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has a composition that can only be inferred) in the same manner as the liquid is treated when doing VLE calculations. Amixturemodelisusedtoaccountforinteractions,whichmaybeassimpleasRaoult’slaw or as involved as Wilson’s equation. These correspond roughly to the Ideal Adsorbed Solution and Vacancy Solution models, respectively. Pure component and mixture equilibrium data are required. The unfortunate aspect is that all versions require iterative root-finding procedures and integration. These add complexity to design or simulation routines, which may already be solving coupled partial differential equations. They may be the only route to acceptably accurate answers, however. It would be nice if adsorbents could be selected to avoid both aspects, but generally the adsorbent is only an accomplice not the cause of complexity. 3.4. Instrument Types and Data Analysis Doing isotherm measurements is painstaking and time-consuming. It is usually even more difficult to set-up the equipment, however, than to do the experiments. Despite that, it is important to know something about how they are done, in order to discuss what they mean. There are three basic types of equipment: volumetric, gravimetric, and chromatographic. The equipment and techniques are reviewed briefly here. The first method, volumetric, generally is a vessel containing adsorbent that is subjected to a measured step change of fluid phase concentration. The ultimate concentration reveals the amount adsorbed via a mass balance. It is easiest if there is a noninvasive way to measure concentration. For gases a pressure transducer will do, since volume and temperature are fixed. For liquids, a variety of instruments exist that can be used in situ, but it is also acceptable to extract small samples with a syringe for individual analysis. This method is probably the best in terms of flexibility, decent accuracy, and low cost. Second, the gravimetric approach, mainly applies to gas-phase adsorption. It involves measuring the amount taken up by the adsorbent by weight. These isotherm measurements are quick and accurate, and the interpretation is easy. Some types of equipment are elaborate, with a small adsorbent-bearing pan suspended from a quartz spring. Then, the main problem is cost, plus the fact that the equipment tends to be finicky (each seal is subject to leaks). Other problems that are sometimes overlooked are: adsorption on the walls rather than on the adsorbent, and buoyancy effects (which can amount to more than 10% error). Another version uses a column of adsorbent, through which is passed gas of a known concentration. Periodically the flow is stopped, the column is sealed then weighed. The adsorption capacity can be determined once steady- state is reached. This is more tedious, but reliable and relatively inexpensive. Alternatively, the adsorbent can be heated strongly, and the off-gases can be trapped and analyzed to infer the adsorbate composition. Third is chromatographic analysis. This is primarily a screening technique in which adsorbents are crushed and placed in a chromatographic column, then a pulse of the components of interest is injected into a nonadsorbing carrier fluid. In principle, the technique applies to both gases and liquids, but the former is much more popular. The Henry’s law coefficient can be determined readily from the retention of each peak. 3.5. Adsorption Dynamics In order to select an adsorbent, one must appreciate the impact of processing conditions on performance. This does not mean becoming familiar with methods to solve the governing partial differential equations. It just means that awareness of the variables and parameters involved in transport phenomena, beyond their definitions, can help when picking an adsorbent. As potentially complicated as that might sound, there are really only three topics that are important in most cases: intraparticle diffusion, interstitial mass transfer, and packed bed flow behavior. Although each of these has been the topic of dozens of technical papers, there are some very simple generalizations that are sufficient to cover most situations. First of all, intraparticle diffusion is characterized by an effective diffusivity, Deff =DAB gP /J (where DAB 17PDF Image | ADSORBENT SELECTION
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