Calculation computer

O Connell, and R. V. Orye "Computer Calculations for Multicomponent Vapor-Liquid Equilibria," Prentice-Hall, Englewood Cliffs, N.J., 1967. 

Discusses the thermodynamic basis for computer calculations for vapor-liquid equilibria computer programs are given. Now out of date. 

In the original study (61), NTU /NTU was calculated for thousands of hypothetical design cases as a function of both Pe and Pep -pu- The results were correlated and empirical expressions were given that can be evaluated on a handheld calculator, just as equations 76 and 77, but which approximate the computer calculation much better, to within about 5%. 

The problem of solvent selection is most difficult for high molecular-weight polymers such as thermoplastic acryHcs and nitrocellulose in lacquers. As molecular weight decreases, the range of solvents in which resins are soluble broadens. Even though solubihty parameters are inadequate for predicting ah. solubhities, they can be useful in performing computer calculations to determine possible solvent mixtures as replacements for a solvent mixture that is known to be satisfactory for a formulation. 

J. M. Prausnit2 and co-workers. Computer Calculations for Multicomponent Vapor—Eiquid and Eiquid—Eiquid Equilibria Prentice-Hall, Inc., Englewood Cliffs, N.J., 1980. 

Ruiter, J. P, Rev. Jnt. Fioid = Jnt. J. Refrig., 13 (1990) 223—236 gives subroutines for computer calculations. See also ASHRAE Handbook—Fundamentals. 

Multicomponent systems containing four or more components become difficult to display graphically. However, process-design calculations can often be made for the extraction of the component with the lowest partition ratio K and treated as a ternaiy system. The components with higher K values may be extracted more thoroughly from the raffinate than the solute chosen for design. Or computer calculations can be used to reduce the tedium of multicomponent, multistage calculations. 

Results The results of computer calculations are summarized for the two operations by Figs. 23-4 and 23-5. In the second design, the equations had to be modified to take account of two feeds with different specific rates. 

Figure 23-36 shows a computer calculation with these specific rates, but which does not agree quantitatively with the figure shown by Swern. The time scales appear to be different, but both predict a peak in the amount of oleic acid and rapid disappearance of the first two acids. 

Equation-of-state measurements add to the scientific database, and contribute toward an understanding of the dynamic phenomena which control the outcome of shock events. Computer calculations simulating shock events are extremely important because many events of interest cannot be subjected to test in the laboratory. Computer solutions are based largely on equation-of-state models obtained from shock-wave experiments which can be done in the laboratory. Thus, one of the main practical purposes of prompt instrumentation is to provide experimental information for the construction of accurate equation-of-state models for computer calculations. 

Published analyses of cascade cycles by means of energy balances under conditions comparable to those used in analyzing expander cycles are very scarce. Longwell and Kruse tabulated computer-calculated compressor and expander powers for a C3Hg-C2Fl4-CF[4 cascade. For a feed of 1,566 Ib-moles/hr at 515 psia and 60°F, 490 lb-moles of LNG and two gaseous products were produced. 

The Smith-Brinkley Method uses two sets of separation factors for the top and bottom parts of the column, in contrast to a single relative volatility for the Underwood Method. The Underwood Method requires knowing the distillate and bottoms compositions to determine the required reflux. The Smith-Brinkley Method starts with the column parameters and calculates the product compositions. This is a great advantage in building a model for hand or small computer calculations. Starting with a base case, the Smith-Brinkley Method can be used to calculate the effect of parameter changes on the product compositions. 

Kaufman, L. and Bernstein, H. (1970) Computer Calculations of Phase Diagrams (Academic Press, New York). 

Equation (16) was tested against some data obtained for (R) 4-phenyl-2-oxazolidinone using a range of mixtures of ethanol, acetonitrile and -hexane as the mobile phase. The column chosen was similar to that previously used for the separation of the 4-phenyl-2-oxazolidinone which was 25 cm long, 4.6 mm I.D. packed with 5 mm silica particles bonded with the stationary phase Vancomycin. The results obtained are shown in Table 1 and this is the data used in subsequent computer calculations. 

Step 8 Solve the Equations. Many material balances can be stated in terms of simple algebraic expressions. For complex processes, matrix-theory techniques and extensive computer calculations will be needed, especially if there are a large number of equations and parameters, and/or chemical reactions and phase changes involved. 

Large computers calculated theoretical models of the secondary processes to produce tables of build-up factors. These tables are for neutrons and gammas of various energies in many geometries and material combinations. 

The equations for calculating the individual velocity components in the. r and y directions are given in rhe source,- where suitable forms for computer calculations are also given. 

Depending on the purpose of the computer calculations, different tools are selected. The modeling methods described in this chapter and their pri maty application are listed in Table 11.1. 

The results of a set of computer calculations for a CBT plant with single-step cooling (i.e. of the first stage nozzle guide vanes) are illustrated in Fig. 5.2, in the form of (arbitrary) overall thermal efficiency (tjq) against pressure ratio (r) with the combustion temperature T. oi as a parameter, and in Fig. 5.3 as tjq against with r as a parameter. 

Once the state points are known round a cycle in a computer calculation of performance, the local values of availability and/or exergy may be obtained. The procedure for e.stimating exergy losses or irreversibilities was outlined in Chapter 2. Here we. show such calculations made by Manfrida et al. [13] which were also presented in Ref. [14]. 

This method is the most popular procedure, as it can be used without problems by both manual and computer calculations (Fig. 14.1). 

The relative fluctuations in Monte Carlo simulations are of the order of magnitude where N is the total number of molecules in the simulation. The observed error in kinetic simulations is about 1-2% when lO molecules are used. In the computer calculations described by Schaad, the grids of the technique shown here are replaced by computer memory, so the capacity of the memory is one limit on the maximum number of molecules. Other programs for stochastic simulation make use of different routes of calculation, and the number of molecules is not a limitation. Enzyme kinetics and very complex oscillatory reactions have been modeled. These simulations are valuable for establishing whether a postulated kinetic scheme is reasonable, for examining the appearance of extrema or induction periods, applicability of the steady-state approximation, and so on. Even the manual method is useful for such purposes. 

Of course, the fact that every problem presents molecular models raises natural questions about the accuracy and meaning of these models. Molecular models are not derived from experiments, but rather from computer calculations. Thus, there will be some differences between modeling data and experimental data, and one must occasionally interpret these data in different ways. 

A concerted [2 + 2] cycloaddition pathway in which an oxametallocycle intermediate is generated upon reaction of the substrate olefin with the Mn(V)oxo salen complex 8 has also been proposed (Scheme 1.4.5). Indeed, early computational calculations coupled with initial results from radical clock experiments supported the notion.More recently, however, experimental and computational evidence dismissing the oxametallocycle as a viable intermediate have emerged. In addition, epoxidation of highly substituted olefins in the presence of an axial ligand would require a seven-coordinate Mn(salen) intermediate, which, in turn, would incur severe steric interactions. " The presence of an oxametallocycle intermediate would also require an extra bond breaking and bond making step to rationalize the observation of trans-epoxides from dy-olefms (Scheme 1.4.5). 

Maas [108] presents a useful analysis for selecting the feed tray in a multicomponent column. For accuracy it involves the use of a tray-by-tray computer calculation. 

Yaw s et al. [141] present a useful technique for estimating overhead and bottoms recoveries with a very good comparison with tray-to-tray computer calculations. The procedure suggested uses an example from the reference with permission ... 

The results of the computer calculation are as summarized by copies of the printouts. Note that Stage one is the product from an overhead condenser and is hquid, as is the bottoms or reboiler outlet product. The results show that the initial criteria have been met for recovery of component 5 however, this does not reflect any optimization of reflux or final number of stages (theoretical trays) that might be required to accomplish the separation in a final design. 

Prausnitz, J. M. and P. L. Cheuh, Computer Calculations for High Pressure Vapor-Liquid Equilibrium, Prentice-Hall Inc. (1968). 

Packed column performance can use either the HETP or HTU concepts, the HTU is somewhat more complicated but no more correct than the HETP concept. The latter adapts itself to direct use from tray-by-tray digital computer calculations, and is thereby a litde more direct. 

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