Calculation of fermentation parameters from the results of a fed-batch test taking account of the volume of biomass in the fermenting medium

ENGINEERING AND TECHNOLOGY

Calculation of fermentation parameters from the results of a fed-batch test taking account of the volume of biomass in the fermenting medium

Walter Borzani^* "in memoriam"

Instituto Mauá de Tecnologia; Escola de Engenharia Mauá; Praça Mauá 1; [e-mail]; 09580-900; São Caetano do Sul - SP - Brazil

ABSTRACT

The volume of biomass in the fermenting medium may significantly affect the values of fermentation parameters calculated from the measured concentrations of the substrates and/or products. The corrections proposed in this paper should be evaluated and, depending on their magnitude, considered in order to obtain more representative results. A numerical example is presented.

Key words: Biomass volume, corrections calculation, fed-batch fermentation, fermentation parameters, medium aqueous phase volume

RESUMO

O volume da biomassa no meio em fermentação pode afetar significativamente os parâmetros do processo calculados a partir das medidas das concentrações de substratos e/ou produtos. Correções propostas neste trabalho deveriam ser avaliadas e, dependendo de seus valores, consideradas a fim de obter resultados mais representativos. Apresenta-se um exemplo numérico.

INTRODUCTION

The values of the fermentation parameters (yield factors; efficiencies; productivities; production and consumption rates), usually calculated from the measured concentrations of the biomass, substrates and products, may be significantly influenced by several factors (e.g. evaporation and stripping losses, addition of the acid or base solutions to control the medium pH, addition of antifoam, production of substances that change the aqueous phase volume, biomass volume, samples withdrawal). Some aspects of the above topics have been discussed elsewhere (Borzani and Perego, 1976; Concone et al., 1978; Wang, 1979; Borzani and Baralle, 1983; Borzani, 1995; Borzani and Jurkiewicz, 1998; Borzani, 2003). The main purpose of this paper was to show to what extent the biomass volume in the fermenting medium could affect the values of the fermentation parameters calculated from results of a fed-batch experiment.

Aqueous Phase Volume

Considering that the biomass concentrations are measured in the whole medium, and that the substrate and product concentrations are measured in the medium aqueous phase, that is, in the filtered (or centrifuged) medium, it is necessary to evaluate the aqueous phase volume in order to calculate the actual masses of the substrate and product in the fermenting medium. Equation (1), where V_a is the volume of the aqueous phase, V is the volume of the fermenting medium, X is the biomass concentration (dry matter), σ is the fraction of dry matter in the biomass, and ρ is the density of the microorganism, permits to calculate the above volume.

Otherwise, the volume of the fermenting medium in the reactor at time t ( t < θ, where θ is the duration of the reactor feeding phase) is calculated by Equation (2), where V_iis the volume of the inoculum, and F is the reactor feeding rate.

Here it was assumed that F was constant and that V was not affected by the other operational conditions.

The actual masses of the biomass (M_X), substrate (M_S) and product (M_P) in the reactor were then calculated by Equations (3), (4) and (5), respectively, where S and P were, the concentrations of substrate and product respectively, measured in the aqueous phase of the fermenting medium.

It was proposed (Borzani, 2003) to replace S and P (measured in g/L aqueous phase), respectively, by S’ and P’ (measured in g/L whole medium) calculated by Equations (6) and (7).

Obviously, depending on both the value of X / θ · ρ and the uncertainty associated with the measured concentration, the difference between the measured and the corresponding calculated concentration could be insignificant (Borzani, 2003).

General Equations

The purpose of this section was to compare the values of a fermentation parameter calculated from the measured concentrations disregarding the biomass volume obtained taking account of the above volume. In the equations presented in this section, S₀ was the substrate concentration of the feeding mash, and the subscript i and f indicate, respectively, the variable values at time t = 0 and t = θ. If the value of a given parameter calculated disregarding the biomass volume was represented by Z, the value calculated taking account of the biomass volume would be represented by Z’.

Biomass yield factors (Y_x and Y'_X)

Equations (6), (8) and (9) show that: a) YX > Y'X when S_i = 0; b) YX < Y'X when S_f = 0; c) YX = Y'X when S_i = S_f = 0. Considering that S_i and S_f were usually relatively small, the difference between Y_Xand would be frequently insignificant.

Product yield factors (Yp and Y'p)

If S_i = S_f = P_i = 0, Equations (6), (7), (10) and (11) lead to Equation (12).

Process productivities (Q and Q’)

If P_i= 0, Equations (7), (13) and (14) give:

Rates during the reactor filling phase

The rates of biomass growth (R_X), product formation (Rp and R'p) and substrate consumption (Rs and Rs) during the reactor filling phase may be calculated by equations (16) to (20).

Equations (7), (17) and (18) give:

Otherwise, Equations (6), (16), (19) and (20) lead to Equation (22).

Numerical Example

Table 1 shows the results obtained during the reactor filling phase of a fed-batch ethanol fermentation of sugar-cane molasses medium carried out under the following experimental conditions (Koshimizu, 1984; Koshimizu et al., 1984): V_i = 4.00 L, S_i = P_i = 0, S₀ = 247 g/L, F = 1.17 L/h and θ = 5 h.

In the case of ethanol fermentation, the concentration of intracellular ethanol would be equal to the concentration of ethanol in the medium aqueous phase (Pamment and Dasari, 1988). Hence, if the purpose of the test is to study the process performance taking account of both the intracellular and the extracellular ethanol, the values of P, P_f and P_i could be used in Equations (11), (14) and (18) instead of P', P'_f and , respectively. If, however, the purpose would be to study the process performance taking account of only the extracellular ethanol, since only the medium aqueous phase is distilled, Equations (11), (14) and (18) must be used. Calling , Q'' and the ethanol yield factor, the process productivity and the ethanol production rate, respectively, calculated taking account of both the extracellular and the intracellular ethanol, Equation (23) to (25) must be used.

Table 2 shows the calculated values of V, D, S' and P' during the reactor feeding phase. The values of θ and ρ were 0.300 and g/L, respectively.

The values of Tables 1 and 2 permit to calculate the biomass yield factors (Y_X = 0.182 g/g; Y'X g/g), the ethanol yield factors (Y_P = 0.426 g/g; Y'P = 0.392 g/g; = g/g) and the process productivities (Q = Q'' 10.3 g/L.h; Q' = 9.6 g/L.h).

The above values showed that Y_X was 1.7% higher than Y'X , Y_P was 1.4% higher than and 8.7% higher than Y'P , and Q = Q'' was 7.3% higher than Q'. It was then possible to conclude that, in this example, the volume of the biomass in the fermenting medium: a) did not affect the calculated value of the biomass yield factor; b) did not affect the calculated values of the ethanol yield factor and process productivity when the intracellular ethanol was also considered; c) affected the values of the ethanol yield factor and process productivity when only the extracellular ethanol was considered.

From the curves representing the variation of S, P, S' and P' during the filling phase, the values of R_S, R_P, R'S and R'P were calculated (see Table 3). The numerical differentiation method (Sinclair and Cantero, 1990) was used to calculate the dS/dt, dP/dt, dS'/dt and dP'/dt.

Assuming that the difference RS – R'S (or RP – R'P) could be considered as negligible if (or ) belonged to the interval 0.980 to 1.020, Table 3 showed that the volume of the biomass in the fermenting medium affected the value of the ethanol production rate. The above volume, however, did not affect the value of the substrate consumption rate when t > 1.75 h.

NOMENCLATURE

D dilution rate (h^-1)

F reactor feeding rate (L/h)

M_Pmass of product in the fermenting medium (g)

M_S mass of substrate in the fermenting medium (g)

M_X mass of biomass in the fermenting medium (g)

P product concentration measured in the aqueous phase (g/L)

P' product concentration calculated by Equation (7) (g/L)

Q process productivity (*) (g/L.h)

Q' process productivity (**) (g/L.h)

R_P product production rate (*) (g/L.h)

R'_P product production rate (**) (g/L.h)

R_S substrate consumption rate (*) (g/L.h)

R'_S substrate consumption rate (**)(g/L.h)

R_X biomass growth rate (g/L.h)

S substrate concentration measured in the aqueous phase (g/L)

S' substrate concentration calculated by Equation (6) (g/L)

S₀substrate concentration of the feeding mash (g/L)

t time (h)

V volume of the fermenting medium (L)

V_avolume of the aqueous phase (L)

V_i volume of the inoculum (L)

X biomass concentration (dry matter) (g/L)

Y_P product yield factor (*) (g/g)

Y'_P product yield factor (**) (g/g)

Y_X biomass yield factor (*) (g/g)

Y'_X biomass yield factor (**) (g/g)

θ duration of the reactor feeding phase (h)

ρ density of the microorganism (g/L)

σ fraction of dry matter in the biomass (-)

i subscript indicating the value at t = 0

f subscript indicating the value at t = θ

(*) calculated disregarding the biomass volume

(**) calculated taking account of the biomass volume

Received: June 01, 2007;

Revised: November 19, 2007;

Accepted: April 03, 2008.

• Borzani, W. (1995), Product inhibition during the feeding phase in fed-batch ethanol fermentation of sugar-cane blasckstrap molasses. Biotechnol. Lett, 17, 1295-1298.
• Borzani, W. (2003), Calculation of fermentation parameters from the results of a batch test taking account of the volume of biomass in the fermenting medium. Biotechnol. Lett 25, 1953-1956. See Erratum: Biotechnol. Lett, 26, 357-362.
• Borzani, W. and Baralle, S.B. (1983), Correction of results obtained in laboratory-scale studies of batch fermentation kinetics. Biotechnol. Bioeng, 25, 3201-3206.
• Borzani, W. and Jurkiewicz, C.H. (1998), Variation of the ethanol yield during very rapid batch fermentation of sugar-cane blasckstrap molasses. Brazil. J. Chem. Eng, 15, 225-233.
• Borzani, W. and Perego Jr., L. (1976), The mash volume decrease during the ethanol fermentation of blackstrap molasses. J. Ferment. Technol, 54, 902-906.
• Concone, B.R.V.; Doin, P.A. and Pinto, A.G. (1978), Some major deviations for biomass determination by indirect method and estimation based on alkali consumption. J. Ferment. Technol, 56, 59-63.
• Koshimizu, L.H. (1984), Influência da concentração inicial de levedura e do tempo de alimentação da dorna no processo descontínuo alimentado de fermentação alcoólica de mosto de melaço de cana-de-açúcar. MSc Thesis, University of São Paulo, São Paulo, Brazil.
• Koshimizu, L.H., Gómez, E.I.V., Bueno Netto, C.L. Cruz, M.R.M., Vairo, M.L.R. and Borzani, W. (1984), Constant fed-batch ethanol fermentation of molasses. J. Ferment. Technol, 62, 205-210.
• Pamment, N.B. and Dasari, G. (1988), Intracellular ethanol concentration and its estimation. In: van Udden, N.F. (Ed.). Ethanol Inhibition in Yeasts and Bacteria CRC Press, Boca Raton, Florida.
• Sinclair, C.G. and Cantero, D. (1990), Fermentation modeling. In: Mc Neil, B. and Harvey, L.M. (Eds.). Fermentation: a practical approach IRL Press, Oxford.
• Wang, H.I. (1979), Volume changes during aerobic fermentations. Biotechnol. Bioeng, 21, 525-532.

*

Author for correspondence

Publication Dates

• Publication in this collection
  16 July 2008
• Date of issue
  June 2008

History

• Accepted
  04 Mar 2008
• Received
  06 Jan 2007
• Reviewed
  19 Nov 2007