Method of Calculations

having discussed the theory, the equipment, the required design data, and the special considerations, an actual design vvill be considered. Crystallization of monosodium glutamate shall be used for this example. The first step is to gather the design data. 

100-125 U.S. standard mesh 316L stainless steel, food grade 

The second step is to select an operating mode and to calculate the heat and material balances. For this example, an evaporative crystallizer will be used. Complete evaporation and crystallization of the feed will be assumed. 

From the preceding information, the nozzles connecting the crystallizer with the remainder of the process can be sized and a heat exchanger design prepared. While these are important to the design of the crystallization, they will not be pursued further at this time. 

The final step to be examined is the sizing of the crystal growth container. 

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To illustrate calculations for a binary system containing a supercritical, condensable component. Figure 12 shows isobaric equilibria for ethane-n-heptane. Using the virial equation for vapor-phase fugacity coefficients, and the UNIQUAC equation for liquid-phase activity coefficients, calculated results give an excellent representation of the data of Kay (1938). In this case,the total pressure is not large and therefore, the mixture is at all times remote from critical conditions. For this binary system, the particular method of calculation used here would not be successful at appreciably higher pressures. 

Porter and Momoh have suggested an approximate but simple method of calculating the total vapor rate for a sequence of simple columns. Start by rewriting Eq. (5.3) with the reflux ratio R defined as a proportion relative to the minimum reflux ratio iimin (typically R/ min = 1-D- Defining Rp to be the ratio Eq. (5.3) becomes... 

LCAO method A method of calculation of molecular orbitals based upon the concept that the molecular orbital can be expressed as a linear combination of the atomic orbitals. 

In 1972, Soave published a method of calculating fugacities based on a modification of the Redlich and Kwong equation of state which completely changed the customary habits and became the industry standard. In spite of numerous attempts to improve it, the original method is the most widespread. For hydrocarbon mixtures, its accuracy is remarkable. For a mixture, the equation of state is ... 

Fiscal allowances for investment in capital items (i.e. capex) are made through capital allowances. The method of calculating the capital allowance is set by the fiscal legislation of the host government, but three common methods are discussed below. 

One way of calculating the IRR is to plot the NPV against discount rate, and to extrapolate/ interpolate to estimate the discount rate at which the NPV becomes zero, as in the Present Value Profile in Figure 13.16. The alternative method of calculating IRR is by... 

Mayorov A.L. The Method of Calculation and Design of Magnetic Systems. -Defectoscope 89 - Int.Conference - Plovdive, Bulgaria, 1989, V2, P583-586,... 

This is Kirkwood s expression for the chemical potential. To use it, one needs the pair correlation fimction as a fimction of the coupling parameter A as well as its spatial dependence. For instance, if A is the charge on a selected ion in an electrolyte, the excess chemical potential follows from a theory that provides the dependence of g(i 2, A) on the charge and the distance r 2- This method of calculating the chemical potential is known as the Gimtelburg charging process, after Guntelburg who applied it to electrolytes. 

Banwell C N and Primas H 1963 On the analysis of high-resolution nuclear magnetic resonance spectra. I. Methods of calculating NMR spectra Mol. Phys. 6 225-56... 

Hazi A U and Taylor H S 1970 Stabilization method of calculating resonance energies model problem Phys. Rev. A 1 1109... 

In periodic boimdary conditions, one possible way to avoid truncation of electrostatic interaction is to apply the so-called Particle Mesh Ewald (PME) method, which follows the Ewald summation method of calculating the electrostatic energy for a number of charges [27]. It was first devised by Ewald in 1921 to study the energetics of ionic crystals [28]. PME has been widely used for highly polar or charged systems. York and Darden applied the PME method already in 1994 to simulate a crystal of the bovine pancreatic trypsin inhibitor (BPTI) by molecular dynamics [29]. 

L. A. Gribov, W. J. Orville-Thomas, Theory and Methods of Calculation of Molecular Spectra, Wdey, Chichester, 1988. 

Bond orders, charges, dipole moments, and reaction orders have been calculated for thiazole and alkylthiazoles. The order of electron density is 2<4<5. Different methods of calculation include LCAO SCF (162)... 

Notice that this generalization follows naturally from the method of calculating oxida tion numbers outlined m Table 2 5 In a C—C bond one electron is assigned to one carbon the second electron to the other In a bond between carbon and some other ele ment none of the electrons m that bond are assigned to carbon when the element is more electronegative than carbon both are assigned to carbon when the element is less elec tronegative than carbon... 

Energy, geometry, dipole moment, and the electrostatic potential all have a clear relation to experimental values. Calculated atomic charges are a different matter. There are various ways to define atomic charges. HyperChem uses Mulliken atomic charges, which are commonly used in Molecular Orbital theory. These quantities have only an approximate relation to experiment their values are sensitive to the basis set and to the method of calculation. 

Foster s neglect of the role of the adsorbed film was unavoidable in the then absence of any reliable information as to the thickness of the film. It is now known that in fact the effect of the film on the calculated result is far from negligible, as will be demonstrated shortly. Since, however, all the methods of calculating pore size distributions involve a decision as to the upper limit of the range to be studied, this question needs to be discussed first. In effect one has to choose a point corresponding to point G in Fig. 3.1, where the mesopores are deemed to be full up. If the isotherm takes the course GH there are no further cores to be considered in any case but if it swings upwards as at GH, the isotherm is usually so steep that the Kelvin-type approach becomes too inaccurate (cf. p. 114) to be useful. 

Fig. 14. Sketch of breakthrough curve showing break time / and the method of calculation of the stoichiometric time // and LUB. From ref. 7.

A. O. PaUingston and M. Weinstein, Method of Calculation of Interior Ballistic Properties of Propellantsfrom ClosedBomb Data, report 2005, PTA, Dover, N.J., 1959. 

High temperature steam cools and eventually condenses as it propagates through the oil reservoir. To maintain foam strength as the steam cools, a noncondensible gas, usually nitrogen or methane, is often added to the injectant composition (196). Methods of calculating the optimum amount of noncondensible gas to use are available (197). 

Power. The power requited to drive a belt conveyor is derived from the tensile forces requited to propel or restrain the belt at the design speed. These include the tensile forces produced by the frictional resistance of the drive, conveyor components, and material the acceleration of the material and the gravitational forces requited to lift or lower the material. Detailed information and methods of calculation can be found in belt conveyor design handbooks and in Reference 9. 

The values given in the following table for the heats and free energies of formation of inorganic compounds are derived from a) Bichowsky and Rossini, Thermochemistry of the Chemical Substances, Reinhold, New York, 1936 (h) Latimer, Oxidation States of the Elements and Their Potentials in Aqueous Solution, Prentice-Hall, New York, 1938 (c) the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards and (d) the tables of Selected Values of Chemical Thermodynamic Properties of the National Bureau of Standards. The reader is referred to the preceding books and tables for additional details as to methods of calculation, standard states, and so on. 

Basic pure component constants required to characterize components or mixtures for calculation of other properties include the melting point, normal boiling point, critical temperature, critical pressure, critical volume, critical compressibihty factor, acentric factor, and several other characterization properties. This section details for each propeidy the method of calculation for an accurate technique of prediction for each category of compound, and it references other accurate techniques for which space is not available for inclusion. 

The dipole moment (A) of a molecule is the first moment of the elec tric charge density of a molecule. Paraffins have dipole moments of zero, while dipole moments of almost all hydrocarbons are small. McClellan lists many dipole moments. The computer method of Dixon and Jurs" is the most useful method for predicting dipole moments. Lyman et al. give other methods of calculation. 

The effect upon total taxes paid, when they are corrected to their purchasing power in Year 0, is shown in Fig. 9-36. Differential inflation not only decreases the profitability of the project to its owner but also decreases the revenue received by the taxing authority. The method of calculation is identical to that of the earlier example. 

The simplified method of calculation outhned includes no allowance for the effect of surface tension. Stroebe, Baker, and Badger (loc. cit.) found that by adding a small amount of surface-... 

For the system water-acetic acid-MIBK in Fig. 15-11 the raffinate (water) layer is the solubility curve with low concentrations of MIBK, and the extract (MIBK) layer is the solubihty curve with high concentrations of MIBK. The dashed lines are tie lines which connect the two layers in equihbrium as given in Table 15-1. Example 2 describes the right-triangular method of calculating the number of theoretical stages required. 

Fig. 6.1. The method of calculating Young s modulus from the stiffnesses of individual bonds.

Prohl, M.A., General Method of Calculating Critical Speeds of Flexible Rotors, Trans. ASME, J. Appl. Mech., Vol. 12, No. 3, September 1945, pp. A142-A148. 

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