Monod-type

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. 

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

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. 

Inserting the Monod-type rate expressions gives For the cell balance... 

The kinetics can be described approximately according to the Monod-type kinetics. 

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... 

General Kinetic Expression. The simplest expression of the Monod type which can account for both factors in microbial fermentation is... 

Figure 29.1 Behavior of batch or plug flow reactors for Monod type microbial fermentation.

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... 

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

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... 

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 7.1. Example of Monod-type uptake (or growth) functions a /j(S) dominates/jlS) for all values of S, and competitive exclusion holds b /,(S) and fi S) cross exactly at the value of D, producing coexistence, the knife-edge phenomenon c / (S) and fi(S) cross, and competitive exclusion holds.

The OMBRE approach is applied to a biomass fermentation model [1], which, assuming Monod-type kinetics for biomass growth and substrate consumption, is described by the following DAEs set ... 

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... 

Effeedveness factor Microbial growth on multiple substrates (here oxygen and glucose) is Q cady modeUed using Monod type kinetics ... 

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