Semi-continuous ethanol production in bioreactor from whey with co-immobilized enzyme and yeast cells followed by pervaporative recovery of product – Kinetic model predictions considering glucose repression

Journal of Food Engineering 91 (2009) 240–249

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Semi-continuous ethanol production in bioreactor from whey with co-immobilized enzyme and yeast cells followed by pervaporative recovery of product – Kinetic model predictions considering glucose repression Marek Staniszewski a,*, Wojciech Kujawski b, Małgorzata Lewandowska a a b

´ ski 1, 10-726 Olsztyn, Poland University of Warmia and Mazury, Faculty of Food Science, pl. Cieszyn ´ , Poland Nicolaus Copernicus University, Faculty of Chemistry, ul. Gagarina 7, 87-100 Torun

a r t i c l e

i n f o

Article history: Received 23 January 2008 Received in revised form 29 July 2008 Accepted 27 August 2008 Available online 5 September 2008 Keywords: Mathematical modeling Saccharomyces cerevisiae b-D-galactosidase Ethanol Fermentation Pervaporation

a b s t r a c t Mathematical models for semi-continuous ethanolic fermentation in a whey medium employing coimmobilized Saccharomyces cerevisiae strain and b-D-galactosidase and for pervaporative product recovery from the resultant broth were developed. Kinetic parameters of biomass growth were estimated using the nonlinear least squares method on the basis of experimental data obtained from culture of suspended yeast cells grown in a mixture of glucose and galactose and during semi-continuous fermentation in a bioreactor in a whey medium with co-immobilized enzyme and yeast cells. Experimentally determined fluxes of ethanol and water from broth were applied for the estimation of kinetic constants of ethanol separation by pervaporation. The degree of sugar utilization and ethanol productivity in bioreactor as well as the time of ethanol separation needed to obtain the desired amount of product can be predicted using this model. The influence of selected operating parameters on the fermentation effectiveness was simulated based on the developed model. Ó 2008 Elsevier Ltd. All rights reserved.

1. Introduction The development of ethanol production methods is stimulated by the possibility of using ethanol as a component of biofuels (Poitrat-Ademe, 1999; Zaldivar et al., 2001; Kim and Dale, 2004; Ryan et al., 2006). According to the Act of Biocomponents and Liquid Biofuels enacted by the Parliament of Republic of Poland on August 25, 2006, which has come in force since 2007, Poland permits the content of biocomponents in petrol and diesel oil above 5% v/v. This act is consistent with the Directives on biofuel and biocomponents added to petrol and diesel oil accepted by European Parliament in 2003. One of the factors limiting a wider use of biofuels is the price of the substrate (Mielenz, 2001; Cardona and Sánchez, 2007). Ethanol can be produced by fermentation of raw materials containing carbohydrates or polysaccharides, including whey – one of by-products of dairy industry. Yeast Saccharomyces cerevisiae are capable to produce ethanol up to a level of 19% (v/v) in a special fed-batch culture (Alfenore et al., 2002). The lack of ability of lactose consumption, demonstrated by yeast S. cerevisiae, constitutes an obstacle to using whey as a raw material. This problem can be solved through the enzymatic hydrolysis of lactose with the use of b-galactosidase (Lewandowska and Kujawski, 2007). This meth* Corresponding author. Tel.: +48 89 5233510; fax: +48 89 5233443. E-mail address: [email protected] (M. Staniszewski). 0260-8774/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2008.08.026

od permits direct lactose fermentation with the use of yeast strains of high activity and stability. Another possibility is the use of yeasts capable of lactose utilization, e.g., Kluyveromyces lactis or Kluyveromyces marxianus (Barba et al., 2001; Kourkoutas et al., 2002; Aktas et al., 2006). The simultaneous usage of the enzyme and the yeast cells is possible through its immobilization. Immobilization of b-galactosidase permits to reuse the enzyme thus significantly prolonging the activity of the preparation as compared to native enzyme (Zhou and Chen, 2001; Atesß and Mehmetog˘lu, 1997). The immobilized yeast cultures demonstrate higher cell densities and higher ethanol productivities in comparison to free cells suspensions (Melzoch et al., 1994; Najafpour et al., 2004). The results of the immobilization tests showed that the co-immobilization of b-galactosidase and cells of yeast S. cerevisiae in calcium alginate gel is the most effective way with respect to ethanol productivity (Lewandowska and Kujawski, 2007). The soluble preparations of b-D-galactosidase from Aspergillus oryzae show the maximal activity at the pH 4.5 (Grosová et al., 2008). It was found that the immobilization of the enzyme does not change significantly the pH at which it shows maximal activity in comparison to a native preparation (Haider and Hussain, 2007). b-D-Galactosidase is activated by manganese ions (Vella and Greenwell, 1997). The presence of calcium ions at higher concentrations can deteriorate the activity of the enzyme. As reported by Haider and Hussain (2007), calcium chloride at concentration

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241

Nomenclature a a1 a2, a3 A Am B cI D Dr k0 KI KM KBU KDI KSA KSU L m0 mE mF ms P PE P0 qA qP

exponent in term for inhibition of cells by ethanol, dimensionless kinetic constant of ethanol transport, kg m2 h1 kinetic constants of water transport, kg m2 h1 concentration of galactose in broth, kg m3 area of membrane, m2 concentration of biomass, kg m3 limiting concentration for sugar uptake by cells, kg m3 concentration of dead cells, kg m3 degree of recovery of ethanol from feed, dimensionless specific death rate of cells, h1 inhibition constant of enzyme by substrate, kg m3 Michaelis–Menten constant for enzyme, kg m3 constant in term for glucose repression, kg m3 inhibition constant of biomass by dead cells, kg2 m6 Monod half-saturation constant for biomass on galactose, kg m3 Monod half-saturation constant for biomass on glucose, kg m3 concentration of lactose in broth, kg m3 initial mass of ethanol in feed, kg mass of ethanol in feed, kg mass of feed, kg maintenance factor, kg kg1 h1 ethanol concentration in broth, kg m3 ethanol productivity, kg h1 ethanol concentration at which cells stop growth, kg m3 rate of galactose consumption, kg kg1 h1 rate of product formation, kg kg1 h1

of 5% w/v decreases nearly twice the activity of soluble b-D-galactosidase. On the other hand, the immobilization of the enzyme increases its resistance for calcium cations. S. cerevisiae strains are able to assimilate a wide range of carbon sources, though hexoses, e.g., glucose, fructose or mannose (Carlson, 1998) are preferred. The growth and metabolism of yeast are regulated by the carbon source. The phenomenon of inactivation of several enzymes in yeast by glucose is known as catabolite repression (Gancedo and Gancedo, 1985; Belinchón and Gancedo, 2003). The presence of transporter proteins plays important role in the yeast metabolism due to glucose transported into cells by facilitated diffusion (Weirich et al., 1997; Carlson, 1998). It is known that glucose induces some genes, including those encoding glucose transporters, depending on varying glucose levels, and represses others involved in the utilization of other carbon sources (Carlson, 1999). As a consequence, if the culture medium contains a mixture of carbohydrates, e.g., glucose and galactose, sugars are consumed by yeast sequentially prolonging the time of fermentation (Gutierrez et al., 1993; Dynesen et al., 1998). One of the directions of investigations aimed at overcoming this problem is an application of metabolic engineering for developing of glucosederepressed strains (Olsson and Nielsen, 2000). Another way would be screening experiments with wild-type strains of S. cerevisiae aimed at identifying strains with exceptional fermentation activity (Keating et al., 2004). Pervaporation is one of the techniques employed in order to remove ethanol from the post-fermentation liquid. It is a membrane separation technique, which is generally applied to separate liquid mixtures (Fleming and Slater, 1992; Karlsson and Trägårdh, 1993; Koros et al., 1996; Böddeker, 1990; Néel, 1991; Kujawski, 2000a). Due to the mechanism of separation, this technique permits also the fractionation of mixtures at azeotropic composition. In this

qU R RPDM r rmax SSR s t U V VB VR xE YBAmax YBUmax YPSmax

rate of glucose consumption, kg kg1 h1 correlation coefficient, dimensionless relative percentage deviation modulus, % rate of enzymatic reaction, kg h1 maximal rate of enzymatic reaction, kg h1 sum of squared residuals, kg2 m6 standard deviation time, h concentration of glucose in broth, kg m3 volume of broth in bioreactor, m3 volume of carrier, m3 volume of broth removed from bioreactor after production cycle, m3 mass ratio of ethanol in feed, dimensionless maximal yield coefficient for biomass on galactose, kg kg1 maximal yield coefficient for biomass on glucose, kg kg1 maximal yield coefficient for product, kg kg1

Greek symbols g ratio of ethanol productivity and theoretical productivity (equal to 0.538 kg of ethanol per 1 kg of lactose), % lA specific growth rate of cells on galactose, h1 lU specific growth rate of cells on glucose, h1 lmax maximal specific growth rate of cells, h1 n ratio of mF and Am, kg m2 u function describing inhibition of cells growth, dimensionless v ratio of molecular masses MGlu/MLac, dimensionless

method, the feed is located on one side of the non-porous polymeric membrane whereas the permeate is received as a vapor on the other side, into a vacuum (vacuum pervaporation) or into a stream of an inert gas (sweeping gas pervaporation) (Böddeker, 1990; Néel, 1991). The separation of vapors and liquids through non-porous membranes results from the differences in the sorption and diffusion of mixture components in the polymeric material of a membrane. When applied on an industrial scale, pervaporation appears to be a competitive approach in relation to traditional methods (O’Brien et al., 2000; Kujawski and Lewandowska, 2005). Models of continuous ethanolic fermentation of lactose medium by the use of the strain Candida pseudotropicalis (Ghaly and El-Taweel, 1997) and sucrose medium by the strain S. cerevisiae (Oliveira et al., 1999a, 1999b, 2000) have been developed. The model presented by Ghaly and El-Taweel (1997) for fermentation of supplemented whey considered the influence of following parameters: substrate limitation, substrate inhibition, ethanol inhibition and cells death. In the model published by Oliveira et al. (2000) for tower bioreactor with cells recycling fed by sugar cane juice the following key points were taken into account: substrate limitation, inhibition related to ethanol and biomass, absence of fermentation in the settler and irreversible cell inactivation. In our former paper (Staniszewski et al., 2007) the model developed for batch fermentation of lactose medium in bioreactor with co-immobilized b-galactosidase and S. cerevisiae yeast cells has been presented. The aim of the present study was to develop the mathematical model of bioreactor describing a semi-continuous ethanol production from whey with co-immobilized enzyme and yeast cells considering consecutive sugars utilization, as well as an attempt to improve the predictability of the model of ethanol concentration by the pervaporation technique. The formulated models would

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enable the prediction of the level of the ethanol as well as the productivity for the successive fermentation cycles and the separation time, with the assumed final concentration of the product recovered from the given volume of broth from bioreactor. 2. Materials and methods 2.1. Batch fermentations on mixed-substrate medium In fermentation experiments commercial yeast strain S. cerevisiae B4 originating from the collection of the Independent Distillery Laboratory in Bydgoszcz, Poland was used. Yeasts were conducted on YPG (2% of glucose) slants at 30 °C (Lewandowska and Kujawski, 2007). The batch fermentations of yeasts cells suspension were performed in glass vessels of volume 250 cm3 on the medium contained both glucose (6% w/w) and galactose (4% or 6% w/w) – the other compounds was the same as in liquid YPG medium. D-(+)Glucose and D-(+)galactose were purchased from Sigma Co. (USA). The culture medium was sterilized at 121 °C for 20 min. During culturing the biomass concentration was determined every 6 h by weighing the dried samples of broth. The glucose and galactose were analyzed quantitatively by gas chromatography (GC-14A, Shimadzu Co., Japan) as silyl derivatives (Halpern et al., 1967). The experiment was performed in duplicate. 2.2. Substrate for semi-continuous fermentation The solution of dried milk permeate from ultrafiltration (Dairy Plant in Wolsztyn, Poland) was used for preparation of a substrate for the semi-continuous fermentation. The concentration of lactose in the substrate was 12% w/w. pH of the substrate was adjusted to 4.7 with HCl solution. After deproteinization, the substrate was supplemented with (NH4)2SO4 and yeast extract and then it was pasteurized at 80 °C for 20 min. Composition and detailed procedure of preparation of substrate were published by Lewandowska and Kujawski (2007). 2.3. Biocatalyst preparation For preparing of biocatalyst applied in the fermenter a commercial preparation of b-D-galactosidase (Sigma Co., USA) and a commercial yeast strain S. cerevisiae B4 (Independent Distillery Laboratory in Bydgoszcz, Poland) were used. The enzyme, crosslinked with glutaraldehyde, and yeast cells were entrapped in sodium alginate gel (2% w/w) as described in Lewandowska et al. (2003). The alginate beads were hardened with calcium chloride solution and stored at pH 4.7. 2.4. Fermentation/pervaporation set-up for semi-continuous process The experimental set-up for semi-continuous conversion of lactose into ethanol consisting of a fermenter and pervaporation unit was presented by Lewandowska and Kujawski (2007). Ethanol formed in the bioreactor was then recovered from the broth and concentrated in the pervaporation unit (Fig. 1). The volume of fermenter was 5 dm3. Every 48 h a part of broth (4 dm3) was withdrawn from the fermenter and replaced by fresh whey medium prepared as described above. The temperature in the fermenter was maintained at 30 °C by water circulation through internal heat exchanger. The flow of broth through the layer of biocatalyst was forced by a peristaltic pump (Watson-Marlow 501 RL, United Kingdom). During fermentation pH, extract, released carbon dioxide and ethanol content were controlled (Lewandowska and Kujawski, 2007). The experiment has been finished after 20 days of fermentation.

The broth removed from bioreactor was transferred for concentration of product into an intermediate tank, which was heated to 65 °C. Recovery and concentration of ethanol from broth were carried out in a laboratory pervaporation unit (membrane area 170 cm3) working in a vacuum pervaporation mode (Kujawski, 2000b). The pressure on the permeate side was kept below 2 hPa by using a vacuum pump. Permeate vapours were frozen out in the glass trap by using liquid nitrogen. A PDMS–PAN–PV composite membrane (Pervatech B.V., the Netherlands) made of poly(dimethylsiloxane) on poly(acrylonitrile) support was used in the pervaporation unit. The permeate fluxes were determined by weighing the sample of permeate collected over a given period of time. The ethanol content in the feed and the permeate was determined by gas chromatography (Varian 3300, Varian Inc., USA) as described by Kujawski (2000b). 3. Mathematical model 3.1. Kinetics of enzymatic hydrolysis of lactose Enzymes efficiently catalyze different kind of reactions at temperature not higher than 50 °C and at pH close to neutral. A characteristic feature of enzymes is their high specificity towards selected substrates. However, the main disadvantage of the use of enzymes is their high sensitivity to inhibitors and denaturing agents present in the reaction environment is (Dixon and Webb, 1958). The immobilization of enzymes preparations can improve their stability against these factors prolonging the time of practical use (Grosová et al., 2008; Haider and Hussain, 2007). To describe the kinetics of enzymatic hydrolysis of lactose with the participation of b-D-galactosidase, the extended Michaelis– Menten scheme, including competitive inhibition, was employed (Steinfeld et al., 1999):

E þ S () ES ) products

ð1Þ

EI () E þ I

ð2Þ

In Eqs. (1) and (2), E is an enzyme, S is a substrate, ES and EI are enzyme–substrate and enzyme–inhibitor complexes. The reaction rate depends on the concentration of both the substrate and the inhibitor. By using the quasi-stationary approximation for that scheme and considering that in the investigated system, the lactose acts as a competitive inhibitor (Zárate et al., 2002), one obtains the following expression for the rate of enzymatic hydrolysis related to lactose concentration:

rðLÞ ¼

r max L K M ð1 þ KLI Þ þ L

ð3Þ

where KM is a Michaelis–Menten constant for a given enzyme and rmax is a maximal reaction rate. Details of derivation of Eq. (3) have been presented in Staniszewski et al. (2007). 3.2. Kinetics of growth of immobilized cells The biomass growth rate depends on the prevailing environment conditions (pH, temperature, presence of nutrients and growth factors) including instantaneous medium composition. The maximum growth is observed at a strictly specified, for a given species, concentration of the substrate. Its increase over this value results in biomass growth inhibition because of the growing osmotic pressure of the fermentation medium (González-Bernáldez et al., 1968). After exceeding a certain level of a main product concentration, a complete inhibition of growth occurs (Schlegel, 1992). In the case of immobilized microorganisms, products of cells degradation accumulated in a carrier cause also an inhibitory effect.

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substrate

CO 2

1 4 3 2

6 5

Fig. 1. Schematic drawing of fermentation/pervaporation system. 1 – Fermenter, 2 – vessel with biocatalyst, 3 – intermediate tank, 4 – pervaporation unit, 5 – product receiver, 6 – vacuum pump.

The original Monod’s model of cell growth (Monod, 1949) was the basis for developing a new pseudomechanistic model considering catabolic repression of galactose for immobilized S. cerevisiae cells operating in long-term semi-continuous process. According to this model the proper cell growth rate lU associated with the utilization of glucose by yeasts is related to the maximum specific rate of microbial growth (lmax) and the half-saturation constant of glucose (KSU) as presented below (Eq. (4))

lU ðU; P; DÞ ¼ lmax

U uu K SU þ U P D

ð4Þ

U denotes concentration of limiting substrate, i.e. glucose. The value of KSU, corresponding to efficiency of microorganism in substrate uptake, can vary with the strain used. Functions uP, uD represent the effects of other compounds of the broth on the biomass production inside the carrier. uP is a function describing the inhibition of cell growth by ethanol according to an exponential relationship (Eq. (5)) (Levenspiel, 1980)



uP ðPÞ ¼ 1 

P P0

a ð5Þ

In Eq. (5) P0 is a concentration of product entirely inhibiting the growth of cells. To describe the drop of fermentation activity observed during semi-continuous process, the following term was incorporated into Eq. (4):

uD ðDÞ ¼

K DI K DI þ D2

ð6Þ

The value of KDI parameter characterizes the inhibition effect of toxic products of cells degradation on biomass growth which correspond to losses of cell viability in the carrier. D is the concentration of cells debris accumulating in the biocatalyst beads with the rate equal to the cell death rate of first order kinetics – related to k0 parameter and biomass concentration B. The value of an exponent at D variable in Eq. (6) has been established as a result of test calculations performed in order to obtain the best conformity with an experiment. As a consequence of catabolic repression in presence of glucose growth rate lA associated with the utilization of galactose is also the function of glucose concentration if a mixture of substrates is used. The sequential assimilation of substrates was modeled by introducing the function uU

uU ðUÞ ¼

K BU K BU þ U

ð7Þ

The value of KBU parameter represents the level of glucose below that the consumption of galactose by cells is repressed. Thus, the equation for growth rate lA is as follows:

lA ðA; U; P; DÞ ¼ lmax

A uu u K SA þ A P D U

ð8Þ

In Eq. (8), KSA is the half-saturation constant of galactose. A denotes concentration of galactose. The above model neglects the effect of substrate inhibition, however, it was proved that the use of the Andrew’s model did not improve significantly the ability for fitting of experimental data. 3.3. Rate of substrate utilization and product formation Considering the composition of the investigated system the rates of glucose and galactose utilization by cells qU, qA calculated per unit of biomass concentration are defined by the following equations:

U lU þ U þ cI Y BUmax A l u þ A qA ðA; U; B; P; DÞ ¼ ms A þ cI U Y BAmax qU ðU; B; P; DÞ ¼ ms

ð9Þ ð10Þ

where ms is a substrate utilization rate directed towards maintenance of the vital processes of cells, and YBUmax, YBAmax are yield coefficients of the biomass for glucose and galactose, respectively. The following modifications, in comparison to classical relationship (Solomon and Erickson, 1981), have been considered. In the equation for qA (Eq. (10)) the term uU, corresponding to the effect of catabolic repression on the assimilation of galactose (non-associated with growth) of the same form as in Eq. (8), was included. MoreU A (Eq. (9)) and Aþc (Eq. (10)) were incorporated. over, the terms Uþc I I Thanks to that, at a substrate concentration below value of cI the rate of sugars uptake by cells approaches zero preventing negative values of concentrations occurring on entire utilization of substrate during solving model equations. The product formation rate qP is related to utilization rate of both sugars, i.e. glucose and galactose and is expressed as follows:

qP ðU; A; B; P; DÞ ¼ ðqU þ qA ÞY PSmax

ð11Þ

where YPSmax is the yield coefficient of the product. Eqs. (4)–(11) define the non-structured model of growth kinetics of immobilized S. cerevisiae cells. This model needs the estimation of less number of parameters as well as control of less number

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of variables in comparison to known structured models (Lei et al., 2001). 3.4. Model equations for the fermentation A mathematical model of the conversion of lactose into ethanol taking place in a bioreactor was obtained by combining Eqs. (3)– (11). The assumption made was that the enzymatic hydrolysis of lactose and ethanol formation by yeast are localized inside the carrier. The model derived from the mass balance of the bioreactor has the form of a set of ordinary differential equations describing time derivatives of component concentrations in broth and biocatalyst

dL r ¼ dt V þ VB dU rv VB  qU B ¼ dt V þ VB V þ VB dA rv VB  qA B ¼ dt V þ V B V þ VB dP VB ¼ qP B dt V þ VB dB ¼ ðlU þ lA ÞB  k0 B dt dD ¼ k0 B dt

4. Evaluation of model parameters

ð12Þ

4.1. Kinetic parameters of lactose hydrolysis

ð13Þ

Fig. 2 presents the progress of lactose hydrolysis (12% w/w) catalyzed with immobilized b-D-galactosidase. The enzyme (0.6 g) was cross-linked with glutaraldehyde and entrapped in alginate gel according to procedure described above. The solid line shows the kinetics of hydrolysis predicted by using Eq. (12) (R2 = 0.9954). In calculations the values of b-D-galactosidase kinetic constants (KM = 78.7 kg m3, KI = 68.4 kg m3) taken from published data by Matioli et al. (2003) were applied. The value of rmax (Eq. (3)) for the immobilized enzyme, found by the fitting of experimental data, was then used for the modeling of the kinetics of the fermentation process.

ð14Þ ð15Þ ð16Þ ð17Þ

where V is the volume of liquid circulating in the bioreactor and VB is a volume of the carrier (alginate beads). The solution of this system of equations needs the use of numerical methods due to the non-linearity of terms representing the reaction kinetics and fermentation kinetics. Eqs. (12)–(17) allow us to calculate the concentrations of the sugar, ethanol and biomass during fermentation for the given initial conditions. The solutions for the semi-continuous operation with partial withdrawal of broth and supplying fresh culture medium were obtained as a result of integration of set of initial value problems for successive fermentation cycles. The calculations were done with the use of backward differentiation method (Stoer and Bulirsh, 1983; Ceynowa et al., 1997; Staniszewski, 1999). 3.5. Model equations for the pervaporative ethanol separation In the pervaporation technique the rate of ethanol transport through a membrane is a function of the instantaneous composition of the feed. This function is dependent on the membrane properties. To obtain more accurate equations the model assumptions made by Staniszewski et al. (2007) have been modified. The kinetics of the separation process of ethanol from post-fermentation broth (with initial ethanol content of 6% v/v), was described by the following equations:

dmE ¼ a1 xE Am dt dmF ¼ ðða1 þ a2 ÞxE þ a3 ÞAm dt

intercept of the dependency of observed water flux on xE, respectively. The values of coefficients a1, a2, a3 expressed in [kg m2 h1] depend on the membrane properties. The above equations were used for all separation experiments done with broth obtained in successive fermentation cycles. Eqs. (12)–(19) permit the prediction of ethanol concentration obtained in semi-continuous fermentation as well as the concentration of the removed ethanol in the permeate and the time needed to remove the assumed amount of EtOH. The model presented here can help in process optimization for a selected criterion and in project calculations.

ð18Þ ð19Þ

Time derivatives of the ethanol mass in a feed (dmE/dt) and the feed mass (dmF/dt) are related to the mass ratio of ethanol in the feed (xE). It was assumed, with good agreement to experimental data, that fluxes of ethanol and water are linear functions of ethanol content in a feed and the effect of other compounds can be neglected. The deviation from the linearity was observed at the beginning of transport experiments only, for time not exceeding 1 h. This phenomenon can be attributed to the transient period of transport under non-stationary conditions. The a1 coefficient denotes the slope of the dependency of observed ethanol flux on the mass ratio of ethanol in the feed (xE). The a2, a3 coefficients denote the slope and the

4.2. Kinetic parameters of fermentation For determining the values of model parameters KSU, KSA, KBU,

lmax, k0, m0, YBUmax and YBAmax (Table 1) the experimental data obtained in free cells cultures of S. cerevisiae B4 strain were applied (Fig. 3). For better recognition of the effect of catabolic repression of glucose on the growth of yeast used, experiments were carried out at different initial ratios of glucose to galactose in the culture medium. The estimation of values of the parameters was done by the Nelder-Mead method (Kre˛glewski et al., 1984) and using Eqs. (13)–(17) to minimize the deviation between the predicted values and the experimental data. The minimized function was a sum of squared residuals (Eq. (20)).

SSR ¼

m X n  2 X ðeÞ ðpÞ Y ij  Y ij i¼1

ð20Þ

j¼1

In Eq. (20) Yij(e) denotes an experimental value, Yij(p) denotes a predicted value, n is the number of observations, and m is the number

Degree of lactose hydrolysis [%]

244

100

80

60

40

Experiment

20

Model

0 0

12

24

36

48

Time [h] Fig. 2. Kinetics of lactose hydrolysis catalyzed by b-D-galactosidase immobilized in calcium alginate (12% w/w of lactose).

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The meanings of symbols: Yi(e) is an experimental value, Yi(p) is a predicted value, and n is the number of observations.

Table 1 Values of kinetic parameters in the fermentation model Parameter KM KI

lmax KSU KSA KBU a P0 KDI k0 m0 YBUmax YBAmax YPSmax

Value 1

7.87  10 6.84  101 3.39  102 6.04  100 1.20  101 9.03  100 6.0  101 6.4  101 1.31  103 5.02  103 1.52  102 1.32  102 2.63  102 4.45  101

Standard deviation

Unit

– – 3.5  104 4.7  101 5.0  101 6.5  101 – – 2.4  101 4.0  105 2.1  103 3.4  104 3.6  104 1.1  103

kg m3 kg m3 h1 kg m3 kg m3 kg m3 – kg m3 kg2 m6 h1 kg kg1 kg kg1 kg kg1 kg kg1

of process variables. Then the other parameters of biomass growth, i.e. KDI and YPSmax (Eqs. (6) and (11)), were determined by the same method using values of parameters found previously, and applying the experimental data obtained in a semi-continuous fermentation in a bioreactor with the co-immobilized b-D-galactosidase and yeast cells of S. cerevisiae B4 (Table 2). The values of a and P0 (Eq. (5)) were taken from our earlier work (Staniszewski et al., 2007). The accuracy of fitting was characterized by two indices: the determination coefficient (R2) and the RPDM (relative percentage deviation modulus). RPDM was calculated according to ðeÞ ðpÞ n jY i  Y i j 100 X RPDM ¼ ðeÞ n i¼1 Yi

ð21Þ

4.3. Kinetic parameters of ethanol removal from fermentation broth The kinetic constants of ethanol separation from post-fermentation broth by the pervaporation method (Table 5) were found by applying the experimentally determined fluxes of permeate together with its composition (Kujawski and Lewandowska, 2005; Lewandowska and Kujawski, 2007). The parameters a2, a3 (Eqs. (18) and (19)) were determined by the linear regression based on the dependency of water flux on the feed composition determined experimentally for each separation experiment. Then the value of a1 parameter was determined by the Nelder-Mead method (Kre˛glewski et al., 1984) using Eqs. (18) and (19) and values of degree of recovery of ethanol Dr calculated from experimental data as

Dr ¼

ð22Þ

In Eq. (22) symbols denote the initial (m0) and the remaining (mE) mass of ethanol in a feed. 5. Results and discussion 5.1. Influence of sugars ratio in multi-substrate culture medium on fermentation kinetics The experimental values of sugars concentrations in the batch fermentations with non-immobilized cells of S. cerevisiae B4 and also the values calculated based on Eqs. (13)–(17) are shown in

70

4

Concentration [kg m-3]

60

Concentration [kg m-3]

m0  mE m0

50 40

Glucose Galactose Model

30 20 10

3

2

Biomass

1

Model 0

0 0

12

24

36

48

60

72

0

84

12

24

48

60

72

84

4

70

Glucose Galactose Model

60 50

Concentration [kg m-3]

Concentration [kg m-3]

36

Time [h]

Time [h]

40 30 20 10

3

2

Biomass

1

Model 0

0 0

12

24

36

48

Time [h]

60

72

84

0

12

24

36

48

60

72

84

Time [h]

Fig. 3. Kinetics of sugar utilization and growth of S. cerevisiae B4 in a suspension on a medium containing glucose and galactose. The lines were calculated with the same set of parameters (Table 1) for each experiment. Error bars represent mean standard deviation for all samples.

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Table 2 Comparison of values of fermentation indices obtained from semi-continuous experiment and predicted by the model Fermentation time [h]

Ethanol concentration P [% v/v]

Fermentation efficiency g [%]

Experimentala

Calculated using the model

Experimentala

Calculated using the model

48 96 144 192 240 288 336 384 432 480 Mean

3.26 4.97 5.40 4.53 5.37 6.19 5.22 4.28 3.42 2.98 4.56

3.43 4.93 5.45 5.49 5.38 5.08 4.65 4.17 3.71 3.19 4.55

27.2 41.4 45.0 37.7 44.7 51.6 43.5 35.7 28.5 24.8 38.0

28.6 41.1 45.4 45.8 44.8 42.4 38.7 34.8 30.9 26.6 37.9

a

Taken from Lewandowska and Kujawski (2007).

Fig. 3. The values of R2 found for the first experiment (6% of glucose, 6% of galactose) were as follows – 0.9893 (glucose), 0.8109 (galactose), 0.9486 (biomass). For the second one (6% of glucose, 4% of galactose) the values were equal to 0.9670, 0.6824 and 0.8891, respectively. In both experiments the glucose is utilized entirely during 30 h. The galactose is consumed slower what was also observed by other researchers (Ramakrishnan and Hartley, 1993). By comparison the kinetic parameters, the twice higher biomass yield on galactose and the seven times higher utilization rate of glucose is found. Similar differences in growth parameters were observed by Ostergaard et al. (2000). In the first experiment, for equimolar mixture of glucose and galactose in the medium, the sequential substrate utilization occurs what corresponds to diauxic growth. From the literature data the level of glucose causing the catabolite repression for S. cerevisiae was found to be 5 kg m3 (Dynesen et al., 1998). This value is comparable to that estimated in our calculations (KBU = 9.0 kg m3). However, it looks that for initial molar ratio of glucose to galactose 3:2 the utilization of both sugars occurs simultaneously. The ethanol content in the broth (4.24% v/v) determined after 24 h of fermentation also proves the partial utilization of galactose by yeast in spite of non-entire glucose assimilation. This is the reason of worse model predictions of the galactose and biomass concentrations for the second experiment. The explanation of this phenomenon needs more detailed studies with the strain B4. From results obtained by Ramakrishnan and Hartley (1993) it is known that repression of enzymes involved in galactose utilization depends also on galactose or lactose level – entire repression of galactokinase was observed at glucose level 5% w/w. However, considering the modeling of semi-continuous process it should be pointed out that the first experiment is more representative with respect to the substrate composition in the bioreactor. 5.2. Influence of operating conditions on dynamics of semi-continuous fermentation The experimental values of ethanol concentration and fermentation efficiency in the bioreactor during 20 days (10 cycles) of semicontinuous fermentation of whey medium (12% w/w of lactose) and also the values calculated based on Eqs. (12)–(17) are presented in Table 2. The ethanol concentration in broth drained from bioreactor increases reaching the maximal value of 6.19% in 6th cycle. In further cycles, the productivity of biocatalyst showed diminishing trend – down to 2.98% in the last cycle. Similar results were obtained with yeast C. pseudotropicalis immobilized in porous agar for fermentation of 10–12% lactose (Szczodrak et al., 1997). The

maximal ethanol concentration reached was 4.15–4.37% and then the drop of yeasts activity was observed in the subsequent cycles. The gradual decrease in the ethanol productivity was also observed by Wendhausen et al. (2001) in backed bed reactor with Saccharomyces sp. adsorbed onto chrysotil during 50 days continuous fermentation with the sugar cane syrup as a substrate (33% w/v). The ability of model for fitting experimental data is characterized by the values of relative percentage deviation modulus RPDM = 7.53% and correlation coefficient R2 = 0.7420. The trend of the fermentation efficiency calculated from the model differs from experimental findings in 8–10 days of fermentation. The model predicts the maximum in 4th cycle whereas during experiment the drop of ethanol productivity was observed after 3rd cycle and then the ethanol concentration in broth increased until its maximal value obtained in 6th cycle of fermentation (Table 2). This phenomenon can be explained by the change in cell distribution in the interior of biocatalyst beads or by growth of cells on the surface of carrier occurring after 3rd cycle. As seen in Table 2, the mean values of ethanol concentration and ethanol yield calculated from the model are close to the values found in the experiment. Mean productivity of ethanol calculated for 20 days of fermentation was 3.80  103 kg h1, whereas the value predicted by model is equal to 3.79  103 kg h1. With the help of the formulated model, the effect of selected process factors on the production rate of ethanol was analyzed. Two factors conditioning the fermentation effectiveness were chosen – cycle length and volume of broth removed after the cycle. The results of bioreactor dynamics on the basis of Eqs. (12)–(17) are shown below. The model predictions of the influence of cycle length of fermentation on the ethanol yield and productivity are presented in Table 3. The calculations were done for the lengths 24 h, 48 h and 96 h. The volume of broth removed from bioreactor was the same as in the experiment (4 dm3). The increase in the cycle length causes an increase in the mean ethanol concentration of broth from 3.36% to 5.32% resulting from higher sugars utilization, as expected. It should be note that high ethanol concentration in broth is preferable for pervaporative concentration of the product. However, the increase in ethanol concentration does not improve fermentation productivity. Mean productivity of ethanol, calculated

Table 3 Effect of cycle length on the ethanol production rate in the bioreactor predicted by the model Fermentation time [h]

Ethanol concentration P [% v/v] Cycle 24 h

24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 384 408 432 456 480 Pmean [% v/v] PE [kg h1]

1.57 2.85 3.78 4.43 4.86 5.05 5.06 4.95 4.73 4.44 4.12 3.77 3.39 2.99 2.60 2.24 1.93 1.67 1.44 1.25 3.36 0.00559

Cycle 48 h

Cycle 96 h

3.43 4.93

5.13

5.45 5.49

5.60

5.38 5.08

5.59

4.65 4.17

5.39

3.71 3.19 4.55 0.00379

4.89 5.32 0.00222

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M. Staniszewski et al. / Journal of Food Engineering 91 (2009) 240–249 Table 4 Effect of volume of broth removed from bioreactor on the ethanol production rate predicted by the model

therefore this value of VR was the highest one in the discussed range.

Fermentation time [h]

5.3. Kinetic of ethanol removal from fermentation broth

Ethanol concentration P [% v/v]

48 96 144 192 240 288 336 384 432 480 Pmean [% v/v] PE [kg h1]

VR = 4.0 dm3

VR = 3.5 dm3

VR = 3.0 dm3

3.43 4.93 5.45 5.49 5.38 5.08 4.65 4.17 3.71 3.19 4.55 0.00379

3.43 4.96 5.45 5.50 5.41 5.18 4.83 4.42 4.00 3.56 4.67 0.00341

3.43 4.99 5.46 5.50 5.43 5.26 4.99 4.66 4.29 3.92 4.79 0.00300

over 480 h of process, drops over twice from 5.59  103 kg h1 to 2.22  103 kg h1 (Table 3). The volume of broth removed after cycle (VR) also influences on the kinetics of semi-continuous fermentation. The results of analysis of the effect of the volume VR in the range 3–4 dm3 on the ethanol productivity is shown in Table 4. In the calculations a cycle length equal to 48 h was assumed. Mean ethanol concentration exhibits a small increase from 4.55% to 4.79% with the decrease of value of VR by 1 dm3. In spite of increase in the ethanol content in the broth the productivity of ethanol calculated for 480 h of process decreases by 20% from 3.79  103 kg h1 to 3.00  103 kg h1 (Table 3). Due to bioreactor construction increasing the volume of the removed broth over 4 dm3 is not possible,

The selected experimental results presenting the kinetics of ethanol recovery from the post-fermentation broth by pervaporation and the values of the degree of recovery of ethanol Dr predicted by the model (Eqs. (18) and (19)) are seen in Fig. 4. The initial ethanol concentration in the broth (cycle 1) was 3.26% w/w (Table 2). For the PDMS–PAN–PV membrane, the following values of kinetic parameters were found: a1 = 21.6 kg m2 h1, a2 = 25.5 kg m2 h1 and a3 = 2.41 kg m2 h1 (n = 118 kg m2). The value of correlation coefficient R2 = 0.9999 indicates the good conformity of model prediction with the experimental data. Similar conformity was achieved for the experiment with broth produced in cycle 3 (R2 = 0.9997, initial ethanol content in the feed 5.4% w/w). For remaining experiments presented in Fig. 4 the convergence was clearly weaker. For broth from cycle 6 and 10 the position of line calculated from Eqs. (18) and (19) and the trend of experimentally determined degrees of recovery of ethanol are divergent at high values of Dr. As seen in Table 3 the values of a1 and a3 parameters do not differ very much regardless of initial ethanol content in the feed. It should be noticed that the a1 parameter is strictly related to the selectivity coefficient of ethanol transported from broth. The constancy of a1 parameter confirms the stability of separation ability of the membrane in the long-term experiment. The values of a2 parameter found for the 3rd, 6th and 10th cycle were equal to zero (Table 5), contrary to the non-zero value found for the broth produced at the beginning of fermentation. The value close to zero

100

100

Cycle 3

80

80

60

60

Dr [%]

Dr [%]

Cycle 1

40

40

Experiment

20

Experiment

20

Model

Model

0

0 4

0

8

12

4

0

Time [h]

12

100

100

Cycle 6

Cycle 10

80

80

60

60

Dr [%]

Dr [%]

8

Time [h]

40

40

Experiment

Experiment

Model

20

Model

20

0

0 0

8

4

Time [h]

12

0

8

4

12

Time [h]

Fig. 4. Kinetics of ethanol recovery from the fermentation broth by the vacuum pervaporation technique with the PDMS–PAN-PV membrane.

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Table 5 Values of parameters in the model of pervaporative ethanol concentration Cycle

1 3 6 10

Total time of membrane work [h] 11 33 67 111

by changing the length of production cycle only, though with a decrease in the concentration of recovered product.

Parameter ± s [kg m2 h1] a1

a2

21.6 ± 0.61 25.5 ± 1.79 19.2 ± 0.85 0.64 ± 0.60 20.7 ± 0.93 0.60 ± 0.48 23.4 ± 0.94 1.20 ± 1.00

a3 2.41 ± 0.029 2.46 ± 0.015 2.48 ± 0.015 2.25 ± 0.016

means that the flux of water was independent of instantaneous ethanol concentration in the feed during separation. This observation indicates a change of transport properties of the membrane in consecutive separation experiments. The change in the value of a2 parameter can be attributed to the decrease in hydrophobicity of the membrane caused by a change of morphology of polymer matrix under the influence of contact with the broth containing electrolytes, i.e. phosphates. However, it should be note that the scale of this change does not bring about a deterioration in the effectiveness of product recovery. Another factor affecting transport rate is a fouling of the membrane surface by a gel layer of proteins originating from the broth. Fouling of the surface increased the transient non-stationary stage of transport for 10–20 min (Fig. 4, cycle 6 and 10). However, this effect did not influence the selectivity of the membrane. The average fluxes of permeate measured in separation experiments reached 2.9 kg m2 h1, and the mean ethanol concentration in the permeate was in the range 10.5–20.5% w/w depending on the initial content of ethanol in the broth. The removal of 90% ethanol (n = 118 kg m2) occurred during the time shorter than 12 h. 6. Conclusions The use of microorganisms as catalysts can be an interesting alternative for technologies currently used in processes of practical importance, e.g. in waste treatment. The progress in the modeling of metabolism of living cells is of essential importance in the design of processes involving these microorganisms. The knowledge of specific behavior of microorganisms with respect to operating parameters is the basis for the choice of optimal conditions guarantying reasonable productivity of the system. The separation technique used for purification of product influences the economics of the process. Modeling of the system coupled with experimental investigation permits better planning of experiments needed for system design. The results of the performed investigations lead to the following conclusions: 1. Two different models were formulated and tested: a mathematical model describing semi-continuous fermentation of lactose to ethanol with the use of co-immobilized b-D-galactosidase and S. cerevisiae yeast cells, and a model for the recovery of ethanol from the fermentation broth by pervaporation. The models can be used to predict the influence of process parameters on the productivity of the fermentation/pervaporation system. 2. The incorporation of glucose repression effect exhibited by S. cerevisiae yeast in kinetics of fermentation enhances the applicability of the developed model. However, the results of performed experiments need for further investigations of the growth of the yeast strain B4 on mixture of sugars. The kinetics of the sugars utilization has a special meaning for a semi-continuous fermentation of lactose with a periodical supply of a substrate. Model predictions point to the possibility of enhancing the bioreactor output

3. The kinetic coefficients of the ethanol concentration process by pervaporation in successive experiments suggest a change in transport properties of the tested membrane. However, this phenomenon has no effect on the selectivity of the membrane. The presence of mineral salts affects transport rate of permeate through the membrane in pervaporative separation of mixtures (Kujawski and Krajewski, 2007). The exploration of the influence of the minor compounds of the broth on the product concentration needs also further investigations.

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