Washout point

Operating near the washout point maximizes the production rate of cells. A feedback control system is needed to ensure that the limit is not exceeded. The easiest approach is to measure cell mass—e.g., by measuring turbidity— and to use the signal to control the flow rate. Figure 12.5 shows how cell mass varies as a function of t for the system of Examples 12.7 and 12.8. The minimum value for t is 2.05 h. Cell production is maximized at F=2.37h. 

In the chemostat, the dilution rate is set at a fixed value, and the rate of cell growth then adjusts itself to the set dilution rate. This type of operation is relatively easy to carry out, but becomes unstable in the region near the washout point. 

In the turbidostat, P and F are kept equal but the dilution rate D is automatically adjusted to a preset cell concentration in the product by continuously measuring its turbidity. Compared to chemostat, turbidostat operation can be more stable in the region near the washout point, but requires more expensive instruments and automatic control systems. 

The chemostat is a biological CSTR where the substrate concentration in the tank is maintained constant. The tur-bidostat is similar to the chemostat except that the cell mass in the reactor is kept constant. The primary distinction between the two reactors is the control mechanism used to maintain continuous operation. A unique feature of a biological CSTR is the washout point. When the flow rate is increased so that the microbes can no longer reproduce fast enough to maintain a population, the microbes wash out of the tank, and the reaction ceases. This washout point represents the limits of maximum flow rate for operation. 

Hence, lysis as well as maintenance may cause the curve of biomass concentration against the dilution rate D to approach zero as the dilution rate tends to zero (see Figs. 6.4 and 6.5). Furthermore, the lysis causes a decrease in the washout point... 

The steady-state values of this model as a function of D are shown in Fig. 6.6. Note that the biomass concentration does not vanish above the washout point (see also Sinclair and Brown, 1970 Toda and Dunn, 1982). Imperfectly mixed bioreactor systems have been summarized recently by A. Moser (1985b). 

Drillstring Failure Prevention. Drillstring failures are mainly due to vibrations, shocks and neutral point positioned too close to the drill pipes. They result in drillstring washouts and twist-offs. 

For most practical purposes, a first-order process may be deemed complete if it is 95% or more complete. Table 1 shows that five half-lives must elapse to reach this point. Thus the elimination of a drug from the body may be considered to be complete after five half-lives have elapsed (i.e., 97% completion). This principle becomes important, for example, in crossover bioavailability studies in which the subjects must be rested for sufficient time between each drug administration to ensure that washout is complete. 

Due to the fact that it is assumed that a washout occurs directly after product is removed, two consecutive batches of product will be separated by a washout. In terms of time points, a unit can only start processing a batch two time points after the first batch starts. This is due to the fact that three time points are used to describe the batch processing and unit cleaning operations. Furthermore, the assumption that a cleaning operation follows product removal negates the need for a separate binary variable to represent the cleaning operation in a unit. Therefore, constraint (8.20) is included to ensure that two product producing tasks do not occur in consecutive time points. 

The bioreactor has two equilibrium points within the physically realizable domain. Such equilibrium points correspond to washout and operation conditions. For the operation condition (i.e., when degradation of the organic... 

Figure 6.14 shows these stationary-state solutions as a function of residence time for various small values of k2. The non-zero states exist over a limited range of ires they lie on the upper and lower shores of a closed curve, known as an isola . The size of the isola decreases as k2 increases. At each end of the isola there is a turning point in the locus, corresponding to extinction or washout. There are no ignition points in these curves. 

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