A mathematical model is developed to simulate the drying of hygroscopic porous media and, in particular, of wood. Drying rate experiments were performed using wood specimens and a nonhygroscopic porous ceramic solid and were simulated using the appropriate version of the drying model. Calculated model predictions are in very satisfactory agreement with experimental results. An examination of the relative impacts on drying of the transport mechanisms that comprise the model leads to meaningful interpretations of observed drying behavior. Controlling rate factors can be identified and different types of drying behavior specific to a given material or drying condition can be explained and understood through model simulation studies. Such capability can provide important guidance for drying process design and control. M. A. Stanish, G. S. Schajer, Ferhan KayihanWeyerhaeuser Technology Center Tacoma, Washington 98477 SCOPEThe drying of moist porous solids is a complicated process involving simultaneous, coupled heat and mass transfer phenomena. Accordingly, drying behavior can be influenced by a rather large variety of independent factors, including, for example, ambient conditions of temperature, air velocity, and relative humidity, and solid properties such as density, permeability, and hygroscopicity. Extensive characterization of drying behavior using a strictly experimental approach constitutes a formidable challenge due to the excessively large number of variables that must be considered. The task becomes more manageable, however, with the help of a reliably realistic mathematical model of the drying phenomenon. Our objective is to develop such a tool to simulate drying behavior and therefore allow us to extend the results of experimental drying investigations. In this way, the impact of the many variables on drying behavior can be examined and interpreted without having to resort to an extensive program of experimental testing.The approach taken here represents advancement of drying modeling and theory on several fronts. The mathematical description of the drying process is derived and maintained for the most general case; a comprehensive set of fundamental heat-and mass-transfer mechanisms is coupled with thermodynamic phase equilibrium expressions in a way that accommodates either hygroscopic or nonhygroscopic materials. Heat transfer by both conduction and convection is included together with mass transfer by gaseous diffusion and bulk flow of gas and liquid through the void space and by bound-water diffusion through the solid matrix. Bound-water migration is expressed in terms of the diffusion of sorbed water driven by the gradient in the chemical potential of the bound molecules. While this concept of bound-water diffusion was previously suggested by Siau (1983) and others (Kawai et al., 1978), in this development a new, uniquely explicit expression for bound-water flux is derived in terms of temperature and vapor pressure gradients. Combination of all of these transport mechanisms in a single generalized ...

The reaction kinetics and physical transport processes governing the thermal dehydration of solid KzCOy3/2HzO particles were investigated. Isothermal reaction rate data were gathered using a thermogravimetric balance in which narrowly-sized KzC03*3/2HzO crystals were dehydrated under a water vapor atmosphere at different pressures and temperatures. The magnitudes of the heat and mass transfer resistances external to and within the solid product were estimated from solutions of the relevant pseudosteady-state transport equations. In the temperature range 320 to 358 K, the vacuum dehydration of K~COs*3/2HzO crystals smaller than 710 pm (-25 +30 mesh) are accurately modeled by the spherical shrinking-core equation for the chemical rate control regime. In the presence of water vapor, external heat transfer to the particles was sufficient to prevent significant self-cooling; heat and mass transfer resistances within the particles were negligible. The activation energy for K2C03*3/2H20 dehydration is approximately 91 kJ/mol in vacuum; the reaction becomes extremely slow at relative pressures SCOPEOf the literature reports concerned with the dehydration of solid inorganic salt hydrates, a majority are based on information from experiments done in vacuum or in dry atmospheres; as a consequence, the dehydration reaction is most often treated as an irreversible thermal decomposition. The possible application of salt hydrates as absorbents in chemical heat pumps (Stanish and Perlmutter, 1981) provides an incentive to investigate the dehydration of these materials in greater detail and suggests that this process should be treated instead as one part of a reversible gas-solid reaction. This paper reports the results of experimental rate studies of the dehydration of KzC03*3/2H20, a salt hydrate that holds promise as a heat pump absorbent. Experimentally-measured particle reaction data are interpreted in terms of a shrinkingcore gassolid reaction model. The dehydration rate dependence on ambient water vapor pressure is of primary interest and is quantitatively determined for temperature in the range 338 to 358 K. Internal and external heat and mass transfer resistances are estimated for the conditions employed and their roles in the overall particle hydration process are evaluated. CONCLUSIONS AND SIGNIFICANCEThe dehydration of small crystals of KzCO3*3/2HzO may be accurately modeled by the spherical shrinking-core equation for the chemical rate control regime. In the presence of water vapor, heat transfer rates to the particles are sufficiently high to prevent significant self-cooling. Under vacuum conditions, self-cooling becomes important; particle temperature corrections were calculated from a heat balance equation that takes account of the radiation heat transfer to the solid particles and supporting sample pan. In either atmosphere, heat transfer resistance within the particle is negligible. Diffusional resistances within the product layer are not important for particles smaller than about 710 pm (-25 +30 mesh), but are...

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Rate studies arc reported of the effect of rehydrationdehydration cycling on the vapor hydration behavior of solid KzCO3. Isothermal rate data were obtained a t different temperatures and water vapor pressures for the reaction of narrowlysized anhydrous particles. Effects of different particle preparation histories on the rehydration rate were investigated and correlations of rate with particle pore structure explored. Rehydration rates of dehydrated K2C03*3/2IIzO were found to depend on the conditions of the prior dehydration. Rehydration is comparatively very slow at relative pressures below PIP,., N 1.5; rates increase linearly with pressure above PIP, -3. Hydration rates of KzCO3 particles obtained as anhydrous are substantianyslower than those of identically-sized crystals produced by prior dehydration of KpC03*3/2II20; after one rehydrationdehydration cycle, rehydration rates are increased by as much as two orders of magnitude and this distinction between sources virtually disappears. Diffusional resistances based on calculated water vapor diffusivities are qualitatively consistent with the observed effects of cycling but d o not by themselves account fully for the observations. M. SCOPEThe hydration reaction of KzCO:, with water vapor is of interest from two different perspectives. First, this system serves as a convenient prototype for the study of kinetics in reversible gas-solid reactions of inorganic salts, a topic of recognized industrial importance. Second, water and KzCO3 were shown (Stanish and Perlmutter, 1981) to hold significant promise as a refrigerant-absorbent pair in a low-temperature heat pump cycle. Since little information is available concerning the kinetics of hydration and dehydration in the water-KzC03 system, a n experimental study of these phenomena is needed to more accurately determine the feasibility and potential of a real KzC03-based heat pump device.The objectives of this study were to identify the variables that are most important in determining the rehydration rate of KzCO3 particles and to quantify their effects. This investigation includes evaluation of the importance of the source of the solid and the method of preparation in determining the rate of rehydration. In addition, the effect of water vapor pressure on reaction rate is quantified. Finally, changes in rehydration rate with rehydrationdehydration cycling are explored, and correlations are sought with the differences in particle pore structure revealed by mercury intrusion porosimctry data. The behavior of this system is compared to that reported for thc rcvcrsiblc decomposition of AglC03. CONCLUSIONS AND SIGNIFICANCEThe rate of rehydration of dehydrated K&O3*3/2HzO crystals is affected by the prior dehydration conditions; samples that were dehydrated more rapidly (at higher temperature and/or lower pressure) were subsequently found to rehydrate more rapidly as well. Slow rehydration and the appearance of induction and acceleration in rehydration conversion time curves were characteristics of KzC03*3/2HzO dehydrat...

A mechanism is proposed for the dehydration-rehydration process in solid inorganic salts, and model rate equations are derived and applied to the observed behavior of potassium carbonate. Quantitative expressions for the effect of pressure on the reaction rates are derived using basic principles from nucleation and heterogeneous phase transformation theory. Model equation predictions agree with experimental dehydration and rehydration rate data at all but extreme pressures. The basic rate equation is also used to interpret the data of Eckhardt and Flanagan (1964) for the effect of pressure on the dehydration of manganous formate dihydrate. The mechanism on which the model equations are based is also consistent with the observed effects of cycling and of high temperature pretreatment on the KzC03 rehydration rate. SCOPEA new mechanistic interpretation is offered for the analysis of the kinetics of gas-solid reactions and applied in detail to the reversible dehydration and rehydration of solid inorganic salts. These processes are considered as solid-solid transformations, and an expression is derived for the intrinsic rate of reaction in terms of the velocity of the movement of the boundary separating the reactant and product phases. The rate dependence on pressure and temperature predicted by the model equations is compared to those observed for both dehydration and rehydration in experiments with potassium carbonate hydrate and to that reported in the literature for the dehydration of manganous formate dihydrate. In addition, the effects of cycling and of high-temperature pretreatment on the reaction rates of KzCO3 are presented, and the ability of the proposed mechanism to account for these effects is discussed.A new mechanistic rate model has been formulated for reversible gas-solid reactions and applied to interpret the dehydration and rehydration kinetics of salt hydrates. Quantitative rate expressions predicting the effects of pressure and temperature were derived using basic principles from nucleation and heterogeneous phase transformation theories. The dehydration model rate equation provides accurate quantitative predictions for the velocity of movement of the KzCOs*3/2HzO dehydration interface at all three temperatures studied. The dehydration equation also provided a close correlation with data from the literature for the dehydration of manganous formate dihydrate.A comparison of the rehydration model equation with experimental KzC03 particle rehydration rates revealed good agreement of the model with the experimental data for reduced pressures within the range 1 < (Pes/P) < 2. At higher rehydration pressure, the reaction rates are not controlled by the transformation process at the reaction interface and the model equations are not applicable. Within the range of moderate pressures both above and below the equilibrium pressure, the model effectively describes the rapid decline of both dehydration and rehydration rates as the equilibrium pressure is approached.The model equations imply that reaction ra...