Heat transfer, sorption processes

A significant feature of physical adsorption is that the rate of the phenomenon is generally too high and consequently, the overall rate is controlled by mass (or heat transfer) resistance, rather than by the intrinsic sorption kinetics (Ruthven, 1984). Thus, sorption is viewed and termed in this book as a diffusion-controlled process. The same holds for ion exchange. 

The discussion above explains why basic information on sorption and diffusion under the reaction conditions, especially at elevated pressures, is required for kinetic and mass- and heat- transfer modelling of catalytic polymerization reactors. If such information is sufficiently available, one should be able, for example, to compare the kinetics of gas-phase and slurry-processes directly by taking into account both gas solubilities in swollen polymers and the hydrocarbons used in slurry processes. 

Duration of a cycle of HHP operation is defined as time required for reaction hydrogenation/dehydrogenation in pair hydride system. This time determines heat capacity of HHP. Duration of a cycle depends on kinetics of hydrogenation reactions, a heat transfer between the heated up and cooling environment, heat conductivities of hydride beds. Rates of reactions are proportional to a difference of dynamic pressure of hydrogen in sorbers of HHP and to constants of chemical reaction of hydrogenation. The relation of dynamic pressure is adjusted by characteristics of a heat emission in beds of metal hydride particles (the heat emission of a hydride bed depends on its effective specific heat conductivity) and connected to total factor of a heat transfer of system a sorber-heat exchanger. The modified constant of speed, as function of temperature in isobaric process [1], can characterize kinetics of sorption reactions. In HHP it is not sense to use hydrides with a low kinetics of reactions. The basic condition of an acceptability of hydride for HHP is a condition of forward rate of chemical reactions in relation to rate of a heat transmission. 

The further perfection of calculated model can consist in the account of a filtration of hydrogen through a porous bed, final speed of heat transfer in sorbers, influences of a kinetics of absorption and allocation of hydrogen. The expediency of use of the model which are taking into account only processes of heat and hydrogen transfer, explains practical absence of the data on the kinetic constants describing processes of a sorption of hydrogen in hydrides. 

Criterion Biot determines the ratio of intensity of external heat exchange processes (numerator) and effective thermal conductivity of a hydride layer (denominator). To carry out frontal chemical reactions of hydrogen sorption -desorption, small numbers Biot (Bi<0.1) are preferable. Number Bi can be decreased by several ways 1) decreasing of the characteristic layer size 2) decreasing of intensity of an external heat transfer (but time of non-stationary processes is growing) 3) increasing of effective hydride bed thermal conductivity. 

The further improvement of mathematical model can include, for example, final rate of heat transfer in sorbers, as well as influence of hydrogen sorption and desorption kinetics. Use of the model, which takes into consideration only heat and hydrogen transfer processes in sorbers volumes, is explained by practical absence of the kinetic constants data describing processes of hydrogen sorption in the hydride forming alloys. 

In the chromatographic method a pulse or step change in sor-bate concentration is introduced into the carrier stream at the inlet of a packed adsorption column and the diffusional time constant is determined from the dispersion of the response signal at the column outlet. Since heat transfer in a packed bed is much faster than in a closed system the chromatographic method may, in principle, be used to follow somewhat faster sorption processes. 

The highest intensity of evaporation occurs in the zone II. The thickness of liquid film in the zone I is close to the size of molecular sorption film and there are no the favorable conditions for process of vaporization. In the zone III the liquid film is thick, so a thermal resistance is higher than in zone II. Thus the optimal conditions for intensive evaporation are in the zone II. There is great number of such zones over all porous surfaces, so the total area of evaporation is very large. Thus we have excellent condition for the intense heat transfer. 

Moreover, the heat transfer process has significant impact on the evaporation process in cotton fabrics but not in polyester fabrics. The process of moisture sorption is largely affected by water vapor diffusion and liquid water diffusion, but not by heat transfer. When there is liquid diffusion in the fabric, the moisture sorption of fibers is mainly determined by the liquid transport process, because the fiber surfaces are covered by liquid water quickly. Meanwhile, the water content distributions in the fibers are not significantly related to temperature distributions. 

All moisture transport processes, on the other hand, affect heat transfer significantly. Evaporation and moisture sorption have a direct impact on heat transfer, which in turn is influenced by water vapor diffusion and liquid diffusion. The temperature rise during the transient period is caused by the balance of heat released during fiber moisture sorption and the heat absorbed during the evaporation process [40],... 

The second stage features the moisture sorption of fibers, which is relatively slow and takes a few minutes to a few hours to complete. In this period, water sorption into the fibers takes place as the water vapor diffuses into the fabric, which increases the relative humidity at the surfaces of fibers. After liquid water diffuses into the fabric, the surfaces of the fibers are saturated due to the film of water on them, which again will enhance the sorption process. During these two transient stages, heat transfer is coupled with the four different forms of liquid transfer due to the heat released or absorbed during sorption/desorption and evaporation/condensation. Sorption/ desorption and evaporation/condensation, in turn, are affected by the efficiency of the heat transfer. For instance, sorption and evaporation in thick cotton fabric take a longer time to reach steady states than in thin cotton fabrics. 

However, the two-sink model as well as other existing adsorption (sink) models do not seem to be able to describe the strong asymmetry between the adsorption/desorption of VOCs on/from indoor surface materials (the desorption process is much slower than the adsorption process). Diffusion combined with internal adsorption is assumed to be capable of explaining the observed asymmetry. Diffusion mechanisms have been considered to play a role in interactions of VOCs with indoor sinks. Dunn and Chen (1993) proposed and tested three unified, diffusion-limited mathematical models to account for such interactions. The phrase unified relates to the ability of the model to predict both the ad/absorption and desorption phases. This is a very important aspect of modeling test chamber kinetics because in actual applications of chamber studies to indoor air quality (lAQ), we will never be able to predict when we will be in an accumulation or decay phase, so that the same model must apply to both. Development of such models is underway by different research groups. An excellent reference, in which the theoretical bases of most of the recently developed sorption models are reviewed, is the paper by Axley and Lorenzetti (1993). The authors proposed four generic families of models formulated as mass transport modules that can be combined with existing lAQ models. These models include processes such as equilibrium adsorption, boundary layer diffusion, porous adsorbent diffusion transport, and conveetion-diffusion transport. In their paper, the authors present applications of these models and propose criteria for selection of models that are based on the boundary layer/conduction heat transfer problem. 

For a partitioning process, the molar heat of sorption Af/sorp that is, transfer of the solute from water to the partitioning phase, in this case SOM, would be expressed... 

Since adsorption is exothermic and the heat of sorption must be dissipated by heat transfer there is, in gpneral, a difference in temperature between an adsorbent particle and the ambient fluid when sorption is taking place. Whether or not this temperature difference is significant depends on the relative rates of mass and heal transfer. By simple theoretical analysis it may be shown that in a batch adsorption experiment it is the dissipation of heat from the external surface of the adsorbent sample, rather than the conduction of heat within the adsorbent, which is generally the rate-limiting heat transfer process. The conditions under which heat transfer resistance may be neglected and the system treated as isothermal as well as a more detailed discussion of the analysis of nonisothcrmal behavior are given in Section 6.6. 

Heat and mass transfers in porous media are coupled in a complicated way. On the one hand, heat is transported by conduction, convection, and radiation. On the other hand, water moves under the action of gravity and pressure gradient whilst the vapor phase moves by diffusion caused by a gradient of vapor density. Thus, the heat transfer process can be coupled with mass transfer processes with phase changes such as moisture sorption/desorption and evaporation/condensation. 

The coupled heat and liquid moisture transport of nano-porous material has wide industrial applications in textile engineering and functional design of apparel products. Heat transfer mechanisms in nano-porous textiles include conduction by the solid material of fibers, conduction by intervening air, radiation, and convection. Meanwhile, liquid and moisture transfer mechanisms include vapor diffusion in the void space and moisture sorption by the fiber, evaporation, and capillary effects. Water vapor moves through textiles as a result of water vapor concentration differences. Fibers absorb water vapor due to their internal chemical compositions and structures. The flow of liquid moisture through the textiles is caused by flber-liquid molecular attraction at the surface of fiber materials, which is determined mainly by surface tension and effective capillary pore distribution and pathways. Evaporation and/or condensation take place, depending on the temperature and moisture distributions. The heat transfer process is coupled with the moisture transfer processes with phase changes such as moisture sorption and evaporation. 

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