (7), a consistent constraint that could be imposed on these input fluxes could be: M
Fi t 0
(8)
i 1
Where M is the number of input fluxes, and M N accounts for the possible combination of nutrients within a single flow. Each flow would also have its own minimum and maximum limits (0 Fi(t) Fi_max), with constant inlet concentration of nutrient i (i_in). Another important operational constraint in fed-batch mode is the maximum volume of the tank (Vmax): t
f
V0
V max
t 0
Fi t dt
(9)
i
Where V0 is the initial volume of the tank, and tf is the total duration of the operation (which starts at t = 0). Maximizing biomass productivity implies maximizing the final biomass concentration xf over the finite horizon tf :
Fig. 4. Algal growth in the presence of bacteria for different feeding approaches
t
xf
x0
f
x t dt
(10)
t 0
Or the overall biomass production: t
P
f
x t v t dt
(11)
t 0
Fig. 5. Bacterial growth for the different feeding approaches (in relation to Fig. 4). 6. CONTROL PROBLEM DEFINITION The previous results support the idea of an alternate feeding approach for large-scale mixotrophic cultures of microalgae. However, as these results have shown, the decision process for the nutrient additions is not trivial. Also, a daily addition of the nutrients only (manual mode) proves inefficient. This section thus aims to propose a control problem definition for automating the decision process and operation of the system. As this is the very first study of the case, the situation shall be limited to the fed-batch mode, the results of which could be easily extended to the semi-continuous mode (periodic fedbatch operation), being a more realistic solution. The main operational constraint to be imposed on the system is that the product of the element concentrations in the culture medium equals zero (assumption that the bacterial growth rate is indeed an interactive Monod or equivalent form for the nutrients considered). To keep the idea as general as possible, N different elemental species can be considered:
To effectively maintain the system on an optimal trajectory, information on all state variables can be important. Indeed, from the previous results, addition of the organic carbon is most effective when it coincides with a high nitrogen quota value. Also, knowledge of the actual i:j ratio (e.g. C:N) in the reactor, as well as a good estimation (prediction) of the autotrophic carbon intake would be necessary to set the right addition of organic carbon. The addition of the nitrogen (or other) source should also be planned to maximize the results. Biomass measurements can be effected quite efficiently with OD (optical density) sensors (Benavides et al., 2015). Also in some cases, nutrients (such as nitrates) can be measured quite effectively by similar correlations in the UV range. Glucose (and other organic carbon forms) can now be estimated quite effectively by FT-IR analyses (Girard et al., 2013), although the equipment is rather expensive and on-line operation can be somewhat elaborate. As for the intracellular quota, a good approach would be to combine the measurements from the available sensors and model-based information to construct a state observer, which was just proven feasible (Feudjio et al., 2016). Future work will thus imply further study of the intricacies of this system, and the development and application of an effective optimal control strategy for this problem. Also, for a
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more realistic behaviour (and significance of the results), the autotrophic part of the model should account for the photoacclimation and photo-inhibition phenomena (Bernard, 2011; Bernard et al., 2009). This is of particular importance in pilot or large-scale systems where light attenuation is significant, due to the size of the vessels. 7. CONCLUSIONS This paper presented a first study on a possible active control approach to favor microalgae over bacteria in mixotrophic cultures, intended for large scale systems where an adequate sterilization is difficult to ensure. Using a simple model based on the Droop formulation for algae growth and the Monod formulation for bacterial growth, it has been shown possible to exploit the dynamical properties of the consortium to limit bacterial growth with minimal impact on microalgal biomass productivity. The approach is appropriate for microalgae with the ability to internalize nutrients more quickly and in more important amounts than the bacteria present, as is the case for the internalization of nitrate by specie Scenedesmus obliquus used as the basis for this study. The study raised important issues on the elemental (e.g. C:N) ratios in such cultures, and discussed potential solutions to these problems. Finally, a control problem formulation was proposed for the first time for this application. Future work will be devoted to determine an appropriate time window of operation using information from more complex models that take light limitation factors into account (the decisive factor for ending the culture cycle will be the point at which CO2 capture becomes negligible), and obtain the optimal control strategy for this problem. ACKNOWLEDGEMENTS The author would like to thank NSERC for funding (grant # DDG-2016-00008). REFERENCES Adesanya, V.O., Davey, M.P., Scott, S.A. and Smith, A.G. (2014). Kinetic modelling of growth and storage molecule production in microalgae under mixotrophic and autotrophic conditions, Bioresour. Technol., 157, 293-304. Benavides, M., Mailier, J., Hantson, A.L., Muñoz, G., Vargas, A., Van Impe, J. and Vande Wouwer A. (2015). Design and test of a low-cost RGB sensor for online measurement of microalgae concentration within a photo-bioreactor. Sensors, 15, 4766-4780. Bernard, O. (2011). Hurdles and challenges for modelling and control of microalgae for CO2 mitigation and biofuel production. J. Process Control, 21, 1378-1389. Bernard, O., Masci, P. and Sciandra, A. (2009). A photobioreactor model in nitrogen limited conditions. in Proc. 6th Conf. Math. Model., Vienna. Brennan, L. and Owende, P. (2010). Biofuels from microalgae - A review of technologies for production, processing, and extractions of biofuels and co-products, Renew. Sustain. Energy Rev., 14, 557-577. Chandra, R., Rohit, M.V., Swamy, Y.V. and Mohan, S.V. (2014). Regulatory function of organic carbon supplementation on biodiesel production during growth
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