Monod rate law

Monod rate laws whose macro-coefficients depend on dilution rate as well as temperature were derived. 

The second term In equation (13a) represents the rate of substrate consumption, or nutrient uptake. It saturates In substrate concentration according to a Monod rate law where both K and Pm/Y are known to vary with temperature and dilution rate (11-21). 

Equation (15a) represents a Monod rate law with a threshold substrate concentration S<] (Figure 2). It can be linearized to a generalized Eadle-Augustlnsson equation (31-33) ... 

A double reciprocal plot of kinetic data for a biochemical reaction that obeys a Monod rate law will yield a value of Pmax from the reciprocal of the intercept of the y-axis. The corresponding slope is equal to At high val-... 

Inspection of the values of qx and qs in Table 113.1-3 indicates that even in terms of our unsophisticated approach to the determination of these parameters, the percentage variations are surprisingly small. The fact that the variations are small can be attributed to a situation in which the Monod parameter Kg in equation (13.1.13) is much less than the substrate concentration (5). Consequently, the Monod rate law reduces to a pseudo-zero-order form... 

Figure 113.3 Mass versus time profiles of substrate and biomass for a batch reaction in a fermenter. Monod rate law with Kg = 2.78 g/L and = 3.16 day-. ...

If cell death and maintenance metabolic effects are negligible, and if the Monod rate law is applicable to this system, the steady-state material balance on the biomass can be expressed as... 

The kinetics of cell growth are governed by a Monod rate law for which the kinetic parameters at the operating conditions proposed are p = 0.7 h" and Kg = 0.2 g glu-cose/L. 

Sue proposes to analyze these data to determine whether or not her analysis yields kinetic parameters for a Monod rate law that are consistent with the parameters reported in Example 11.1 of J. M. Santamarfa, J. Herguido, M. A. Mendndez, and A. Monzdn, Ingenien a de Reactores, Editorial Sintesis, Madrid, 1999. Does the Monod model provide a good fit of the data Comment on your faith in the vahdity of the kinetic parameters that you would determine from the fit of an appropriate form of the following equation to the data ... 

If the feed for the fed hatch phase of the process is sterile (Xq = 0) and if the Monod rate law is applicable, the material balance for the fungus becomes ... 

Appending Ft to the Monod equation, we write a thermodynamically consistent rate law,... 

If the concentrations of only the electron donor and acceptor are considered to vary, each mD+ is invariant and the term ] [ n/ 1 in Equation 18.23 reverts to a half-saturation constant K[y Similarly, the corresponding term in Equation 18.24 may be represented by K A. Now, we see the dual Monod equation (Eqn. 18.16) is a specific simplification of the general rate law (Eqn. 18.22). 

P7-29a a CSTR is being operated at steady state. The cell growth follows the Monod growth law without inhibition. The exiting substrate and cell concentrations are measured as a function of the volumetric flow rate (represented as the dilution rate), and the results are shown below. Of course, measurements are not taken until steady state is achieved after each change in the flow rate. Neglect substrate consumption for maintenance and the death rate, and assume that is zero. For run 4, the entering substrate concentration was 50 g/dia and the volumetric flow rate of the substrate was 2 dmVs,... 

Because there is no growth during the stationary phase, it is clear that Equation (7-112) cannot be used to account for substrate consumption, nor can the rate of product formation be related to the growth rate [e.g., Equation (7-113)]. Many antibiatics, such as penicillin, are produced in the stationary phase. In this phase, the nutrient consumed for growth has become virtually exhausted and a different nutrient, called the secondary nutrients, is used for cell maintenance and to produce the desired product. Usually, the rate law for product formation during the stationary phase is similar in form to the Monod equation, that is,... 

We now need to determine the rate law parameters and Ks in the Monod equation... 

Lag II. Exponential III. Stationary IV. Death [Pg.448]

One can consider other peiturbations to the preceding analysis by considering the reaction kinetics to follow a lirst-order rate law, -r = or Monod kinetics,... 

The ability of Monod s empirical relation to fit kinetic data for biochemical reactions has its foundations in generalizations of two phenomena frequently observed for fermentation processes (1) nature places a cap on the quantity of microorganism that can be achieved during the exponential phase of growth in a bioreactor operating in a batch mode and (2) as the concentration of the limiting substrate approaches zero, the rate laws for biochemical reactions approach pseudo-first-order behavior with respect to that substrate. The cap indicated on the cell growth rate has been associated with the natural limit on the maximum rate at which replication of DNA can be achieved. 

This simple approach was adopted in order to circumvent the complications that are introduced by the fact that the volume of the liquid phase in the reactor varies with time. When the volume of the aqueous growth medium varies during the course of the reaction, an approach based on integration of a proposed rate law is problematic, although numerical integration would be possible. An additional reason for employing the differential approach below is that for rate laws that are other than those of the simple nth-order form (such as a Monod rate expression) a differential method of data analysis is often adequate for preliminary considerations involved in the design of a bioreactor that is intended to operate in a batch mode. 

The corresponding concentration of the substrate in the effluent from the CSTBR can be determined by recognizing that (1) at steady state, equation (13.2.59) is again applicable, and (2) in the absence of cell death and cell maintenance effects, the biochemical reaction obeys a biomass-specific rate law of the Monod form ... 

Here we have also assumed that the rate law is of the simple Monod form. Equations of the form of equations (13.2.81) to (13.2.83) can be written for each reactor in a cascade and the resulting set of equations can be readily solved using engineering software. Students should note... 

In equation (13.3.2) we have also assumed that the rate at which biomass enters in the original wastewater is negligible (xq = 0) compared to the rate at which biomass enters the contaimnent vessel via the recycle stream. Readers should note the presence of different subscripts on the specific growth rate (p) in equations (13.3.2) and (13.3.3). The subscript net implies the presence of a cell death term, whereas the subscript max does not. For the substrate, the Monod form of the rate law is appropriate for use. 

Consider the operation of a chemostat with a working volume of 2 L. The results of preliminary batch cultivation studies of the biochemical reaction and growth medium of interest indicate that the rate law is of the Monod form with p = 0.1 h . However, the reported value of the half-saturation constant is suspect, although it is thought to be quite small compared to the concentration of substrate in the feed Sq Kg). Use this information to obtain a preliminary estimate of the maximum feed flow rate that can be accommodated by this apparatus when it operates at steady state. Employ two approaches for part A, obtain a crude estimate of the feed rate by assuming that Kg is zero then refine this estimate to obtain an improved value of Kg based on the information in part B. For Part B the effluent concentration of substrate may differ from that of Part A. 

For purposes of the analysis, you may assume that cell death and cell maintenance metabolism effects are negligible, as is formation of any products other than biomass. The concentration of substrate in the feed is 25 g/L and the yield coefficient x/s is 0.52 g cells (dry weight)/g substrate. The kinetics of cell growth are characterized by a rate law of the Monod form with = 0.6 h" and Kg = 0.5 g/L. The dilution rate for the CSTBR is 0.95 h" and the concentration factor / is 2.5. 

The rate law for secondary metabolite formation often takes the form of the familiar Monod equation therefore. 

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