NomenclatureARt

mole fraction of BAin original mixtureXBAlX OCBAcrystallization temperature

L = liquid phase[-][-] Literature Cited[q

mole fraction of precipitated crystalswith respect to original mixturemole fraction of BAin differential

crystallizationmole fraction of OCBAin differential

crystallizationaverage mole fraction of BAin crystalsobtained by batch crystallization

1) Abu Elamayen, M. A.: J. Inorg. Nucl. Chem., 26, 2159 (1964).2) Chlopin, V.: Z. Anorg. Allgem. Chem., 143, 97 (1925).

3) Doener,H.A. andW. M. Hoskins: J. Am. Chem. Soc,47, 662(1925).

4) Feibush, A. M., K. Rowley and L. Gordon: Anal. Chem., 30,1605 (1958).

5) Kitamura, M. and T. Nakai: Kagaku Kogaku Ronbunshu, 8,442 (1982).

6) Klein, D. H. and B. Fontal: Talanta, 12, 35 (1965)... .. . . , ,, ,, ,, (Presented at the 47th Annual Meeting of The Society of

= distr.but.on coefficent defined by Eq. (1) [-] Chemica, EngineerS; Japan> at Tokyo> 19g2>)(Superscript)S = solid phase

AIR DRYING BY PRESSURE SWING ADSORPTION

Kazuyuki CHIHARAand Motoyuki SUZUKIInstitute of Industrial Science, University of Tokyo, Tokyo 106

Air drying experiments by pressure swing adsorption (PSA) were carried out, using two columns packed withsilica gel as adsorbent. Measurementswere also madeof batch adsorption of water vapor on silica gel to obtaininput data for the authors' PSAsimulation program. Experimental PSAresults were compared with this computersimulation. Good agreement was obtained and the trend of experimental results was well explained by simulationfor both isothermal and non-isothermal cases. In the simulation, however, mass transfer coefficients two or threetimes larger than those estimated conventionally from batch measurement were used to obtain good coincidence.These larger masstransfer coefficients were determined by a recently developed methodfor short adsorption anddesorption cycle.5} The simulation method is useful in predicting the performance of air drying PSA.

IntroductionPressure swing adsorption (PSA) processes are

cyclic processes for the separation of gaseous mix-tures. They were developed during the 1960's as highthroughput replacements for adsorption processesemploying thermal regeneration.

The principal steps involved in a pressure swingcycle are adsorption during pressurization, removal ofpurified product during a high-pressure feed step, anddesorption during blowdown to low pressure. Apurge step may follow depressurization. A portion ofthe purified product is used as purge stream.The higher throughput in pressure swing processes

compared to temperature swing processes resultsfrom the more rapid response of a gas-solid system topressure change than to temperature change. The

Received August 7, 1982. Correspondence concerning this article should be addressedto Kazuyuki Chihara, Dept. of Industrial Chemistry, Meiji Univ., Kawasaki 214.

VOL. 16 NO. 4 1983

more rapid response permits shorter cycle times andhence greater throughput. Additional advantagesclaimed for pressure swing processes include lowenergy requirement and low capital investment costs.

Pressure swing processes are widely used indus-trially in air drying, hydrogen purification and pro-duction of low-purity oxygen from air.6) These PSAseparation processes utilize the difference amongad-sorption equilibria of componentsin gas mixture.Few theoretical analyses of the operation have been

reported for PSA separation in the literature.3>7)Recently a simulation method of nonisothermalpressure swing adsorption (PSA) was developed byChihara and Suzuki.1} In their method, non-equi-librium and nonisothermal pressure swing adsorp-tion for the removal of one adsorbing impure com-ponent, such as air drying, was simulated numericallyfrom start-up until steady cyclic modeis established.Further, the dependence of product gas concentration

293

on the volumetric purge to feed ratio could be esti-mated by their simulation method. The previousdesign method3J) did not give any estimation ofproduct concentration nor of relations between prod-uct concentration and purge to feed ratio, thoughthis volumetric purge to feed ratio is the key point ofPSA design.Comparison of air drying experiments with a simu-

lation by Chihara and Suzuki's method was the focusin this work, which consists of three parts. Thepurpose of the first part was to obtain input data ofadsorption equilibrium and rate for computation.The second part was the PSAexperiments. The thirdpart was the comparison of PSA data with thesimulation. The experimental results were comparedwith the simulation with no fitting parameter.1. Experimental

1.1 Batch gravimetric adsorptionPellets of silica gel (Fuji Davidson type A, spherical

and blue, 5 to 10 Tyler mesh) were used as adsorbentfor air drying PSA experiments. The adsorptionproperties of the adsorbent were measured for usein computation as follows.A quartz spring balance was installed in a Pyrex

glass vessel. An MKSBaratron (1000 torr head) wasconnected with the vessel to detect the inside pressure.About 1.0x 10~3kg of adsorbent pellets were hungfrom the balance in a glass tube which was immersedin a constant-temperature bath. After degassing theadsorbent sample at 423 K for 1 hr, a small amount ofwater vapor was introduced. The change in weight ofadsorbent corresponding to small step change ofadsorbate pressure was measured by the balance. Thepressure decay after the initial step change was alsorecorded. Data were obtained at several small pres-sure intervals in the range between 0 to saturationvapor pressure, Ps, at 308K, 323K and 353K.Isotherms were determined from the final uptake atthe same time.

The weight and pressure change curves obtainedwere analyzed to obtain surface diffusivity, Ds, bycurve-fitting of these experimental curves with thefollowing theoretical curves,2) assuming the surfacediffusion controlling.

6^+l)e--2tMt=i-E

p_=1 LMi.Po 1+1 Mm

where q 's are the -th root oftang =

3ft,3+^n2

T = DJ/Rp2

294

(1)

(2)

1+f= Wsq0/V(P0/RT)

and

1.2 PSAoperationThe original pellets of silica gel were crushed and

screened to yield the desired size (14 to 20 Tyler mesh)of small particles. This fraction was packed in thePyrex glass tube as the adsorbent columnof PSA.Twotypes of column, thick and thin, were used. Aschematic diagram of the apparatus for PSAexperi-ments is shown in Fig. 1. Adjustable check valves keepthe column pressure at a fixed value in the adsorptioncycle. A rotameter was used to measure both productand reflux gas flow rates. Dewpoints offeed, productand purge were measured by a Panametric hygrom-eter. The operation mode of PSA cycle is as de-scribed in the article1) by Chihara and Suzuki.Experimental conditions are listed in Tables l(a) and(b).

The dew point of product gas was continuallydetected by hygrometer during each run to checkwhether cyclic operation had reached steady state.The operation was judged as steady-state whenthedew point was kept within 2K for all day long.Location of the boundary between pink zone andblue zone in the adsorbent column was another indi-cator of steady operation. Though this locationchanges slightly during a cycle, average locationwas kept within 0.01m in steady operation. Afterstarting up at one set of operational conditions, cy-clic operation were continued for more than tendays until steady operation was observed. Thenoperational conditions were changed to reach an-other steady state. In the initial several runs, dewpoints of feed and purge were measured after steadystate was reached to check the mass balance.

For the thick column experiments, stainless tube(0.002m I.D., 0.04m O.D.) was set along each axis ofthe cylindrical adsorbent columns. A thermocouplewas inserted into each tube through the end flange ofthe column. Temperature was measured at severallocations along with the axes. This temperaturechange was also used as an indicator of steady opera-tion in addition to the product dew point and thepink-blue boundary location. After getting steadydew point and boundary location for each run, tem-perature change was measured for one cycle atnondimensional longitudinal locations, 0, 0.25, 0.5,0.75 and 1.0.

2. Result and Discussion2.1 Adsorption isotherm and adsorption rate of watervapor on silica gelFigure 2 shows the adsorption isotherm of water

vapor on original silica gel pellets. The solid line in

JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

Fig. 1. PSA dryer, experimental apparatus. 1, Silica gelbed; 2, compressor; 3, needle valve; 4, solenoid valve; 5, checkvalve; 6, hygrometer; 7, flow meter; 8, gas meter.

Fig. 2. Adsorption isotherm ofH2O on silica gel.

Fig. 3. Surface diffusivity of H2O on silica gel.

Table 1. Experimental conditions for PSA operation

a) thick column caseAdsorbent bedL = 0.127or0.15mr = 0.025ms = 0.40y = 0.73xl03kg/m3ps = 1.22xl03kg/m3

Cps = 9.21xlO2J/kg-Kpg = 1.2kg/m3 (at atmospheric pressure)Cpg = 1.00xl03J/kg-K

Q = 6.3xl04J/mol

Feed gasvH = 0.058to0.061m/sPH = 4.44x105Pac0 = 0.48to0.71mol/m3To = 287to293K^ - 600or1800s

Purge gasvL =ol-vhm/sPL = 1.01xl05Paa = 0.75to1.23t2 = 600or1800s

b) thin column caseAdsorbent bedL = 0.3m

r = 0.012mOther conditions were the same as those forthick column runs.Feed gas

vH = 0.263m/sPH = 5.07x105Pac0 = 1.067mol/m3To = 298K

tx = 600or300s

Purge gasvL = a"vHm/si>L = 1.01xl05Paa = 1.25to2.1?2 = 600or300s

Fig. 2 shows the Freundlich equation as follows.q*=1.92x 10-2(P/Ps)1/1 6 [mol/g] (6)

Ps-PsO exp (-A/^r)c=P/RT

Apparently the experimental results can be explained

by the above equation. Isosteric heat of adsorption is5x lO4 to 6.3x 104J/mol.

Surface diflfusivity of H2Oon silica gel as a functionof amount adsorbed is shown in Fig. 3. On the samebasis of driving force expressed by amount adsorbedgradient, the obtained surface diffusivity was com-pared with the effective diffusivity, which was esti-mated by assuming that the diffusion is governed bydiffusion of Knudsentype at an average pore diam-eter of 2.2nm. Experimental diffusivity as surface

diffusion was almost ten times faster than that esti-mated. Hence it is concluded that intraparticle dif-fusion is controlled by surface diffusion. The acti-vation energy of surface diffusion at 0.03kg/kg ofamount adsorbed was 4.2x 104J/mol, which was

about 0.8 of the isosteric heat of adsorption.2.2 PSA operationIn the thick column experiments, dew points ofproduct gas, temperature changes and locations of

boundary between pink zone and blue zone at steadyoperation were obtained at several conditions by.

changing volumetric purge to feed ratio, a, and half-cycle time, tx. These three kinds of information (dewpoints, boundary locations and temperature changes)were compared with three simulated profiles (gas-

phase concentration, amount adsorbed and tempera-ture) to check the suitability of the simulation meth-od. Figures 4(a), (b), (c) and (d) show examples of

VOL 16 NO. 4 1983295

Fig. 4(a). Example of temperature profile (RUN A).

Fig. 4(b). Example of temperature profile (RUN B).

Fig. 4(c). Example of temperature profile (RUN C).

Fig. 4(d). Example of temperature profile (RUND).

the experimental results, noted as RUNA, B, C, andD, respectively. In each of these figures, experimen-tally obtained product concentration (dew point, D.P.

exp), boundary location (the arrow, BL exp, pointsthe location in the axial direction) and two tempera-ture profiles at the ends of both adsorption and

desorption cycles are shown. f=0 is the inlet at high-pressure flow and the outlet at low-pressure purge

flow. By batch gravimetric adsorption, color changeof the silica gel was checked and found to correspondto 8wt%to 10wt%of water adsorption. Thereforethe region of color changing, i.e. boundary location,means that the amount of water adsorbed is 8 to 10%in that region. In RUNA, B and C, volumetric purgeto feed ratio, a, was changed from 1.23 to 0.75, whilehalf-cycle time, tl9 was kept constant (600s) to keepthroughput ratio, t1/t0, almost constant as shown in

Figs. 4(a), (b) and (c) and other conditions were fixed(Table l(a)).As a decreases, product concentration becomes

worse from D.P.=201 K to 253K, and the tempera-ture peak at the end of adsorption cycle and the

boundary location shift to the outlet at high-pressureflow. Figure 4(d) (RUN D) can be compared withFig. 4(a) (RUN A), since only t1 was changed (to1800s) in RUND from RUNA. As a result, dewpoint rises, and temperature peak and boundary

location shift to the outlet at PH in RUND.Figure 5 shows an example of the temperature

changes at various positions in the axial direction, asobtained in RUNA.Dew points of product gas and locations of

boundary between pink zone and blue zone atsteady operation were experimentally obtained atseveral conditions by changing volumetric purge to

feed ratio, a, and half-cycle time, tl9 for the thin col-umn experiments also. Figures 6 and 7 show the de-pendence of product dew points and boundary lo-cations, respectively, on a. Experimental dew pointsare in the range between 213K to 183K and fallreasonably with the increase of a. Also, dew points

shift to lower value by changing the half-cycle timefrom 600s to 300s. Experimental location of the

boundary goes up from 0.03m to 0.18m by reducingthe volumetric purge to feed ratio. Also, operation at300s half-cycle time lowers the boundary location

from that at 600 s half-cycle time operation.2.3 Comparison of PSA data with simulation

Theoretical temperature profiles, boundary loca-tions (BL 10 and BL 8 correspond to 10wt% and

8 wt% respectively) and product concentrations (D.P.cal) are shown in corresponding figures (Figs. 4(a),(b), (c) and (d)) for thick column experiments (RUNA, B, C and D). Simulated product concentrations asisothermal are also shown (D.P. iso). Input data forsimulation are adsorption isotherm of Eq. (6), overall

296 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

Fig. 5. Temperature change at various positions in axialdirection during one steady cycle.

Fig. 6. Dependence of dew points of product gas onvolumetric purge to feed ratio.

Fig. 7. Location of boundary between pink zone and bluezone.

mass transfer coefficient, Ksav and complex heattransfer coefficient through the wall, h0, with thosedesign and operation conditions shown in Table l(a).h0 is estimated to be 62.8J/m2 -s-K for high-pressureflow.

The adsorption isotherm (Eq. (6)) was used forcomputation just as shown. The values of Km,,,

however, were checked as follows. Whenadsorptionuptakes are approximated by linear driving force, theoverall mass transfer coefficient is usually expressed as

follows.

Ksav = \5yDjRp2 (7)Surface diffusivity is experimentally determined in thefirst part of this work. First, Ksav determined by Eq.(7) was used for simulation (DS=S.2x 10~12rn2/s,Ksav=0.35kg/m3-s at 293K). Agreement with ex-perimental data was not good.Recently Nakao and Suzuki5} proposed an esti-mation method for mass transfer coefficient, Ksav,defined by including the adsorption and desorptioncycle time for the single spherical particle. Ksavin-

creases with decreasing cycle time in this new con-ception. Though the conditions under which they

determined Ksavare not strictly the same as those inthis work, Ksajs for PSAsimulation were deter-mined again by their method.5) Using the larger Ksavvalues thus obtained (Ksav=0.$2kg/m3-s for 600s

half-cycle and 0.44 for 1800 s), fairly good agreementwas obtained between experimental results and simu-lation as for temperature profile, boundary location

and product dew point. Also, the trend of the experi-mental data with change of operational condition,

i.e. volumetric purge to feed ratio, a, and throughputratio, tjto, is well explained by the simulation.

Longitudinal heat conduction is neglected here.In Fig. 5, an example of the theoretical curve, whichcorresponds to the temperature change at z=0.5, isplotted. Amplitude is in good agreement, but thesimulation curve shows rather quick response. The

reason is not yet known, but the difference as the timeconstant is not so great.In Figs. 6 and 7, theoretical curves by computersimulation are shown for the thin column experi-ments. Input data for computation except the designand operation condition in Table l(b) are the adsorp-tion isotherm (Eq. (6)) and overall mass transfercoefficient, Ksav. Equation (6) was used for com-putation just as shown. As for mass transfer coef-ficient, Ksav determined by Eq. (7) was first used forsimulation (Ds= l.l x 10~n m2/s, Ksav=0Alkg/m3 -sat 298 K). Agreement with experimental data was notgood. Then, larger values (Ksav=0.96kg/m3-s for^=600s, 7CX=1.35kg/m3-s for 300s) determinedby Nakao and Suzuki's method5) were examined toobtain the curves in Figs. 6 and 7, though theexperimental conditions are slightly different fromthose of their estimation method. These Ksav valuesare two to three times larger than Ksav by Eq. (7). Thesimulation curves well explained the trend and theabsolute value of the experimental results for both theproduct concentration and the boundary location.Longitudinal heat conduction was neglected in these

VOL. 16 NO.4 1983 297

Fig. 8. Dependence of product gas dew points on tw.

considerations because of its low sensitivity.In these simulations, isosteric heat of adsorption,

g, was assumed to be zero for thin column experi-ments. Heat generation effect was checked, however,by inputting the exact heat of adsorption and esti-mated complex heat transfer coefficient through thewall, h0, with column diameter to the computer.Figure 8 shows the computation results (chained linewith three circles) (a=0.17, ^=600s), which showsthe dependenceof product concentration on the walleffect parameter, tw. The lower horizontal line is thatfor the isothermal case and the circle which cor-responds to tw= 1500 is that for the nonisothermalcase with estimated h0 (=182J/m2-sK at PH).4)Circles for tw=500 and 50, and upper horizontal line(tw= 0), are hypothetical calculations. Therefore, theisothermal assumption is found to be reasonable inthis operation condition of thin column.

Figure 8 shows also the dependence of outletconcentration on tw at the condition of RUNA bychanging only h0 (dotted line, tw=850 is the actualcondition). Therefore, nonisothermal treatment isreasonable for thick column.C onclusion

Continuous air drying experiments by pressureswing adsorption (PSA) were carried out, using twocolumns packed with silica gel as adsorbent. Columnsof 0.024m and 0.05m in diameter were used. Also,batch adsorption equilibrium and rate measurementswere made to obtain input data for the computersimulation developed by Chihara and Suzuki.1}Experimental PSAresults were compared with thecomputer simulation. Goodagreement was obtainedand the trend of experimental results was well ex-plained by simulation for both isothermal (small-diameter column) and non-isothermal (large-diametercolumn) cases. In the simulation, however, masstransfer coefficients two or three times larger thanthose estimated originally from batch measurementwere used to obtain good coincidence. These larger

mass transfer coefficients were determined by Nakaoand Suzuki's recently developed method, which de-fines Ksav by including the adsorption and desorptioncycle time. It is concluded that the simulation methoddeveloped previously1} is useful in predicting theperformance of air drying PSAwith the new esti-mation method for Ksav.5) Further improvement ofthe simulation might be possible by improving the

treatment of heat transfer and the estimation of heattransfer coefficient.

AcknowledgmentThe authors express their gratitude to Mr. Ryuichi Shimoyoshi,

on leave from Kanagawa University, for his assistance in theexperimental part of this work.

NomenclatureCpg = heat capacity of gas [J/kg"K]Cps = heat capacity of adsorbent [J/kg " K]c - adsorbate concentration in gas phase [mol/m3]c0 = adsorbate concentration in feed gas [mol/m3]Ds = surface diffusivity [m2/s]

h0 = overall heat transfer coefficientthrough the wall [J/m2 " s " K]

Ksav = overall mass transfer coefficient [kg/m3 " s]L = adsorbent bed length [m]

Mt = uptake in batch adsorption [kg]M^ = final uptake in batch adsorption [kg]p = water vapor pressure [Pa]Po = initial P increased [Pa]PH = pressure in adsorbent column at adsorption

step [Pa]PL = pressure in adsorbent column at purge step [Pa]Ps = saturated water vapor pressure [Pa]P^ = constant in Eq. (6) [Pa]Q = isosteric heat of adsorption [J/mol]q0 = final increase of amount adsorbed in

infinite volume by increase of Po [kg/kg]qn = nth root ofEq. (3) [-]q* = equilibrium amount adsorbed [kg/kg]q0* = equilibrium amount adsorbed with c0 [kg/kg]R = gasconstant [J/mol"K]Rp = adsorbent particle radius [m]

r = radius of adsorbent bed [m]T = bed temperature [K]To = ambient temperature [K]

t = time [s]r0 = (Lyqo*)/(evHco): saturation time [s]

tt = adsorption cycle time [s]t2 = purge cycle time [s]V - volume of vessel [m3]

vH = interstitial velocity at high pressure flow [m/s]vL = interstitial velocity at low pressure flow [m/s]Ws = weight of adsorbent [kg]z = position in bed [m]2 = z/L [-]

a = volumetric purge to feed ratio [-]y = bed density [kg/m3]8 = bed porosity [-]pg = gas density [kg/m3]ps = adsorbent particle density [kg/m3]X = heat of water vaporization [J/mol]z = dimensionless time defined by Eq. (4) [-]

298 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

=to/{(pgCpg+yCps)r/2ho}= defined by Eq. (5)

Literature Cited1) Chihara, K. and M. Suzuki: J. Chem. Eng. Japan, 16, 53(1983).2) Crank, J.: "The Mathematics of Diffusion," Oxford (1975).3) Mitchell, J. E. and L. H. Shendalman: AIChESymp. Ser., 69,

No. 134, 25 (1973).

4) Mizushina, T. et al\ "Heat Transfer and Heat Exchanger,"in Kagaku Kogaku Binran, pp. 255-385, Maruzen, Tokyo

(1978).

5) Nakao, S. and M. Suzuki: J. Chem. Eng. Japan, 16, 114(1983).6) Skarstrom, C. W.: "Recent Developments in SeparationScience," Vol. 2, pp. 95-106, CRC Press, Cleveland, Ohio

(1972).

7) Shendalman, L. H. and J. E. Mitchell: Chem. Eng. Sci., 27,1449 (1972).

TURBULENT COAGULATION OF PARTICLESDISPERSED IN A VISCOUS FLUID

Ko HIGASHITANI, Kiyoyuki YAMAUCHI, Yoshizo MATSUNOand Gijiro HOSOKAWADepartment of Environmental Engineering, Kyushu Institute of Technology, Kitakyushu 804

A kinetic equation for the turbulent coagulation of particles in a viscous fluid in which the hydrodynamicinteraction between colliding particles is taken into account is proposed. The theoretical prediction of the time-dependent behavior of particle concentration is compared with results of experiments in which latex particles inKC1 solutions are coagulated in a stirred tank. It is found that the effect of the hydrodynamic interaction is notnegligible, and that changes of particle concentration under various experimental conditions are quantitativelypredicted by the present theory. On the other hand, the Saffman-Turner theory is found to overestimate thecoagulation rate considerably and to yield a systematic error in the dependence of coagulation rate on thedissipation energy.

IntroductionThe coagulation of colloidal particles is found in

manynatural phenomenaand industrial processes. Inmost situations the coagulation is caused by the flowof turbulence, where particles collide because of theirrelative motion induced by the velocity field of themedium. If there exists no repulsive surface forcebetween particles, every collision leads to coagulation.This process, called rapid coagulation, in a turbulentviscous fluid is treated in this paper.

A theoretical treatment of turbulent coagulationwas carried out approximately by Camp and Stein,2)assuming that the collision mechanismof particles isanalogous to that of the shear coagulation proposedby Smoluchowski.12) Levich7) also derived a kineticequation of turbulent coagulation, assuming that theproblem of coagulation of particles transported byturbulent eddies is reduced to a diffusion problemcharacterized by a turbulent diffusion coefficient. A

Received September 27, 1982. Correspondence concerning this article should beaddressed to Ko Higashitani. Y. Matsuno is at Dept. of Industrial Chemistry, KyushuInstitute of Tech., Kitakyushu 804. K. Yamauchi is now with Fuji Electric Co., Ltd., Hino191.

VOL. 16 NO. 4 1983

theory developed by Saffman and Turner11} is some-what more rigorous. However, it is assumed in theiranalysis that particles encounter each other withoutinteracting hydrodynamically; that is, each particlebehaves as though the others were not present. Thistheory is approximately applicable to the collision inwhich the effect of inertia of particles is predominant,or the interparticle attractive force acts such that itcancels the effect of the hydrodynamic interaction.But it is unlikely that the theory is applicable to thecollision between sufficiently small particles dispersedin a viscous fluid. The theories described above weredeveloped to predict the coagulation process in whichparticles follow the fluid motion completely. There isanother mechanismof turbulent coagulation in whichthe particle collision is attributed to the inertia ofparticles. This mechanism is not treated here becauseit is applicable to rather large particles in a vigorousturbulence.

Experimental investigations on turbulent coagula-tion have been carried out for aerosols,1'10) but norigorous measurements for colloidal dispersions inaqueous solutions are found.

299