Modelling microalgae growth in nitrogen-limited continuous culture
Xinping Zhou a, *, Shuo Yuan a, Ranchi Chen b, Bao Song c
a Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, Chinab School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USAc School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e i n f o
Article history:Received 13 April 2013Received in revised form7 June 2014Accepted 14 June 2014Available online xxx
Please cite this article in press as: Zhou X, edx.doi.org/10.1016/j.energy.2014.06.058
a b s t r a c t
In this paper, based on the mathematical models of microalgae growth, the performance of microalgaegrowth in nitrogen-limited and light-limited continuous culture is investigated and the effect ofimportant factors on the growth is examined. The dilution rate and the influent inorganic nitrogenconcentration have been shown to have a significant influence on the growth of microalgae in contin-uous culture. In order to obtain a maximum productivity of microalgae, lower dilution rate is better for alower influent inorganic nitrogen concentration and an optimal dilution rate can be obtained for a higherinfluent inorganic nitrogen concentration. There is an optimal influent inorganic nitrogen concentrationcorresponding to maximum microalgae productivity, and the optimal value for lower dilution rate is farhigher than that for higher dilution rate. This paper will lay a foundation for the design of the operationalparameters of continuous culture PBR (photobioreactor).
With the continuous reduction of the fossil fuels and the ac-celeration of global greenhouse effect mainly due to carbon dioxide(CO2) emissions, energy supplymay be in trouble in the near future.It is urgent and significant to find reliable clean energy resourcesalternative to fossil fuels [1]. Microalgae may become one of themost promising new resources to supply energy and mitigate CO2in the future [2,3]. Compared to the first generation biofuels,microalgae have several advantages in sustainability, economicsand environment. Microalgae not only have higher productivity,but also can be fed in saline/brackish water/coastal seawater onnon-arable and deserted land. The concept of using microalgae forbiofuels as a potential biofuel source is not new, and many re-searchers have done plenty of work on planktons [4e7]. Technol-ogies for producing microalgae and using microalgae for biodieselhave been known for more than 50 years. Now the technology ismuch accounted of owing to the current high price of depletingfossil fuels and the global warming induced by combustion of fossilfuels.
t al., Modelling microalgae g
Microalgae cultures are effective technologies to producemicroalgae in artificial bioreactors. The bioreactors mainly consistof open ponds and closed PBRs (photobioreactors). The advantagesof the open ponds include high surface/volume (s/v) ratio, relativelycheap, easy to clean, to utilise non-agricultural land, low energyinputs, and easy maintenance. But there are poor biomass pro-ductivity, large area of land required, limited to a few strains ofalgae, poor mixing, and poor utilization of light and CO2, and cul-tures are easily contaminated. Open ponds are suitable for a smallquantity of algal species which can tolerate extreme environmentalconditions, e.g., Chlorella, and Spirulina. They belong to fast growersand can thrive in highly alkaline or saline environments. Comparedto the open systems, the closed systems have a higher s/v ratio,showing a larger surface area exposed to the light source to reducethe shadow effect, and can better control the culture conditions,e.g., mass flux, contamination, temperature, pH, gaseous transfer,and nutrient distributions. A large quantity of algal species cantherefore be used in PBRs. The PBR has therefore been moreaccounted of researchers and companies recently [8,9].
By now, how to improve the biomass or oil productivity frommicroalgae has been the aim of all the researchers' and companies'work. Experiment is a good method to investigate the technology.But it will take a long period of time and a lot of funds to doexperiment. Modelling may be an effective method to help re-searchers to investigate the process of microalgae growth in
rowth in nitrogen-limited continuous culture, Energy (2014), http://
bioreactors. Recently, some models have been proposed to studythe performance of the phytoplankton growth, among which thereexist differences to some extent.
Droop [10,11] proposed a dynamicmodel of algae growth, whichtakes the dilution rate and the influent inorganic nitrogen con-centration into account. The model is classical, but practical, whichdescribes the dynamic model of the algae growth and the nitrogenuptake. Some new models were developed based on Droop’smodel. Geider et al. [12] proposed a new model which includedgrowth process, nitrogen uptake, chlorophyll synthesis, tempera-ture and respiration aspects, but ignored depth dependence. Cherifand Loreau [13] proposed a more biologically realistic use ofDroop's equations to model growth under multiple nutrient limi-tation, and examined the effect of the dilution rate on the equi-librium densities of two species. Bougaran et al. [14] proposed amodel of continuous cultures of microalgae colimited by nitrogenand phosphorus, but did not examine the effect of the dilution rateor the influent inorganic nitrogen concentration. Quinn et al. [15]proposed a model for industrial scale systems based on Ref. [12].Packer et al. [16] developed a dynamic model to predict the growthand neutral lipid synthesis of green algae by taking into consider-ation the influences of the photosynthesis and the nitrogen uptakeon the growth rate. In Bernard's dynamic model [17], the light-limited and nitrogen-limited factors simultaneously have effectson the growth rate. In Mairet et al.' model [18], the biomass isdivided into three compartments, i.e., the function part, carbohy-drates, and neutral lipids, which can be transformedmutually. Yuanet al. [19] studied several main models of microalgae growth innitrogen-limited and light-limited culture system for estimatingbiomass productivity by comparing different expressions and co-efficients used in these models.
By now, little work has been done to analyze the effects of bothdilution rate and influent inorganic nitrogen concentration on themicroalgae growth in continuous culture. In this paper, based onthe Bernard's dynamic model [17], the effects of the importantfactors including the dilution rate and the influent inorganic ni-trogen concentration on the microalgae growth in nitrogen-limitedand light-limited continuous culture are studied. The performanceof the microalgae growth manifested by the two important pa-rameters is investigated. Optimal values of culture parameters arediscussed for maximum microalgae productivity.
2. Model description
Many models have been proposed up to now, which usedvarious expressions to calculate the parameters e.g. light distribu-tion, pigment dynamics, nitrogen uptake, growth rate, respirationrate, temperature dependence, dilution rate, and influent inorganicnitrogen concentration. In this paper, we will use Bernard's modelto model microalgae growth in nitrogen-limited PBR [17]. Themodel is introduced below.
The model [17] describes four variables in the ordinary differ-ential equations: s(t), which denotes the concentration of dissolvedinorganic nitrogen, the nitrate or ammonium, q(t), which is internalnitrogen cell quota, x(t) which is algae biomass concentration, andI*(t) which is not the real radiation but a conceptual variabledenoted radiation. The unit of I*(t) is mmolm�2 s�1, which meansthe number of photons absorbed per unit area per unit time. Theexpression of calculating variable I* will be discussed later. The fourordinary differential equations were expressed as:
_s ¼ Dsin � rs
sþ Ks
�1� q
Q1
�x� Ds (1)
Please cite this article in press as: Zhou X, et al., Modelling microalgae gdx.doi.org/10.1016/j.energy.2014.06.058
_q ¼ rs
sþ Ks
�1� q
Q1
�� m
�I0; I
*; x; q�ðq� Q0Þ (2)
_x ¼ m�I0; I
*; x; q��
1� Q0
q
�x� Dx� Rx (3)
_I* ¼ m
�I0; I
*; x; q��
1� Q0
q
��I � I*
�(4)
where D denotes the dilution rate, r is the maximum nitrogenuptake rate, sin is influent inorganic nitrogen concentration, R is theinspiration rate, I is the average radiation along culture volume, Q0is the minimum nitrogen quota, Q1 is the maximum nitrogen quota,and m denotes the average growth rate, which is calculated by:
mðI0; xÞ ¼ ~m2KiI
lffiffiffiffiD
p arctan
0@ I0
�1� e�l
� ffiffiffiffiD
p
2I20e�l þ I0
�1þ e�l
�KiI þ 2I2opt
�qC0
�1A
(5)
where I0 represents the light intensity at the bioreactor surface, and~m is the maximum growth rate. The average radiation along culturevolume I is given by:
I ¼ I0l
�1� e�l
�(6)
where the optical depth, l, is the product of the depth of the cultureL multiplied by light attenuation rate x:
l ¼ xL (7)
The light attenuation rate x can be calculated by:
x ¼ aChlþ bxþ c (8)
where, a, b, and c are the constants, and the chlorophyll concen-tration Chl can be calculated by:
Chl ¼ g�I*�xq (9)
The proportion of chlorophyll concentration to nitrogen con-centration g(I*) can be given by:
g�I*� ¼ gmax
kI*I* þ kI*
(10)
where gmax is the maximum value of g(I*).The parameters D and Iopt which denote the radiation providing
maximum rate of photosynthesis in Eq. (5) are calculated by:
D ¼ 4I2opt�qC0
�� K2
iI (11)
Iopt ¼ffiffiffiffiffiffiffiffiffiffiffiffiKsIKiI
p(12)
where KsI is:
KsI ¼K*sI
qC0
(13)
The initial value of Chl/x is denoted by a parameter qC0:
rowth in nitrogen-limited continuous culture, Energy (2014), http://
Table 1Parameters values used in simulation.
Parameters Values Units
~m 1.7 day�1
Q0 0.05 g N (g C)�1
Q1 0.25 g N (g C)�1
K*sI 1.4 molm�2 s�1
KiL 295 molm�2 s�1
r 0.073 g N (g C)�1 day�1
Ks 0.0012 g Nm�3
R 0.0081 day�1
gmax 0.68 g Chl (g N)�1
kI* 63 molm�2 s�1
I0 100 molm�2 s�1
X. Zhou et al. / Energy xxx (2014) 1e6 3
qC0 ¼ Chl0x0
(14)
where Chl0 is the initial value of Chl, and x0 is the initial value of x.
3. Results and discussion
3.1. Model validation
Bernard's model has been validated by Bernard [17] with theexperiment data [20]. In this paper, we also do this work in order toshow the validation of our code for this model. The parametersused in the simulations with the model are presented in Table 1.
Fig. 1 shows the simulation results using the model and com-pares them with the experiment. In the experiment, both dilutionrate D and influent inorganic nitrogen concentration sin were 0.Isochrysis galbana used widely in research was used in the experi-ment. Culture was grown at 18 �C, and illuminated at100 molm�2 s�1. No additional nutritionwas added into the cultureonce the growth of microalgae began. Concentration dissolvedinorganic nitrogen s was run out on the 12th day. The increase ofintracellular particulate carbon approached to saturation on the25th day which is the end of the experiment. As shown in Fig. 1, themodel simulations have a good agreement with the experiment
Fig. 1. Comparison of simulations with Bernard's
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data. This figure also indicated that the extracellular nitrogen wasexhausted on the 12th day. At the same time, the synthesis ofchlorophyll ceased. The growth process of biomass content withtime could be divided into four phases [20]. The first five days wereat the lag phase, during which the cells increased at a slow rate.Following the lag phase was the exponential phase (from the 5thday to the 12th day), during which the growth rate of cells was0.4 day�1. The cells didn’t stop growing until the 19th day, andthese days (from the 12th day to the 19th day) were at the post-exponential phase. After that, the culture entered the stationaryphase, during which the content of biomass, chlorophyll andintracellular nitrogen were stable.
3.2. Dilution rate effect
Dilution rate (D) and influent inorganic nitrogen concentration(sin) are two important factors influencing themicroalgae growth incontinuous culture PBRs. In order to illuminate the influence of Dvalue on the results, simulations by using different D values areperformed and compared. Fig. 2 shows the variations of four mainparameter values including the concentration of the dissolvedinorganic nitrogen (s), the particulate carbon concentration in thecell (x), the chlorophyll concentration (Chl) and the particulate ni-trogen concentration in the cell (x� q) with time calculated basedon the model by using D values of 0, 0.04, 0.08, 0.12, 0.16 and0.2 day�1 when sin¼ 1 gNm�3. While Fig. 3 shows the variationsby using D values of 0, 0.04, 0.05, 0.06, 0.1 and 0.2 whensin¼ 5 gNm�3.
As shown in Fig. 2, for a lower sin value of 1 g Nm�3, with anincrease in D value, the particulate carbon concentration in the cell(x), the chlorophyll concentration (Chl) and the particulate nitrogenconcentration in the cell (x� q) increase, while the concentrationsof the dissolved inorganic nitrogen (s) on the 10th day for all the Dvalues are nearly equal. As shown in Fig. 3, for a higher sin value of5 g Nm�3, the variations of the four main parametric values with Dvalue increasing differ with those as shown in Fig. 2. In Fig. 3, withan increase in D value, the particulate carbon concentration in thecell (x), the chlorophyll concentration (Chl) and the particulate ni-trogen concentration in the cell (x� q) on the 50th day initially
model [17] and experimental data from [20].
rowth in nitrogen-limited continuous culture, Energy (2014), http://
Fig. 2. Four main parametric values calculated at various D values when sin¼ 1 g Nm�3.
X. Zhou et al. / Energy xxx (2014) 1e64
increase, then reach the peak for the dilution rate (D) of 0.05 day�1,and finally decrease. While, with an increase in D value, the con-centration of the dissolved inorganic nitrogen (s) gradually in-creases and becomes 0 at a later time.
The results show that in order to obtain maximum microalgaeproductivity in a continuous culture process, lower dilution rate isbetter when influent inorganic nitrogen concentration is lower at1 g Nm�3, and an optimal dilution rate of 0.05 day�1 can be
Fig. 3. Four main parametric values calculated
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obtained when influent inorganic nitrogen concentration is higherat 5 g Nm�3.
In order to illuminate the influence of sin value on the results,simulations by using different D values are performed andcompared. Fig. 4 shows the variations of four main parametric
at various D values when sin¼ 5 g Nm�3.
rowth in nitrogen-limited continuous culture, Energy (2014), http://
Fig. 4. Four main parametric values calculated at various sin values when D¼ 0.02 day�1.
X. Zhou et al. / Energy xxx (2014) 1e6 5
values including the concentration of the dissolved inorganic ni-trogen (s), the particulate carbon concentration in the cell (x), thechlorophyll concentration (Chl) and the particulate nitrogen con-centration in the cell (x� q) with time calculated based on themodel by using sin values of 0, 10, 26, 27, 28 and 50 gNm�3 whenD¼ 0.02 day�1. While Fig. 5 shows the variations by using sin valuesof 0, 3, 6, 7, 8 and 30 gNm�3 when D¼ 0.1 day�1.
Fig. 5. Four main parametric values calculated
Please cite this article in press as: Zhou X, et al., Modelling microalgae gdx.doi.org/10.1016/j.energy.2014.06.058
As shown in Figs. 4 and 5, for D¼ 0.02 or 0.1 day�1, with anincrease in sin value, the particulate carbon concentration in the cell(x), the chlorophyll concentration (Chl) and the particulate nitrogenconcentration in the cell (x� q) initially increase and then decrease,and the concentration of the dissolved inorganic nitrogen (s)gradually increases. The optimal values of influent inorganic ni-trogen concentration corresponding to maximum microalgae
at various sin values when D¼ 0.1 day�1.
rowth in nitrogen-limited continuous culture, Energy (2014), http://
X. Zhou et al. / Energy xxx (2014) 1e66
productivity reach 27 gNm�3 for a lower dilution rate (D) of0.02 day�1, and 7 gNm�3 for a higher dilution rate (D) of 0.1 day�1,respectively.
4. Conclusions
Microalgae acted as the second generation biofuels could beproduced in quantity with culture technologies in artificial bio-reactors. Modelling microalgae growth is an effective method topredict the growth process, and then estimate the production andhelp to improve the productivity of microalgae under a givenculturing condition at a given site. In this paper, the effects of twoimportant factors (i.e., dilution rate and influent inorganic nitrogenconcentration) on the growth of microalgae in continuous culturehave been investigated. The dilution rate and influent inorganicnitrogen concentration have been shown to have a significant in-fluence on the growth of microalgae in continuous culture. It isfound that in order to obtain a maximum productivity of micro-algae, lower dilution rate is better for a lower influent inorganicnitrogen concentration of 1 g Nm�3 and an optimal dilution rate of0.05 day�1 can be obtained for a higher influent inorganic nitrogenconcentration of 5 g Nm�3. There is an optimal influent inorganicnitrogen concentration corresponding to maximum microalgaeproductivity. The optimal value of the influent inorganic nitrogenconcentration for lower dilution rate of 0.02 day�1 reaching27 gNm�3 is higher than that for higher dilution rate of 0.1 day�1
reaching 7 gNm�3. This paper will guide the researchers to designthe operational parameters in order to improve the microalgaegrowth and produce more microalgae in continuous culture.
(molm�2 s�1)I* conceptual radiation (molm�2 s�1)I average radiation along culture volume (molm�2 s�1)KiI Inhibition coefficient (mol m�2 se1)Ks Half saturation constant (g N me3)L depth of culture (m)p photosynthesis rate (day�1)pm maximum value of p at temperature T (day�1)prefC maximum photosynthesis rate (day�1)
q internal nitrogen cell quota (g N (g C)�1)Q0 minimum nitrogen quota (g N (g C)�1)Q1 maximum nitrogen quota (g N (g C)�1)R respiration rate (day�1)s concentration dissolved inorganic nitrogen, (nitrate or
ammonium)(g Nm�3)sin influent inorganic nitrogen concentration (g Nm�3)t time (day)Topt optimum microalgae growth temperature (�C)
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