Curve Method

In this example, the minimum utility requirements for a HEN involving the four streams in Example 10.1 are determined using the graphical approach by Umeda et al. (1978). 

F re 10.7 Graphical method to determine MER targets (a) heating and cooling curves for the streams (b) composite hot and cold curves. 

H2 coexist, and hence, their cooling requirements are combined. Note that the combined heat-capacity flow rate is increased, and consequently, the slope of the hot composite curve is reduced. Finally, ftoB 160 to 130°F, only stream H2 appears. 

the cold composite curve is graphed. For Ar jn = 10°F, the TI method determined a minimum cooling utility of 60 X 10 Btu/hr. Therefore, the graph begins with an enthalpy datum of that value. From Table 10.2, the cold composite enthalpies are 

Many additional observations are noteworthy in connection with the hot and cold composite curves. One is that the slopes of the composite curves always decrease at the inlet temperature of a stream and increase at the outlet temperature of a stream. It follows that points at which the slope decreases are candidate pinch points, and furthermore, when a pinch temp -ature exists, one of the inlet temperatures is always a pinch temperature. Hence, to locate a potential pinch temperature, one needs only to examine the inlet temperatures of Hk streams. 

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Heyer, R. H., Fracture toughness evaluation by R-curve methods. ASTM, STP 527... 

The EasQ for Hg, as well as for other liquid metals has been obtained using the Lippman electrometer12 (y, E curve method) modified by Gouy, Frumkin, Koening, and others. The principles of the technique and its problems have been extensively described in previous reviews1,10,16 and will not be dealt with further here. 

There have been many attempts to apply the surface tension (y, E curve) method to solid electrodes, and various experimental approaches... 

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

The ratio kJK, is obtained as /cobs/[I] at low inhibitor concentrations. With efficient inhibitors, parameters Kr and kt can be obtained using the progress curve method in which the enzyme substrate competes with the inhibitor as described for example in Ref. 21. 

Hasegawa et al. [76] measured miconazole serum concentration by a high performance liquid chromatographic method. The authors assessed whether the internal standard method produced an intra-assay error and found that the method gave more precise and more reproducible results compared to the absorption calibration curve method. With 0.5 pg/mL of miconazole, the coefficient of variation produced by that method was 3.41%, whereas that of the absorption calibration curve method was 5.20%. The concentration of absorptions calibration curve method showed higher values than the internal standard method. This indicated that the internal standard method was far more precise in measuring the miconazole serum concentrations than the absorption calibration curve method. 

Yamamoto et al. [6] studied preservation of arsenic- and antimony-bearing samples of seawater. One-half of the sample (201) was acidified to pH 1 with hydrochloric acid immediately after sampling, and the remaining half was kept without acidification. In order to clarify the effect of acidification on storage, measurements were made over a period of a month after sampling. Results are given in Table 1.1. In this study, a standard addition method and calibration curve method were used for comparison and it was proven that the two gave the same results for the analyses of seawater. 

Walters [24] examined the effect of chloride on the use of bromide and iodide solid state membrane electrodes, and he calculated selectivity constants. Multiple linear regression analysis was used to determine the concentrations of bromide, fluorine, and iodide in geothermal brines, and indicated high interferences at high salt concentrations. The standard curve method was preferred to the multiple standard addition method because of ... 

If desired, the model and program can be extended by adding a continuous inlet and outlet stream and by incorporating the E-curve methods found in Example CSTRPULSE. 

Jenc, F. (1983), The Reduced Potential Curve Method for Diatomic Molecules and Its Applications, Adv. Atom. Mol. Phys. 19, 265. 

ISO 3597-2 2003 Textile-glass-reinforced plastics - Determination of mechanical properties on rods made of roving-reinforced resin - Part 2 Determination of flexural strength ISO 5893 2002 Rubber and plastics test equipment - Tensile, flexural and compression types (constant rate of traverse) - Specification ISO 6721-3 1995 Plastics - Determination of dynamic mechanical properties - Part 3 Flexural vibration - Resonance-curve method... 

Confidence bands are direct precision data, and the maximum reportable concentration can be defined as the maximum concentration at which the method yields adequate precision ( ) (excluding measurements near the minimum reportable concentration, where poor precision is unavoidable). Table III shows RCB for the determination of iron in water by AAS. The analyst may consider a RCB of say, 15% to be adequate. The maximum reportable concentration would be 15 pg/ml from a single, weighted least-squares curve, and 20 pg/ml by the multiple-curve method. Samples containing > 20 pg/ml should be diluted to 1-10 pg/ml and analyzed using standards containing 0.05 - 15 pg/mL. (Note that it is always better to include a standard above the maximum desired concentration. The precision of this standard measurement will be poor, but poor data at this level are better than none.)... 

Mitchell has scattered points that do not conform to plotted data. It was uncertain which plot should have been used to compare to therefore the general consensus of all three was taken in this comparison and only obvious differences noted. For the single curve method the 6.4 amount in A was different from the plot. In B the 0.33, 0.082, 0.92, and 6.3 points were different. In F the 0.023 point was different and the 1.18 point appears to be in error. There was an improvement in precision when the multiple curve method was used. In A all three points conform. 

In B only the extreme points 0.31 and 24.9 do not appear to be similar. There were essentially no differences in F, save for the erroneous 1.18 point, over the single curve method. 

In general, the calibration curve method is suitable for all samples where the test substance is not bound in complexes or when it can be liberated from complexes by suitable sample pretreatment. Otherwise, the compositions of the samples and of the standard solutions must be as similar as possible to obtain results with acceptable accuracy. In view of the ISE potential drift, the calibration must be repeated often (at least twice a day). As mentioned above, the precision of the determination is not particularly high with a common precision of the potential measureihent at a laboratory temperature of 1 mV the relative error is 4% for univalent and 8% for divalent ions [58], However, this often suffices for practical analytical purposes. An advantage is that the same precision... 

Physical Measurements on Supports. Pore diameter and volume were determined by mercury poroslmetry. Micropores were estimated by the BET and t-curve methods (2i, 22). 

Comparison of surface areas as determined by the BET and t-curve methods (21) Is another measure of mlcroporoslty since the latter technique will estimate the surface area of pores under ISA In diameter. A SynChropak GPC-lOO sample gave 201 m /g by the BET method and 216 m /g by the t-curve method. 

ISA. In contrast, 7SA pore diameter Glycophase CPG was found to have 137 m /g of surface area by both the BET and t-curve methods Indicating the absence of micropores. 

Continuous steam distillation, 147, 148 Cooling baths, 61 Cooling curve method, 26 Copper bronze, activated, 193 Copper - chromium oxide catalyst, for aldehyde synthesis, 318, 321 for hydrogenation, 872, 873 hydrogenolysis with, 872J Copper phthalocyanine, 983 Copper powder, 192 Copper sulphate, as desiccant, 40, 41 Cork stoppers, 55 boring of, 56... 

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