Monod kinetics equation

When microorganisms use an organic compound as a sole carbon source, their specific growth rate is a function of chemical concentration and can be described by the Monod kinetic equation. This equation includes a number of empirical constants that depend on the characteristics of the microbes, pH, temperature, and nutrients.54 Depending on the relationship between substrate concentration and rate of bacterial growth, the Monod equation can be reduced to forms in which the rate of degradation is zero order with substrate concentration and first order with cell concentration, or second order with concentration and cell concentration.144... 

Baughman and colleagues145 derive a second-order kinetic rate expression as a special case of the Monod kinetic equation. It appears to describe biodegradation of organics in natural surface waters reasonably well ... 

The shape of the performance curve for a continuous stirred-tank fermenter is dependent on the kinetic behaviour of the micro-organism used. In the case where the specific growth rate is described by the Monod kinetic equation, then the productivity versus dilution rate curve is given by equation 5.137 and has the general shape shown by the curve in Fig. 5.58. However, if the specific growth rate follows substrate inhibition kinetics and equation 5.65 is applicable then, at steady state, equation 5.131 becomes ... 

Figure 4.25. Model identification and parameter estimation of the Monod kinetic equation using differential methods and a simple reciprocal plot (Eadie, 1942 Hofstee, 1952). (---), 95% confidence interval.

A Langmuir-Hanes plot based on the Monod rate equation is presented in Figure 8.7. The Monod kinetic model can be used for microbial cell biocatalyst and is described as follows ... 

Equation (2.19), which concerns a situation without processes in the biofilm, can be extended to include transformation of a substrate, an electron donor (organic matter) or an electron acceptor, e.g., dissolved oxygen. If the reaction rate is limited by j ust one substrate and under steady state conditions, i.e., a fixed concentration profile, the differential equation for the combined transport and substrate utilization following Monod kinetics is shown in Equation (2.20) and is illustrated in Figure 2.8. Equation (2.20) expresses that under steady state conditions, the molecular diffusion determined by Fick s second law is equal to the bacterial uptake of the substrate. 

For limiting nutrients, cellular concentrations are constant under conditions of steady-state growth. To ensure that the limiting nutrient is not diluted in the microbial population, kmt must be greater than the maximal growth rate, /imax. This limiting condition sets a minimum for the value of the Monod constant, Kmd = / max /[7]- Note that while Monod kinetics are more applicable than first-order kinetics for many ecological uptake processes, solutions of the above equations require considerably more a priori information [48]. 

The growth of biomass in the reactor is assumed to follow Monod kinetics with a first-order death rate. A mass balance on the biomass in the reactor yields the following differential equation (assuming that no biomass enters the reactor in the feed) ... 

The oxygen demand of the heterotrophic microbes can be measured as the loss of COD. In the absence of oxygen limitation this was also described by equations (6, 7 8) developed from Monod kinetics (15). 

The equations, developed from the model based on Monod kinetics and the additional equations, developed empirically to describe the effects of oxygen limitation on aerobic treatment of piggery slurry, will provide this information as the most suitable mean treatment time, reaction temperature, and DO level. 

Assume Monod kinetics (no product poisoning), constant fractional yields 9, and no cells entering in the feed stream. Then the mixed flow performance equation becomes... 

With sufficient food and harmonious environment, cells multiply freely. However, no matter how much food is available, eventually either cells crowd each other out or their waste products inhibit their growth. We call this product poisoning. Hence, Monod kinetics always is a special case of a more general rate form which includes product poisoning. A simple equation of the general rate form for this situation is... 

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... 

An understanding of the influence of environmental conditions on the kinetics of enzyme reactions is essential for the design of processes based upon the use of these materials as catalysts. Their growth kinetics are also governed by similar kinetic equations (c.f. Monod growth equations, Section S.9). 

Temperature is recognised as having an effect on the growth yield, the endogenous respiration rate and the Monod kinetic parameters Ks and pm. Within the temperature range of 25 to 40°C these have been shown to have dependencies which could be accounted for by Arrhenius-type exponential equations (Topiwala and Sin-CLAIR<52)). If the temperature-dependent nature of the constants has to be taken into account, equation 5.70 must be written as ... 

Assuming that the local rate of enzyme reaction follows Michaelis-Menten kinetics, or that the microbe film follows Monod kinetics regardless of immobilisation, then equation 5.86 becomes ... 

The deviation of the reaction rate 31, from the rectangular hyperbola which would be shown by a true Michaelis-Menten reaction law, is best illustrated by considering the data as represented by an Eadie-Hofstee plot. The original equation for the Michaelis-Menten or Monod kinetics ... 

If the growth follows the Monod kinetic model, then equation 5.62 may be substituted into equation 5.115 to give ... 

If the growth rate can be described by Monod kinetics, then using equation 5.157 to substitute into equation 5.62, the substrate concentration at steady-state is given by ... 

The conditions for washout with the recycle stream of biomass can be determined by putting S -> S0 as D - Z)crit so that with the incorporation of Monod kinetics into equation 5.157 ... 

The Monod kinetic parameters, and Ks, cannot be estimated with a series of batch runs as easily as the Michaelis-Menten parameters for an enzyme reaction. In the case of an enzyme reaction, the initial rate of reaction can be measured as a function of substrate concentration in batch runs. However, in the case of cell cultivation, the initial rate of reaction in a batch run is always zero due to the presence of a lag phase, during which Monod kinetics does not apply. It should be noted that even though the Monod equation has the same form as the Michaelis-Menten equation, the rate equation is different. In the Michaelis-Menten equation,... 

F. L., et al, Development and Demonstration of an Explicit Lumped Parameter Biofilter Model and Design Equation Incorporating Monod Kinetics, /. Air Waste Manage. Assoc., 2002, 52(2) 208-219 Margulis, L., Microcosmos, Summit Books, New York, 1986. 

It was considered a stirred tank reactor where the Desulfovibrio Alaskensis (DA) bacteria growth is carried out. The DA bacterium is a sulfate reducing bacteria used, in this case, to degrade some undesirable sulfate compounds to sulfides. It was previously determined that the Monod s kinetic equation adequately describes our reactor [2], where its kinetics parameters were determined via standard methodology in a batch culture [3]. 

Depending on the nature of the class, the instructor may wish to spend more time with the basics, such as the mass balance concept, chemical equilibria, and simple transport scenarios more advanced material, such as transient well dynamics, superposition, temperature dependencies, activity coefficients, redox energetics, and Monod kinetics, can be skipped. Similarly, by omitting Chapter 4, an instructor can use the text for a water-only course. In the case of a more advanced class, the instructor is encouraged to expand on the material suggested additions include more rigorous derivation of the transport equations, discussions of chemical reaction mechanisms, introduction of quantitative models for atmospheric chemical transformations, use of computer software for more complex groundwater transport simulations, and inclusion of case studies and additional exercises. References are provided... 

The growth rate for cells in a bioreactor can follow a variety of growth equations. Monod kinetics is represented by part (1) of Problem 8.3. A substrate-inhibition growth rate is given by (see Shuler, 1988) ... 

While the Monod equation is an oversimplification of the complicated mechanism of cell growth, it often adequately describes fermentation kinetics. The Monod kinetic parameters can be determined by making a series of ideal continuous stirred-tank bioreactors, which will be discussed later. Table 19.6 shows the typical values of the Monod s kinetic parameters when glucose is a limiting substrate. 

From Equation (19.47), Q can be calculated with a known residence time and the Monod kinetic parameters as... 

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