Separative capacity calculation example

May [M6] has calculated the effect of varying the circulation rate N on the separative capacity of this centrifuge example operated at peripheral speeds of 400, 500, and 700 m/s, at a feed rate of 0.03171 g UFg/s, using the parameters of Table 14.14, with results shown in Fig. 

To reliably select separate thermodynamic parameters for the compoimds under consideration, we must improve the suitable calculation procedures and/or criteria that allow the validity of the available experimental data to be estimated. To this end, we have selected lanthanide trifluorides as example. They are much less sensitive to hydrolysis although they have noticeable corroding action on container materials at high temperatures. In view of this, we have chosen the method of heat capacity calculations over a wide temperature range, up to the melting point, based on an analysis of the experimental low-temperature heat capacities and high-temperature enthalpy increments. This method is described below. Its application to lanthanide di- and trichlorides will be presented later on. 

If the capacity factor and a are known, then equation 12.21 can be used to calculate the number of theoretical plates needed to achieve a desired resolution (Table 12.1). For example, given a = 1.05 and kg = 2.0, a resolution of 1.25 requires approximately 24,800 theoretical plates. If the column only provides 12,400 plates, half of what is needed, then the separation is not possible. How can the number of theoretical plates be doubled The easiest way is to double the length of the column however, this also requires a doubling of the analysis time. A more desirable approach is to cut the height of a theoretical plate in half, providing the desired resolution without changing the analysis time. Even better, if H can be decreased by more than... 

Having chosen the test mixture and mobile diase composition, the chromatogram is run, usually at a fairly fast chart speed to reduce errors associated with the measurement of peak widths, etc.. Figure 4.10. The parameters calculated from the chromatogram are the retention volume and capacity factor of each component, the plate count for the unretained peak and at least one of the retained peaks, the peak asymmetry factor for each component, and the separation factor for at least one pair of solutes. The pressure drop for the column at the optimum test flow rate should also be noted. This data is then used to determine two types of performance criteria. These are kinetic parameters, which indicate how well the column is physically packed, and thermodynamic parameters, which indicate whether the column packing material meets the manufacturer s specifications. Examples of such thermodynamic parameters are whether the percentage oi bonded... 

The breakthrough curves measured for the monolithic columns with different proteins are very sharp and confirm again the fast mass transport kinetics of the monoliths [133, 134]. The frontal analysis used for the determination of the breakthrough profile can also be used for calculation of the dynamic capacity of the column. For example, the capacity for the 60x16mm i.d. monolith at 1% breakthrough is 324 mg of ovalbumin and represents the specific capacity of 40.0 mg/g of separation medium or 21.6 mg/ml of column volume. 

This equation indicates that minimal separation time depends on plate numbers, capacity factor, and resistance to mass transfer. It should be pointed out that the analysis times calculated from Equation 2.121 also depend on the desired resolution. Our example calculations were made on the basis of resolution, =... 

Although the thermal demands of crystallization processes are small compared with those of possibly competitive separation processes such as distillation or adsorption nevertheless, they must be known. For some important systems, enthalpy-composition diagrams have been prepared, like those of Figure 16.4, for instance. Calculations also may be performed with the more widely available data of heat capacities and heats of solution. The latter are most often recorded for infinite dilution, so that their utilization will result in a conservative heat balance. For the case of Example 16.3, calculations with the enthalpy-concentration diagram and with heat of solution and heat capacity data are not far apart. 

Once the list is narrowed down, the relief capacity for each of the remaining failures must be determined separately. At this stage, the premises must be reexamined, and any credits must be carefully reviewed. The desired location of the relief device must be determined, since this will have some effect on its capacity. Common practices for setting relief device capacity, credit pitfalls, and preferred location are discussed in subsequent sections. Examples of the premises and calculations are presented elsewhere (293, 351). Each failure will lead to a different relief requirement. The largest requirement sets the size of the relief device. 

As mentioned in section 2.2.2, treatment of hindered internal rotators is not included in SMCPS instead a more exact contribution from hindered rotations is calculated by use of the ROTATOR program. The calculated entropy and heat capacities are then added to those calculated with SMCPS. The example input file shown in Scheme 2.5 evaluates the rotation of the first oxygen about the next carbon (C=C—OOC). It is important to emphasis that each rotor is computed separately. Required data are all extracted from Gaussian computation, geometry of the optimized structure and the rotational energy from which the parameters of the Fourier equation are derived. 

The buffer capacity can become important in separations of extended duration. For example, a CGF separation requiring 30 min on a 30 cm capillary will require 300 minutes on a 300 cm capillary if the same electric field strength is used. The 10-fold increase in analysis time results in 10-fold the amount of electrolysis products that must be dealt with by the buffer. The moles of OH at the cathode can be calculated from the electrophoretic current i) ... 

In order to optimize a separation and produce it in the minimum time, the capacity ratios and separation ratios must be measured for a given pair of enantiomers under known conditions of mobile phase composition and temperature (this will be discussed in detail later in this chapter). Unfortunately, when two peaks are eluted close together, which frequently occurs in chiral chromatography, the positions of the peak maxima are distorted due to the immediate presence of the other peak. An example of this problem is shown in figure 10.1, where the peaks are simulated and added, and the composite envelope plotted over the envelope of each individual peak. It is seen that the actual retention difference, if taken from the maxima of the envelope, will give a value of less than 60% of the true retention difference. Unfortunately, this type of error will probably not be taken into account by most data processing software. It follows, that if such data is used in an attempt to calculate the... 

Taking a practical example of a column 40 cm long, 2 cm ID., having a dead volume of 75.4 ml (s tz r l), the maximum sample volume can be calculated for a range of separation ratio values (a) and capacity ratio values (k) for the first eluted peak. The results are shown in figure 12.2... 

This relationship allows us to calculate the constant-volume heat capacity in the ideal-gas state from tabulations of the constant-pressure heat capacity. For this reason, V is not tabulated separately. Example 3.16 Isothermal Compression of Steam... 

In writing this equation, it is very important that, unless otherwise stated, each reactant and product is understood to be the pure component in a separate and designated phase gas, liquid, or solid. A reaction is characterized by two important thermodynamic quantities, namely the heat of reaction and the Gibbs (free) energy of reaction. Furthermore, these two quantities are functions of temperature and pressure. Thermodynamic data are widely available in simulators and elsewhere, for more than a thousand components, for the calculation of these two quantities under standard state conditions, for example, at a reference temperature of 25°C and 1 bar with all components in a designated phase, usually as an ideal gas. The effect of temperature on the heat of reaction depends on the heat capacities of the reactants and products and the effect of temperature on those heat capacities. For... 

EXAMPLE 1.7-1. Heating of Fermentation Medium A liquid fermentation medium at 30°C is pumped at a rate of 2000 kg/h through a heater, where it is heated to 70°C under pressure. The waste heat water used to heat this medium enters at 95°C and leaves at 85°C. The average heat capacity of the fermentation medium is 4.06 kJ/kg- K, and that for water is 4.21 kJ/kg K (Appendix A.2). The fermentation stream and the wastewater stream are separated by a metal surface through which heat is transferred and do not physically mix with each other. Make a complete heat, balance on the system. Calculate the water flow and the amount of heat added to the fermentation medium assuming no heat losses. The process flow is given in Fig. 1.7-1. 

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