Modelling thermophilic cheese whey bioremediation in a one-stage process

Biochemical Engineering Journal 35 (2007) 281–288

Modelling thermophilic cheese whey bioremediation in a one-stage process M.R. Kosseva b,∗ , A. Fatmawati c , M. Palatova d , C.A. Kent a a

Department of Chemical Engineering, The University of Birmingham, Edgbaston B15 2TT, Birmingham, UK b School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland c Chemical Engineering Department, The University of Surabaya, Jl. Raya Kalirungkut, Surabaya 60292, Indonesia d Department of Computing and Control Engineering, Institute of Chemical Technology Prague, 166 28 Prague 6, Czech Republic Received 22 June 2006; received in revised form 19 January 2007; accepted 20 January 2007

Abstract A one-stage bioremediation process for the treatment of cheese whey has been developed, involving use of a mixed population including Bacillus sp. isolated from fruit–vegetable wastes, at elevated temperatures (55, 60, 65 ◦ C), in an aerated system. Based upon a reaction scheme which combined the activities of Lactococcus sp. and thermotolerant yeasts, found in unpasteurised whey, with that of a thermophilic Bacillus sp., we modelled this process using mass balances for a batch culture. We obtained adequate fits to experimental data by simulating the biodegradation of whey components and consequent biomass growth rates using models containing one “lumped” biomass and three “equivalent” substrates (lactose, lactic and acetic acids), with a further simplification of biomass specific growth rate into one constant, “pseudo-exponential” value over the batch. Values of “best fit” model parameters were generated to predict biomass specific growth rates. The average specific growth rate calculated from the models was 0.075 h−1 whilst the experimental one was 0.088 h−1 . The results obtained suggest that temperature may be of greater importance to the biodegradation process than dissolved oxygen, as the composition of the microbial community changed with temperature within the range 55–65 ◦ C. High COD removal efficiencies were achieved: up to 93% at 55 ◦ C, and up to 70% at 65 ◦ C. Our investigations suggest that modelling of complex bioreaction systems via “lumping” of key substrates and microbial species into a limited number of “equivalent clusters” is worthy of consideration as a possible means of facilitating rapid process development and practical process operation. © 2007 Elsevier B.V. All rights reserved. Keywords: Aerobic processes; Bioremediation; Dynamic modelling; Thermophiles; Whey

1. Introduction A sustained worldwide increase in the production of dairy products has led to the generation of vast amounts of one of the main liquid by-products, cheese whey. Despite its use in many food products, approximately half of world cheese whey production is not treated, but discarded as effluent [1]. Cheese whey has a high chemical oxygen demand (COD), mainly owing to its 4.5–5% (w/v) lactose content, but also to soluble proteins (0.6–0.8%, w/v) and lipids (0.4–0.5%, w/v) [1]. Two main whey varieties are produced: acid (pH < 5) and sweet (pH 6–7) whey, depending upon the procedure used for casein precipitation. The lack of affordable methods for COD elimination in whey still

∗

Corresponding author. Tel.: +353 1 716 1955; fax: +353 1 716 1177. E-mail addresses: [email protected], maria [email protected] (M.R. Kosseva), [email protected] (C.A. Kent). 1369-703X/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.bej.2007.01.022

forces industries to dump large volumes into sewage lines or on to the land, a fact that poses a permanent hazard in terms of environmental pollution [2–5]. A dairy farm processing 100 t of milk per day produces approximately the same quantity of organic products in its effluent as would a town with 55,000 residents [1]. However, legislative regulations for the dumping of whey are forcing industries to come up with alternatives to make this process of elimination environmentally safer. One with attractive potential involves the use of thermophilic microorganisms to produce a pasteurised, easily dewatered sludge at temperatures that facilitate enhanced levels of energy recovery [6]. Processing options include the associated production of low COD treated wastewater [7], or of added-value products such as xanthan gum [8] and polyhydroxyalkanoates [9]. Aerobic treatment involving generally mixed populations of thermophilic bacteria offers many benefits. One of these is the potential for the biodegradation of organics in high-temperature wastewaters [10,11], which eliminates the need for cooling them

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prior to treatment. Operation under thermophilic conditions gives a high rate of biodegradation [12]. High temperatures also support the inactivation of the pathogens present in the wastewater [13–15], which is one of the main aims of the treatment process. That makes aerobic thermophilic processing suitable for stabilisation of the sludge and for rendering it hygienic, so that it can be exploited as a fertilizer. For example, the end product of thermophilic biodegradation of olive-mill wastewater provides a series of beneficial effects on the land, including: increased microporosity, hence improved oxygenation of the surface profile of the soil; increased stability of aggregates; better hydrodynamic retention of the land; and greater bioavailability of microelements for vegetable nutrition [16]. As part of a project funded under the Fifth FRAMEWORK programme of the European Commission, we sought to develop a one-stage bioremediation technology for cheese whey, associated with reduction of COD of the treated waste at elevated temperatures. This novel approach is a potential application of the standards for food industry environmental management systems, notably ISO 14000 [17]. In order to support this technology, and enable its effective exploitation, we also wished to produce an appropriate mathematical model to describe the one-stage biodegradation process, and also to estimate optimal values of model parameters. This model was intended for two areas of use: (a) to facilitate the rapid development of process conditions most suited to given remediation tasks by means of predictive simulation of bioreaction patterns, and (b) as the centre of a bioreactor control system, for example to regulate the feeding regime of a continuous or fed-batch bioreactor according to a given cost function related to the process aim. Because of the complexity of the reacting system – multiple substrates and multiple organism species – we considered that the most realistic approach was likely to be to develop a model that simplified the description of substrates or organisms or both, and yet enabled reasonable approximations of process behaviour. Our investigations have shown that mass balance-based models, including modifications and developments of the IAWQ Activated Sludge Model “family” [18,19], could be used successfully to describe the main characteristics of the biodegradation processes, not only for cheese whey but for other food industry wastes studied within our FP5 project. In this work, we describe our developments of a one-stage bioremediation process for the treatment of cheese whey at elevated temperatures, and a simplified model to support the technology. 2. Materials and methods Stilton “acid” whey (pH ≤ 5) (Glanbia Foods Tuxford Tebbutt, UK) was used as the main material for our development of the bioremediation technology. 2.1. Cultivation of microorganisms Lactococcus sp. was isolated from whey using general purpose medium supplemented with skimmed milk powder; the

thermotolerant yeast Kluyveromyces sp. was isolated from whey using yeast and mould broth/agar. These were employed as starting cultures in cheese making [20] and have been used to carry out biodegradation of lactose in whey at elevated temperatures [7]. Thermophilic Bacillus sp. was isolated from a fruit-andvegetable waste, using nutrient agar. The Bacillus sp. organisms were grown in tryptone solution (1%, w/w) with addition of (g l−1 ): lactate (13.8), citrate (5.0) and ethanol (8.0) in shakeflasks at 150 rpm at 45 ◦ C for 24 h. Fermentations were carried out in batch mode in a PreludeTM bioreactor system (Biolafitte & Moritz, France), equipped with pH, temperature and dissolved oxygen tension (DOT) control. The working volume of the system was 1.3 l:1 l of cheese whey with pH adjusted to 7 was inoculated with a 0.3 l inoculum of Bacillus sp. Experiments were carried out at 55, 60 and 65 ◦ C at DOT levels of 20, 40, 60 to 80% of saturation. These levels of dissolved oxygen tension were kept constant (±3–4%) by cascade control on to agitation speed. More information on our cultivation strategies is given in [12]. The difference in this set of experiments was in the aeration rate (1 vvm) and the use of lower agitation rates. The maximum rate of agitation achieved at 60 and 65 ◦ C during the cascade control was in the range of 900–1000 rpm. 2.2. Analytical methods Biomass concentration was measured spectrophotometrically (optical density at 600 nm) and by dry cell weight (DCW). The optical density of samples was measured against a blank of crude whey. The dry cell weight was measured by weighing the dried biomass after centrifuging 1 ml samples for 30 min at 13,000 × g. The solids were washed with distilled water and centrifuged once again. The washed, centrifuged biomass samples were dried in an oven at 90 ◦ C for 15 h until a constant weight was achieved. The specific growth rate of biomass was estimated from the following equation:   X = μt (1) ln X0 This is valid for the exponential phase of growth, when μ is constant at its maximum value, μmax . However, an approximation was made to the model of total biomass growth by assuming a constant value of μ throughout the batch, based upon that estimated from the data points obtained until the end of exponential growth. Determinations of organic acids, lactose and ethanol were carried out using an HPLC system (Gilson Medical Electronics, USA/France), using simultaneously an RI (Gilson 132) detector and a UV (Cecil series 1000, CE 1220) variable wavelength monitor at 220 nm. A 300 mm × 7.8 mm Rezex RHM-Monosaccharide column (Phenomenex UK Ltd.) was used for analysis of samples containing carbohydrates in combination with organic acids, alcohols, or inorganic salts. Separation of compounds was performed at a column temperature of 80 ◦ C [21]. A Mass Spectrometer (VG Gas Analysis Systems Ltd.,

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UK) was used for the on-line analysis of exit gas (e.g., CO2 , O2 , N2 ) from the bioreactor.

(2) Thermotolerant yeasts shift their metabolism to acetic acid and biomass production in aerobic conditions: Yeast

C12 H22 O11 + H2 O−→6C2 H4 O2

2.3. Modelling and simulation The simulation language PSI was used to solve the model equations and also for identification of the model parameters. PSI is an interactive, expression-oriented simulation program for studying the behaviour of dynamic and discrete systems [22]. The following criterion was used for optimisation of the parameters:  ftime crit = ((C1m − C1 )2 + (C2m − C2 )2 + (C3m − C3 )2 0

+ (Xm − X) ) dt 2

(2)

This represents the integral of the sum of the squares of the model output errors for the four main reaction species, and was minimised for parameter estimation. 3. Results and discussion In order to develop a one-stage thermophilic bioremediation technology, and to study the effects of temperature and DOT on the biodegradation pattern of whey, we performed a series of experiments and subsequently obtained the biodegradation profiles described below. 3.1. Biodegradation profiles at 55 ◦ C Biodegradation profiles at 55 ◦ C and 40% DOT are shown in Fig. 1. Knowing the composition of the microbial consortium, which consists of lactic acid bacteria, thermotolerant yeast and thermophilic Bacillus sp. (inoculum), we proposed the following reaction scheme for the aerobic one-stage process. (1) Lactic acid bacteria (LAB), Lactococcus sp. available in the Stilton cheese whey, consume lactose, producing lactate: LAB

C12 H22 O11 + H2 O−→4C3 H6 O3

Fig. 1. Variation in whey composition at 55 ◦ C and DO = 20%.

(3)

283

(4)

(3) Thermophilic bacteria, Bacillus sp., consume lactate and acetate with main products carbon dioxide and biomass: C3 H6 O3 + 3O2 → 3CO2 + 3H2 O

(5)

C2 H4 O2 + 2O2 → 2CO2 + 2H2 O

(6)

(4) Biomass formation occurs simultaneously: eCHx Oy + f O2 + gHl Om Nn → CHδ Oε Nφ + hH2 O + iCO2

(7)

where CHx Oy is a carbon source, Hl Om Nn is a nitrogen source, and CHδ Oε Nφ is biomass. High conversions in the range of 80–100% were obtained at 55 ◦ C and DOT = 20, 40, 60 and 80%. Maximum product removal was observed at DOT = 20 and 40%; the efficiency of COD removal was approximately 93–94%, and the efficiency of consumption of lactose and organic acids was more than 96%. 3.2. Biodegradation profiles at 60 ◦ C Significant concentrations of acetate were found in the range 6–7.5 g l−1 during the biodegradation process at 60 ◦ C, which is evidence of metabolic activity of yeast and lactose degradation (Fig. 2). Efficiency of COD removal was in the range of 60–65.7%; efficiency of consumption of lactose and organic acids was in the range of 65–74%. 3.3. Population changes over the period of operation of each run We observed that the structure of the microbial community changed with operating temperature, in the range 55–65 ◦ C. Biodegradation profiles at 65 ◦ C and a dissolved oxygen level of 40% are shown in Fig. 3. There was no lactose consumption in the broth, and concentrations of acetate found at this temperature were less than 2–3 g l−1 . Microscopic observations showed the

Fig. 2. Variation in whey composition at 60 ◦ C and DO = 40%.

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Carbon-substrate consumption: 1 dC1 μ1 X, =− dt YX/C1

C1 (0) = C10

(9)

dC2 1 1 μ2 X + μ1 X, =− dt YX/C2 YX/C1

C2 (0) = C20

(10)

dC3 1 1 =− μ3 X + μ1 X, dt YX/C3 YX/C1

C3 (0) = C30

(11)

Biomass growth kinetics: μ = μ1 + μ2 + μ3

(12)

Fig. 3. Variation in whey composition at 65 ◦ C and DO = 40%.

μ1 = μ1max

C1 K1C + C1

(13)

absence of LAB and live yeast in the fermentation broth at the highest temperature (65 ◦ C). The efficiency of COD removal was in the range of 60–77%, 20% lower than that observed at 55 ◦ C. At 65 ◦ C thermophilic bacteria grew mainly on lactate. The efficiency of lactate consumption was in the range of 87.5–92%. In comparison, LaPara et al. [23] reported that the extent of soluble COD removal in a batch reactor treating a pharmaceutical wastewater declined as temperature increased by an average of 60 mg l−1 ◦ C−1 . The effects of a temperature increase from 55 to 65 ◦ C on bacterial community structure and microbial population dynamics were reported for both cases of aerobic biological treatment of a synthetic wastewater [24] and an anaerobic reactor treating cattle manure [25].

μ2 = μ2max

C2 K2C + C2

(14)

μ3 = μ3max

C3 K3C + C3

(15)

3.4. Mathematical modelling Biodegradation patterns of the one-stage process showed that lactose was the first substrate to be degraded by the LAB and yeast, with lactate and acetate production, respectively, following by consumption of lactate and acetate by Bacillus sp. at 55 and 60 ◦ C. 3.5. Approach I We have suggested a mathematical model for aerobic biodegradation of the whey based on the following assumptions: • A mixed culture of LAB, “lactic” yeast and Bacillus sp. was used, but biomass is lumped into one “equivalent culture” with a total specific growth rate, μ. • The carbon sources in whey are expressed as three “equivalent substrates”: 1, lactose; 2, lactate; 3, acetate. • Separate specific growth rates, one for each “substrate”: μ1 for LAB, μ2 for yeasts, μ3 for thermophiles. • Multiple Monod-type kinetics, for every C-source. Biomass growth: dX = μX − Kd X, dt

X(0) = X0

(8)

Fig. 4a–d show “best fit” solutions of the mathematical model, related to biomass (a), lactose (b), lactic acid (c) and acetic acid (d) concentrations. Values of yield coefficients calculated for each experimental run (at different temperatures and DOT levels) and from the model are shown in Table 1. Specific growth rates were estimated using biomass concentrations obtained from experiments and from the model; these are also shown in Table 1. The average specific growth rate estimated from the experimental data was approximately 0.09 h−1 , whereas that found from the model data was approximately 0.08 h−1 . The highest specific growth rates, in the range 0.12 and 0.16 h−1 , were observed at DOT = 40% and temperatures of 60 and 65 ◦ C. A similar trend was observed for the yield coefficients on lactic acid: the highest values were observed at 55 and 65 ◦ C and DOT = 40%. The average yield coefficients are given below in Table 1. These vary from 0.350 g g−1 (on lactose substrate) to 0.430 g g−1 (on lactic acid substrate); that on the acetic acid substrate is more than 0.90 g g−1 . This is valid for all the three groups of microorganisms. At 55 ◦ C, the highest yields on lactose and growth rates were observed at DOT = 20%. This is consistent with the properties of LAB which are microaerophilic bacteria. Their yield and specific growth rate declined with an increase in DOT. At 60 ◦ C, growth of thermotolerant yeast on lactose predominated. This could be an explanation of the highest yield at that temperature being at DOT = 80%. An increase in yields on acetic acid with a rise in DOT at 55 ◦ C can be explained by increased production of yeast when they shift their metabolism to acetic acid production under aerobic conditions, also with the aerobic growth of thermophilic biomass on acetic acid produced by yeast. It has been claimed that thermophilic aerobic treatment may be limited by a poor oxygen transfer rate owing to lower oxygen solubility at higher temperatures. However, Boogerd et al. [26] found that the oxygen transfer rate showed only minor changes in a temperature range between 15 and 70 ◦ C in a mechanically

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Fig. 4. Simulation results (Approach I) and experimental data for 55 ◦ C, DO = 80%. Assessments of levels of error in analytical measurements (shown in this figure and in Figs. 5 and 6) were made on the basis of triplicate samples, for biomass dry weight determinations, and manufacturer’s information, for HPLC determinations of concentrations of lactose, lactic acid and acetic acid.

mixed bioreactor. Vogelaar et al. [27] showed that the reduced oxygen saturation concentration in thermophilic sludge was offset by the increased overall oxygen transfer coefficient, and that the oxygen transfer rate was only slightly affected by the liquid temperature in the range of 20–55 ◦ C. We performed a statistical assessment on our data of the impact of DOT on Y and μ, using the correlation data analysis tool in Microsoft® Excel. Correlation coefficients varied from −0.39 to −0.20 for YX/C1 and YX/C2 (Y1 and Y2 ), which demonstrated a small negative correlation. The correlation coefficient obtained for YX/C3 (Y3 ) was 0.50, showing a medium positive correlation between DOT and yield coefficient on acetate, as acetate is produced by yeast under aerobic conditions. The correlation coefficient determined for μ was −0.52—a negative correlation between DOT and specific growth rate of biomass. These statistics were in general agree-

ment with the trends observed and explained above. Therefore, in our work we can generally conclude that no clear influence of dissolved oxygen tension on the biomass parameters studied (Y and μ) was shown. 3.6. Approach II If we consider the biodegradation profile at 65 ◦ C, there is no evidence of lactose degradation and acetate production, so the following simplifications were applied. Growth rates of LAB and yeast are neglected: μ1 = 0 (for LAB) and μ2 = 0 (for yeasts) and the model is modified as shown below: dX = μX − Kd X, dt

X(0) = X0

(16)

Table 1 Values of the yield coefficients and the specific growth rates calculated for each experimental run and from the model Experimental T (◦ C) DO Y1 ((g biomass) run (%) (g lactose)−1 )

Y1m ((g biomass) (g lactose)−1 )

Y2 ((g biomass) Y2m ((g biomass) (g lactate)−1 ) (g lactate)−1 )

Y3 ((g biomass) Y3m ((g biomass) (g acetate)−1 ) (g acetate)−1 )

μ (h−1 )

μm (h−1 )

1 2 3 4 5 6 7 8 9

0.443 0.355 0.327 0.275 0.356 0 0 0 0

0.422 0.274 0.319 0.281 0.331 0 0 0 0

0.352 0.496 0.494 0.473 0.383 0.422 0.530 0.372 0.32

0.323 0.30 0.570 0.462 0.496 0.439 0.508 0.454 0.14

0.751 0.857 0.865 0.941 0.90 0 0 0 0

0.60 0.812 1.0 1.18 1.466 0 0 0 0

0.11 0.094 0.087 0.12 0.056 0.087 0.16 0.017 0.06

0.086 0.06 0.09 0.08 0.061 0.078 0.145 0.028 0.05

0.351

0.325

0.427

0.410

0.863

1.010

0.088

0.075

Average

55 55 55 60 60 65 65 65 65

20 40 80 40 80 20 40 60 80

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Fig. 5. Simulation results (Approach II) and experimental data for 65 ◦ C, DO = 20%.

dC1 = 0, dt

C1 (0) = C10

1 dC2 μ2 X, =− dt YX/C2 dC3 = 0, dt

C3 (0) = C30

(17) C2 (0) = C20

(18)

(19)

μ = μ2 = μ2max

C2 K2C + C2

(20)

Graphical “best fit” solutions for this approach are given in Fig. 5a–d for biomass (a), lactose (b), lactic (c) and acetic acid (d) concentrations. If we apply the original model (Approach I), the results of the simulation are given in column 5 of Table 2. It may be seen that the values of μ1max and μ3max approach

Fig. 6. Simulation results (Approach I) and verification: experimental data for 60 ◦ C, DO = 80%.

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Table 2 Values of the model parameters calculated for different experimental runs, using Approach I and Approach II Parameters

55 ◦ C (DO = 80%)

55 ◦ C (DO = 40%)

60 ◦ C (DO = 80%)

65 ◦ C (DO = 20%)

65 ◦ C (DO = 20%)

K1C (g l−1 ) K2C (g l−1 ) K3C (g l−1 ) μ1max (h−1 ) μ2max (h−1 ) μ3max (h−1 ) Kd (h−1 ) YX/C1 (g g−1 ) YX/C2 (g g−1 ) YX/C3 (g g−1 )

6.274 9.617 5.452 0.158 0.144 0.0515 0.0855 0.319 0.570 0.865

7.99 8.07 3.34 0.218 0.095 0.065 0.094 0.286 0.108 0.120

17.158 3.586 5.9813 0.2091 0.0972 0.0579 0.0949 0.7085 0.3874 0.1713

6.11 0.001 3.98 0.014 0.111 0.0457 0.046 0.537 0.565 0.551

– 0.0013 – – 0.096 – 0.0179 – 0.531 –

zero, which is our assumption for the simplified model applied at 65 ◦ C (Approach II, given in column 6 of Table 2). This suggests that our model can be simplified at 65 ◦ C and is valid over a range of temperatures. Experimental verification of the model (Approach I) was carried out, and one of the three independent experimental results is shown in Fig. 6a–d at 60 ◦ C and 80% DOT. 4. Conclusions We have developed a one-stage thermophilic bioremediation process for the treatment of cheese whey. The thermophilic microbial populations with which we worked have successfully reduced the polluting load of this waste stream. We have shown that the process is capable of reducing pollution loads in cheese whey up to 93% at 55 ◦ C, and up to 70% at 65 ◦ C in a conventional aerated stirred tank bioreactor, in a way that complies with EU guidelines on sanitisation of bio-waste. Further process intensification could well improve the economic performance of such a route, and make more attractive the adoption of this means of waste conversion. We have further developed design tools, notably process models, and operating strategies, to facilitate the development and use of efficient processes for the thermophilic, aerobic treatment of an important dairy industry-related waste stream. Mass balance based mathematical models have been developed using simplified modifications of the IAWQ Activated Sludge Model’s concepts of “lumping” mixed populations and mixed substrates into a small number of “clusters” of “equivalent” substrate or biomass. Reasonably good fits to process data were obtained using these models over a range of temperatures, including those within the thermophilic region. Values of “best fit” model parameters were generated to predict biomass specific growth rates. The average specific growth rate calculated was 0.097 h−1 at 55 ◦ C whilst the experimental one was 0.079 h−1 . At 65 ◦ C the calculated average specific growth rate was 0.075 h−1 whilst the experimental one was 0.089 h−1 . The results obtained suggest that temperature may have exerted a larger influence on the biodegradation process than dissolved oxygen, as the composition of the microbial community changed with temperature over the range 55–65 ◦ C. The average biomass yields generated varied from 0.350 g g−1 (on lactose substrate) to 0.430 g g−1 (on lactic acid substrate) and were 0.86 g g−1 on acetic acid sub-

strate, whereas yields calculated using the model varied from 0.325 g g−1 (on lactose substrate) to 0.410 g g−1 (on lactic acid substrate), being 1.01 g g−1 on acetic acid substrate. Our investigations suggest that modelling of complex bioreaction systems via “lumping” of key substrates and microbial species into a limited number of “equivalent clusters” is worthy of consideration as a possible means of facilitating rapid process development and practical process operation. Further work on the models reported here will be needed to improve some of their predictions, including allowance for time-varying specific growth rates. However, in cases where approximate predictions are all that is required, such models could have much to commend them. Acknowledgement The authors acknowledge the financial support of this work by the European Commission, under the Fifth FRAMEWORK programme, contract number QLK3-CT-1999-00004. References [1] M.I. Gonzalez Siso, The biotechnological utilization of cheese whey: a review, Biores. Technol. 57 (1996) 1–11. [2] J.K. Arora, S.S. Marwaha, R. Grover, Biotechnology in Agriculture and Environment, Asiatech Publishers Inc., New Delhi, 2002, pp. 129–149. [3] A.J. Mawson, Bioconversions for whey utilization and waste abatement, Biores. Technol. 47 (1994) 195–203. [4] S.T. Yang, E.M. Silva, Novel products and new technologies for use of a familiar carbohydrate, milk lactose, J. Dairy Sci. 78 (1995) 2541– 2562. [5] M. Rubio-Texeira, Endless versatility in the biotechnological applications of Kluyveromyces LAC genes, Biotechnol. Adv. 24 (2006) 212–225. [6] C.F. Chiang, C.J. Lu, L.K. Sung, Y.S. Wu, Full-scale evaluation of heat balance for autothermal thermophilic aerobic treatment of food processing wastewater, Water Sci. Technol. 43 (11) (2001) 251–258. [7] M.R. Kosseva, C.A. Kent, D.R. Lloyd, Thermophilic bioremediation of whey: effect of physico-chemical parameters on the efficiency of the process, Biotechnol. Lett. 23 (2001) 1675–1679. [8] M. Papagianni, S.K. Psomas, L. Batsilas, S. Paras, D.A. Kyriakidis, M. Liakopoulou Kyriakides, Xanthan production by Xanthomonas campestris in batch cultures, Process Biochem. 37 (2001) 73–80. [9] A.A. Pantazaki, M.G. Tamvaka, V. Langlois, P. Guerin, D.A. Kyriakidis, Polyhydroxyalkanoates (PHA) biosynthesis in Thermus thermophilus: purification and biochemical properties of the PHA synthase, Mol. Cell. Biochem. 254 (2003) 173–183. [10] A.F. Rozich, K. Bordacs, Use of thermophilic biological aerobic technology for industrial wastewater treatment, Water Sci. Technol. 46 (4–5) (2002) 83–89.

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[25]

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Glossary C1 : Concentrations of lactose (g l−1 ), experimental data. C2 : Concentration of lactate (g l−1 ). C3 : Concentration of acetate (g l−1 ). C1m , C2m , C3m : Model results of simulations; C1 , C2 , C3 : experimental data. ftime: Duration of the experiment (h). Kd : Decay coefficient (h−1 ). K1C , K2C , K3C : Saturation constants (g l−1 ). X: Lumped biomass concentration (g l−1 ). YX/C1 , YX/C2 , YX/C3 : Yield coefficients ((g biomass) (g substrate)−1 ). μ: Specific growth rate (h−1 ).