Feed function/rate

Fig. 32. Maximum flux obtained with various protein solutions as a function of protein concentration according to equation 3. Feed flow rates, cm /min = A, 3000 B, 2000 C, 1000 and D, 500. The flux decreases exponentially as the protein concentration increases. The extrapolated protein concentration at no flux is the gel point for this type of solution (approx 28%). These results were obtained in a flow-through cell and demonstrate the...

During operation, the immobilized enzyme loses activity. Most commercial enzymes show decay as a function of time (Eig. 12). The glucose isomerase ia a reactor is usually replaced after three half-Hves, ie, when the activity has dropped to around 12.5% of the initial value. The most stable commercial glucose isomerases have half-Hves of around 200 days ia practical use. To maintain the same fmctose content ia the finished symp, the feed-flow rate is adjusted according to the actual activity of the enzyme. With only one isomerization reactor ia operation, the result would be excessive variations ia the rate of symp production. To avoid this, several reactors at different stages ia the cycle of enzyme decay are operated ia combiaation. 

Optimisation may be used, for example, to minimise the cost of reactor operation or to maximise conversion. Having set up a mathematical model of a reactor system, it is only necessary to define a cost or profit function and then to minimise or maximise this by variation of the operational parameters, such as temperature, feed flow rate or coolant flow rate. The extremum can then be found either manually by trial and error or by the use of numerical optimisation algorithms. The first method is easily applied with MADONNA, or with any other simulation software, if only one operational parameter is allowed to vary at any one time. If two or more parameters are to be optimised this method becomes extremely cumbersome. To handle such problems, MADONNA has a built-in optimisation algorithm for the minimisation of a user-defined objective function. This can be activated by the OPTIMIZE command from the Parameter menu. In MADONNA the use of parametric plots for a single variable optimisation is easy and straight-forward. It often suffices to identify optimal conditions, as shown in Case A below. 

Thus, the specific growth rate in a chemostat is controlled by the feed flow rate, since // is equal to D at steady state conditions. Since ft, the specific growth rate, is a function of the substrate concentration, and since fi is also determined by dilution rate, then the flow rate F also determines the outlet substrate concentration S. The last equation is, of course, simply a statement that the quantity of cells produced is proportional to the quantity of substrate consumed, as related by the yield factor Yx/s-... 

A total continuity equation for the liquid phase is also needed, plus the two controller equations relating pressure to heat input and liquid level to feed flow rate Fq. These feedback controller relationships will be expressed here simply as functions. In later parts of this book we will iscuss these fhnctions in detail. 

A new value of frequency is specified and the calculations repeated. Table 12.3 gives a FORTRAN program that performs alt these calculations, The initial part of the program solves for all the steadystate compositions and flow rates, given feed composition and feed flow rate and the desired bottoms and distillate compositions, by converging on the correct value of vapor boilup Vg. Next the coeflicients for the linearized equations arc calculated. Then the stepping technique is used to calculate the intermediate g s and the final P(j transfer functions in the frequency domain. 

Remark 1 Since the light and heavy key recoveries of each column are treated explicitly as unknown optimization variables, then the cost of each nonsharp distillation column should be a function of its feed flow rate, feed composition, as well as the recoveries of the key components. 

Figure 2.79 Composition of dry reformate as a function of reaction temperature. Liquid feed flow rate 6 Ncm3 h-1. Circles, S/C 1.1 squares, S/C 1.5 triangles, S/C 2.0 [124] (by courtesy of ACS).

The results show that the feed flow rate and the temperature can be adequately chosen in order to obtain total tocopherol recovery. In addition, the behavior of the tocopherols on the evaporator as a function of the temperature and feed flow rate can be verified. In future works, the validation of the model and of the simulation will be demonstrated. 

Tables 9.2 and 9.3 list the recommended feed water and concentrate flow rates, respectively, as functions of feed water source quality.1 Higher feed water flow rates result in water and its contaminants being sent to the membrane more rapidly, leading to faster rates of fouling and scaling. As Table 9.2 shows, an RO operating on a well water source can have a feed flow rate as higher as 65 to 75 gpm per pressure vessel, while a surface water source RO should not exceed 58 to 67 gpm per pressure vessel. The well water RO would require 12% fewer pressure vessels than the surface water RO.

Table 9.2 listed the recommended feed flow rates as a function of water source.1 At higher feed water flow rates, contaminants such as colloids and bacteria that may be present in the source water, are sent to the membrane more rapidly, resulting in faster fouling of the membrane. This is why lower flow rates are recommended for water sources that contain high concentrations of contaminants. 

The variable that has the most significant impact on the economics of an extractive distillation is the solvent-to-feed flow rate ratio S/F. For close-boiling or pinched nonazeotropic mixtures, no minimum-solvent flow rate is required to effect the separation, as the separation is always theoretically possible (if not economical) in the absence of the solvent. However, the extent of enhancement of the relative volatility is largely determined by the solvent composition in the lower column sections and hence the S/F ratio. The relative volatility tends to increase as the S/F ratio increases. Thus, a given separation can be accomplished in fewer equilibrium stages. As an illustration, the total number of theoretical stages required as a function of S/F ratio is plotted in Fig. 13-95a for the separation of the nonazeotropic mixture of vinyl acetate and ethyl acetate using phenol as the solvent. 

The decision variables used for the optimization of the reactor must be selected among the operating ones. After considering industry requirements, the effect of each of the operating variables on the objective function and the easiness of how these variables can be changed in the plant, the feed flow rate of hydrogen (FAo) and the reactor feed temperature (Tfo) were chosen as the decision ones. Thus the optimization routine searches for the values of FAo and Tfo that, with the current value of o-cresol flow rate, lead to maximal reactor profit. 

Multiobjective optimization of the SMB and Varicol processes by a non-dominated sorting genetic algorithm (NSGA) which does not require any initial guess of the optimum solution was carried out by Zhang et al. [80] who used in that process an objective function that maximizes the feed flow rate (maximum throughput). 

Optimization of an existing SMBR system Maximizing the purity of a fraction and the yield of a compormd and minimizing the solvent consumption are chosen as the three objective functions. Six decision variables were used in this optimization study, the switching time (fj), the number of columns in sections II, III, and IV, the amormt of raffinate produced, and the eluent consumed. Since the optimization of an existing system is considered, the number of columns, their lengths and their diameters were kept fixed, but the sensitivity of the results to the number of columns on the Pareto shift was studied. The flow rate in section II and the temperature of the columns were also kept constant in order to allow a comparison of the optimum results at constant operation cost. Of the two throughput parameters, the raffinate flow rate (j3) was selected as a decision variable, in order to determine the optimum raffinate flow rate for a constant feed flow rate. 

Thus, the specific growth rate in a chemostat is controlled by the feed flow rate, since p is equal to D at steady state conditions. Since p, the specific growth rate, is a function of the substrate concentration, and since p is also determined by... 

Any control system which is properly designed to control the evaporation process must maintain both an energy and material balance across the evaporator boundaries. The control system must be able to accommodate some fluctuation in the feed flow rate or composition within a specified range, and still enable the evaporation system to perform the required separation with stable operation. The control system should function to reduce heat input with a reduction in feed rate, or change the evaporation rate as changes in the feed composition occur. 

RDX in feed). During the 90-d feeding study, four females (three at 420 and one at 187 ppm) and one male (exposed to 420 ppm) died within 56 d of exposure. It is likely the exposures to 420 ppm are of consequence, and that the moribund individual at 187 ppm was an anomaly, particularly since there were no statistical differences in organ weights, body mass, egg production, hematology, histopathology, and various functional and descriptive immune assays that were also conducted as part of the 90-d study [44], The feed consumption rates and mean body masses resulted in calculated RDX intakes of 0,6.0, 8.7,10.6,12.4, and 18.4 mg RDX kg-1 bw d 1 for both sexes for the 0, 83,125,187, 280, and 420 ppm feed treatments, respectively. 

The dynamic adsorption capacity of the annular bed was calculated by integrating the concentration vs. time curves up to a point close to the dynamic equilibrium time. Typical results of the dynamic adsorption capacity as a function of the SO2 inlet partial pressure, the feed flow rate and the feed concentration are shown in Figures 3 to 5. The effect of temperature on the dynamic adsorption capacity is shown in Figure 6 where the higher temperature data were taken from reference (5). 

Fig. 4. Ri4 vs. / 4 + i 6 as a function of temperature for the following conditions commercial low temperature shift Cu catalyst loading of 0.14 g/cm total feed flow rate of 236 cm (STP) min residence time r = 1.8 s feed composition of H2O(10%), CO(10%) and Nilbalance)...

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