The Ratio Method

The ratio method is a simple technique whereby known capital cost data for an existing chemical plant are adjusted to provide a cost estimate for the desired plant capacity. This method is also able to update figures to account for inflationary effects of past years. Finally the capital cost figure is adjusted for exchange rate differences between countries. The method is centred around the use of key cost estimation indices such as the CE Plant Cost Index and the Marshall and Stevens (M S) Index. 

The method used is outlined in Ref. CE9 (Chapter 4). The capital cost estimate is adjusted to the correct plant capacity by applying a scaling index. The appropriate scaling index for nitric acid plants is 0.6 (Ref. CE9 Table 19, p.184). Therefore  

The plant cost must be updated to account for inflation and technological advances over the 7 years from 1979 to 1986. This is achieved by the use of the CE Plant Cost Index (Ref. CE8 p.7). The cost is calculated from  

Present Cost = Previous Cost x (Present Index/Previous Index) 

The present index is evaluated using a formula that applies a weighting for the various capital cost components. The weighting scheme is shown below  

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A second order-of-magnitude approach is the ratio method, based on the assumption that capital investment can be correlated with plant capacity in a manner similar to that used for equipment. This gives... 

The ratio method is also particularly useful for quick estimates over a range of capacities after a calculated estimate for one size has been made (10). The calculated estimate can be separated into groups C, C2,. .., according to individual equipment exponents n, n2,. Then an overall plant capacity exponent n can be calculated from... 

An alternative approach to the quantitative analysis formalism is the ratio method. Here we consider the ratio of the intensities of any two edges A and B. Using Equation (3) we can show that... 

The accuracy achievable by the ratio method amounts to approximately 5-10 atom% when ionization edges of the same type are used, i. e. only K edges or only L edges, whereas the error in quantification increases to +15-20 atom% for the use of dissimilar edges. Improvement of the quantification accuracy up to approximately 1 atom% is possible if standards are used. 

Modern instruments capable of obtaining excitation-emission matrices (EEMs) allow use of new data-analysis techniques to resolve overlapped spectra. Resolution techniques such as the ratio method (28) and others (29,30) may provide further differentiation of the components present in the phases separated by solvent extraction. 

The absorbance ratio AnlAxi for the solute peak should be close to zero. If it is not, then this suggests that the peak is not what we think it is. For example, there may be another component that elutes at the same time, so the ratio method is a simple way of indicating the purity of the peaks. 

If there is no emission shift, but only variation in the fluorescence quantum yield on protonation, one follows the fluorescence intensity at one emission wavelength when the acid and the base forms of the probe are excited. All the advantages of the ratio method described with two emission wavelengths also apply to this fluorescence excitation method. 

Where N is the effective number of bonds along the normal and in plane directions, as tabulated in Table 3. From this expression, the variation of the Debye-Waller factor between 300 K and 77 K is derived by the ratio method ... 

This approximation, known as the "ratio method" (16), is particularly attractive for applications in solid-state chemistry because it should apply under the normal working conditions of a transmission electron microscope. If the approximation holds, then a determination of k using any well-characterised compound containing x and y will then afford a simple method for measuring the x y ratio in any other compound. This approach will be illustrated below with the results obtained for some standards... 

There are a number of potential difficulties with our method. In the first instance, we must ask whether the ratio method (equation (2)) is reliable under all circumstances if the crystals are sufficiently thin. We believe that in the vast majority of instances this will be the case, but we have encountered... 

The use of a line source and the ratio method (i. e. 7/7) tend to minimize errors in AAS. Thus, if the wavelength setting is seriously incorrect, it is unlikely that any absorption will be observed. If the wavelength is incorrectly tuned, the effects on the value of7 will roughly equal those on the value of I , and the error may not be too serious. 

The intense absorption of water over most of the infrared spectrum restricts the regions where aqueous solutions of carbohydrates can be usefully studied. Absorbance subtraction makes it possible to eliminate water absorbance and magnify the remaining spectral features to the limit of the signal-to-noise ratio. Many other data-processing techniques, such as the ratio method,4 the least-squares refinement,5 and factor analysis,6 should be of benefit in the study of carbohydrate mixtures. 

Peters and Timmerhaus (Ref. CE9) was the most used book in this category. It explains the ratio method and factored cost method of capital cost estimation. It also contains nomographs and correlations so that many plant equipment items can be costed. There are tables of typical values for costs such as insurance, depreciation and engineering. 

The capital cost is estimated by the ratio method at AS1 2.9 million. 

The economic evaluation is an important and integral part of the overall feasibility study of the project. First, a capital cost estimate is obtained using two estimation techniques. The ratio method and factorial cost estimation techniques are used to determine separate capital cost estimates for the proposed 280 tonne/day plant. Finally an investigation into the expected return on investment from this project is performed. 

The accuracy of the ratio method improves if more recent plant cost data are available. This figure is probably accurate to within + 30%. The exchange rate used was taken at 16th October 1986 (US I = AsO.6332). 

The ratio method provides an estimate of AS1 2.9 million. This can be regarded as reasonably accurate ( 30%) considering the original plant cost data is 7 years old. The factorial method has produced a surprisingly similar result. This is probably due to the fact that the plant is not particularly large, and the possibility of estimation cost inaccuracies is reduced. The estimate of AS1 3.5 million determined by the factorial cost technique should therefore also be regarded as an acceptably accurate value. 

Process in reasonable control the indirect proficiency test will be most economical of resources when the participating laboratories are consistently producing PT material lots having good quality. This condition facilitates use of the ratio methods mentioned in the previous section of this paper, and thus reduces the number of accurate, traceable measurements that are required. 

In this Sample Problem, you will see two different methods of solving the problem the algebraic method and the ratio method. Choose the method you prefer to solve this type of problem. 

Figure 10 The magnetic field dependence of H-ESEEM spectra (solid lines) obtained for Fe(II)NO-TauD samples treated with aKG and Ci- H-taurine using the ratio method described for Figure 9. The field positions displayed are (a) 171.0mT (b) 190.0 mT (c) 290.0 mT and (d) 346.0 mT. Simulations of these H-ESEEM spectra (dashed lines) are plotted along with the data. Hamiltonian parameters used for the simulations were principal g-values, 4.0, 4.0, 2.0 principal deuterium hyperfine values, —0.25, —0.25, 0.50 MHz Euler angles forhyperfine tensor, 0, 17°, 0 Q, 0.20 MHz ], 0 and Euler angles relating nqi to hyperfine, 0, 23°, 0...

The RATIO method table (Table I) includes provision for specifying upper and lower limits of integration for both primary and reference bands with the peak area evaluation procedure. The practical limits of the integration can be determined empirically by evaluating a set of spectra stored on microfloppy disks with varying limits set in the appropriate locations in the method table. Optimum limits can be determined from the calibration plots and related error parameters. The calibration plots shown in Figures 4 and 5 indicate that both evaluation procedures, peak height and peak area provide essentially the same level of precision for the linear least squares fit of the data. The error index and correlation coefficients listed on each table are both indicators of the relative scatter in the data from the least squares fit line. The correlation coefficient is calculated as traditionally defined in statistics. 

Raman spectroscopy is a scattering, not an absorption technique as FTIR. Thus, the ratio method cannot be used to determine the amount of light scattered unless an internal standard method is adopted. The internal standard method requires adding a known amount of a known component to each unknown sample. This known component should be chemically stable, not interact with other components in the sample and also have a unique peak. Plotting the Raman intensity of known component peaks versus known concentration in the sample, the proportional factor of Raman intensity to concentration can be identified as the slope of the plot. For the same experimental conditions, this proportional factor is used to determine the concentration of an unknown component from its unique peak. Determining relative contents of Si and Ge in Si—Ge thin films (Figure 9.38 and Figure 9.39) is an example of quantitative analysis of a Raman spectrum. 

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