SERI/TP-252-2952

UC Category: 59a

Preprint

DEB6014502

Moisture Transport in

.Silica Gel Packed Beds

II. Experimental Study

Ahmad A. Pesaran (SERI)

Anthony F. Mills (University of California)

August 1986

To Appear in

International Journal of

Heat and Mass Transfer

Prepared under Task No. 3022.210

FTP No. 01-540

Solar Energy Research Institute

A Division of Midwest Research Institute

1617 Cole Boulevard

Golden, Colorado 80401-3393

Prepared for the

U.S. Department of Energy

Contract No. DE-AC02-83CH10093
NOTICE

This report was prepared as an account of work sponsored by the United States

Government. Neither the United States nor the United States Department of Energy,

nor any of their employees. nor any of their contractors. subcontractors, or their

employees, makes any warranty, express or implied. or assumes any legal liability

or responsibility for the accuracy, completeness or usefulness of any information,

apparatus, product or process cisclosec. or represents that its use would not

infringe privately owned rights.

, .
..

TP-2952

MOISTURE TRANSPORT IN SILICA GEL PACKED BEDS

II. EXPERIMENTAL STUDY

Ahmad A. Pesaran* Anthony F. Mills

Solar Energy Res~arch Institute School of Engineering and Applied Science

Golden, CO 80401, USA

ABSTRACT

University of California

Los Angeles, CA 90024, USA

Experiments have been performed to obtain the transient response of a thin

adiabatic packed bed of silica gel after a step change in inlet air condit i ons , Comparisons are made with predictions using a solid-side resistance

model and a pseudo-gas-side controlled model and better agreement obtained

with the former model. An apparent dynamic hysteresis for adsorption!

desorption with microporous silica gel is clearly in evidence, which could be

due to solid side effective diffusion coefficient which decreases with

increasing moisture content, or to a lesser extent to a hysteresis in the

adsorption isotherm itself.

*At the School of Engineering and Applied Science, UCLA during the course of

this work.

1
a

A

NOMENCLATURE

average pore radius

cross section area of bed

specific heat of liquid water

constant pressure specific heat of humid air

constant pressure specific heat of water vapor

desiccant to air ratio, PbAL/mGT (dimensionless)

TP-2952

D

D*

ID

total diffusivity, defined by Eq. 13

DT/R2 (dimensionless)

Knudsen diffusion coefficient

surface diffusion coefficient

equilibrium isotherm, pml' = g (W,T)

derivative of equilibrium isotherm, g'(W) = p(aml/aW)T

convective heat transer coefficient

heat of adsorption

Intermediate Density (macroporous)

gas-side mass transfer coefficient

effective mass transfer coefficient

length of bed

water vapor mass fraction (kg water/kg humid air)

2
NOMENCLATURE (Continued)

me mass flow rate of gas mixture

TP-2952

Nt u number of transfer units, KG L/mG or KC,eff Lime (dimensionless)

P pressure

PGC pseudo-gas-side controlled

p perimeter of bed

r radial coordinate in a particle

r* r/R (dimensionless)

R particle radius

R H20 gas constant

Re Reynolds number, 2RV/~ (dimensionless)

RD Regular Density (microporous)

RH relative humidity, P1/psa t (dimensionless)

SSR solid-side resistance

t time

t* dimensionless time, tiT (dimensionless)

T temperature

V superficial velocity of alr

W desiccant water content (kg water/kg dry desiccant)

z axial distance

z* z/L (dimensionless)

Greek

6 ppD/KGR (dimensionless)

porosity (dimensionless)

3
NOMENCLATURE (Concluded)

v kinematic viscosity

TP-2952

p density of humid air

Pp particle density

, duration of experimental run

'g tortousity factor for intraparticle gas diffusion (dimensionless)

's tortousity factor for intraparticle surface diffusion (dimensionless)

Subscripts

1 water vapor

2 dry air

avg average value

b bed; bulk

e surrounding humid air

eff effective value

K Knudsen diffusion

tn inlet value

o initial value

out outlet value

p particle

S surface diffusion

s s-surface, in gas phase adjacent to gel particles, or dry solid phase

of the bed

sat saturation

4
TP-2952

1.0 INTRODUCTION

Part I of this series [1] reported an analytical study of the transient

response of thin silica gel packed beds to a step change in inlet air humidity

or temperature. Special attention was given to moisture transport within the

silica gel particles since earlier investigators [2,3,4] showed that the

solid-side moisture transfer resistance is generally larger than the gas-side

resistance. A model which accounts for both Knudson and surface diffusion of

moisture within the particles was proposed and incorporated into a simultaneous heat and mass transfer model for predicting the transient response of

thin silica gel packed beds. The model is called the Solid Side Resistance

(SSR) model and includes both solid- and gas-side resistances. The predictions of the SSR model were compared with predictions of the widely used

Pseudo-Gas-side Controlled (PGC) model. In the PGC model the overall mass

transfer from the air stream to the silica gel is represented by a gas-side

coefficient which is reduced to account for solid side resistance.

Part II of this .series describes an experimental program which obtained data

for the evaluation of the analytical models. A bench-scale test rig was

bui 1t , and adsorpt ion and desorpt ion experiments performed on microporous

Regular Density (RD) and macroporous Intermediate Density (10) silica gel in

adiabatic thin packed beds. Section 2 describes the experimental rig, instrumentation, procedure, and test materials; Section 3 presents the results and a

discussion. Section 4 presents our conclusions.

5
2.1 Apparatus

2.0 EXPERIMENTAL KETHOD

TP-2952

A schematic of the experimental system is shown in Fig. 1. The system consists of a dryer, an air heater, a humidifier, a blower, a heat exchanger, and

a desiccant bed in a test chamber. The dryer, air heater and humidifier are

used to generate the desired inlet air conditions for the test chamber; the

a~r heater is also used to regenerate the silica gel both in the test chamber

and in the dryer.

The dryer used to provide dry air for step change experiments is a stainless

steel cylinder 0.55 m high, and 0.19 m in diameter. A packing height of

0.42 m of 3-8 mesh RD silica gel (Davison, Grade 01) is used. A computer code

[3,4,6] was used to design the dryer and for prediction of its performance.

The dryer can be isolated from the system by closing valves 2 and 4.

The a~r heater ~s used to regenerate the silica gel in both the test chamber

and the dryer. It 1S a commercial 1.5 kW electrical heater manufactured by

Pacific Chromalox. It consists of two electrical heating elements contained

in a well-insulated stainless steel casing. The outlet air temperature can be

controlled by controlling the power supplied to the heater with an AC Variac.

The humidifier for providing humid a1r for the experiments 1S a cast acrylic

cylinder 0.73 m high and 0.72 m inside diameter, packed with 1/2 inch ceram~c

Berl saddles. The height of the packing in the original design was 0.5 m,

However, after some preliminary tests the hei.ght was reduced to 0.25 m for

6
TP-2952

better control of humidity. The packing is supported by a perforated acrylic

plate. The process air enters from below and contacts with water sprayed on

top of the packing. Tap water is fed to the top of the packing. The humidifier can be removed from the system by closing valves 5 and 7.

Air flow is provided by a positive displacement rotary blower manufactured by

Gardner-Denver (model 2PDR) with a capacity range of 1.4x 10-3 to 0.1 m3/s ,

The blower is driven by a 3 HP, 230 VAC, 3 phase induction motor, through a

belt and pulley system. The blower capacity can be changed by operating at

different shaft speeds using different pulleys, and/or by varying the rate of

air by-pass, i.e., controlling valve 1. Since the blower blows the air

through the system, all components are under a slight pressure.

The test chamber is a 0.13 m I.D. Pyrex glass cylinder with a wall thickness

of 6.5 mm , The test chamber has three sections: the main section, a top

section, and a lower section. Air enters through the top, passes through a

flow straightener of about 0.18 m height of Berl saddle packing to provide a

uniform flow before entering the silica gel bed. The uniformity of flow was

satisfactory as checked with a hot wire anemometer. The silica gel bed is

supported by a copper screen, which, in turn, 1 s supported by the lower

section of the test chamber. The height of the bed is varied by adding more

or less silica gel from the top of the test chamber. To approximate the

adiabatic operation, the test chamber is insulated with fiberglass during

testing.

The purpose of the heat exchanger is to cool the hot process alr after

adsorption to a dry bulb temperature in the useful range of the hygrometer

7
TP-2952

sensor used for measuring humidity. The heat exchanger consists of a copper

coil welded to an aluminum cylindrical casing. Tap water is fed to the top

of the coil and the process a i r is passed through the aluminum cylinder

cocurrently with the water. The system components are connected through

1.25 inch (0.0.) galvanized pipes and 1.5 inch rubber hose connectors. The

pipes are insulated for a better temperature control and to reduce heat loss

during regeneration.

2.2 Instrumentation

The volume flow rate 1S determined by a calibrated Rockwell Testmeter (model

No. 415). Associated air pressure and temperature measurements are made using

a mercury manometer and thermocouple, respectively, to convert volume flow

water rate to mass flow rate. A standard ASME orifice system with required

manometer calibrated the Testmeter. The expected error in measurement of air

flow rate is less than 3%.

The pressure drops across the desiccant bed, dryer and humidifier are measured

using water manometers. The air temperatures upstream (at station D) and

downstream (at station E) of the bed, outlet from the humidifier (at

station C), and outlet from dryer (at station B) are measured uSlng dry

thermocouples made from 30 gauge (0.0. = 0.25 mm) type K, chromel-alumel

wires. Chromel-alumel thermocouples were chosen because of their resistance

to corrosion in water and humid air, and also for their low conductivity so as

to reduce lead conduction errors. The dry thermocouples are provided with

radiation shields for reduction of radiation losses and the readings corrected

where appropriate. The expected error in temperature measurement is less than

a.soc.

8
TP-2952

The relative humidity of the process air is measured us mg a hygrometer

manufactured by Weather Measure Corp. (Model HMS-14) with a single dielectric

polYmer sensor with a very short response time (90% of final relative humidity

in one second) • The sensor of the hygrometer can be mounted at several

locations (stations C, F and G) in the system for various purposes. At each

mounting station a thermocouple junction is provided for measurement of tem--

perature along with measurement of relative humidity so that the water vapor

concentration can be calculated. A resistance type hygrometer manufactured by

Hydrodynamics Inc. (Model 15-3001) is also used with sensors appropriate to

different humidi ty ranges. These sensors have a slower response than the

Weather Measure sensor and thus are used for measurement of uniform humidities

from the dryer or humidifier to the desiccant bed. The bed outlet humidity

measurement was corrected for time lag due to the distance between the bed

outlet and the measuring- station. The error i n measurement of relative

humidity is 3%. Considering other errors in measurement of temperature and

total pressure the estimated error in measurement of water vapor mass fraction

is less than 6%.

All thermocouple junctions are spot welded and connected to a millivolt

recorder and a cold junction compensator manufactured by Fluke Company

(model 2240A Datalogger). The voltage outputs of all the thermocouples and

the hygrometers are recorded simultaneously at a preprogrammed time interval

by the Datalogger.

9
TP-2952

2.3 Procedure

Tests were performed to determine the transient response of thin silica gel

packed beds to a step change in inlet conditions. A bed of known initial

water content and temperature was prepared using the heater of the humidifier,

and then sealed. Commencing at time t=O process air with selected constant

humidity and temperature was passed through the bed. The outlet air conditions (temperature and relative humidity) from the bed were measured as a

function of time and the data collected. Two types of experiments were

performed, namely, adsorption and desorption. In adsorption experiments, the

initial bed water content is lower than the equilibrium value corresponding to

the process air, i.e., Wo < W (m1,in' Tin' p). In desorption experiments, the

initial bed water content is higher than the equilibrium value corresponding

to the process air, i.e., Wo > W (m1,in' Tin' p). The experiments were terminated after 20-30 minutes which 1S typical of cycle times between adsorption

and desorption processes encountered in operation of dehumidifiers 1n

desiccant cooling systems. The collected data were converted to engineering

units and plotted and compared with the model predictions as shown 1n

Section 3.

2.4 Test Material

Both micr opo rous silica gel (Regular Density, Davison Grades 01, 03, 40 and

408) and macroporous silica gel (Intermediate Density, Davison Grade 59) were

tested to investigate the effect of average pore diameter and equilibrium

isotherm on bed performance. The major difference in various grades of RD gel

is their range of particle size. It is reasonable to assume that the solid

10
TP-2952

S=~II.I

side resistances varies with gel particle size and thus a wide range of gel

sizes was tested (0.6-5 mm in diameter). Since the particle size range in

some of the grades are wide, they were sieved to obtain a narrow range of

particle size. The average pore sizes supplied by the manufacturer are 11 A

for RD gel, and 68 A for ID gel.

3.0 RESULTS AND DISCUSSION

Thirty-five tests were performed: due to space limitations only the results

of selected tests are used here to evaluate the validity of the theoretical

models. Table 1 summarizes the pertinent parameters of the tests. We have

presented 13 tests to show the results for two types of gel, adsorption and

desorption cases, various particle sizes, and initial and inlet air

conditions. The outlet air temperature and outlet water vapor mass fraction

as functions of time after a step charge 1n inlet air conditions to the bed

are shown by symbols in Figures 2 through 1S for thirteen tests. Predictions

using both the solid-side (SSR) model and the pseudo-gas-side controlled (PCC)

model are also shown in these figures by solid lines.. For convenience the

essential differences between these models are summarized in Table 2 ..

3.1 Adsorption on Regular Density Silica Gel

Figures 2 through 7 show results for adsorption tests with RD gel.. The

general trends of the curves for the experimental results and the theoretical

predictions are simi lar and are explained in Part I for their series [1] ..

Unless otherwise specified Eq.. (A-l) was used for the equilibrium isotherm and

11
Eq, (A-3) for the test of adsorption in the predictions. Eq, (A-6) was used

for the effective surface diffusion coefficient. Since the parameter Do,eff

had not been previously established for the H20- s i l i ca gel system, we

determined a suitable value by making calculations for a range at Do,eff

values and comparing predictions with experiment: Figures 3 and 4 show

typical results of such predictions. Based on a number of such comparisons a

value of Do,eff = 1.6 x 10-6 m2/s was chosen [5]. Theoretical predictions

with the SSR model were not made for tests on gel particles of 0.87 mm radius

and smaller: the large values of Nt u for these tests required a large number

of time and spatial node points to avoid numerical instability and thus the

computational cost was prohibitive.

By comparing predictions with experiments the following general observations

can be made. Predictions of ml,out using the SSR model are generally superior

to those of the PCC model, especially at small times. The initial slopes of

the ml,out curves from SSR model are steeper than those of PCC model and

usually match the experimental results. The PCC model usually underpredicts

the experimental ml,out' i.e., more water 1S adsorbed due to less mass

transfer resistance. In most of the experiments the measured Tout is within

the range of the predicted values of both SSR and PCC models; at small times

the agreement with SSR model is generally better. The SSR model tends to

predict peak values of T t which are higher than those for PCC model with the ou

peaks occurring earlier.

12
TP-2952

S=~II.I

3.2 Desorption from Regular Density Gel

Fig~res 8 through 11 show results for desorption tests on RD gel. Again the

theoretical predictions using both models follow the general trend of the

experimental results. Again Eqs. A-l and A-3 are used for the equilibrium

isotherm and heat of adsorption, respectively. For the moisture diffusivity,

Eqs. (A-5 and A-8) are used, i.e., 'only surface diffusion is considered for RD

gel. Figures 12, 13, and 14 show that Do,e£f = 0.8 x 10-6 m2/s gives a better

match with experiment than the value of 1.6 x 10-6 used for the adsorpc i.on

experiments. The lower value of Do,eff increases the solid side resistance

and thus decreases the desorption rate: ml,out is overp-cedicted by both

models (even when the reduced value of Do,eff is used in the SSR mode), while

Tout is predicted satisfactorily by the SSR model, and is underpredicted by

the PGC model. The p-cediction of ml,out by the PCC model matches better than

that by the SSR model for Test 25 (Fig. 8), while the reverse is true for

Tests 29 and 30 (Figs. 9 and 10), when Do,eff = 0.8 x 10-6 m2/s is used in the

SSR model. A theoretical prediction for Test 35 (Fig. 11) using the SSR model

was not obtained owing to a prohibitive computer cost associated with the

large Nt u value. For this test the PGe model predicts Tout satisfactorily,

while m1,out is again overpredicted. The discrepancy between predictions of

the SSR and PCC models 1n Figures 8-10 is because they differ fundamentally as

can be seen from Table 2.

It is clear that there is a fundamental difference between the behavior of the

bed during adsorption and desorption. For example, the experimental responses

of an adsorption test (:fj24) and a desorption .test Ci!29) with similar bed and

flow conditions shown in Figure 12 present this difference. As discussed in

13
Part I [1],

TP-2952

the SSR model shows that there should be a difference due to

concentration dependence of DS,eff in the Sladek theory, Eq. (A-8): initial

rates of desorption should be higher than initial rates of adsorption with all

other pertinent parameters the same. However a comparison of figures shows

that exactly the opposite is true. Furthermore our comparison of predictions

with experiments has shown that solid side effective diffusion coefficients

appear to be one half of those for adsorption. The SSR model lacks an

essential feature: either there 1S a marked hysteresis in the adsorption

isotherm, or solid side effective diffusion coefficients decrease with

increasing gel moisture content W. Indeed, Kruckels [1,9] found it necessary

to include such a feature in correlating his experimental data for adsorption

on RD gels at low moisture contents, as discussed in Part I of this series.

The isotherm of RD gel usually does not show a strong hysteresis [e.g., 7 and

8]. However, decrease of solid side effective diffusion coefficient with

increasing gel moisture content is quite possible. The negative exponential

dependence of DS,eff in Eq. (A-B) is due to the decrease of heat of adsorption

with increasing moisture content and has a rational basis; hence, one must

look elsewhere for an explanation. A similar behavior (i.e., good agreement

for adsorption and poor agreement for desorption) was observed by Barlow [10]

and thus this apparent dynamic hysteresis can now be regarded as a firmly

established feature of RD silica gel behavior. Further experiments are

needed, in which the initial gel moisture content 1S varied over a wide range

so as to resolve whether the apparent dynamic hysteresis is due to a gel

moisture content dependent effective surface diffusion coefficient, or whether

there is a more fundamental difference between the adsorption and desorption

processes on a molecular scale. It should be noted than an. effective porosity

which decreases with increasing moisture content 1S not an unreasonable

explanation.

14
TP-2952 5='1'.1

3.3 Adsorption on Intermediate Density Silica Gel

The resul ts for adsorption on ID gel are shown in Figures 13 through 15.

Equations A-2 and A-4 were used for the equilibrium isotherm and heat of

adsorption, respectively. For the moisture diffusivity Eqs. A-6, A-1 and A-a

are used, i.e., both Knudsen and surface diffusion are considered for IO gel.

The Do,eff value used was the same as that established for adsorption on RD

gel, i.e., 1.6 x 10-6 m2/s, and a reasonable match between SSR model

predictions and experiment is obtained.

The general shapes of the Tout and ml,out curves are the same as those of RD

gel. However, since the equilibrium capacity of ID gel is much lower than

that of RD gel (as shown in Fig. A.l), the ID gel bed loses its adsorption

capacity faster. Thus, ml,out increases very rapidly initially and then there

is a smooth transition to a more gradual increase; Tout also increases to its

peak value very quickly, and subsequently decreases rapidly to the inlet alr

temperature. The predictions of m1,out of SSR model is better than those of

PCC model, especially at small times. This behavior is similar to that noted

before for adsorption experiments on RD gel. At longer times, ml,out is

overpredicted by SSR model. Usually, the PCC model underpredicts the experimental initially and overpredicts later. 1S generally

underpredicted by both models, especially after the peak value is reached,

with PCC model doing somewhat better than SSR model.

15
TP-2952

4.0 CONCLUSIONS

1. Reasonable agreement between prediction and experiment for RO gels is

possible with both the solid-side resistance (SSR) model and the pseudogas-side controlled (PCC) model, though in general the SSR model gives the

better agreement.

2. The effective surface diffusion coefficient 1n the SSR model required to

match desorption data for RO gels is about one half of that required to

match adsorption data for RO and 10 gels.

3. There is an apparent dynamic hysteresis for adsorption/desorption with RO

gel, which could be due a solid-side effective diffusion coefficient which

decreases with in~reasing moisture content; a less likely possibility is a

hysteresis in the adsorption isotherm itself.

4. Further experiments, in which the initial moisture content of the gel is

varied over a wide range, are required to clarify the cause of the

apparent hysteresis.

16
TP-2952

ACKNOWLEDGMENTS

This work was supported by a grant from the Solar Energy Research Institute/

U.S. Department of Energy, Grant No. DE-FG02-80CS84056. The Technical Monitor

was T. Penney. Computer time was supplied by the Campus Computing Network of

the University of California, Los Angeles. The Publication Development Branch

of the Solar Energy Research Institute assisted in preparing this paper.

17
TP-2952

S - !!!!tl ,~ =~ I~~I

REFERENCES

1. Pesaran, A. A. and A. F. Mills, Moisture Transport in Silica Gel Packed

Particle Beds 1. Theoretical Study, Intemational Journal of Heat and Mass

Transfer, in press.

2. Clark, J. E., "Design and Construction of Thin, Adiabatic Desiccant Beds

with Solar Air Condi tioning Applications," M. S. Thesis , School of

Engineering and Applied Science, University of California, Los Angeles

(1979).

3. Clark, J. E., A. F. Mills and H. Buchberg, Design and Testing of Thin

Adiabatic Desiccant Beds for Solar Air Conditioning Applications, J. Solar

Energy Engineering, 103, (May 1981).

4. Pesaran, A. A., "Air Dehumidification i n Packed Silica Gel Beds,"

M. S. Thesis, School of Engineering and Applied Science, University of

California, Los Angeles (1980).

5. Pesaran, A. A., "Moisture Transport i n Silica Gel Particle Beds," Ph.D.

Dissertation, School of Engineering and Applied Sciences, University of

California, Los Angeles (1983).

6. Nienberg, J. W. "Modeling of Desiccant Performance for Solar DesiccantEvaporative Cooling Systems," M. S. Thesis, School of Engineering and

Applied Science, University of California, Los Angeles (1977).

18
TP-2952

7. W. R. Grace and Co., Davison Silica Gel, Bulletin No. lC-15-378; and

W. R. Grace and Co., Fluid Processing Handbook, Baltimore, Maryland (1966).

8. Jury, s. H. and H. R. Edwards, The Silica Gel Water Vapor Sorption Therm;

Can. J. Chern. Engr. 49, 663-666 (October 1979).

9. Kruckels, W. W., On Gradient Dependent Diffusivity, Chern. Engs. Sci., 28,

1565-1576 (1973).

10. Barlow, R. S., Analysis of Adsorption Process and of Desiccant Cooling

Systems--A Pseudo-Steady-State Model for Coupled Heat and Mass Transfer,

SERI/TR-631-1329 , Solar Energy Research Institute, Golden, CO, USA (1982).

19
TP-2952

APPENDIX A. AUXILIARY DATA

Beside the information already given for KG and hc and in Table 2, data are

required for specific heats cp,e' cpl' and cb' heat of adsorption and

equili brium isotherm relation, and bed density, silical gel density and

diffusivities. The specific heats are assumed to be independent of

temperature which is a reasonable assumption for the range of temperature

encountered for the application of this work, namely, solar desiccant cooling

systems.

The specific heats are:

cpl = 1884 J/kg K

Cp,e = C m + c (l-ml ) pI l,e p2 ,e = 1884 m1 + 1005 (1-m1 ) ,e ,e J/kg K

cb = ci Wavg + csilica gel = 4178 Wavg + 921 J/kg K

Equilibrium isotherms were obtained by fitting fourth degree polynomials to

the manufacturer's data [9] for Regular Density (Davison, Grades 01, 03 and

40) and Intermediate Density (Davison, Grade 59) silica gels.

RH = 0.0078 - 0.05759W + 24.16554 W2 - 124.478 W3 + 204.226 W4

and for ID gel,

20

(A-I)
TP-2952

S=~II.1

RH =1.235 W+ 267.99 W2 - 3170.7 W3 + 10087.16 W4 W 0.07

RH = .3316 + 3.18 W W::> 0.07 (A-2)

Fig. A-1 compares the equilibrium isotherm of RD and ID silica gels. The heat

of adsorption is a function of gel water content and is the summation of heat

of condensation and heat of wetting. A summary of the literature on heat of

adsorption of H20 on RD silica gel is given in [4]. A recommended correlation

that fits the available data for RD gel is

H = 3500 - 13400 W ads

Hads = 2950 - 1400 W

w 0.05 I kJ/kg water

W ::> 0.05

(A-3)

For heat of adsorption on IO gel no satisfactory data was found, thus the

Clausius-Clapeyron equation

was applied to the equilibrium isotherm of ID silica gel. The equilibrium

isotherm was replotted on the 1n PI versus 1/ (T + 273.15) plane, where an

approximate straight line for a constant gel water content was obtained. The

slopes of these lines gave the average heat of adsorption at each gel water

content. The following equation was fitted to the results,

H = -300 W + 2095 ads

H = 2050 ads

W< 0.15

w 0.15

21

kJ/kg water (A-4)
TP-2952

~~- The bulk density of RD silica gel bed is 721.1 kg/m3, and that of ID silica

gel is 400.6 kg/m3• The particle density of RD silica gel is 1129 kg/m3 , and

that of ID gel is 620 kg/m3•

As discussed in Appendix A of Part I of this work [1] the total diffusivity D

depends on only surface diffusion coefficient for microporous RD gel

D = DS,eff (A-5)

and depends on both surface and Knudson diffusion coefficients for macroporous

ID gel

g'(W) D = DS eff + DK ----- , Pp

where the effective diffusion coefficients are given by

(A-6)

DK eff = 22.86 (T + 273.15)1/2a (A-7) , Tg

DS,eff = Do,eff exp [-0.947 Hads/(T + 273.15)] (A-8)

where Hads is in kJ/kg water and T in °c and a is pore size in meter. The

particle porosity (€p) and gas tortousity factor ('g) for ID gel are 0.716 and

2.0, respectively.

22
Table 1. Bed and Flow Conditions for the Experiments UlIII

Test Gel Process* R L W - o To' ml,in Tin V Re Nt u1,* DAR T ItI}1 "'!!~

II Type (10-3 m) (10-3 m) (oC) (oC) {m/s} (9)

1 RD AD 1.94 77.5 0.0417 23.3 0.0100 23.3 0.21 49.30 22.65 0.1285 1800

4 RD AD 1.94 75.0 0.0410 24.2 0.0105 24.2 0.32 78.60 18.74 0.0819 1800

6 RD AD 1.94 75.0 0.0450 22.1 0.0088 22.1 0.55 150.9 14.25 0.0547 1500

7 RD AD 1.27 65.0 0.0410 24.7 0.0106 24.1 0.39 10.0 26.29 0.0604 1800

21 RD AD 0.435 45.0 0.0640 20.2 0.0088 20.6 0.30 16.34 98.61 0.0554 1800

24 RD AD 2.60 50.0 0.0668 22.6 0.0109 25.6 0.40 129.8 7.62 0.0440 1800 N

w

25 RD DE 2.60 50.0 0.260 25.4 0.0007 25.4 0.67 218.5 6.12 0.039 1200

29 RO DE 2.60 50.0 0.368 25.0 0.0051 23.9 0.40 131.0 7.59 0.042 1800

30 RD DE 2.60 50.0 0.370 23.8 0.0090 23.5 0.65 205.0 6.28 0.040 1200

35 RD DE 0.33 30.0 0.220 24.3 0.0008 24.3 0.28 11.32 101.1 0.040 1800

13 JD AD 1.94 17.5 0.0088 23.1 0.0097 23.6 0.45 109.41 16.85 0.050 1200

14 ID AD 1.94 71.5 0.0084 23.3 0.0074 23.3 0.18 44.0 24.70 0.0813 1860

17 10 AD 1.94 77.5 0.005 24.4 0.0063 24.4 0.67 164.19 14.21 0.033 1200

..··AD: adsorption; DE: desorption

."

I

••t ~·;1'h i s value of Nt u is for SSR model, Nt u for PGC model is about 1/3.4 of this value. t-,)

\D

VI

t-,)