Product criteria

We might say that if Pv is used as the elemental criterion, a weighing factor is automatically built into the (sum or product) criterion for the entire chromatogram, which puts the emphasis either on the major or on the minor components in the sample. 

Nevertheless, the use of eqn.(4.32) may result in a slower optimization process than if a simple sum or product criterion were used. It is also unclear at the outset how the process would respond to chromatograms with the same value for Cp but widely different values f or C. In other words, the criterion cannot differentiate between a bad resol ution in a short time and a good resolution in a long time. 

In section 4.3.2 we have seen that the normalized resolution product criterion r aims at achieving a chromatogram in which all peaks appear at constant resolution intervals from the first one. If r is used instead of r, then the regular intervals start at an imaginary peak at t=t0. A chromatogram for which r = 1 is one of a series for which the constant intervals can be found. Once the absolute value of S, the number of peaks and the plate number are known, the chromatogram is defined unambiguously. 

If a product of peak-valley ratios is used as the optimization criterion, then two values would need to be used for every peak, one describing its resolution from the preceding peak in the chromatogram and the other one describing its resolution from the following peak. Because a product criterion is used, the weighting factors (g) will appear as powers in the product. If we assume the weighting factors to be positive, we may write... 

In order to investigate the conditions governing the precipitation of the particles Equations 7.6.7-7.6.9 may be used for mathematical modelling of the process. Assuming the solubility product criterion to be satisfied, that is the system is saturated with regards to the compound formed, the combined activity coefficients for the precipitated compounds may be calculated. According to Equation 7.6.8, the slope of the saturation content of... 

The flash point of a petroleum liquid is the temperature to which it must be brought so that the vapor evolved burns spontaneously in the presence of a flame. For diesel fuel, the test is conducted according to a closed cup technique (NF T 60-103). The French specifications stipulate that the flash point should be between 55°C and 120°C. That constitutes a safety criterion during storage and distribution operations. Moreover, from an official viewpoint, petroleum products are classified in several groups according to their flash points which should never be exceeded. 

The type of development, type and number of development wells, recovery factor and production profile are all inter-linked. Their dependency may be estimated using the above approach, but lends itself to the techniques of reservoir simulation introduced in Section 8.4. There is never an obvious single development plan for a field, and the optimum plan also involves the cost of the surface facilities required. The decision as to which development plan is the best is usually based on the economic criterion of profitability. Figure 9.1 represents a series of calculations, aimed at determining the optimum development plan (the one with the highest net present value, as defined in Section 13). 

The reservoir model will usually be a computer based simulation model, such as the 3D model described in Section 8. As production continues, the monitoring programme generates a data base containing information on the performance of the field. The reservoir model is used to check whether the initial assumptions and description of the reservoir were correct. Where inconsistencies between the predicted and observed behaviour occur, the model is reviewed and adjusted until a new match (a so-called history match ) is achieved. The updated model is then used to predict future performance of the field, and as such is a very useful tool for generating production forecasts. In addition, the model is used to predict the outcome of alternative future development plans. The criterion used for selection is typically profitability (or any other stated objective of the operating company). 

In teclmology, an economic separation of tlie products of a reaction from tlie solution containing tlie catalyst is necessary. Distillation is a commonly used metliod and, for it to work successfully, tlie products and catalyst must be stable at tlie temperatures of tlie distillation, which are often relatively high some organometallic compounds, for example, may not meet tliis criterion. 

We now turn specifically to the thermodynamics and kinetics of reactions (5. EE) and (5.FF). The criterion for spontaneity in thermodynamics is AG <0 with AG = AH - T AS for an isothermal process. Thus it is both the sign and magnitude of AH and AS and the magnitude of T that determine whether a reaction is thermodynamically favored or not. As usual in thermodynamics, the A s are taken as products minus reactants, so the conclusions apply to the reactions as written. If a reaction is reversed, products and reactants are interchanged and the sign of the AG is reversed also. 

The first criterion was associated with improved secondary and tertiary petroleum recovery processes. This is the justification for the patent appHcations issued to the Dow (50) and Exxon (51) corporations. The additional costs of production and the increased adsorption of such modified water-soluble polymers are detrimental to the commercial appHcation of such polymers and even the academic studies in this area have decreased in recent years. 

Spices are natural agricultural products and exhibit a range of variations of many specific characteristics. The most important quaUty assessment is the subjective physical observation of the whole or ground spice by an expert. The macroscopic and microscopic examination of spice is the criterion for the continued analysis of the product to determine adherance to specifications. 

High temperature is an important requirement for the attainment of fusion reactions in a plasma. The conditions necessary for extracting as much energy from the plasma as went into it is the Lawson criterion, which states that the product of the ion density and the confinement or reaction time must exceed 10 s/cm in the most favorable cases (173). If the coUisions are sufficiently violent, the Lawson criterion specifies how many of them must occur to break even. Conventional magnetic confinement involves fields of as much as 10 T (10 G) with large (1 m ) plasmas of low densities (<10 particles/cm ) and volumes and reaction times of about 1 s. If the magnetic flux can be compressed to values above 100 T (10 G), then a few cm ... 

Loss of elongation is the most sensitive criterion for aging measurement regardless of mechanism, and it is favored over measurement of tensile loss for cured compounds. In synthetic mbber production (SBR, in particular), viscosity increases with aging and can affect processing if not prevented. 

Elastic Properties. The abiUty of a fiber to deform under below-mpture loads and to return to its original configuration or dimension upon load removal is an important performance criterion. Permanent deformation may be as detrimental as actual breakage, rendering a product inadequate for further use. Thus, the repeated stress or strain characteristics are of significance in predicting or evaluating functional properties. 

Performance. Consumer acceptance is a criterion on which cosmetic marketers caimot compromise. Whereas the likes and dislikes of consumers are in a state of constant flux, some product features are critical. A deodorant that does not deodorize or a hair coloring that fades in sunlight is unacceptable. Performance is tested by in vitro techniques during formulation, but the ultimate test of a product s performance requires in-use experience with consumers and critical assessment by trained observers. Performance tests can sometimes be combined with in-use safety tests, and protocols for such programs have been developed. 

By employing successive substitution of the tear variables and the criterion of Eq. (13-83), convergence was achieved slowly, but without oscillation, in 23 iterations. Computed products are. 

Rejection Rejection is defined in Background and Definitions. The highest-rejection membranes are those designed for single-pass production of potable water from the sea. The generally accepted criterion is 99.4 percent rejection of NaCl. Some membranes, notably cellulose triacetate fibers are rated even higher. A whole range of membranes is available as rejection requirements ease, and membranes with excellent chlorine resistance and hydrolytic stability can be made with salt rejection over 90 percent. 

As with all of die processes described, drese are first studied in detail in the laboratoty with an industrial application as dre objective. Those processes which pass the criterion of economic potential are used in a pilot plant smdy, and dretr, if successful, at the production level which must be optimized. The materials which are produced are mainly, in the present instance, for application in the elecU onics industry where relatively high costs are acceptable. It will be seen drat the simple kinetic theory of gases is adequate to account for dre rates of these processes, and to indicate the ways in which production may be optimized on dre industrial scale. 

An important practical question is, what is the representative pipe diameter in loading circuits comprising different sizes of pipe This has a large effect on the values calculated for velocity and velocity-diameter product. As an example, static ignition of ester mist in a rail car (5-1.3.1) involved 1450 gpm through a 6-in. pipe (v = 5 m/s and vd = 0.76 mVs) followed by a short 4-in. dip pipe assembly (y = 11 m/s and vd = 1.15 mVs). Were nonconductive liquid flow rate restrictions applied to the semiconductive ester (time constant —0.01 s) involved in this fire, the flow rate based on the 4-in. pipe would be unacceptably large based either on a 7 m/s maximum velocity or a 0.80 mVs maximum vd product. However, based on the 6-in. pipe upstream the flow velocity is less than 7 m/s and also meets API s vd < 0.80 mVs criterion. 

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