Exhaustion profiles

As with the steam turbine, if there was no stack loss to the atmosphere (i.e., if Qloss was zero), then W heat would he turned into W shaftwork. The stack losses in Fig. 6.34 reduce the efficiency of conversion of heat to work. The overall efficiency of conversion of heat to power depends on the turbine exhaust profile, the pinch temperature, and the shape of the process grand composite. 

Fig. 2. CEC methanol-fueled vehicle exhaust profile for (a) HC, hydrocarbons (b) NO and (c) CO. SoHd line represents State of California standard...

Figure 12.16 Exhaustion profiles for Cl Reactive Red 180 in the presence of 1.711N sodium chloride or 1.711N sodium citrate [139]...

What can be presently said about the contribution of automobile exhaust to the general PAH pollution in our environment This question certainly can not be answered as it has been tried in the introduction of this paper, calculating the benzo(a)pyrene concentration from automobile exhaust profiles and fuel consumption, since temporary and local variations have to be taken into account. In 196 a concentration of l60 ng benzo(a)pyrene/m was measured in the Essen area of Northrhine-Westphalia (FRG) (l4), whereas nowadays the mean concentration there varies between 1.2-27 ng/m- ... 

The resolution of geometrical isomers is readily accomplished on reversed-phase sorbents based on Vydac-type polymeric silica, unlike on monomeric phases on which all cis isomers usually co-elute. The exhaustive profiling of carotenoids in complex samples often requires the complementary use of a reverse phase (Cig) plus a polar (cyano) sorbent. With modern equipment it is possible to achieve accurate and reproducible separation and quantitation of the major classes of carotenoids, retinoids, and... 

Key words dyeing, dyes, textile fibres, dyeing quality, dyeing rate, levelness, dyeing vessels, package dyeing, dyeing automation, exhaustion profiles. 

Brooks showed that, for a given flow direction within a package, the difference in concentration across the radios was found to be proportional to the overall rate of exhaustion of the dye nsed. For a constant rate of depletion of dye, this difference must be constant thronghont the dyeing. This has cast serious doubts on the linear function being the optimnm exhaustion profile. He stated that neither linear exhaustion curves nor the time-temperature profile recotmnended by dye manufacturers result in best level dyeing. He showed that exponential curves and exhaustion curves proportional to the square root of time t give superior levelness compared with previous models. 

Ren stndied the exhaustion profiles and concluded both theoretically and experimentally that the quadratic exhaustion profile is more likely to result in better levelness than any other profile. The control of the exhaustion of a dyeing process to achieve the various profiles will be discussed in Chapter 7. 

Variation of the concentration of dye in the dyebath during the dyeing is referred to as the exhaustion profile, and the shape of this profile has been believed by many researchers to be the greatest determining factor in levelness of dyeing. ... 

Exhaustion control has been developed theoretically and in the laboratory by several workers. The earlier workers used knowledge of the dyeing kinetics to devise a time/temperature profile to give a particular exhaustion profile later workers attempted direct control of the exhanstion rate. 

Carbonell et al. developed a mathematical representation of various exhaustion profiles and went on to calculate practical time/temperature profiles that would result in linear exhaustion profiles. Cegarra et al. carried out more work aimed at establishing detailed kinetic relationships in order to carry out isoreactive dyeings, in which the dyeings have a linear exhaustion profile. ... 

Medley and Holdstock developed a mathematical model of the dyeing process, defined as simple depletion theory . Using this theory, they were able to show that an exponential exhaustion profile should give the optimum levelness for the same reasons as Brooks empirical argument - that at the end of the exhanstion phase the risk of nnlevelness is greatest. Their work also involved the development of a commercial dyebath monitoring system in order to apply their theoretical work to a real dyehorrse situation. ... 

Ren/ in collaboration with Nobbs, developed a theoretieal model of the package dyeing process, which can be used to quantify the diffeienee between the amount of dye inside and outside of the paekage over the whole of a dyeing cycle, which leads to the proposal of a new type of optimum exhaustion profile, the quadratic profile. 

Medley J.A., Holdstock C.R. (1980), The Choice of Optimum Dye Exhaustion Profiles in the Direct Control of Dyeing Journal ofthe Society of Dyers and Colourists, 96,286-92. 

Models that are based on the physico-chemical laws that describe the dyeing process, and introduce explicit mathematical equations, but which have a restricted description of the flow of the dye liquor around the machine and within the package. These models are generally used to determine dyeing conditions likely to produce a given desired exhaustion profile. 

The woik of Nobbs and Ren, unlike that of Hoffmann and Mueller, does not produce solutions which provide the concentration of dye at aity positions in the package at aity time. It gives a relationship between a number of variables and the unlevelness of dyeing. The control scheme developed and described subsequently by the authors was aimed at achievement of any of the three exhaustion profiles -linear, exponential or quadratic - by on-hne measurement of the dye bath conditions and manipulation of the temperature. 

Feed-forward predictive control models are among several that may be used in the control of the dyeing to obtain set pre-defined exhaustion profiles. This is achieved by altering the temperature of the system based on the prediction of exhaustion at any given stage. The model, based on dyeing kinetics, assumes an Arrhenius-type relationship between the exhaustion rate and the temperature. 

The control parameter for different exhaustion profiles is then defined as follows Linear ... 

Therefore, a general control parameter for all exhaustion profiles can be expressed as ... 

As was shown earlier, three exhaustion profiles were used in this model linear, quadratic and exponential. The general equation defining the exhaustion rate can be shown as ... 

The other correction is based on the fact that as the current concentration decreases the exhaustion rate will also decrease. Gilchrist also showed that 1-min look-forward times resulted in a good control for exponential and quadratic exhaustion profiles. Therefore, the equations for the desired exhaustion rate can be modified to those shown below. 

The final correction to the model is based on adjusting the exhaustion rate at the end of the non-linear exhaustion profiles, when it drops to very low values which would result in the control program trying to cool off the machine. The controller may be adjusted to accommodate a pre-set final ramp rate when the target exhaustion rate drops below 0.2%. 

Simulation results demonstrating a comparison of set and achieved exhaustion values using a linear exhaustion profile. 

A close look at the reported exhaustion values at the end of each dyeing profile suggests that complete exhaustion of dye from dyebath is impractical in many cases. Given the number of factors that could affect the outcome of the dyeing process, it is difficult to suggest any one profile as the best profile in terms of overall performance. Various researchers, however, have promoted different exhaustion profile shapes as producing the overall best results compared with the average. However, no conclusive evidence in support of any of the models for use on all fibres has so far been reported. 

Display of critical attributes on exhaust profile for a typical dyeing. 

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