Operating Conditions Theoretical Considerations

The choice of optimal operating conditions for a two-bed cyclic adsorption system presents a complex optimization problem since the effects of all the process variables (cycle time, bed length, adsorption and desorption temperatures, purge gas velocity) are coupled. However some general guidance may be derived from a comparatively simple theoretical analysis. 

The mathematical models used to simulate die dynamic behavior of a cyclic adsorption system are essentially similar to those described in Chapters 8 and 9. There is however one important difference. In most of the models discussed in Chapters 8 and 9 an initially sorbate free-adsorbent bed was 

Theoretical simulations of a two-bed adsorption system with a single adsorbable component have been carried out by Tan and Spinner for linear systems and by Bunke and Gelbin and Chao for nonlinear systems. In Gelbin s analysis the advantages of reverse-flow regeneration are clearly shown but the quantitative conclusions are of limited practical value since the analysis is restricted to systems in which both temperature and flow rate are maintained constant throughout the entire cycle. For the reasons already discussed it is impractical to operate an adsorption system in that way except when the adsorption isotherm is linear. 

With these assumptions the behavior of the system is described by the following set of equations  

These conditions imply that the initial distribution of sorbate at the start of the adsorption cycle, q(z, 0), is the same as the final distribution at the end of the desorption cycle, q z, Q, where is the duration of both adsorption and desorption cycles. Distances during desorption are measured from the bed outlet (z ) to take account of the flow reversal. 

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It will be realized as the discussion develops that adequate data for strict comparison of the various equipment types are not available. Nevertheless, some relative measure of performance is desirable, and the ratio of throughput to volume of a theoretical stage has been chosen as a simple characterizing device. Typical values of this criterion have been quoted, under conditions which represent as nearly as possible the best available performance. The figures must be used with considerable caution, since operating conditions were not usually comparable. Furthermore it will be clear from the discussion that this criterion alone is not the only one which should be applied in deciding upon the merits of a particular apparatus. 

Performances of dryers with simple flow patterns can be described with the aid of laboratory drying rate data. In other cases, theoretical principles and correlations of rate data are of value largely for appraisal of the effects of changes in some operating conditions when a basic operation is known. The essential required information is the residence time in the particular kind of dryer under consideration. Along with application of possible available rules for vessel proportions and internals to assure adequate contacting of solids and air, heat and material balances then complete a process design of a dryer. 

Finally, it should be pointed out once again that obtaining as precise and complete information on a studied chemical or physical system as possible, with a minimal number of experiments and the lowest possible expenses, is the necessary condition for efficient research work. Therefore, application of modern mathematical and statistical methods in designing and analyzing experimental results is a real necessity in all fields and phases of work, starting with purely theoretical considerations of a process, its research and development, all the way to designing equipment and studying optimal operational conditions of a plant. 

The required number of actual plates, Ap, is larger than the number of theoretical plates, App, because it would take an infinite contacting time at each stage to establish equilibrium. The ratio Aj Ap is called the overall column efficiency. This parameter is difficult to predict from theoretical considerations, however, or to correct for new systems and operating conditions. It is therefore customary to characterize the single plate by the so-called Alurphree vapor plate efficiency, Ey (98) ... 

ABSTRACT As a step in the application of the cracking of tar in fuel gas amelioration the characteristics of the endothermic reaction potential of tar was studied experimentally and theoretically. In this context, however, due to the structural complexity of tar and/or tany constituents in fuel gas well defined hydrocarbons as tar model compounds were applied with inexpensive and readily available materials (dolomites, dolomitic magnesium oxide [MgO], quicklime [CaO]). The effects of operation condition on extent of hydrocarbon conversion, gas product composition, and corresponding endotherai of the reaction potential have been explored. The results obtained in this work provide a basis for ture considerations of catalytic tar cracking. 

The possible reactions taking place within the wet lime/limestone SO2 removal system have been studied. Our conclusions relative to the controlling reactions are based on consideration of theoretical equations in light of operating experience in both field and pilot systems. Because there is considerable difference in operating conditions required to provide adequate SO2 removal in the absence of scale or deposit formation when utilizing lime or limestone as additives, the chemical reactions of the systems are treated separately. The essential reactions governing these systems are ... 

Increased reflux ratio has the effect of decreasing the required number of theoretical contacts, but it increases the internal flow, equipment diameter, and energy requirements. It is frequently necessary to solve the separation problem a considerable number of times, imposing various operating conditions and carefully ascertaining the effect on the total cost of the particular solution proposed. Optimum design conditions are discussed in Chapter 13. 

As can be seen from Fig. 8.3 the maximum efficiencies are higher for the electrochemical energy conversion than for heat engines at temperatures below 1150 K. However, this theoretical advantage has to be realized in practical systems and therefore the losses of fuel cells under realistic operation conditions have to be taken into consideration. 

The performance of trickle-bed reactors may be affected by many factors, such as interphase mass transfer, intraparticle diffusion, axial dispersion and incomplete catalyst wetting. Therefore, knowledge about these influenced factors is important for their mathematical description by an unsteady-state reactor model. Until now, the literature analysis shows the experimental and theoretical understanding of trickle-bed reactors under unsteady-state-operation conditions has improved, but not considerably. The following studies are focused on the trickling regime under unsteady-state-operation conditions. 

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