Exactness

The most reliable estimates of the parameters are obtained from multiple measurements, usually a series of vapor-liquid equilibrium data (T, P, x and y). Because the number of data points exceeds the number of parameters to be estimated, the equilibrium equations are not exactly satisfied for all experimental measurements. Exact agreement between the model and experiment is not achieved due to random and systematic errors in the data and due to inadequacies of the model. The optimum parameters should, therefore, be found by satisfaction of some selected statistical criterion, as discussed in Chapter 6. However, regardless of statistical sophistication, there is no substitute for reliable experimental data. 

It cannot be said at this stage exactly how great an excess of decane would be required in order to make Fig. 4.7d feasible. This would have to be established experimentally, but the size of the excess does not change the basic structure. 

A refrigeration system is a heat pump in which heat is absorbed below ambient temperature. Thus the appropriate placement principle for heat pumps applies in exactly the same way as for refrigeration cycles. The appropriate placement for refrigeration cycles is that they also should be across the pinch. As with heat pumps, refrigeration cycles also can be appropriately placed across utility pinches. It is common for refrigeration cycles to be placed across a utility pinch caused by maximizing cooling water duty. 

In general, the final network design should be achieved in the minimum number of units to keep down the capital cost (although this is not the only consideration to keep down the capital cost). To minimize the number of imits in Eq. (7.1), L should be zero and C should be a maximum. Assuming L to be zero in the final design is a reasonable assumption. However, what should be assumed about C Consider the network in Fig. 7.16, which has two components. For there to be two components, the heat duties for streams A and B must exactly balance the duties for streams E and F. Also, the heat duties for streams C and D must exactly balance the duties for streams G and H. Such balemces are likely to be unusual and not easy to predict. The safest assumption for C thus appears to be that there will be one component only, i.e., C = 1. This leads to an important special case when the network has a single component and is loop-free. In this case, ... 

These expressions define Pn-2n for number of 1-2 shells in series in terms of R and Xp in each shell. The expressions can be used to define the number of 1-2 shells in series required to satisfy a specified value of Xp in each shell for a given R and Pjv 2n- Hence the relationship can be inverted to find the value of N which satisfies Xp exactly in each 1-2 shell in the series ... 

Boyle s law At constant temperature the volume of a given mass of gas is inversely proportional to the pressure. Although exact at low pressures, the law is not accurately obeyed at high pressures because of the finite size of molecules and the existence of intermolecular forces. See van der Waals equation. 

After the primary step in a photochemical reaction, the secondary processes may be quite complicated, e.g. when atoms and free radicals are fcrnied. Consequently the quantum yield, i.e. the number of molecules which are caused to react for a single quantum of light absorbed, is only exceptionally equal to exactly unity. E.g. the quantum yield of the decomposition of methyl iodide by u.v. light is only about 10" because some of the free radicals formed re-combine. The quantum yield of the reaction of H2 -f- CI2 is 10 to 10 (and the mixture may explode) because this is a chain reaction. 

Vegard s law In phases in which there is a range of composition of solid solution then the cell dimensions vary linearly with the molar proportions of the constituents. The (aw is rarely followed exactly. 

When it comes to the heaviest of petroieum fractions, modern analytical methods are not able to isolate and characterize the molecules completely. In the absence of something better, the analyst separates the heavy fractions into different categories, which leads merely to definitions that are workable but are no longer in terms of exact structure. 

All have molecular weights of 226 to the nearest integer (C = 12, H = 1, S = 32), but the exact molecular weights differ slightly. A resolution of 2500 is necessary to separate molecules 1, 2 and 3 but 75,000 is required to separate molecule 4 from molecule 3 which explains why high resolution mass spectrometers are sdiiglit. 

Adaptations of this method have been proposed in order to take into account the band displacement due either to substitution on the aromatic ring, or to chains of different lengths. The variations consist, instead of measuring the absorbance at maximum absorption, of an integration of the absorbance curve over a specified range (Oelert s method, 1971). More exact, this method is used less often mainly because the Brandes method is simpler... 

A panoply of methods whose results can be widely scattered are available to the process engineer not knowing the pitfalls attached to this activity, he would like to have a unique method or an exact guideline for applying these methods. 

The acentric factor can be determined as a function of temperature by finding the exact properties supplied by the DIPPR. 

The exact calculation of the index is given in the ASTM D 2270 standard. The kinematic viscosity at 40°C (f/) of an oil whose viscosity index (V7) is being calculated is compared with those of two reference oils for which the viscosity indices are 0 and 100 respectively, and which have at 100°C the same kinematic viscosity as that of the oil being examined )... 

The experimental conditions used to determine the CFPP do not exactly reflect those observed in vehicles the differences are due to the spaces in the filter mesh which are much larger in the laboratory filter, the back-pressure and the cooling rate. Also, research is continuing on procedures that are more representative of the actual behavior of diesel fuel in a vehicle and which correlate better with the temperature said to be operability , the threshold value for the Incident. In 1993, the CEN looked at two new methods, one called SFPP proposed by Exxon Chemicals (David et al., 1993), the other called AGELFI and recommended by Agip, Elf and Fina (Hamon et al., 1993). 

These are carbon monoxide, CO, unburned hydrocarbons (HC), and the nitrogen oxides, NO. In the U.S.A., a program called Auto/Oil (Burns et al., 1992), conducted by automotive manufacturers and petroleum companies, examined the effect of overall parameters of fuel composition on evaporative emissions and in the exhaust gases. The variables examined were the aromatics content between 20 and 45%, the olefins content between 5 and 20%, the MTBE content between 0 and 15% and finally the distillation end point between 138 and 182°C (more exactly, the 95% distilled point). 

The TBP (True Bolling Point) distillation gives an almost exact picture of a crude petroieum by measuring the boiling points of the components making up the crude whence its name. 

When the two components are mixed together (say in a mixture of 10% ethane, 90% n-heptane) the bubble point curve and the dew point curve no longer coincide, and a two-phase envelope appears. Within this two-phase region, a mixture of liquid and gas exist, with both components being present in each phase in proportions dictated by the exact temperature and pressure, i.e. the composition of the liquid and gas phases within the two-phase envelope are not constant. The mixture has its own critical point C g. 

An alternative and commonly used representation of the range of reserves is the proven, proven plus probable, and proven plus probable plus possible definition. The exact cumulative probability which these definitions correspond to on the expectation curve... 

A Monte Carlo simulation is fast to perform on a computer, and the presentation of the results is attractive. However, one cannot guarantee that the outcome of a Monte Carlo simulation run twice with the same input variables will yield exactly the same output, making the result less auditable. The more simulation runs performed, the less of a problem this becomes. The simulation as described does not indicate which of the input variables the result is most sensitive to, but one of the routines in Crystal Ball and Risk does allow a sensitivity analysis to be performed as the simulation is run.This is done by calculating the correlation coefficient of each input variable with the outcome (for example between area and UR). The higher the coefficient, the stronger the dependence between the input variable and the outcome. 

The exact relationship will depend upon both fluid and reservoir properties, and will be investigated during well planning. 

Schedule of Rates contract the cost of the labour is agreed on a rate basis, but the cost of materials and the exact hours are not specified. 

If you were offered 7,130 today, or 10,000 in exactly 5 years time, you should be indifferent to the options, unless you could find an alternative investment opportunity which yielded a guaranteed interest rate better than the bank (in which case you should accept the money today and take the alternative investment opportunity). 

The basic condition of the Standard application - the availability of stable coupled probabilistic or the multiple probabilistic relations between then controlled quality indexes and magnetic characteristics of steel. All the probabilistic estimates, used in the Standard, are applied at confidence level not less than 0,95. General requirements to the means of control and procedure of its performance are also stipulated. Engineers of standard development endeavoured take into consideration the existed practice of technical control performance and test at the enterprises that is why the preparation of object control for the performance of nondestructive test can be done during the process of ordinary acceptance test. It is suggested that every enterprise is operated in correspondence with direct and non-destructive tests, obtained exactly at it, for detailed process chart and definite product type, however the tests have long since been performed after development of the Standard displayed that process gives way to unification. 

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