Dynamics modeling of hydrogen production by sulfur-deprived Chlamydomonas reinhardtii culture in tubular photobioreactor

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 2 1 7 7 e1 2 1 8 5

Available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/he

Dynamics modeling of hydrogen production by sulfur-deprived Chlamydomonas reinhardtii culture in tubular photobioreactor T. Zhang Institute of Northern Engineering, University of Alaska Fairbanks, 306 Tanana Drive, Duckering Building, Fairbanks, AK99775, USA

article info

abstract

Article history:

A heterogeneous hydrogen production system induced by light attenuation across the

Received 11 April 2011

culture in a photobioreactor and the boundary conditions is studied by solving the

Received in revised form

advective-diffusive reaction equation (ADRE) used to describe the system. A uniform light

8 June 2011

intensity is prescribed on the cylindrical surface of the tubular bioreactor and attenuated

Accepted 26 June 2011

by Chlamydomonas reinhardtii culture toward the center. The rate constants and the

Available online 30 July 2011

kinetics orders of the S-system based kinetics equations were determined by correlating with the available experimentally measured data. The photobioreactor was operated for

Keywords:

200 h and the dynamics behavior of O2 evolution and H2 production were analyzed. The

Bioreactor

effects of different initial chlorophyll concentrations and quantities of sulfur re-added to

Hydrogen

the sulfur deprived culture on H2 production were studied. The results demonstrate that H2

Advective-diffusive reaction

production decreases with the light attenuation along radial direction. The overall H2

Kinetics

production increases with the initial cell concentration and the amount of re-added sulfur,

S-system

respectively, within the simulated range. The modeled results indicate that optimal

Chlamydomonas reinhardtii

combination of the culture parameters under the given light intensity and the mixing condition may exist for high H2 production. Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

1.

Introduction

Sustainable hydrogen production by Chlamydomonas reinhardtii under anaerobic condition induced by the deprivation of sulfur in the medium has been realized in laboratory under continuous light illumination [1,2]. This technique circumvents the severe O2-sensitivity of the reversible Fehydrogenase by temporally separating photosynthetic O2 evolution and carbon accumulation from H2 production in the culture. During the early stage of sulfur deprivation, photosynthetic O2 evolution reaches its maximum level which prohibits the induction of the expression of Fe-

hydrogenase and hence H2 production. As the photosynthetic activity of PSII is down-regulated by the decrease in the turnover of the D1 protein due to the lack of sulfur, O2 evolution drops abruptly below the level required by cellular respiration, which results in the establishment of anaerobiosis, the induction of the expression of Fe-hydrogenase enzyme, and the production of H2 for a few days. This novel technique has since inspired numerous studies in understanding the biochemical mechanisms behind the phenomenon [3e6], in improving the duration and efficiency of H2 production [7,9], and the effects of culture parameters [8,10]. It has been found that the parameters affecting H2

E-mail address: [email protected]. 0360-3199/$ e see front matter Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2011.06.132

12178

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 2 1 7 7 e1 2 1 8 5

production include: cell growth condition prior sulfur deprivation, pH value of the medium, re-addition of small quantity of sulfur back to sulfur deprived medium, initial cell concentration, and light intensity and illumination pattern [8,11]. It has also been found that H2 production could be improved by optimizing the combination of the initial cell concentration, light intensity, and mixing technique [11]. Mathematical models have been proposed to explain the interplay of different culture parameters during H2 production [12e14]. These mathematical models are mainly based on S-system (power law) [15,16] and assumed the culture being homogeneous in space, which is actually not the case in practice, especially for a large scale photobioreactor. Indeed, as indicated by experimentation [11], homogeneous culture is hardly obtained even under continuous mixing. To consider the inhomogeneity of the biochemical process for H2 production in a photobioreactor induced by light attenuation and the boundary conditions, a spatial- and temporaldependent mathematical model based on advectivediffusive reaction equation was proposed to describe the biochemical process [17]. In this paper, we use the proposed mathematical model to study the spatial- and temporaldependent dynamic process for H2 production by C. reinhardtii in sulfur deprived medium, exam the interplay of different culture parameters during H2 production, and the possibility to improve and optimize the bioreactor performance and design.

2.

Governing equations

The governing differential equations are based on the advective-diffusive reaction equation, which are given by C_ i þ U$VCi ¼ V$ðDi VCi Þ þ Ri ði ¼ 1; 2; /; NÞ

(1)

where i denotes the ith species in the system, Ci ð! x ; tÞ is the concentration function of spatial position and time, U is the average velocity of the fluid flow within the bioreactor, Di is the diffusion coefficient, Ri counts for all local biochemical reaction, and V is the gradient operator. By some mathematical manipulation, the advective-diffusive reaction equation could be separated into temporal-dependent kinetics terms and spatial-dependent advective-diffusive terms. By treating the spatial-dependent advectiveediffusive terms as the constraints, i.e., 8 0 V$ðDi VXi ð! x ÞÞ U$VXi ð! xÞ <  ¼ constant ! ! : Xi ð x Þ Xi ð x Þ f ðX ð! x ÞÞ;

3. Analytical solution of advective-diffusive equations Since the light intensity and O2 concentration play the key roles in H2 production in a photobioreactor, we only consider the spatial distribution of O2 in the system and assume, for the time being, U ¼ 0 and Di being a constant. The first equation in Eq. (2) is then reduced to x Þ ¼ 0: DV2 X2 ð!

(4)

For a tubular bioreactor with radius R, length H, and the boundary conditions of spatial-dependent O2 due to solar radiation prescribed on cylindrical surface and a constant O2 concentration at two ends as shown in Fig. 1, an approximate analytical solution was obtained for the advectiveediffusive equation Eq. (4) [17] as N npr npr npznh X sin Xðr; 4; zÞ ¼ A0;n I0 þ A1;n I1 cosð4Þ H H H n¼1 npr npr i þ A2;n I2 cosð24Þ þ / þ Am;n Im cosðm4Þ H H npr npr h sinð4Þ þ B2;n I2 sinð24Þ þ / þ B1;n I1 H H npr io sinðm4Þ ; (5) þ Bm;n Im H where Im ðnpr=HÞ is Bessel function, Am;n and Bm;n are the constant coefficients calculated by 8 gþ2p < Z 4ð2n  1Þ1   f0 cosðm4Þd4 Am;n ¼ R : Hp2 Im ð2n  1Þp gþp H 9 = 2f00  sin½ð2m  1Þg (6a) ; ð2m  1Þ 8 gþ2p < Z 4ð2n  1Þ1 2f00   f0 sinðm4Þd4  Bm;n ¼ : R ð2m  1Þ Hp2 Im ð2n  1Þp gþp H 9 = cos½ð2m  1Þg ;

ð6bÞ

(2)

i

the reaction equation (specifically for S-system based [19]), is reduced to # 8 " 0 < nY þm nY þm 1 gij hij ai Cj  bi Cj þ constant  Ti ðtÞ T_ i ðtÞ ¼ / : Xi ðx Þ j¼1 j¼1 f ðXi ð! x ÞÞTi ðtÞ:

(3)

x ÞTi ðtÞ, Xi ð! x Þ and Ti ðtÞ are the spatialin which Cð! x ; tÞ ¼ Xi ð! dependent and temporal-dependent concentration functions, respectively, ai and bi are the rate constants, gij and hij are the kinetics orders, and f ðXi ð! x ÞÞ is a known function. Detailed description of these equations were given in [17].

Fig. 1 e Diagram of the bioreactor used in the simulation.

12179

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 2 1 7 7 e1 2 1 8 5

(6c)

Am;n ¼ Bm;n ¼ 0; A0;n

Light attenuation data Ca=5mg/L Giannelli (2009) Ca = 12mg/L Ca = 24mg/L fitting function for Ca = 5mg/L Ca = 12mg/L Ca = 24mg/L

80

where angle g depends on the parameters of solar beam and time, f0 is the local spatial- and temporal-dependent O2 concentration and f00 is a constant O2 concentration due to solar radiation. For the special case considered in this paper, in which a uniformly distributed light with a constant intensity prescribed on the cylindrical surface, the analytical solution is independent of angular coordinate, 4, and the coefficients in Eq. (6) are reduced to

60

40

20

0 0

8 > > <

4f 0 0  for odd n R ¼ npI0 np > H > : 0 for even n

a 100

Light attenuation (%)

A0;n

9 8 gþ2p = < Z 4ð2n  1Þ1 0   ¼ f0 d4 þ pf0 ; : R Hp2 I0 ð2n  1Þp gþp H

(7)

2

4

6 8 10 Culture depth (cm)

12

14

16

b

Ip ¼ I0 eKa Ca r can be used to describe light attenuation across the medium, in which Ip is the attenuated light intensity, I0 is the reference light intensity, Ka is the light attenuation coefficient of the medium, Ca is the culture density, and r is the culture depth. It was found that cell division is arrested under sulfur deprivation condition [18] and hence a constant attenuation coefficient could be possibly used in LamberteBeer’s law for a given initial cell concentration. The attenuation coefficients used in the current study were obtained by fitting the experimentally measured data [11], which gives the coefficients 5.32, 3.5, and 3.2 for the initial chlorophyll concentrations 5, 12, and 24 mg/ L, respectively. The empirical equation for the variation of light attenuation coefficient with initial cell concentration is given by 3:0

Ka ¼ 3:2 þ 8:6e10:8 Ca :

2.3 2.2 2.1 2 1.9

)

(m

ce

an

12

st

10

14 16 18 20 Chlorophyll 22 concentratio n (mg/L)

24 0

Fig. 2 e Light attenuation by the culture across the reactor.

was conducted without mixing. However, most experiments of H2 production were conducted with mechanical mixing to improve light penetration depth by moving the cells (C. reinhardtii) around. In this case, the light attenuation level should be lower than that given by the empirical equation, Eq. (9). We modified Eq. (9) by including a pre-factor, i.e., 2

3

Ka ¼ K0a 43:2 þ 8:6e



3:0 C 10:8 a 5:

(10)

to describe both the culture absorption property and the effect of mechanical mixing, by which the forced advection is considered indirectly. The uniform light prescribed on the cylindrical boundary surface travels toward the center and in opposite directions with each other within the tubular bioreactor. The light intensity at any position is calculated by the superposition of the two light rays in opposite directions, i.e.,

(9) Ip ¼

The light attenuation using the fitted Ka is also plotted in Fig. 2 along with experimentally measured data. Light attenuation coefficients obtained by fitting the measured data [11] are mainly characterization of the absorption property of the culture since the measurement

0.025 0.02 0.015 0.01 0.005

1.8

di

in which (O2)max is maximum O2 concentration (mmole), Ip is the light intensity (mEm2 s1), and sPSU ¼ fm a =NPSU with fm being the maximum yield in Chlorophyll, a being the in vivo absorption coefficient normalized to the concentration of Chlorophyll a, and NPSU being the amount of Chlorophyll a in a photosynthetic unit (PSU). The uniformly distributed light prescribed on the cylindrical boundary surface is attenuated by the culture in the bioreactor toward the center. The decrease in light intensity along the beam path depends on cell concentration. Light attenuation by C. reinhardtii culture has been measured for different cell concentrations [11] and is shown in Fig. 2. For low cell concentration medium, LamberteBeer’s law

2.4

al

(8)

id

ðO2 Þmax  1 þ exp  sPSU $Ip

Ra

f00 ¼

Light intensity (Ip x 100)

where f00 is calculated by

 I0 eKa Ca ðRrÞ þ eKa Ca ðRþrÞ 1 þ e2Ka Ca R

ignoring deflection and scattering effects for simplicity. The light attenuation along radial direction of the bioreactor with different initial cell concentrations studied in this paper is shown in Fig. 2.

12180

4.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 2 1 7 7 e1 2 1 8 5

Kinetics equation

The kinetics equations are based on Biological System Theory (BST) [15,16,19] with the variables, rate constants, and kinetics orders being derived from a metabolic map [14] and modified to include spatial-dependence for inhomogeneous system [17] as below g g g h h h T_ 1 ¼ a1 T161;16 T181;18 T211;21  b1 T11;1 T181;18 T251;25  1 g g g h h h a2 T162;16 T182;18 T212;21  b2 C22;2 T182;18 T292;29 T_ 2 ¼ X2

g g g h g g h h h T_ 5 ¼ a5 T95;9 T125;12 T305;30  b5 C25;2 T55;5 ; T_ 6 ¼ a6 C26;2 T56;5  b6 T66;6 T236;23 g h h h g h T_ 7 ¼ a7 C27;2 T57;5  b7 C27;2 T77;7 T297;29 T317;31 g g g g h h h h T_ 8 ¼ a8 T38;3 T68;6 T188;18 T238;23  b8 T88;8 T108;10 T208;20 T328;32 g g g g h g g h T_ 9 ¼ a9 T89;8 T199;19 T249;24 T329;32  b9 T99;9 ; T_ 10 ¼ a10 C210;2 T1710;17  b10 T1010;10

  a17 T34 a17 T34   T17 ð0Þ eb17 t b17 b17   a16 T22 T33 a16 T22 T33 ¼   T16 ð0Þ eb16 t b16 b16

T17 ¼ T16

g g g h h g g g h h T_ 3 ¼ a3 T163;16 T183;18 T213;21  b3 T33;3 T233;23 ; T_ 4 ¼ a4 T34;3 T64;6 T194;19  b4 T44;4 T254;25

g g g g T_ 11 ¼ a11 C211;2 T811;8 T1011;10 T1911;19

experimentally measured data. By careful examination, we found that Eqs. 1017, 1016, 101, 103 are actually ordinary differential equations since the independent variables T34, T33, T25, T22, T21, and T18 are constants. The analytical solutions for these equations are simply given by

(12)

a16 T22 T33  T16 ð0Þ a1 a16 T21 b T22 T33  16 a1 T18 T21 eb16 t T1 ¼ b1 T18 T25  b16 b1 b16 T25 8 > < a1 a16 T21 þ T1 ð0Þ  T22 T33 > b1 b16 T25 : 9 a16 > T22 T33  T16 ð0Þ = b16 þ a1 T18 T21 eb1 T18 T25 t > b1 T18 T25  b16 ;

h  b11 T1111;11

g g g g g h h T_ 12 ¼ a12 T112;1 T412;4 T2512;25 T2612;26 T2712;27  b12 T1212;12 T2812;28

(13)

for b1 T18 T25  b16 s0 and

g g h h T_ 13 ¼ a13 C213;2 T3113;31  b13 T1313;13 T2913;29 g g g h g h T_ 14 ¼ a14 C214;2 T3114;31  b14 T1414;14 ; T_ 15 ¼ a15 C215;2 T715;7  b15 T1515;15

T1 ¼

g g h g h T_ 16 ¼ a16 T2216;22 T3316;33  b16 T1616;16 ; T_ 17 ¼ a17 T3417;34  b17 T1717;17 :

(11) The definition of these dependent and independent variables along with their constant values or initial values are given in Table 1 (also see [14]). A systematical method to determine the rate constants, ai, bi and the kinetics orders, gij and hij has been described in [15,16]. This method relies on in vivo measurement of metabolite concentration and fluxes which are currently very limited and are difficult to obtain. To circumvent the difficulties in determining the rate constants and kinetics orders in Eq. (4), we need to consider the possible analytical solutions of uncoupled equations and fitting the general solution to the

  a1 a16 T21 a1 a16 T21 T22 T23 þ T1 ð0Þ  T22 T33 eb1 T18 T25 t b1 b16 T25 b1 b16 T25

(14)

for b1 T18 T25 ¼ b16 . T3 ¼

  a3 a b3 b eb16 t eb3 t  3 þ T3 ð0Þ  3 þ b3 b3 b3  b16 b3  b16

(15)

for b3  b16 s0, with a3 ¼ a3 a16 =b16 ; b3 ¼ ða16 =b16  T16 ð0ÞÞa3 ; a3 ¼ a3 T18 T21 , b3 ¼ b3 T23 . The rate constant and kinetics order for hydrogenase expression T17 have been given in [14]. T17 determines hydrogenase kinetics along with O2 evolution. Photosynthesis activity and cellular respiration in C. reinhardtii culture have been measured in numerous experimentations [1,8]. These data could be used to determine rate constant and kinetics order in T16, the PSII activity. By fitting the function T16 to the

Table 1 e Designation of variables used in power-law model and their initial values. Dependent variable (value) Protons from PSII (T1) Oxygen (X2 T2 ) e from PSII (T3) Protons from PQ (T4) Starch (T5) e from starch oxidation (T6) Pyruvate (T7) e from PSI (T8) NADPH T9 Hydrogenase (T10) Hydrogen (T11) ATP (T12) Acetate (T13) Formate (T14) Intrcellular CO2 (T15) PSII (T16) H2ase (T17)

Independent variable (value) 1 0.1 108 1 104 103 106 106 106 109 108 107 5 106 103 14.485 105

Light (T18) Protons in stroma (T19) Ferredoxin oxidized (T20) Water (T21) Sulfate (T22) PSI (T23) NADPþ ðT24 Þ ATPase (T25) ADP (T26) Phosphate (T27) ATP consumers (T28) Mitochondrial respiration (T29) Extracellular CO2 (T30) Fermentation (T31) FNR (T32) Precursor to PSII (T33) DNA (T34)

2.363 10 105 0.8 0.01 1 10 1 10 10 0.01 e 3$103 104 1 1 1

12181

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 2 1 7 7 e1 2 1 8 5

T_ 29 ¼ a29 T22  b29 T29

(16)

70

and its analytical solution is given by T29 ¼

a29 b29

  a29 T22  T22  T29 ð0Þ eb29 t : b29

Photosynthetic activity Celluar respiration Photosynthetic activity data (Kosourov (2002)) Cellular respiration data (Kosourov (2002))

60

O2 (mmols/mol Chl/s)

experimentally measured data, we found these parameters to be 0.25 for a16 and 0.075 for b16. The analytical solutions are plotted in Fig. 3 along with experimentally measured data. To consistent with photosynthesis activity function, T16, we introduced the kinetics equation for cellular respiration which is simply assumed to depend on sulfur concentration, i.e.,

50 40 30 20 10 0

(17)

20

40

60 80 Time (hour)

100

120

140

By fitting the function to the experimentally measured data, we found a29 to be 0.75 and b29 to be 0.032. The solution is also plotted in Fig. 3 along with the measured data. Once the rate constants and kinetics orders in the analytical solutions are determined, they can be used to determine those in the coupled kinetics equations. For example, by introducing a16 and b16 into T1 and T3, the functions for proton and electron from PSII can be determined (in the current case a1, b1, a3, and b3 have been given in [14]). Based on these results and the available experimentally measured data, we could determine the parameters in T2 for which an analytical solution is hardly to obtain. By examining the measured data, we found that T2 has to satisfy the following requirements

Fig. 3 e Normalized photosynthesis activity and cellular respiration data [8] and functions describing these activities.

T2 ðt ¼ 0Þ ¼ T2 ð0Þ € ðt ¼ t1 Þ < 0; T2 ðt ¼ t1 Þ ¼ ðT2 Þ T_ 2 ðt ¼ t1 Þ ¼ 0; < T 2 max € ðt ¼ t2 Þ > 0 T 2 T_ 2 ðt ¼ t3 Þ ¼ 0; T2 ðt ¼ t3 Þ ¼ ðT2 Þ

Unlike S-system based kinetics equation in which single solution of the equation represents the whole system, the solution of the advectiveediffusive reaction equation varies across the space of the reactor. To describe the overall O2 evolution and H2 production for a given bioreactor, we need to calculate the volumetric average of O2 evolution and H2 production. The following volumetric integration may be used to evaluate the volumetric average of O2 and H2 Z 1 f¼ f ðr; 4; zÞrdrd4dz: (21) V

(18)

min

in which t1 and t3 are the moments at which T2 reaches its maximum, ðT2 Þmax , and minimum, ðT2 Þmin , respectively, T2 ð0Þ is the initial value, and t2 is the time when transition point occurs. Introducing the solutions of T16 in Eq. (4) and T29 in Eq. (17) into the requirements Eq. (4), we obtained the following equations and constraints

from the analytical solutions Eqs. 4 and 17. ðC2 Þmin andðC2 Þmax can be estimated from the experimentally measured data and therefore n and b2 can be determined. Based on the experimentally measured data, we found n ¼ 0:5 and b2 ¼ 0:321.

5.

Volumetric average O2 and H2

V

a2 T21 T16 ðt1 Þ  b2 T29 ðt1 ÞðC2 Þnmax ¼ 0 

a2 T21 ½T16 ðt1 þ DtÞÞ  T16 ðt1  DtÞ  b 2 Cn2 ðt1 þ DtÞT29 ðt1 þ DtÞ  Cn2 ðt1  DtÞT29 ðt1  DtÞ  0 a2 T21 ½T16 ðt2 þ DtÞ  T16 ðt2  DtÞ  b2 Cn2 ðt2 þ DtÞT29 ðt2 þ DtÞ  Cn2 ðt2  DtÞT29 ðt2  DtÞ 0 a2 T21 T16 ðt3 Þ  b2 Cn2 min T29 ðt3 Þ ¼ 0:

The second and the third equations in Eq. (4) provide the constraints on the range of the values of the parameters can be used. From the first and the last equations in Eq. (4), we could determine the power n and the rate constant b2,   T16 ðt3 ÞT29 ðt1 Þ a2 T21 T16 ðt3 Þ T16 ðt1 ÞT29 ðt3 Þ   : and b2 ¼  n ðC2 Þmin C2 min T29 ðt3 Þ log ðC2 Þmax

n¼

For the special case considered here, the light intensity is axisymmetrically distributed on the cylindrical surface and therefore is independent of 4 and so do O2 evolution and H2 production. The integration in Eq. (21) is reduced to f¼

log

(20)

The parameter of a2 is determined by the constraint a1 ¼ a2 ¼ a3 . T16 ðt1 Þ, T16 ðt3 Þ, T29 ðt1 Þ, and T29 ðt3 Þ can be calculated

(19)

2p V

Z f ðr; zÞrdrdz:

(22)

A

For the discrete data of O2 and H2 obtained from the analysis, the integration can therefore be carried out in 2D domain (rz plane) using the composite Trapezoidal rule. The 2D

12182

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 2 1 7 7 e1 2 1 8 5

8 pDrDz< f¼ r0 f ðr0 ; z0 Þ þ rm f ðrm ; z0 Þ þ r0 f ðr0 ; zn Þ þ rm f ðrm ; zn Þ 2V : 3 2 m1 m1 n1 n1 X X X   X ri f ðri ; z0 Þ þ ri f ðri ; zn Þ þ r0 f r0 ; zj rm f rm ; zj 5 þ 24 i¼1

þ4

j¼1

6.

i¼1

n1 m1 X X

 ri f ri ; zj

i¼1

!9 =

j¼1

;

j¼1

ð23Þ

Example

The photobioreactor considered here is a cylinder with R ¼ 0.025 m and H ¼ 0.5 m as shown in Fig. 1. The uniform light is prescribed on the cylindrical surface of the reactor. In this case, the light distribution within the bioreactor is axisymmetric and independent of angular coordinate 4. The light intensity prescribed on the cylindrical surface is 236.3 mEm2 s1 (also see [14]). A constant O2 concentration of 0.632 mmoles/ml is prescribed at the two ends. The bioreactor is divided into 5 equal divisions along r direction and 10 equal divisions in z direction for the current analysis. The initial value for the dependent variables and the constants for the independent variables as well as their definitions in the kinetics equations are given in Table 1. The parameters used to calculate O2 evolution due to light illumination in Eq. (8) are fm ¼ 4:0, a ¼ 0:8, NPSU ¼ 200. We used the first 100 terms of the solution given in Eq. (3) for all the calculations presented in this paper. The MATLAB [20] functions were coded for Eqs. 3e5. The default convergence criterion for the solver of differential equations, ode45, was used for all the analyses presented.

7.

Results and discussion

7.1.

Light attenuation

The light attenuation coefficient, Ka, obtained by fitting the experimentally measured data [11] or calculated by the empirical equation, Eq. (9) characterizes only the culture absorption property without counting the effect of mechanical mixing and therefore will result in very low H2 production when used in modeling. To characterize both the culture absorption property and the effect of mechanical mixing on light penetration, we modified Eq. (9) by a prefactor as given in Eq. (10). K0a ¼ 0:4 was used in the current dynamics analysis such that the results are consistent with the experimentally measured data in photobioreactor. Fig. 2 shows the results of light attenuation in r direction for different chlorophyll concentrations used in the current study. These results indicate the light intensity decreases exponentially with the culture depth in r direction of the reactor and following a power law with the initial chlorophyll concentration.

The kinetics equation based on a homogeneous culture assumption is an idealized case, which could lead to the conclusion that H2 production increases monotonically with culture volume and cell concentration, which is actually not validated in most experiments. On the other hand, the light intensity reduces rapidly in the cultures without mechanical mixing and the cultures collapse as the initial cell concentration increases. Hence, the actual H2 production in a photobioreactor with mixing should lie somewhere between the two extreme cases depending on the culture initial condition, the boundary condition, and the mixing condition of the system. Optimization with respect to the culture parameters, light intensity, mechanical mixing condition, and reactor configuration is therefore important for improvement on H2 production. To this end, the proposed spatial- and temporaldependent advective-diffusive reaction model could be a quick and powerful tool for identifying those key parameters.

7.2.

O2 evolution

The spatial distribution of O2 evolution for initial chlorophyll concentration of 10 mg/L is shown in Fig. 4. The results indicate that the distribution is nearly uniform across the bioreactor only with small variation in r and z directions. The large variation occurring near the two ends is due to the O2 concentration prescribed on the boundaries. The dynamics behavior of O2 evolution for four different initial chlorophyll concentrations, i.e., 10, 14, 18, 24 mg/L is shown in Fig. 5. The significant difference in O2 concentrations among the cultures with different initial chlorophyll concentrations occurs during O2 evolution phase, but is hardly noticeable during H2 production phase.

7.3.

H2 production

The dynamics behavior of H2 production for the initial chlorophyll concentration of 10 mg/L at z ¼ 0 and z ¼ 0.25 m is shown in Fig. 6. These results demonstrate the variation of the

Chl concentration is 10mg/L and sulfur quantity is 10.0

1.2 O2 ( moles/ml)

domain is equally divided along radial and axial directions, i.e., ri ¼ r0 þ iDr, zi ¼ z0 þ jDz with i ¼ 0, 1, 2, /, m and j ¼ 0,1,2, /, n. The volumetric integration can be evaluated by

1.1 1 0.9 0.8 0.7 0.6

0.025

0.5 0.4

0.02

0.3

0.015

Radia

0.01 0.005 nce ( r in m )

l dista

0.2 0.1 0 0

z in

ce (

tan l dis

m)

a

Axi

Fig. 4 e The spatial distribution of O2 concentration due to diffusion in the culture with the initial chlorophyll concentration of 10 mg/L and the re-added sulfur of 10 mM.

12183

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 2 1 7 7 e1 2 1 8 5

H2 (ml)

Spatial distribution of H2 production at 130 hour

110 105 100 95 90 85 80 75 70

0.025

0.5 0.02

0.015 0.01 l dista 0.005 nce (r in m)

Radia

Fig. 5 e O2 evolution for the cultures with different initial chlorophyll concentration under given sulfur quantity of 20.0 mM.

dynamics behavior of H2 production along radial direction at the given axial positions. The variation in H2 production is mainly due to light attenuation since the spatial variation in O2 concentration is very small as indicated in Fig. 4. The variation of H2 production across the bioreactor at a given time (of 130 h) is shown in Fig. 7 for the culture with the initial chlorophyll concentration of 10 mg/L. These results indicate that light attenuation plays a major role in H2 production in addition to the spatial distribution of O2 concentration.

7.4.

Variation of re-added sulfur and cell concentration

Re-addition of small quantities of sulfur back to the sulfur deprived culture (TAP-S) has been shown to increase the initial specific rate of H2 production and to extend the duration of H2 production phase to a longer period of time [8,9]. To model the process and to study the effects of re-added sulfur on H2 production, we simulated the dynamics of H2 production in the cultures with five different quantities of re-added sulfur, i.e., 10, 20, 30, 40, and 50 mM in combination with four

Fig. 7 e Spatial distribution of H2 production in the culture with the initial chlorophyll concentration of 10 mg/L at 130 h.

different initial chlorophyll concentrations, 10, 14, 18, 24 mg/L. These results are represented by the surface plots in Fig. 8. Each surface in Fig. 8 represents the dynamics of H2 production for four different initial chlorophyll concentrations under a given amount of re-added sulfur. The surface for a given quantity of re-added sulfur indicates that H2 production increases with the initial chlorophyll concentration. The different elevations of these surfaces indicate that H2 production also increases with the quantity of sulfur added back to the sulfur deprived culture. We could also see from the figure the initial specific rate of H2 production increases with the amount of re-added sulfur. For a given quantity of readded sulfur, the modeled H2 production increases with initial chlorophyll concentration, but in a decreased gradient, i.e., the increment of H2 production between two chlorophyll concentration decreases with the increase in the initial chlorophyll concentration. This trend is clearly shown in Fig. 9 for the re-added sulfur quantity of 20 mM. H2 production increases with the initial chlorophyll concentration has been observed in the experiments [8]. However, the experimental data show

H2 (ml)

H2 production at z=0 H2 production at z=0.25 120

H2 (ml)

100 80 60 40 20

0 0

0.4 0.3 ) in m 0.2 z ( e 0.1 anc t s i ld Axia

350 300 250 200 150 100 50 0

Sulfur quantity 10.0 20.0 30.0 40.0 50.0

M M M M M

0

0.025

200

0.02

150 100 Time (h our)

0.015 0.01 50

0.005 0 0

)

in m

ista

ial d

Rad

(r nce

Fig. 6 e Spatial variation of the dynamics of H2 production in the culture with the initial chlorophyll concentration of 10 mg/L at z [ 0 and z [ 0.25 m.

24 22 Ch l co 20 nc 18 20 en 16 60 40 tra 14 100 80 tio 140 120 12 n( 160 180 mg (hour) /L) 10 200 Time

Fig. 8 e Dynamics of H2 production with different quantities of re-added sulfur back to the medium with different initial chlorophyll concentrations.

0

12184

a

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 2 1 7 7 e1 2 1 8 5

140 Chl concentration 24mg/L 120

18mg/L

20.0 M sulfur

14mg/L 100

H2 (ml)

10mg/L 80 60 40 20 0 20

40

60

80

100

120

140

160

180

200

Time (hour)

b

300 Sulfur quantity 20.0 M 250 Chl concentration 24mg/L

H2 (ml)

200

18mg/L

150

14mg/L

100

10mg/L

50

0 20

40

60

80

100

120

140

160

180

200

light intensity under well mixed condition is more favorite for H2 production. Since as the initial cell concentration increases, optical density of the medium will also increase, therefore, the increase in H2 production with cell concentration observed in the experiments [8] could be resulted from a well mixed medium in which a uniform distribution of light intensity and nutrient concentration must have been reached. To testify this idea, we modeled the dynamics of H2 production in the reactor with a uniformly distributed light intensity for four different initial chlorophyll concentrations. The results show that H2 production increases with the initial chlorophyll concentration in an increased gradient as shown in Fig. 9. These modeled results have consistent trend with the observations in the experiments presented in [8]. Fig. 10 shows the comparison between the modeled results and the experimentally measured data. H2 production started earlier in the experiments than the modeled H2 dynamics. Therefore, the experimental data is shifted toward to the analytical solution for a better comparison in the figure. From the shifted curves, we found the measured initial specific rate of H2 production is much higher than the modeled results. The modeled specific rate of H2 production is very close to the measured data for the re-added sulfur quantity of 50 mM during production stage. For the re-added sulfur quantity below 25 mM, the measured specific rate of H2 production is higher than the modeled results during middle and late production stages.

Time (hour)

Fig. 9 e Dynamics of H2 production.

8.

the increase in H2 production with the initial chlorophyll concentration in an increasing gradient. The interplay among the initial chlorophyll concentration, the light intensity, and the mixing condition was further studied in [11] by testing two different initial chlorophyll concentrations (12 and 24 mg/L) under two light intensities (70 mEm2 s1 and 140 mEm2 s1) using two different mixing mechanisms. Those results showed that high initial chlorophyll concentration with high

250 Initial Chl concentration 10 mg/L Modeled results 50 20 Test data (Kosourov 2002) 25 50

200

M SO4 M SO4 M SO4 M SO4

H2 (ml)

150

100

Conclusion

Light attenuation across a photobioreactor induces inhomogeneous metabolic process for H2 production, for which spatial- and temporal-dependent advective-diffusive reaction equation has to be used to describe the process. It has been shown that the proposed advective-diffusive reaction equation based mathematical model is able to model the dynamics behavior of a bioreactor for H2 production with the inhomogeneity being induced by light attenuation across the reactor as well as boundary conditions. The empirical method correlating the S-system based kinetics equation with available experimentally measured data is able to determine the rate constants and the kinetics orders used in the equations. The simulated results demonstrated that H2 production increases with the quantities of re-added sulfur and the initial cell concentration, respectively, within the simulated range. From these results, it can be anticipated that the combination of the culture parameters could be potentially optimized under the given light intensity and mixing condition to target for high H2 production.

50

Acknowledgements 0 0

20

40

60

80

100 120 Time (hour)

140

160

180

200

Fig. 10 e Comparison of H2 production between measured data and the modeled results.

The author would like to thank Arctic Region Supercomputer Center (ARSC) and Institute of Northern Engineering (INE) of University of Alaska Fairbanks for granting the access to the computing resources and facilities.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 6 ( 2 0 1 1 ) 1 2 1 7 7 e1 2 1 8 5

references

[1] Melis A, Zhang LP, Forestier M, Ghirardi ML, Seibert M. Sustained photobiological hydrogen gas production upon reversible inactivation of oxygen evolution in the green alga Chlamydomonas reinhardtii. Plant Physiol 2000;122:127e35. [2] Ghirardi ML, Zhang JP, Lee JW, Flynn T, Seibert M, Greenbaum E, et al. Microalgae: a green source of renewable H2. Trends Biotechnol 2000;18:506e11. [3] Zhang L, Happe T, Melis A. Biochemical and morphological characterization of sulfur-deprived and H2-producing Chlamydomonas reinhardtii (green alga). Planta 2002;214: 552e61. [4] Antal TK, Krendeleva TE, Laurinavichene TV, Makarova VV, Ghirardi ML, Rubin AB, et al. The dependence of algal H2 production on Photosystem II and O2 consumption activities in sulfur-deprived Chlamydomonas reinhardtii cells. Biochim Biophys Acta 2003;1607:153e60. [5] Hemschemeier A, Happe T. The exceptional photofermentative hydrogen metabolism of the green alga Chlamydomonas reinhardtii. Biochem Soc Trans 2005;33(Pt 1):39e41. [6] Antal TK, Volgusheva A, Kukarskih GP, Krendeleva TE, Rubin AB. Relationships between H2 photoproduction and different electron transport pathways in sulfur-deprived Chlamydomonas reinhardtii. Int J Hydrogen Energy 2009;34: 9087e94. [7] Kim JP, Kang CD, Park TH, Kim MS, Sim SJ. Enhanced hydrogen production by controlling light intensity in sulfurdeprived Chlamydomonas reinhardtii culture. Int J Hydrogen Energy 2006;31:1585e90. [8] Kosourov S, Tsygankov A, Seibert M, Ghirardi ML. Sustained hydrogen photoproduction by Chlamydomonas reinhardtii: effects of culture parameters. Biotechnol Bioeng 2002;78(7): 731e40. [9] Kim JP, Kim KR, Choi SP, Han SJ, Kim MS, Sim SJ. Repeated production of hydrogen by sulfate re-addition in sulfur deprived culture of Chlamydomonas reinhardtii. Int J Hydrogen Energy 2010;35:13387e91.

12185

[10] Kosourov S, Patrusheva E, Ghirardi ML, Seibert M, Tsygankov A. A comparison of hydrogen photoproduction by sulfur-deprived Chlamydomonas reinhardtii under different growth conditions. J Biotechnol 2007;128:776e87. [11] Giannelli L, Scoma A, Torzillo G. Interplay between light intensity, Chlorophyll concentration and culture mixing on the hydrogen production in sulfur-deprived Chlamydomonas reinhardtii cultures grown in laboratory photobioreactors. Biotech BioEng 2009;104:76e90. [12] Jo JH, Lee DS, Park JM. Modeling and optimization of photosynthetic hydrogen gas production by green alga Chlamydomonas reinhardtii in sulfur-deprived circumstance. Biotechnol Prog 2006;22:431e7. [13] Park W, Moon II . A discrete multi states model for the biological production of hydrogen by phototrophic microalga. Biochem Eng 2007;36:19e27. [14] Jorquera O, Kiperstok A, Sales EA, Embirucu M, Ghirardi M. S-systems sensitivity analysis of the factors that may influence hydrogen production by sulfurdeprived Chlamydomonas reinhardtii. Int J Hydrogen Energy 2008;33:2167e77. [15] Savageau MA, Voit EO, Irvine DH. Biochemical systems theory and metabolic control theory: 1. Fundamental similarities and differences. Math BioSci 1987;86:127e45. [16] Savageau MA, Voit EO, Irvine DH. Biochemical systems theory and metabolic control theory: 2. The role of summation and connectivity relationships. Math BioSci 1987;86:147e69. [17] Zhang T. Advection-diffusion constrained metabolic reaction in bioreactor analysis for biohydrogen production. Submitted to a journal and currently under revise. [18] Hase E, Otsuka H, Mihara S, Tamiya H. Role of sulfur in the cell division of Chlorella, studied by the technique of synchronous culture. Biochim Biophys Acta 1959;35:180e9. [19] Savageau MA. Metabolite channeling - implications for regulation of metabolism and for quantitative description of reactions in vivo. J Theor Biol 1991;152:85e92. [20] Matlab. The language of technical computing, 7.10.0. The MathWorks, Inc; 2010.