Favourable isotherm

A constant wave-pattern develops when adsorption is governed by a favourable isotherm. In Figure 17.16a, a typical wave is assumed to move a distance dz in a time dr. If the wave is already fully developed, it will retain its shape. A mass balance gives ... 

The adiabatic profile may be further complicated by the shape of the isotherm. Under isothermal conditions, a favourable isotherm produces a single transfer zone, although an isotherm with favourable and unfavourable sections may generate a more complex profile, as shown in Figure 17.21. 

In numerous industrial processes, VOCs and/or air streams containing odorous substances, sometimes in very large quantities, are generated by production. These substances must be concentrated if they are to be disposed of economically. Conventional concentration processes are usually limited to a factor of 10 or a maximum of 20. Due to considerably faster adsorption kinetics, compared to commercial granular activated carbon as well as more favourable isotherm trends for low concentrations, commercial activated carbon cloths (ACC) are particularly suitable for VOC removal at low concentrations ranging from several pg/m ... 

Cooney, D.O., Rapid approximate solutions for adsorption bed concentration profile and breakthrough curve behavior Favourable isotherms and both phase resistances important, Chem. Eng. Commun.. 91, l-IO (1990). Cooney, D.O., On the basis for the Freundlich adsorption isotherm, Chem. Eng. Commun.. 94.27-34 (1990). 

It is fortunate that for many fixed bed adsorption processes of commercial interest the shape of the mass transfer zone remains unaltered as it progresses through the majority of the bed because this leads to substantial simplifications in design. For a favourable isotherm, particularly one of Type I, the mass transfer wave spreads from a shock front as it progresses through the initial region of the bed. As explained earlier in this chapter the... 

The LUB design method requires that constant pattern behaviour occurs. It provides the basis for a very simple design method which allows the design and scale-up from small-scale laboratory experiments particularly for dilute single-component systems in which there is a favourable isotherm. A dilute system implies that the process will be isothermal. Care must be taken if the process is not isothermal because it is possible for the temperature effects to cause a favourable isotherm to take on effectively an unfavourable shape. 

An interesting example of a large specific surface which is wholly external in nature is provided by a dispersed aerosol composed of fine particles free of cracks and fissures. As soon as the aerosol settles out, of course, its particles come into contact with one another and form aggregates but if the particles are spherical, more particularly if the material is hard, the particle-to-particle contacts will be very small in area the interparticulate junctions will then be so weak that many of them will become broken apart during mechanical handling, or be prized open by the film of adsorbate during an adsorption experiment. In favourable cases the flocculated specimen may have so open a structure that it behaves, as far as its adsorptive properties are concerned, as a completely non-porous material. Solids of this kind are of importance because of their relevance to standard adsorption isotherms (cf. Section 2.12) which play a fundamental role in procedures for the evaluation of specific surface area and pore size distribution by adsorption methods. 

The computation of mesopore size distribution is valid only if the isotherm is of Type IV. In view of the uncertainties inherent in the application of the Kelvin equation and the complexity of most pore systems, little is to be gained by recourse to an elaborate method of computation, and for most practical purposes the Roberts method (or an analogous procedure) is adequate—particularly in comparative studies. The decision as to which branch of the hysteresis loop to use in the calculation remains largely arbitrary. If the desorption branch is adopted (as appears to be favoured by most workers), it needs to be recognized that neither a Type B nor a Type E hysteresis loop is likely to yield a reliable estimate of pore size distribution, even for comparative purposes. 

A particle size effect has been detected by Chou and Olson [486] in the isothermal decomposition of isothiocyanatopentammine cobalt(III) perchlorate. Below a = 0.09, the larger crystals decompose relatively more rapidly than the smaller, whereas for a > 0.09, the reverse is true. This behaviour was attributed to enhanced nucleation in the larger particles due to strain, but this favourable factor was later offset by the inhibiting influence of the product ammonia which accumulated in the larger crystals. 

Essentially, extraction of an analyte from one phase into a second phase is dependent upon two main factors solubility and equilibrium. The principle by which solvent extraction is successful is that like dissolves like . To identify which solvent performs best in which system, a number of chemical properties must be considered to determine the efficiency and success of an extraction [77]. Separation of a solute from solid, liquid or gaseous sample by using a suitable solvent is reliant upon the relationship described by Nemst s distribution or partition law. The traditional distribution or partition coefficient is defined as Kn = Cs/C, where Cs is the concentration of the solute in the solid and Ci is the species concentration in the liquid. A small Kd value stands for a more powerful solvent which is more likely to accumulate the target analyte. The shape of the partition isotherm can be used to deduce the behaviour of the solute in the extracting solvent. In theory, partitioning of the analyte between polymer and solvent prevents complete extraction. However, as the quantity of extracting solvent is much larger than that of the polymeric material, and the partition coefficients usually favour the solvent, in practice at equilibrium very low levels in the polymer will result. 

Equation 17.75 is important as it illustrates, for the equilibrium case, a principle that applies also to the non-equilibrium cases more commonly encountered. The principle concerns the way in which the shape of the adsorption wave changes as it moves along the bed. If an isotherm is concave to the fluid concentration axis it is termed favourable, and points of high concentration in the adsorption wave move more rapidly than points of low concentration. Since it is physically impossible for points of high concentration to overtake points of low concentration, the effect is for the adsorption zone to become narrower as it moves along the bed. It is, therefore, termed self-sharpening. 

As is the case with adsorption isotherms, those curves in Figure 18.3 which are concave to the concentration axis for the mobile phase are termed favourable and lead to self-sharpening ion exchange waves. 

The maximum conversion of reactants which can be achieved in an isothermal batch reactor is determined by the position of thermodynamic equilibrium. If this conversion is regarded as unsatisfactory, the use of a simple batch reactor may be abandoned in favour of a reactor which permits removal of products from the reaction mixture. Alternatively, the reactor temperature may be changed to obtain a more favourable equilibrium however, this may result in an unacceptable reduction in the net reaction rate. Such conflicts are often resolved by the use of optimisation procedures (see Sect. 8). 

Via DSC measurements it was shown that the new bis(vinylbenzyl)ethers can undergo a homopolymerization and a copolymerisation with BMI. In a BMI/-divinylbenzylether blend the Diels-Alder copolymerization is favoured over the divinylbenzylether homopolymerisation. The Tgs of the new copolymers are well in excess of 270 °C when the BMI/divinylbenzylether molar ratio is 1 1 (Table 9). Isothermal weight loss studies over a period of 4000 hours indicate that the BMI-MDA/divinylbenzylether copolymer is the most stable system of this family. 

Optimal compressor- types for the various power ranges are plotted in Fig. 4.1-29, which was calculated on the bases of 1 bar intake pressure and an isothermal efficiency of 64% [24]. It can give only approximate reference points for the most favourable area of application, which varies depending on the manufacturer. If the intake pressure is greater than 1 bar, as is the rule, it is necessary to recalculate. For example the compression of ethylene at a flow-rate of 64000 kg/h 51 130 Nm3/h (Standard cubic metre per hour) from 231 to 2151 bar, corresponds to a real intake volume flow-rate at 231 bar of 161 m3/h, and a power consumption of 8200 kW. 

Solid surfaces are usually heterogeneous therefore, since adsorption at the more active sites is favoured, heats of both monolayer physical adsorption and chemisorption might, in this respect, be expected to become significantly less exothermic as the surface coverage increases, as, for example, shown at low pressures in Figures 5.12a and 5.12b. This, in turn would cause the initial slope of an adsorption isotherm to be steeper than that predicted according to the Langmuir equation or the BET equation. 

Both systems are suitable to check whether or not there is a directly proportional relationship between the width of the homogeneity range of a compound and the growth rate of its layer, predicted by the diffusional theory.5 It is clear that in view of the presence of the liquid zinc phase during preparation of Ni-Zn and Co-Zn reaction couples, all the inter-metallic phases had equal and favourable conditions to form their nuclei at the interface between nickel or cobalt and zinc, which could then readily grow during subsequent isothermal annealing. 

---