Skip to main content

The modeling of ethanol production by Kluyveromyces marxianus using whey as substrate in continuous A-Stat bioreactors


We investigated the kinetics of whey bioconversion into ethanol by Kluyveromyces marxianus in continuous bioreactors using the “accelerostat technique” (A-stat). Cultivations using free and Ca-alginate immobilized cells were evaluated using two different acceleration rates (a). The kinetic profiles of these systems were modeled using four different unstructured models, differing in the expressions for the specific growth (μ) and substrate consumption rates (r s), taking into account substrate limitation and product inhibition. Experimental data showed that the dilution rate (D) directly affected cell physiology and metabolism. The specific growth rate followed the dilution rate (μD) for the lowest acceleration rate (a = 0.0015 h−2), condition in which the highest ethanol yield (0.52 g g−1) was obtained. The highest acceleration rate (a = 0.00667 h−2) led to a lower ethanol yield (0.40 g g−1) in the system where free cells were used, whereas with immobilized cells ethanol yields increased by 23 % (0.49 g g−1). Among the evaluated models, Monod and Levenspiel combined with Ghose and Tyagi models were found to be more appropriate for describing the kinetics of whey bioconversion into ethanol. These results may be useful in scaling up the process for ethanol production from whey.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5


a :

Acceleration rate (h−2)

D :

Dilution rate (h−1)

D 0 :

Initial dilution rate (h−1)

K p :

Product inhibition for growth (g L−1)

K s :

Saturation growth constant (g L−1)

m s :

Maintenance energy coefficient (g g−1 h−1)

P :

Product concentration (g L−1)

P xmax :

Product concentration where microbial growth ceases (g L−1)

r p :

Product formation rate (g L−1 h−1)

r x :

Cell growth rate (g L−1 h−1)

r s :

Substrate consumption rate (g L−1 h−1)

S :

Substrate concentration (g L−1)

S i :

Inlet substrate concentration (g L−1)

S 0 :

Outlet substrate concentration (g L−1)

t :

Time (h)

X :

Cell concentration (g L−1)

Y P/S :

Yield coefficient for product on substrate (g g−1)

Y X/S :

Yield coefficient for cells on substrate (g g−1)

α :

Growth-associated constant for product formation (g g−1)

β :

Non-growth-associated constant for product formation (g g−1 h−1)

μ :

Specific growth rate (h−1)

μ max :

Maximum specific growth rate (h−1)


  1. Adamberg K, Lahtvee P-J, Valgepea K, Abner K, Vilu R (2009) Quasi steady state growth of Lactococcus lactis in glucose-limited acceleration stat (A-stat) cultures. Antonie Van Leeuwenhoek International J Gen Mol Microbiol 95:219–226. doi:10.1007/s10482-009-9305-z

    Article  Google Scholar 

  2. Albergaria H, Duarte LC, Amaral-Collaco MT, Girio FM (2000) Study of Saccharomyces uvarum CCMI 885 physiology under fed-batch, chemostat and accelerostat cultivation techniques. Food Technol Biotechnol 38:33–38

    CAS  Google Scholar 

  3. Barbosa MJ, Hoogakker J, Wijffels RH (2003) Optimisation of cultivation parameters in photobiore actors for microalgae cultivation using the A-stat technique. Biomol Eng 20:115–123. doi:10.1061/s1389-0344(03)00033-9

    CAS  Article  PubMed  Google Scholar 

  4. Birol G, Doruker P, Kirdar B, Onsan ZI, Ulgen K (1998) Mathematical description of ethanol fermentation by immobilised Saccharomyces cerevisiae. Process Biochem 33:763–771. doi:10.1016/s0032-9592(98)00047-8

    CAS  Article  Google Scholar 

  5. Cheng JJ, Timilsina GR (2011) Status and barriers of advanced biofuel technologies: a review. Renew Energy 36:3541–3549. doi:10.1016/j.renene.2011.04.031

    CAS  Article  Google Scholar 

  6. Christensen AD, Kadar Z, Oleskowicz-Popiel P, Thomsen MH (2011) Production of bioethanol from organic whey using Kluyveromyces marxianus. J Ind Microbiol Biotechnol 38:283–289. doi:10.1007/s10295-010-0771-0

    CAS  Article  PubMed  Google Scholar 

  7. da Cunha-Pereira F, Hickert LR, Sehnem NT, de Souza-Cruz PB, Rosa CA, Ayub MAZ (2011) Conversion of sugars present in rice hull hydrolysates into ethanol by Spathaspora arborariae, Saccharomyces cerevisiae, and their co-fermentations. Bioresour Technol 102:4218–4225. doi:10.1016/j.biortech.2010.12.060

    Article  PubMed  Google Scholar 

  8. de Andrade RR, Maugeri Filho F, Maciel Filho R, da Costa AC (2013) Kinetics of ethanol production from sugarcane bagasse enzymatic hydrolysate concentrated with molasses under cell recycle. Bioresour Technol 130:351–359. doi:10.1016/j.biortech.2012.12.045

    Article  PubMed  Google Scholar 

  9. Dodic JM, Vucurovic DG, Dodic SN, Grahovac JA, Popov SD, Nedeljkovic NM (2012) Kinetic modelling of batch ethanol production from sugar beet raw juice. Appl Energy 99:192–197. doi:10.1016/j.apenergy.2012.05.016

    CAS  Article  Google Scholar 

  10. Fonseca GG, Heinzle E, Wittmann C, Gombert AK (2008) The yeast Kluyveromyces marxianus and its biotechnological potential. Appl Microbiol Biotechnol 79:339–354. doi:10.1007/s00253-008-1458-6

    CAS  Article  PubMed  Google Scholar 

  11. Furlan SA, Carvalho-Jonas MF, Merkle R, Bértoli GB, Jonas R (1995) Aplicação do sistema Microtiter Reader na seleção de microrganismos produtores de ß galactosidase. Braz Arch Biol Technol 38:1261–1268

    CAS  Google Scholar 

  12. Gabardo S, Rech R, Ayub MAnZc (2011) Determination of lactose and ethanol diffusion coefficients in calcium alginate gel spheres: predicting values to be used in immobilized bioreactors. J Chem Eng Data 56:2305–2309. doi:10.1021/je101288g

    CAS  Article  Google Scholar 

  13. Gabardo S, Rech R, Ayub MAZ (2012) Performance of different immobilized-cell systems to efficiently produce ethanol from whey: fluidized batch, packed-bed and fluidized continuous bioreactors. J Chem Technol Biotechnol 87:1194–1201. doi:10.1002/jctb.3749

    CAS  Article  Google Scholar 

  14. Gabardo S, Rech R, Rosa CA, Ayub MAZ (2014) Dynamics of ethanol production from whey and whey permeate by immobilized strains of Kluyveromyces marxianus in batch and continuous bioreactors. Renew Energy 69:89–96. doi:10.1016/j.renene.2014.03.023

    CAS  Article  Google Scholar 

  15. Ghaly AE, ElTaweel AA (1997) Kinetic modelling of continuous production of ethanol from cheese whey. Biomass Bioenergy 12:461–472. doi:10.1016/s0961-9534(97)00012-3

    CAS  Article  Google Scholar 

  16. Ghose TK, Tyagi RD (1979) Rapid ethanol fermentation of cellulose hydrolysate. II. Product and substrate inhibition and optimization of fermentor design. Biotechnol Bioeng 21:1401–1420

    CAS  Article  Google Scholar 

  17. Guimaraes P, Teixeira J, Domingues L (2010) Fermentation of lactose to bio-ethanol by yeasts as part of integrated solutions for the valorisation of cheese whey. Biotechnol Adv 28:375–384. doi:10.1016/j.biotechadv.2010.02.002

    CAS  Article  PubMed  Google Scholar 

  18. Hill GA, Robinson CW (1988) Morphological behavior of saccharomyces-cerevisiae during continuous fermentation. Biotechnol Lett 10:815–820. doi:10.1007/bf01027579

    CAS  Article  Google Scholar 

  19. Hinshelwood CN (1946) Kinetics of bacterial cell. Oxford University Press, Oxford

    Google Scholar 

  20. Jamai L, Sendide K, Ettayebi K, Errachidi F, Hamdouni-Alami O, Tahri-Jouti MA, McDermott T, Ettayebi M (2001) Physiological difference during ethanol fermentation between calcium alginate-immobilized Candida tropicalis and Saccharomyces cerevisiae. FEMS Microbiol Lett 204:375–379. doi:10.1111/j.1574-6968.2001.tb10913.x

    CAS  Article  PubMed  Google Scholar 

  21. Kargi F, Ozmihci S (2006) Utilization of cheese whey powder (CWP) for ethanol fermentations: effects of operating parameters. Enz Microb Technol 38:711–718. doi:10.1016/j.enzmictec.2005.11.006

    CAS  Article  Google Scholar 

  22. Kasemets K, Drews M, Nisamedtinov I, Adamberg K, Paalme T (2003) Modification of A-stat for the characterization of microorganisms. J Microb Method 55:187–200. doi:10.1016/s0167-7012(03)00143-x

    CAS  Article  Google Scholar 

  23. Kosseva M, Panesar P, Kaur G, Kennedy J (2009) Use of immobilised biocatalysts in the processing of cheese whey. Int J Biol Macromols 45:437–447. doi:10.1016/j.ijbiomac.2009.09.005

    CAS  Article  Google Scholar 

  24. Kourkoutas Y, Bekatorou A, Banat I, Marchant R, Koutinas A (2004) Immobilization technologies and support materials suitable in alcohol beverages production: a review. Food Microbiol 21:377–397. doi:10.1016/

    CAS  Article  Google Scholar 

  25. Kumar S, Singh SP, Mishra IM, Adhikari DK (2011) Continuous ethanol production by Kluyveromyces sp. IIPE453 immobilized on bagasse chips in packed bed reactor. J Pet Technol Altern Fuels 2:1–6

    Google Scholar 

  26. Lane MM, Burke N, Karreman R, Wolfe KH, O’Byrne CP, Morrissey JP (2011) Physiological and metabolic diversity in the yeast Kluyveromyces marxianus. Antonie Van Leeuwenhoek Inte J Gen Mol Microbiol 100:507–519. doi:10.1007/s10482-011-9606-x

    CAS  Article  Google Scholar 

  27. Lewandowska M, Kujawski W (2007) Ethanol production from lactose in a fermentation/pervaporation system. J Food Eng 79:430–437. doi:10.1016/j.jfoodeng.2006.01.071

    CAS  Article  Google Scholar 

  28. LsGS Longhi, DbJ Luvizetto, Ferreira LS, Rech R, Ayub MAZ, Secchi AR (2004) A growth kinetic model of Kluyveromyces marxianus cultures on cheese whey as substrate. J Ind Microbiol Biotechnol 31:35–40. doi:10.1007/s10295-004-0110-4

    Article  Google Scholar 

  29. Luedeking R, Piret EL (2000) A kinetic study of the lactic acid fermentation. Batch process at controlled pH (Reprinted from Journal of Biochemical and Microbiological Technology and Engineering, vol 1, pg 393, 1959). Biotechnol Bioeng 67:636–644. doi:10.1002/(sici)1097-0290(20000320)67:6<636:aid-bit3>;2-u

    CAS  Article  PubMed  Google Scholar 

  30. Monod J (1950) The growth of bacterial culture. Ann Review Microbiol 3:371–394

    Article  Google Scholar 

  31. Moser A (1985) Kinetics of batch fermentations. In: HJ Rehm, Reed G Biotechnology (ed), 243–283

  32. Mussatto SI, Dragone G, Guimaraes PMR, Silva JPA, Carneiro LM, Roberto IC, Vicente A, Domingues L, Teixeira JA (2010) Technological trends, global market, and challenges of bio-ethanol production. Biotechnol Adv 28:817–830. doi:10.1016/j.biotechadv.2010.07.001

    CAS  Article  PubMed  Google Scholar 

  33. Najafpour G, Younesi H, Ismail K (2004) Ethanol fermentation in an immobilized cell reactor using Saccharomyces cerevisiae. Bioresour Technol 92:251–260. doi:10.1016/j.biortech.2003.09.009

    CAS  Article  PubMed  Google Scholar 

  34. Nelder JA, Mead R (1965) Comput. A simplex-method for function minimization 7:308–313

    Google Scholar 

  35. Nigam JN (2000) Continuous ethanol production from pineapple cannery waste using immobilized yeast cells. J Biotechnol 80:189–193. doi:10.1016/s0168-1656(00)00246-7

    CAS  Article  PubMed  Google Scholar 

  36. O’Shea DG, Walsh PK (2000) The effect of culture conditions on the morphology of the dimorphic yeast Kluyveromyces marxianus var. marxianus NRRLy2415: a study incorporating image analysis. Appl Microbiol Biotechnol 53:316–322

    Article  PubMed  Google Scholar 

  37. Ozmihci S, Kargi F (2007) Continuous ethanol fermentation of cheese whey powder solution: effects of hydraulic residence time. Bioprocess Biosyst Eng 30:79–86. doi:10.1007/s00449-006-0101-0

    CAS  Article  PubMed  Google Scholar 

  38. Ozmihci S, Kargi F (2009) Fermentation of cheese whey powder solution to ethanol in a packed-column bioreactor: effects of feed sugar concentration. J Chem Technol Biotechnol 84:106–111. doi:10.1002/jctb.2013

    CAS  Article  Google Scholar 

  39. Paalme T, Elken R, Vilu R, Korhola M (1997) Growth efficiency of Saccharomyces cerevisiae on glucose/ethanol media with a smooth change in the dilution rate (A-stat). Enz Microb Technol 20:174–181. doi:10.1016/s0141-0229(96)00114-7

    CAS  Article  Google Scholar 

  40. Paalme T, Kahru A, Elken R, Vanatalu K, Tiisma K, Vilu R (1995) The computer-controlled continuous culture of Escherichia coli with smooth change of dilution rate (A-stat). J Microbiol Method 24:145–153. doi:10.1016/0167-7012(95)00064-x

    Article  Google Scholar 

  41. Paalme T, Vilu R (1992) A new method of continuous cultivation with computer-controlled change of dilution rate. In: Karim MN, Stephanopoulos G (eds) Modeling and control of biotechnical processes, Ifac Symposia Series, vol 10, pp 299–301

  42. Parrondo J, Garcia LA, Diaz M (2000) Production of an alcoholic beverage by fermentation of whey permeate with Kluyveromyces fragilis I: primary metabolism. J Instit Brewing 106:367–375

    CAS  Article  Google Scholar 

  43. Sansonetti S, Hobley TJ, Calabro V, Villadsen J, Sin G (2011) A biochemically structured model for ethanol fermentation by Kluyveromyces marxianus: a batch fermentation and kinetic study. Bioresour Technol 102:7513–7520. doi:10.1016/j.biortech.2011.05.014

    CAS  Article  PubMed  Google Scholar 

  44. Sansonetti S, Hobley TJ, Curcio S, Villadsen J, Sin G (2013) Use of continuous lactose fermentation for ethanol production by Kluveromyces marxianus for verification and extension of a biochemically structured model. Bioresour Technol 130:703–709. doi:10.1016/j.biortech.2012.12.080

    CAS  Article  PubMed  Google Scholar 

  45. Silveira WB, Passos F, Mantovani HC, Passos FML (2005) Ethanol production from cheese whey permeate by Kluyveromyces marxianus UFV-3: a flux analysis of oxido-reductive metabolism as a function of lactose concentration and oxygen levels. Enz Microb Technol 36:930–936. doi:10.1016/j.enzmictec.2005.01.018

    CAS  Article  Google Scholar 

  46. Siso MIG (1996) The biotechnological utilization of cheese whey: a review. Bioresour Technol 57:1–11. doi:10.1016/0960-8524(96)00036-3

    Article  Google Scholar 

  47. Soares RDP, Secchi AR (2003) EMSO: a new environment for modelling, simulation and optimisation. Comput Aided Chem Eng. 14:947–952

    Article  Google Scholar 

  48. Staniszewski M, Kujawski W, Lewandowska M (2009) 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. J Food Eng 91:240–249. doi:10.1016/j.jfoodeng.2008.08.026

    CAS  Article  Google Scholar 

  49. Szajani B, Buzas Z, Dallmann K, Gimesi I, Krisch J, Toth M (1996) Continuous production of ethanol using yeast cells immobilized in preformed cellulose beads. Appl Microbiol Biotechnol 46:122–125

    CAS  Article  PubMed  Google Scholar 

  50. van der Sluis C, Westerink BH, Dijkstal MM, Castelein SJ, van Boxtel AJB, Giuseppin MLF, Tramper J, Wijffels RH (2001) Estimation of steady-state culture characteristics during acceleration-stats with yeasts. Biotechnol Bioeng 75:267–275. doi:10.1002/bit.1181

    Article  PubMed  Google Scholar 

  51. Verbelen P, De Schutter D, Delvaux F, Verstrepen K, Delvaux F (2006) Immobilized yeast cell systems for continuous fermentation applications. Biotechnol Lett 28:1515–1525. doi:10.1007/s10529-006-9132-5

    CAS  Article  PubMed  Google Scholar 

  52. Yang K-M, Lee N-R, Woo J-M, Choi W, Zimmermann M, Blank LM, Park J-B (2012) Ethanol reduces mitochondrial membrane integrity and thereby impacts carbon metabolism of Saccharomyces cerevisiae. FEMS Yeast Res 12:675–684. doi:10.1111/j.1567-1364.2012.00818.x

    CAS  Article  PubMed  Google Scholar 

  53. Yu JL, Yue GJ, Zhong J, Zhang X, Tan TW (2010) Immobilization of Saccharomyces cerevisiae to modified bagasse for ethanol production. Renew Energy 35:1130–1134. doi:10.1016/j.renene.2009.11.045

    CAS  Article  Google Scholar 

  54. Yu JL, Zhang X, Tan TW (2007) An novel immobilization method of Saccharomyces cerevisiae to sorghum bagasse for ethanol production. J Biotechnol 129:415–420. doi:10.1016/j.jbiotec.2007.01.039

    CAS  Article  PubMed  Google Scholar 

  55. Zafar S, Owais M, Salleemuddin M, Husain S (2005) Batch kinetics and modelling of ethanolic fermentation of whey. Int J Food Sci Technol 40:597–604. doi:10.1111/j.1365-2621.2005.00957.x

    CAS  Article  Google Scholar 

Download references


The authors wish to thank CNPq and CAPES (Brazil) for the financial support of this research and scholarships for the first author.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Marco Antônio Záchia Ayub.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gabardo, S., Pereira, G.F., Rech, R. et al. The modeling of ethanol production by Kluyveromyces marxianus using whey as substrate in continuous A-Stat bioreactors. J Ind Microbiol Biotechnol 42, 1243–1253 (2015).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Bioprocess modeling
  • Ethanol
  • Kluyveromyces marxianus
  • Continuous fermentation
  • A-stat control
  • Whey