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** Calculation of the Activation Energy by Iterative Procedure **

** Iterative Minimization Technique for Total Energy Calculations **

START ITERATIVE CALCULATION OF ACTUAL VAPCR COMPOSITION, ZKI) [Pg.302]

Figure 15, Iterative calculation of the instanton path. The labels 1-9 show gradual improvement of the instanton trajectory shape using the MP2/cc-pVDZ ab initio data. After switching to the CCSD(T)/(aug-)cc-pVDZ ab initio method, only two more steps needed to achieve convergence and obtain the final results. Taken from Ref. [104]. |

X is calculated from Eq. (2-37) and Tf is calculated from Eq. (2-38). Iterative calculation maybe required. [Pg.390]

Using Eqs. (5-42)-(5-46) in Section 5.3.2.2 with iterative calculations, the predicted CHF were compared with Columbia University data (Fighetti and Reddy, 1983). The comparison was made by examining the statistical results of critical power ratios (DNBRs), where [Pg.456]

Internal return rate. The internal return rate (IRR), also known as the discounted cash flow return rate, is the iteratively calculated discounting rate that would make the sum of the annual cash flows, discounted to the present, equal to zero. As shown in Figure 2, the IRR for Project Chem-A is 38.3%/yr. [Pg.109]

Shooting Methods The first method is one that utihzes the techniques for initial value problems but allows for an iterative calculation to satisfy all the boundaiy conditions. Consider the nonlinear boundaiy value problem [Pg.475]

Because the calculation of these residuals does not require any iterative calculations, the overall computational requirements are significantly less than for the explicit estimation method using Equation 14.15 and the explicit LS estimation method using Equations 14.16a and b (Englezos et al. 1990a). [Pg.236]

Multicomponent distillation is by far the common requirement for process plants and refineries, rather than the simpler binary systems. There are many computer programs which have been developed to aid in accurately handling the many iterative calculations required when the system involves three to possibly ten individual components. In order to properly solve a multicomponent design, there should be both heat and material balance at every theoretical tray throughout the calculation. [Pg.90]

Many different manipulations of these equations have been used to obtain solutions. As discussed by King (1971), many of the older approaches work in terms of V/L, which has the disadvantage of being unbounded and which, in the classical implementation, leads to poorly convergent iterative calculations. A preferable arrangement of this equation system for solution is based on the ratio V/F, which must lie between 0 and 1. If we substitute in Equation (7-1) for L from Equation (7-2) and for y from Equation (7-4), and then divide by F, we obtain [Pg.113]

As in Example BSTILL, a column containing four theoretical plates and reboiler is assumed, together with constant volume conditions in the reflux drum. The liquid behaviour is, however, non-ideal for this water-methanol system. The objective of this example is to show the need for iterative calculations required for bubble point calculations in non-ideal distillation systems, and how this can be achieved with the use of simulation languages. [Pg.610]

The design of any of the distillation processes discussed requires choosing an operating pressure, bottoms temperature, reflux condenser temperature and number of trays. This is normally done using any one of several commercially available process simulation programs which can perform the iterative calculations discussed in Chapter 6. [Pg.251]

Example 2 Calculation of Kremser Method For the simple absorber specified in Fig. 13-44, a rigorous calculation procedure as described below gives results in Table 13-9. Values of were computed from component-product flow rates, and corresponding effective absorption and stripping factors were obtained by iterative calculations in using Eqs. (13-40) and (13-41) with N = 6. Use the Kremser method to estimate component-product rates if N is doubled to a value of 12. [Pg.1277]

The primary purpose for expressing experimental data through model equations is to obtain a representation that can be used confidently for systematic interpolations and extrapolations, especially to multicomponent systems. The confidence placed in the calculations depends on the confidence placed in the data and in the model. Therefore, the method of parameter estimation should also provide measures of reliability for the calculated results. This reliability depends on the uncertainties in the parameters, which, with the statistical method of data reduction used here, are estimated from the parameter variance-covariance matrix. This matrix is obtained as a last step in the iterative calculation of the parameters. [Pg.102]

Unconstrained Optimization Unconstrained optimization refers to the case where no inequahty constraints are present and all equahty constraints can be eliminated by solving for selected dependent variables followed by substitution for them in the objec tive func tion. Veiy few reahstic problems in process optimization are unconstrained. However, it is desirable to have efficient unconstrained optimization techniques available since these techniques must be applied in real time and iterative calculations cost computer time. The two classes of unconstrained techniques are single-variable optimization and multivariable optimization. [Pg.744]

See also in sourсe #XX -- [ Pg.559 ]

** Calculation of the Activation Energy by Iterative Procedure **

** Iterative Minimization Technique for Total Energy Calculations **

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