Monod-type equation

The reaction rate is expressed by a Monod-type equation... 

Here the cells are in a uniform environment. No adaptation is needed and cell multiplication proceeds at a constant rate determined by the composition of the fluid in the vessel. This is frequently represented by a Monod-type equation... 

Monod-type equation. One expression used (Aiba et al. 2)) is ... 

In the cases of the cultures in sugar-containing media, it was reported that the Rg value is not greatly affected by light exposure [14]. The specific elongation rate, ju, of heterotrophic and photomixotrophic hairy roots is expressed as a Monod-type equation where fructose is a limiting substrate ... 

Figure L Hybrid model containing Monod-type equations, ANN (Artifical Neural Network), mass balance equations and evidence monitor for the ANN.

Levenspiel (1980), with a Monod-type equation replacing by... 

Substituting a Monod-type equation into Equ. 5.117 results in a hyperbolic function for production in the case of growth association... 

In the present study, the UASB reactor was modeled in terms of the dispersed plug flow and the Monod type of rate equations to constmct the differential mass balance equations fcs- the anaerobic biodegradation of single and multiple substrates components of the volatile fetty acids. 

Equation (5.3) includes the influence of both the electron donor (organic substrate) and the electron acceptor (DO) on the growth of biofilm biomass. The expressions for these dependencies are of the Monod type and 1/2-order kinetics, respectively (cf. Section 2.2). 

A Monod type of DO dependency as used in Equations (5.1) and (5.2) can be added to this equation. 

The fourth assumption is probably the least accurate in low DO systems because BOD decay is actually closer to a Monod type of reaction. With these assumptions, we still have two governing equations to solve. The first is for BOD ... 

The Kq saturation coefficient of oxygen in the Monod-type kinetic equation is an important parameter, too. Its value strongly influences the specific growth rate, especially when the value of oxygen concentration is of the same order of magnitude as or lower than the Kq value. Its effect is illustrated in Fig. 10 in the presence of a dispersed organic phase, e = 0.2. The increasing value of Kq (Kq was chosen to be equal to 0.64 x 10 0.16 x 10 and 0.016 x 10 kg m ) has a... 

A usual modification for this equation considers the influence of substrate concentration on the non-associated term, usually expressed as a Monod-type limitation (Equation 32). 

Table 8.1 summarizes a set of mathematical expressions for the description of the specific growth rate during culture. Most of these formulations employ Monod-type structures for cell growth limitation by substrates (Monod, 1949), and structures for byproduct inhibition (Aiba and Shoda, 1969 see Equations 16 and 24). 

Similar to what has been shown in Table 8.1 for specific growth rate, many mathematical expressions listed in Table 8.3 employ Monod-type structures for limiting phenomena, and Aiba and Shoda-type structures for inhibitory behavior. Limiting components for cell death are lactate and ammonia, that is, the presence of these byproducts increases the specific cell death rate. On the other hand, substrates, such as glucose and glutamine, inhibit cell death (Equations 48 to 52). 

For Equations 62 and 63, the maintenance coefficient appears limited by substrate through a Monod-type formulation. 

Considering the influence of media components on specific production rate, only one expression makes serum relevant (Equation 69), while glutamine appears as a limiting substrate in three formulas (Equations 69 to 71), always with a Monod-type structure. Glucose shows either an inhibitory effect over production (Equations 71 and 72), or a limiting and inhibitory pattern simultaneously (Equations 70). Instead of the classical... 

Frequently, the specific byproduct formation rate is presented as a function of specific substrate consumption rate and substrate-to-product yield (see Equation 12), but other structures can be assumed. The specific production rate can be limited by a precursor substrate and modeled by a Monod-type expression, as in Equation 73, or it may be inhibited by a substrate that is not, in principle, linked to its production, as in Equation... 

Monod-Type Empirical Kinetics Many bioreactions show increased biomass growth rate with increasing substrate concentration at low substrate concentration for the limiting substrate, but no effect of substrate concentration at high concentrations. This behavior can be represented by the Monod equation (7-92). Additional variations on the Monod equation are briefly illustrated below. For two essential substrates the Monod equation can be modified as... 

In this type of dispersed system some of the cells will be adsorbed at the drop surface and the others will be suspended in the continuous phase also. However if the dispersed phase is pure substrate, those cells attached to the drop surface will have a specific growth rate equal to the maximum specific growth rate, and those cells suspended in the continuous phase will have a specific growth rate that can be represented by Monod s equation. When mass transfer is important, the rate of growth in the continuous phase is limited by the quantity of substrate that diffuses into that phase. Since the growth at the drop... 

Assuming that oxygen supply is sufficient to avoid local oxygen limitations, the kinetic model required for the simulation includes only the material balance equation for the substrate. As suggested in earfier simulations based on recirculation models (micro-macromixer) by Bajpai and Reuss [60], the uptake kinetics are only considered in the vicinity of the so-called critical sugar concentration. Thus, a rather simple unstructured empirical model is chosen for the purpose of this study. It involves a Monod type of kinetics for substrate uptake... 

This short presentation of integral solution techniques for biokinetic equations shows that integration of the function incorporating the hypothesis works only in the simplest cases. In addition, the integrated form lacks much of the flexibility desired for fitting data there is an immediate tendency to resort to descriptive polynomial functions. One also tries to use simplified forms of enzyme kinetics such as Monod kinetics, and this involves power law -type equations (cf. type 1 in Fig. 4.12 or Equ. 2.2a). 

Other formal kinetic equations for the quantification of lag phases in microbial growth are found in the literature. A simple extension of Monod-type kinetics using the lag time as model parameter is given by Bergter and Knorre (1972) ... 

Another generalization of the Monod-type kinetics was suggested by Tsao and Hanson (1975) and by Tsao and Yang (1976). They assumed the existence of growth-enhancing substrates Si and of essential substrates resulting in an equation... 

Population dynamics and stability analyses in the case of commensalism and other interactions are widespread in the literature (e.g., Lee et al., 1976 Miura et al., 1980). A modified approach to commensalistic modeling in the case of yeast growth and nicotinic acid production employed Monod-type functions for species 1 and 3 but the following equation for (Tseng and Phillips, 1981) ... 

For both types, one may recognize Monod-type relationships that omit Dg. For biological films, one actually has a realistic zero-order equation (Equ. 5.244). Higher substrate concentrations are attainable with floes, so that here zero order also dominates. 

The pseudohomogeneous biofilm model, given in Equs. 6.116 and 6.121, can be readily adapted to quantify the behavior of a rotating biological disk reactor. The setup of a similar balance equation for S using Monod-type kinetics yields for the case of rds kinetics... 

Inhibition as a result of product formation (viz., ethanol production) is also handled by modifying the Monod-type cell growth equation ... 

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