Modelling Of Micro Algal Growth In Tubular Photo Bio Reactor

Modelling of Microalgal Growth in Tubular Photobioreactor: Hybrid Multicompartment/CFD Approach Štěpán Papáček 1,2, Rudolf Žitný 4, Josef Kuba 4, Jiří Kopecký 2,3, Jiří Masojídek 2,3, Dalibor Štys 2,3 1

2

Faculty of Mechatronics, Technical University of Liberec, Czech Republic Institute of Physical Biology, University of South Bohemia, Nove Hrady, Czech Republic 3 Institute of Microbiology, Academy of Sciences, Trebon, Czech Republic 4 Faculty of Mechanical Engineering, Czech Technical University in Prague, Czech Republic E-mail: [email protected]

Abstract. Klíčovým bodem matematického modelování fotobioreaktorů je propojení popisu biochemických procesů s režimem proudění. V článku je formulován hybridní multicompartment/CFD přístup k modelování růstu mikrořas v tubulárním fotobioreaktoru (PBR) při vsádkovém módu kultivace. Je navrženo rozdělení PBR na nejmenší možný počet jednotek, které zohledňují heterogenitu intenzity osvětlení (což je příčinou rozdělení trubice v radiálním směru), změny v režimu proudění (což je příčinou rozdělení v axiálním směru) a dále i změny při přechodu z osvětlené části PBR do části neosvětlené (tj. do retenční nádrže a do čerpacího zařízení). Biochemický proces (tj. fotosyntéza s uvažováním fotoinhibice) je popsán pomocí jednoduchého strukturovaného modelu, jehož proměnné se vyhodnocují zvlášť v každé jednotce. Váženou sumací dle objemů jednotlivých jednotek je pak z lokálních koncentrací biomasy vypočítána hodnota průměrné koncentrace biomasy na konci každého časového kroku simulace růstu. Vše je implementováno v programu FEMINA. CFD kód FLUENT pak v každém časovém kroku pro simulaci růstu, řeší velikosti toků mezi jednotkami. Parametry proudění (hustota a viskozita řasové suspenze, průtok) a hranice jednotek, které závisí na koncentraci biomasy a na intenzitě osvětlení dopadajícího na stěnu trubice, jsou aktualizovány vždy tehdy, když dojde k jejich „významné“ změně. Model umožňuje predikci produktivity procesu nárůstu řasové biomasy v závislosti na hodnotách konstrukčních parametrů PBR (tj. průměr trubice, délka osvětlené části PBR, objem neosvětlených částí PBR) a na hodnotách operačních proměnných (tj. průtok, počáteční koncentrace biomasy, hodnota intenzity ozáření dopadajícího na stěnu trubice) a bude využit v projektu vypracování metodologie optimálního návrhu fotobioreaktorů pro kultivaci mikrořas. Keywords: microalgae, photobioreactor, mathematical modelling, Computational Fluid Dynamics

1. Introduction The objective of this study is mathematical modelling of microalgal growth in tubular recycle photobioreactor. As a case study, a novel tubular photobioreactor, shown in Fig. 1, was being tested at the Academic and University Centre in Nové Hrady, Czech Republic. The main difference between the cultivation of chemoheterotrophs (fungi, bacteria, heterotrophic microalgae) and phototrophs (microalgae and cyanobacteria) is that, in case of the latter, the

Štěpán Papáček et al. energy source can not be stored in the culture medium, but it must be continuously provided. Delivering the light to achieve maximum productivity is a key issue in photobioreactor (further PBR) design. Mathematically the problem consists in extremum seeking for the integral in the equation (1). The PBR instantaneous process productivity can be expressed as: P(t)=µ(t)x(t)V ; thus, obviously, mass culture should be kept dense if the specific growth rate does not shut down. That leads the culture to be light-limited, if the others factors, i.e. nutrient, temperature, pH, shear stress, are optimal. The conditions of light use (so-called light regime) depend on cell density, incident irradiance (on the wall), length of the optical path (i.e. tube diameter), and flow pattern. The biochemical process (photosynthesis) should be modelled taking into account photoinhibition and the flashing light effect, i.e. the photosynthetic efficiency enhancement as a function of the light/dark cycles parameters. T

P =V

() () T ∫ µ t x t dt

(1)

0

2. Problem Formulation The suspension of microalgae flows periodically between the illuminated part of the PBR (photic stage) and the dark part (retention tank, pump and non-transparent tubes). The illuminated part is composed of the glass tubes, which are uniformly irradiated (e.g. from outside) and form a loop (see Fig. 2). The light availability is thus heterogeneous within the culture volume. This spatial heterogeneity results in local reaction rates, which is leading us to the Eulerian multicompartment approach. Another approach, the so-called Lagrangeian, takes into account “individual” reaction rates of algal cells. This approach leads us to the concept of the “irradiance history” of an individual algal cell and statistical treatment of received data. According to the work of Bezzo et al. [Bezzo (2003)], the authors of this study Fig.1 consider the Eulerian approach more appropriate. To couple the flow field description with the biochemical process, we have to select a model of photosynthetic growth, which can consistently explain three phenomena: (i) photoinhibition, (ii) cell damage due to shear stress, and (iii) flashing light effect. Consequently, to calculate the local specific growth rate it is possible to use: • The unstructured model based either on the modified Monod kinetics, or according to equation (3) in [Muller-Feuga (2003)], or a generalised model, which consider the photosynthetic efficiency enhancement due to flashing light effect [Terry (1986)], • The structured model (e.g. based on [Wu and Merchuk (2002)].

Modelling of Microalgal Growth in a Tubular Photobioreactor: Hybrid Multicompartment/CFD Approach

output

input

Fig. 2

3. Model Derivation 3.1. Irradiance Field Distribution The microalgal growth in the tubular PBR depends mainly on light intensity, which is not uniform in the cross section. The section area can be divided into three zones (see Fig. 3): (i) zone I intensively irradiated near the wall (photoinhibited zone), (ii) zone II, where the culture is light limited, and (iii) zone III in the axis, where no growth occurs. Derivation of local physical laws Fig. 3 for irradiance field distribution is well developed. Based on Lambert-Beer’s law, the one-dimensional problem can be modelled as folows (see Equation 2): (2) I = I 0 exp( − k x x − k w )r 3.2. Model of Photosynthesis and Photoinhibition A structured three-state model integrating photosynthesis and photoinhibition has been proposed elsewhere [Wu and Merchuk (2002)] as schematically presented in Fig. 4. This model is based on the concept of the photosynthetic factory (PSF), which is defined as the sum of the light trapping system, activated by a given amount of light energy. The three possible states are assumed for the PSF: the resting state (open), designated x1, the activated state x2 , and the inhibited state x3 .The kinetic equations may be written as follows: dx1 = −αIx1 + γx2 + δx 3 (3) γ dt I I dx 2 = αIx1 − γx2 − βIx2 (4) αI dt X1 X2 x1 + x2 + x3 = 1 (5) where α, β, γ, δ are rate constants. δ

For the specific growth rate: dx 1 µ= (6) dt x is proposed the next equation: µ = kγx 2 − Me (7) where k is the photosynthesis yield and Me is the maintenance term.

X3

βI

Fig. 4

Štěpán Papáček et al. 3.3. Multicompartment Model

1,1

1,j

1,M

2,1

2,j

2,M

Degasser

Pump i,1

N,1

i, j

i, M

N,j

N, M Fig. 5

The model of algal growth can be implemented as a compartment model with mutual mass exchange, dividing the PBR into a small number of regions, according the particularities of illumination and fluid flow. Specifically for the tubular PBR, the multicompartment model is composed of (N*M)+2 compartments. The (N*M) compartments in the illuminated part of the PBR respect the light attenuation in radial direction (discretisation into N levels) and the changes of fluid pattern in axial direction (discretisation into M levels). One compartment is reserved for a pumping device, and one compartment for a degasser and other non-illuminated parts of the PBR (see Fig. 5). Due to the changes of the physical parameters and operating conditions (i.e. viscosity, density, concentration, flow rates and irradiation), the boundaries of the compartments should be dynamically changed during the numerical simulation. 3.4. Flow Field Description For some simple cases, the mass exchange (i.e. flow rate coefficients) among the compartments can be estimated or calculated analytically. Nevertheless, for the complex flows (e.g. for a specific boundary conditions), the numeric values of the flow rates deliver a CFD code (e.g. FLUENT). 3.5. Solution Scheme Time courses of the PSF states and algal biomass concentrations in each compartment can be described by the system of ordinary differential equations similar to (3) and (4), which have to be completed in terms considering mass transfer through the boundary, and algebraic equations similar to (5) and (7). This system can be defined and solved as a problem file

Modelling of Microalgal Growth in a Tubular Photobioreactor: Hybrid Multicompartment/CFD Approach

bio.mdt by Open Source Software for finite elements FEMINA (for more information about FEMINA, see: http://www.fsid.cvut.cz/~zitny/index.htm). Input parameters are PBR design parameters (geometrical structure), operating conditions (flow rates, incident irradiance, initial concentration at inlet), and of course physical parameters and rate coefficients, which are to be determined from literature or batch experiments. Thus for each time step, the system of [(N*M)+2]*2 ordinary differential equations and [(N*M)+2]*2 algebraic equations is calculated. Integrating the equations (6), the „local“ algal biomass concentrations at the end of each time step can be determined. The overall biomass concentration is received after the weighted summation (the weights are defined by the respective compartment volumes).

4. Conclusion A new approach for mathematical modelling of microalgae growth in tubular recycle photobioreactor has been worked out. The proposed hybrid multicompartment/CFD approach for modelling of algal growth in the PBR allows the prediction of biotechnological process productivity for known values of model parameters. At the same time, the multicompartment/CFD model may be used for the sensitivity analysis, i.e. for the simulation how the different model parameters influence the process productivity. The future goal is the elaboration of methodology for optimal PBR design. The optimisation can be aimed either on the operating conditions (i.e. flow rate, initial cell concentration, incident irradiance), or on the PBR design parameters (i.e. for tubular PBR: tube diameter, bend radius, length of a straight part of the tube, volume of the degasser and other non-illuminated parts). The reason of this effort is that traditional scale-up methodology does not work and the recently proposed method [Papáček (2003)], based on the best adequacy of the so-called relevant light regime parameters of the model with the optimal, experimentally determined parameters, was not fully validated.

Nomenclature I I0 x kx kw r µ Me V t T P(t) P N, M

irradiance in culture (µE m-2 s-1) incident irradiance (µE m-2 s-1) biomass concentration (g L-1) extinction coefficient for biomass (L g-1 m-1) extinction coefficient for water (m-1) distance of considered point to centre of tube (m) specific growth rate (h-1) Maintenance (h-1) PBR culture volume (L) time, i.e. independent variable Batch cultivation cut-off time (h-1) Instantaneous volumetric productivity (g h-1) Overall volumetric productivity (g h-1) Number of tube division into zones in radial and axial direction respectively.

Štěpán Papáček et al. Acknowledgement This research was supported by the project "Mechanism, Ecophysiology and Biotechnology of Photosynthesis", LN00A141 of the Ministry of Education of the Czech Republic and by grant no. MSM1231001. References [Bezzo (2003)] Bezzo F., Macchietto S., Pantelides C.C.: General Hybrid Multizonal/CFD Approach for Bioreactor Modeling. AIChE Journal 49, 2133–2148, 2003. [Masojídek (2003)] Masojídek, J., Papáček, Š., Jirka, V., Červený, J., Kunc, J., Korečko, J., Sergejevová, M., Verbovikova, O., Kopecký, J., Štys, D, Torzillo, G.: A Closed Solar Photobioreactor for Cultivation of Microalgae under Supra-High Irradiances: Basic Design and Performance of Pilot Plant. J. Appl. Phycol., 15, (2003), 239–248. [Muller-Feuga (2003)] Muller-Feuga, A. Le Guèdes, R., Pruvost, J.: Benefits and limitations of modeling for optimization of Porphyridium cruentum cultures in an annular photobioreactor. Journal of Biotechnology 103, 153-163, 2003. [Papáček (2003)] Papáček Š., Rálek P., Hokr M., Kopecký J., Masojídek J., Štys D. and Petera K.: Methodology for Algal Photobioreactor Design: Mathematical Modelling of Hydrodynamic Mixing and Prediction of Light Regime Parameters. Proceedings of the SIMONA 2003, the 2nd international workshop on Simulation, Modelling, and Numerical Analysis. Liberec (CZ), 2003 [Terry (1986)] Terry K. L.: Photosynthesis in Modulated Light: Quantitative Dependence of Photosynthetic Enhancement on Flashing Rate. Biotechnology and Bioengineering 28, 988-995, 1986. [Wu and Merchuk (2002)] Wu X., Merchuk J.C.: Simulation of Algae Growth in a BenchScale Bubble Column Reactor. Biotechnology and Bioengineering 80, 156-168, 2002.