Conductance of a bed

The factor of the resulted heat emission of a hydride bed generally is proportional to effective heat conductivity of a bed and inversely proportional to thickness of a bed. The analysis of these equation shows, that factor of a heat transfer less than smaller factor of a heat emission and consequently it is of no used to increase strongly one of them, thus, not changing another. Results of experiments show, that for brazed and diffusion welded connections of the sorber case and heat-conducting insert R=(0.5-1.5) TO 5 (m2 K)/W. At contact of an insert and the case on tight fit R increases in 10-100 times and influence of contact resistance becomes comparable with influence of the resulted heat emission of a hydride bed. 

Works on increase of an overall performance of HHP were simultaneously carried out. For example, in [2] a number of the factors influencing specific output power of HHP has been considered. Properties of metal hydrides (absorbing ability, speeds of reactions, porosity of a covering, the characteristic of a heat transmission of a hydride bed) were analyzed for optimum selection. It has been shown that in pressings from powder metal hydrides gas permeability and effective specific heat conductivity of a bed Xes should be in common optimized in the certain range of a weight share of an additional heat-conducting material. 

Figure 23.25. Thermal conductance and the corresponding apparent thermal conductivity of a bed of silica aerogel granulate with a thickness of 22.3 mm as a function of gas pressure. The dashed line is the result of the theoretical modeling of the heat transfer [57].

These authors also measured the electrical conductivity of the irrigated bed in the horizontal and vertical directions. The ratio between the liquid holdup multiplied by the conductivity of the liquid and the effective conductivity of the bed was assumed to be a measure of the tortuosity of the liquid flow. 

ILLUSTRATION 12.7 DETERMINATION OF THE EFFECTIVE THERMAL CONDUCTIVITY OF A PACKED BED OF CATALYST PELLETS... 

Here, the densities of the gaseous and solid fuels are denoted by pg and ps respectively and their specific heats by cpg and cps. D and A are the dispersion coefficient and the effective heat conductivity of the bed, respectively. The gas velocity in the pores is indicated by ug. The reaction source term is indicated with R, the enthalpy of reaction with AH, and the mass based stoichiometric coefficient with u. In Ref. [12] an asymptotic solution is found for high activation energies. Since this approximation is not always valid we solved the equations numerically without further approximations. Tables 8.1 and 8.2 give details of the model. 

The relatively poor conductivity of a packed bed makes it difficult to get the heat of regeneration into the bed, either from a jacket or from coils embedded in the packing. This is more easily achieved by preheating the purge stream. Even in the best conditions, it takes time for the temperature of the bed to rise to the required level. Thermal regeneration is normally associated with long cycle times, measured in hours. Such cycles require large beds and, since the adsorption wave occupies only a small part of the bed on-line, the utilisation of the total adsorbent in the unit is low. 

Figure 12.11. Conceptual representation of models for evaluating the effective thermal conductivity of a fixed bed (from Kunii and Levenspiel, 1991) (a) Simple parallel path model (b) Modified model of Kunii and Smith (1960).

Ke Apparent thermal conductivity of a gas-solid suspension flowing through an empty bed... 

Ke Effective thermal conductivity of a fixed bed with stagnant gas... 

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. 

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. 

Values of effective thermal conductivity for a cell modeling tube sorber A,ef=5 0.5 W/(m-K) with a corrugated foil and 1.0-1.5 W/(m K) without it were found in experiments. Corrugated aluminium foil increases effective thermal conductivity of powder bed approximately 3-5 times. Value of effective thermal conductivity in mathematical model for calculations of tube sorbers was assumed to be f=5.8 W/(m-K). 

Porosity, gas permeability, effective heat conductivity of a hydride bed... 

The criterion for a flat velocity profile requires that the first term >100, the second term is also larger than one since the effective conductivity of the bed is smaller than that of a particle, and the last term is only slightly smaller than one. Therefore, the temperature gradient in the catalyst bed will be the first that develops to an unacceptable extent and should be verified first. In case of concern, bed dilution with a well conducting inert material will improve the situation considerably. 

Specific heats of metals and hydrides are easily determined and typically fall in the range of 0.1-0.2 cal/g°C. Thermal conductivity is a little more difficult to determine. The conductivity of the metal or hydride phase is not sufficient the effective conductivity of the bed must be determined. This depends on alloy, particle size, packing, void space, etc. Relatively little data of an engineering nature is now available and must be generated for container optimization. Techniques to improve thermal conductivity of hydride beds are needed. As pointed out earlier, good heat exchange is the most important factor in rapid cycling. 

Fluidized-bed electrode — A - three-dimensional electrode consisting of a bed of individual electronically conducting particles fluidized by an appropriate upward flow of electrolyte. The solid particles/solution system behaves like a single fluid. A perforated distributor through which the electrolyte is admitted to operate the fluidization supports the bed. Current enters (or leaves) the bed via metallic feeders (or collectors) in contact with the particulate suspension. 

In separation processes and chemical reactors, flow through cylindrical ducts filled with granular materials is important. In such systems conduction, convection, and radiation all contribute to the heat flow, and thermal conduction in axial ke x and radial ke r directions may be quite different, leading to highly anisotropic thermal conductivity. For a bed of uniform spheres, the axial and radial elements are approximated by... 

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