Terms for Heat Water Nutrients and Gases

The following sections cite some typical values for the relevant coefficients that have been used in the literature. However, it must be realized that the values of these parameters will be affected to a large extent by the organism and substrate used and the conditions under which the fermentation is carried out.

17.2.1 Metabolic Heat Production

Waste heat production will be associated with both growth-related and maintenance metabolism:

where rg is the overall rate of metabolic waste heat production (J h-1). As will be seen in the bioreactor modeling section, this waste heat production term appears within the overall energy balance equation, the equation that is used to describe changes in the temperature of the bed. YgX is the yield of heat from the growth reaction (J kg-dry-biomass-1), and mg is the coefficient for heat production associated with maintenance metabolism (J kg-dry-biomass-1 h-1).

Direct determination of Yg and mg requires careful calorimetric studies, although reasonable estimates can probably be obtained by relating these values to O2 consumption, given that, for aerobic growth of a number of different microorganisms, the heat yield based on O2 consumption is about 519 kJ mol-O2-1 (Coo-ney et al. 1968). Various values that have been used in the SSF literature are shown in Table 17.1.

Table 17.1. A selection of reported metabolic heat yield and maintenance coefficients

Symbol

Organism

Valuea,b

Reference

YQX

Rhizopus oligosporus

8.366x106 J kg-X-1

Sargantanis et al. (1993)

mQ

Rhizopus oligosporus

329.3 J kg-X-1 h-1

Sargantanis et al. (1993)

YQX

Gibberella fujikuroi

1.54x107 J kg-X-1

Pajan et al. (199l)

mQ

Gibberella fujikuroi

3.3x105 J kg-X-1 h-1

Pajan et al. (199l)

YQC

Gibberella fujikuroi

l.0233x106 J kg-CO2-1

Lekanda and Pérez-

Correa (2004)

a Where appropriate, values have been converted from the units used by the authors. b "X" in the units stands for "dry-biomass" (this also applies to other tables in this chapter).

Correa (2004)

a Where appropriate, values have been converted from the units used by the authors. b "X" in the units stands for "dry-biomass" (this also applies to other tables in this chapter).

17.2.2 Water Production

The equation for water production is:

dt where rW is the overall rate of metabolic water production (kg h-1). This term may be included in a water balance equation within the bioreactor model. YWX is the yield of water from the growth reaction (kg-H2O kg-dry-biomass-1) and mW is the coefficient for water production associated with maintenance metabolism (kg-H2O kg-dry-biomass-1 h-1).

The parameters YWX and mW need to be determined in careful studies, because the production of metabolic water may be small compared to the total water in the system, and there is the possibility of condensation or evaporation occurring. Further, it is not possible to distinguish experimentally between water that was produced by respiration and water that was already in the medium. Estimated values may include the contribution of the consumption of water by extracellular hydrolysis reactions, although this is generally a minor contributor to the overall water balance and is often neglected.

Estimates of the yield coefficient can be made on the basis of assumptions about the stoichiometry of the growth reaction, which will be significantly affected by the types of nutrients being consumed and whether growth is aerobic or anaerobic. In the same way, the maintenance coefficient can be simply correlated to mo, on the basis of an assumed stoichiometry of the maintenance reaction, rather than being measured experimentally. Values that have been used in the literature are shown in Table 17.2.

Table 17.2. A selection of reported metabolic water yield and maintenance coefficients

Sym- Organism Value Reference bol

YWX Rhizopus oligosporus 0.304 kg-H2O kg-X-1 Sargantanis et al. (1993)

mW Rhizopus oligosporus 0.0106 kg-H2O kg-X-1 h-1 Sargantanis et al. (1993)

YWO Aspergillus oryzae 1.22 mol-H2O mol-O2-1 Nagel et al. (2001b)

YWO Gibberella fujikuroi 0.79 mol-H2O mol-O2-1 Lekanda and

Pérez-Correa (2004)

17.2.3 Substrate and Nutrient Consumption

Section 16.2 presented an equation for consumption of the overall residual dry substrate (Eq. 16.10), it being necessary to calculate this in order to convert absolute biomass concentrations into relative values.

Even though it is not appropriate to try to model intra-particle diffusion of nutrients in bioreactor models (Sect. 13.2.1), it may be of interest to calculate the residual quantity of a specific nutrient. In this case the basic equation is:

1 dx yxn dt

where rN is the overall rate of nutrient consumption (kg-nutrient h-1), which will be subtracted in the appropriate place within a balance equation. YXN is the yield of biomass from that nutrient (kg-dry-biomass kg-nutrient-1) and mN is the maintenance coefficient for that nutrient (kg-nutrient kg-dry-biomass-1 h-1).

Given that solid substrates are typically complex mixtures of various carbon-containing nutrients, it is not necessarily a simple matter to determine the yield and maintenance coefficients experimentally. In the case of overall residual dry substrate it may be possible to obtain estimates of YXS and mS by the method shown in Fig. 16.2. Values reported in the literature for parameters related to the overall residual dry substrate (YXS and mS) and specific nutrients (YXN and mN) are shown in Table 17.3.

Table 17.3. A selection of reported metabolic nutrient yield and maintenance coefficients

Symbol

Organism

Value

Reference

mS

Coniothyrium

1.82x10-4 kg-S kg-X-1 day-1

Ooijkaas et al. (2000)

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