Apparent diffusivity of water in silica gel and NaX zeolite pellets

Transcription

1 High Temperatures ^ High Pressures, 2001, volume 33, pages 435 ^ ECTP Proceedings pages 1003 ^ 1007 DOI: /htwu90 Apparent diffusivity of water in silica gel and NaX zeolite pellets Jose M Gurgel, Luiz S Andrade Filho, Pedro P Souza Couto Laboratörio de Energia Solar, Universidade Federal de Paraiba, Joa o Pessoa, PB, Brazil; fax: ; gurgel@les.ufpb.br Presented at the 15th European Conference on Thermophysical Properties, Wu«rzburg, Germany, 5 ^ 9 September 1999 Abstract. The apparent mass diffusivity of water vapour (moist air) in silica gel and zeolite particles was measured at 2 kpa with a simple constant volume/pressure apparatus. A theoretical simple model is presented, with the overall kinetics controlled by an apparent diffusivity identified by a curve-fitting method which consists of a comparison of experimental and theoretical results. The model presents good agreement with experimental results and is in good agreement with earlier publications. The results are useful for the optimisation of the heat and mass transfer in adsorbent beds of thermal adsorption devices and desiccant systems of cooling by low temperature from solar heating or industrial waste heat. There is a different rate of sorption between silica gel and zeolite at the working pressures of the desiccant device. 1 Introduction Desiccant cooling systems are being studied currently because of environmental concerns and the currently increased demand for space cooling. Because of this, there is a great need to develop low energy cooling systems that do not depend on ozone-depleting refrigerants. Such alternative systems based on solid sorption have been explored all over the world, particularly in the USA. They operate with less electric consumption (which is necessary to run the ventilation fans), without chlorofluorocarbons (CFC) or other toxic components, and they are limited to air and water circulations and control devices. Humid ambient air is blown and dried through a packed adsorbed reactor and subsequently is cooled by water evaporation. The water adsorbed is removed by the use of low-temperature process heat available as solar heat or industrial waste heat. These systems have been accepted as economical means of improving the environment in residences in hot climates. Both silica gel and zeolite are commonly suggested for this purpose; mainly silica gel, because it can be regenerated at relatively low temperatures. The analysis of the thermal behaviour of devices using solid adsorbents shows that their performance is very sensitive to heat and mass transfer rates inside the adsorbent beds. Therefore, it is necessary to measure the thermal diffusivity and sorption rates in these beds. The thermal conductivity of silica gel from different makers has been previously investigated by Bju«rstro«m et al (1984) and Gurgel (1998), and that of zeolite by Sahnoune and Grenier (1989). The silica gel studied here is commercially produced by Kalichemie Õ (Kali-Chemie Aktiengesellschaft, Hans-Bo«ckler-Allee 20,30173 Hannover, Germany), and is known as ``type R Sorbead''. It is also presented as spheroidal beads and, in addition, it is available with a pellet diameter between 2 and 5 mm. The zeolite pellets which we studied are marketed by Union Carbide (Union Carbide Corporation, 39 Old Ridgebury road, Danbury, CN , USA). They consist of an agglomeration of crystals about 2 mm in diameter with a clay binder (about 20%). Likewise they are presented as spheroidal beads with an average diameter d ˆ 4 mm. Silica gel and zeolite data are given in table 1. Several experimental and theoretical investigations of rate adsorption have been carried out over the last 30 years and different techniques for the measurement of diffusion

2 µ µ 436 J M Gurgel, L S Andrade Filho, P P Souza Couto 15 ECTP Proceedings page 1004 Table 1. Data for silica gel (Gurgel 1998) and zeolite (Sahnoune and Grenier 1989). Data are given for particle diameter d, porosity e, thermal conductivity l s,densityr s, and specific heat C p. W 0 and N are parameters of the Dubinin ^ Astakhow equation (3) determined by Khelifa (1984) for silica gel/water and by Guilleminot (1978) for zeolite/water. Parameter Silica gel Zeolite d/mm 2.3, 3.5, 4.0, e l s /W m 1 K r s /kg m C p /J kg 1 K W 0 /m 3 kg N 1 2 coefficients have been used by: Ka«rger and Ruthven (1989), Grenier et al (1995), Anderson et al (1985), and Lu et al (1991). This work is intended to determine the effective diffusivity of water in silica gel and zeolite under pressures of 2.0 kpa, which corresponds to an average partial pressure of water vapour in moist ambient air. 2 Experimental setup for determination of mass diffusion The experimental setup was placed inside a climate-controlled room and can be seen in figure 1. It consists of a digital balance where the sample is placed along with the instruments for measuring the psychrometric properties (temperature and wet bulb temperature). The experimental procedure consists of putting the dry sample on thin stainless-steel sheet inside a balance. The pellets are properly spaced in order to prevent interference between the particles. The sample weighed less than 2 g. The initially dry sample was exposed to the initial temperature and moist air pressure of the room. The partial water vapour pressure into the room is calculated by means of psychrometric relationships. The increase of the charging on the sample is measured per unit time. Four different silica-gel particle size samples (2.3 mm, 3.5 mm, 4.0 mm, and 5 mm) were tested and only one size (4 mm) of zeolite. The samples before the measurement were prepared by heating them in an oven at about 200 8C for25h. control system for room temperature wet bulb temperature sensor temperature sensor µ thin stainless-steel sheet sample digital balance Figure 1. Experimental equipment.

3 Apparent diffusivity of water ECTP Proceedings page Theoretical model for mass diffusivity Adsorbent pellets offer various resistances to mass transfer: external surface diffusivity resistance, micropore resistance of the microparticles or crystals, and macropore diffusivity resistance (phase molecular or Knudsen regime). Detailed models have been presented by Sun and Meunier (1987a, 1987b). Here, an effective simplified one dimensional model is presented. In this model an effective mass diffusivity, D eff (macropore and crystal), is assumed. The particles are spherical and have a uniform size with radius R. The pressure, p, and temperature, T, of the surrounding gas are constant. The temperature field inside the particles is only dependent on time, t, by the assumption of the lumped-heat-capacity system. The governing diffusion equation for a spherical particle is: q 2 w qr 2 qw 2 r qr ˆ 1 qw D eff qt, (1) where w is the amount of water per amount of adsorbent, and r is the radial coordinate. The corresponding boundary conditions are: qw qr and r ˆ 0 ˆ 0, (2) w r, t j r ˆ R ˆ W 0 r T exp K R g T ln ps p c N. (3) Here, mass transfer surface resistance is negligible and the surface concentration of the grain (r ˆ R) is at equilibrium with the partial pressure of the moist air of the room and the particle temperature. The concentration can be calculated by the Dubinin ^ Astakhow equilibrium state equation as indicated above (Ruthven 1984), where W 0 is the maximum possible sorbate content, r is the specific gravity of the bed, K ˆ 4: kg H 2 O kj 1, R g ˆ 0:462 kj kg 1 K 1 ; these and N are Dubinin ^ Astakhow parameters (table 1). Also, p s is the saturation pressure, p c is the partial pressure of water vapour in moist ambient air, and T is the pellet temperature. The initial condition for the problem is: w r, 0 ˆ0 dry pellets, (4) T r, 0 ˆroom temperature. (5) The amount of sorbate, M a, that penetrates into the grain by each time Dt is: qw M a ˆ DtAr s D eff qr, (6) r ˆ R where A is the external surface area of the grain, and r s is the density of the adsorbent. The heat balance for a particle is: M s C s SM a C a qt qt ˆ QsM a h Dt r h c T T a, (7) where (M s C s SM a C a ) is the volumetric heat capacity of the wet sample, M s is the absorbent mass, C s is the adsorbent specific heat, M a is the water content mass in the adsorbent, C a is the specific heat of water, Q s is the mass sorption enthalpy, (h r h c ) is the overall heat transfer coefficient (radiation and conduction), and T a is the ambient temperature.

4 438 J M Gurgel, L S Andrade Filho, P P Souza Couto 15 ECTP Proceedings page Mass transfer results Some results are shown in table 2 and in figures 2, 3, and 4. All the experiments were performed inside the room at 22 8C and with a pressure corresponding to 2 kpa of partial water vapour pressure in moist air. Figures 2 and 3 and table 2 show that effective mass diffusivity of water in silica gel increases with particle size. This observation is consistent Table 2. Results for zeolite ^ water and silica gel ^ water. Experiment Adsorbent T/K p c /kpa d/mm D eff /m 2 s 1 1 zeolite silica gel silica gel silica gel silica gel s 1 D eff m w gg d mm t h Figure 2. Dependence of effective diffusivity, D eff, on pellet size, d, for water in silica gel at 2.0 kpa and 295 K. Figure 3. Influence on particle size d on sorption rate for water in silica gel: T ˆ 295 K, p v ˆ 2:0 kpa. Experimental data: *, d ˆ 2:3 mm; &, d ˆ 5:0 mm. Model: öö, D eff ˆ 3: m 2 s 1 ;----,D eff ˆ 1: m 2 s w gg t h Figure 4. Sorption of water in silica gel and zeolite: T ˆ 295 K, p v ˆ 2:0 kpa. Data: &, zeolite, d ˆ 4:0 mm; ~, silica gel, d ˆ 5:0 mm. Model curve fitting: öö, D eff ˆ 1: m 2 s 1 ; ----, D eff ˆ 5: m 2 s 1.

5 Apparent diffusivity of water ECTP Proceedings page 1007 with the model developed and it is not due only to the temperature effect. There is also a geometric effect that causes this increase, which is proportional to the relationship between the size of the diameters (if the thermal effect is ignored at the particle). According to equation (3), the amount of water adsorbed also depends on the particle temperature, because of the lower specific surface for the bigger particles. Figure 4 shows the difference between the sorption rate for water in silica gel and water in zeolite. This result is very attractive with regard to utilising zeolite as the adsorbent for desiccant systems of cooling if the regeneration procedure can be effected at high temperatures close to 200 8C. The diffusivities in this study are consistent with those of other investigators (Tempelhoff and Feldmann 1975; Anderson et al 1985; Grenier et al 1995). 5 Conclusion Measurements of the rate of sorption of water in silica gel show that D eff increases with particle size. This observation is consistent with the model developed and it is due to geometric and temperature effects, according to equation (3). With concentrated solar energy or waste thermal energy from exhaust combustion, the high temperatures allow one to take advantage of the very high regeneration kinetics of the water in zeolite. The sorption rate for water in silica gel is slower, but silica gel has the advantage of a lower temperature for regeneration, close to 80 8C. This is compatible with solar applications with simpler technology. The effective diffusivity values found here take into account the mass diffusivity between air and water vapour. The Knudsen diffusivity in micropores has a value of about m 2 s 1, and the effective diffusivity is of the order of magnitude of m 2 s 1. It is not clear whether the dominant diffusion is in the micropores or in the macropores. This question needs further investigation and it is necessary to find out (measure) details of the sizes of the macropores. The model developed presents good agreement with the experimental data and it is very simple to couple to a complete model for sorption bed reactors. Acknowledgements. This work was sponsored by CNPq (Conselho Nacional de Desenvolvimento Cient fico e Tecnolögico) AI number /95-6. References Anderson J Y, Bjurstrom H, Azoulay M, Carlsson B, 1985 J. Chem. Soc. Faraday Trans. I ^ 2692 Bju«rstro«m H, Karawachi E, Carlsson B, 1984 Int. J. Heat Mass Transf ^ 2036 Grenier Ph, Bourdin V, Sun L M, Meunier F, 1995 AIChE J ^ 2057 Guilleminot J J, 1978 Caractërisation de l'e tat stationnaire liquide-gaz-adsorbant lors de l'adsorption de gaz facilement condensable sur les zëolithes PhD thesis, Dijon University, France Gurgel J M, 1998 High Temp. ^ High Press ^ 320 Ka«rger H, Ruthven D, 1989 Zeolites 9 267^281 Khelifa N, 1984, ``Das Adsorptionspaar Silicagel ^ Wasserdampf, Anwendung als Solares Klimatisierungsystem'', dissertation, Ludwig-Maximillians-Universita«t, Munich, Germany Lu T L, Charoensupaya D, Lavan Z, 1991 J. Sol. Energy Eng ^ 263 Ruthven D, 1984 Principles of Adsorption and Adsorption Process (New York: John Wiley) Sahnoune H, Grenier Ph, 1989 Chem. Eng. J ^ 54 Sun L M, Meunier F, 1987a Chem. Eng. Sci ^1593 Sun L M, Meunier F, 1987b Chem. Eng. Sci ^ 2907 Tempelhoff K, Feldmann K, 1975 Z. Phys. Chem ^ 378

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