Tao Ai ,Aslam M.Mudassar ,Ziqi Cai ,*,Zhengming Gao ,2,*

1 State Key Laboratory of Chemical Resource Engineering,School of Chemical Engineering,Beijing University of Chemical Technology,Beijing 100029,China

2 Beijing Advanced Innovation Center for Soft Matter Science and Engineering,Beijing University of Chemical Technology,Beijing 100029,China

Keywords:High-speed disperser Mean droplet diameter Mass transfer area Split packing

ABSTRACT In thisstudy,the mean droplet diameter in the cavity zone and the total masstransfer area of a multi-stage highspeed disperser(HSD)reactor with different packing combinations were measured and evaluated.The effectsof rotational speed and packing radius,asw ell asthe packing ring radius and numbers,on the mean droplet diameter and the total masstransfer area were evaluated.Amodel wasestablished to calculate the masstransfer area in the cavity zone in the HSD reactor,and it w as found that the packings contribute 61%-82%of the total mass transfer area.Acorrelation for predicting the mass transfer areain the packing zone wasregressed by the dimensionless analysis method.An enhancement factor based on the mass transfer area in the packing zone was proposed to evaluate the effect of packing combination on mass transfer area.Two optimum packing combinations were proposed in consideration of the mean droplet diameter and the enhancement factor.

1.Introduction

Global w arming resulted from the emission of greenhouse gases has been widely concerned in recent years.It hasbeen predicted by the International Panel of Climate Change(IPCC)that by the year 2100,the increasing CO2content in the atmosphere may lead to the rise of 3.8 m in the sea level and 2°Cin the global mean temperature[1-3].Carbon dioxidecaptureand storage(CCS)isconsidered asacrucial strategy for reducing CO2emission[4,5].There are various technologies for CCS[6],including chemical absorption[7],physicochemical adsorption[8],membrane separation[9],and chemical loopingcombustion[10].Among these options,chemical absorption is comprehensively accepted for its advantages of high ef fi ciency,low cost,and mature technology[11].

The conventional gas-liquid absorption contactors,such as packed tow er,spray column,and bubble column,have been applied in various fi elds,however,mass transfer limited by the interfacial area in these traditional reactors w ould w eaken the absorption performance.Rotating packed bed(RPB)is regarded as a promising reactor for gas absorption due to its high mass transfer ef fi ciency and dramatic reduction in equipment size[12,13].The interfacial area in RPBw as several times higher than that in conventional packed columns.For example,the interfacial area in a typical RPB is theoretically betw een 200 m2·m-3and 500 m2·m-3[14],w hile the interfacial area in a packed column only ranges from 80 m2·m-3to 250 m2·m-3[15].

Mass transfer area is an important parameter to evaluate the mass transfer performance.Munjal et al.[16]fi rstly conducted the chemical absorption method to determine the mass transfer area in RPBs.By thesamemethod Yang et al.[17]studied theeffectsof packing thickness in radial direction and the operating parameters on the interfacial area,and it w as reported that the mass transfer contribution of the cavity zone accounted for about 13%-25%of the overall mass transfer.Similarly,Guo et al.[18]estimated that themasstransfer area in the packing zone takes up 70%of the total mass transfer area in RPBs.

The packing is of much importance in RPBs as it can enhance the mass transfer greatly by shearing the liquid into small droplets and increasesthe mass transfer area.The relationship betw een packing structure and mass transfer performance in RPBs has been investigated[19-21].Recent efforts have been devoted to the intensi fi cation of the split packing on the mass transfer in RPBs.Chandra et al.[22]proposed to split the packing into annular rings with gaps,and the results show that the split packing w ould promote the tangential slip velocity to enhance the gas-side mass transfer coef fi cient,leading to the enhancement of mass transfer.In contradiction to this view,Shivhare et al.[23]found that the mass transfer difference betw een co-rotation and counter-rotation of split packing is marginal,and reported that the enhancement of split packing may not result from the gas-liquid slip velocity.Liu et al.[24]also revealed the interfacial area of split packing superior over theconventional block packing,and proposed that theenhancement is derived from the high gas-liquid turbulence in the split packing.

RPBscan bedivided into three parts:the end effect zone(from inner surface of the packing into 15 mm thickness of packing radially in the areaw herethe liquid interactsw ith the packing),thebulk zone(the remaining zone of the packing)and the cavity zone[25].Due to the large relative velocity betw een the liquid and packing in the end effect zone,themasstransfer areaisseveraltimesof that in thebulk zone.Yang et al.[26]con fi rmed the existence of end effect zone w ith high interfacial area even if in an RPBw ith small packing.Considering that the turbulence can be enhanced by the end effect zones,Chu et al.[27]developed a multi-inlet RPBto create extra end effect zones,and results show that the mass transfer area of multi-inlet RPBis larger than that of a traditional single inlet RPB.Yi et al.[28]established a mass transfer model based on the droplet diameter pro fi le along the radial direction of packing to describe the end effect zone in RPBs.

Becausethedroplet diameter issigni fi cant to themasstransfer performance,special attentionshave been paid to thedroplet sizein high-speed rotating reactors with various packing structures.Li et al.[29]observed thedroplet size in the rotor-stator reactor and found that the mean droplet diameter decreases when increasing the number of rotor-ring/statorring.Sang et al.[30]focused on the effect of packing radius on the droplet size and concluded that the mean droplet diameter in the cavity zone of RPBwould increaseif decreasingthepacking radius.Despitemany papers published for the case of droplet size under block packing,the impact of split packing on the droplet diameter has rarely been reported.

In our previous w ork[31],droplet diameter and mass transfer area in amulti-stage HSDreactor without packing wasmeasured,and the results show that the mass transfer area increases w ith the increasing rotor radius.Considering the enhancement of packing in mass transfer process,the mean droplet diameter in a multi-stage HSD reactor w ith various packing combinations is measured in this w ork.The effects of packing ring radius and numbers,as w ell as the packing radius,on the mean droplet diameter in the cavity zone is studied.A mass transfer areamodel isestablished to calculatethemasstransfer areain thecavity zone and the mass transfer contribution of the packing zone.An enhancement factor isproposed to evaluatetheeffect of packing combination on the mass transfer area in the packing zone.

2.Experimental

2.1.Visual study experiments

Fig.1 show s the schematic of the visual study experiment for the measurement of the droplets diameter.During the operation,deionized liquid(w ater at 25°C)w as introduced from the storage tank into the inner edge of the rotor through a tube distributor w ith fourholes.The liquid fl ow ed outw ards radially through the rotor,then it sprayed onto the reactor wall and was collected at the bottom.

The HSD reactor mainly consists of four rotors that are used to support the packing(Fig.1(b)).The rotational speed of the four rotors keeps the same as they are fi xed on a plate.

The picture of HSD rotor,photo capture area and camera position in the visual study experiment are exhibited in Fig.2.The droplets were captured by a high-speed camera(GO5000M,JAI,Denmark)w ith lens(Tamron 180 mm)right above the cavity zone.Fig.2(a)show s the HSDrotor with single block packing in the experiment.The HSDrotor can be divided into the packing zone and cavity zone,and the camera capture area(shadowed square,31.5 mm×25.5 mm)is shown in Fig.2.Then the images(1280×1024 pixel)w ere analyzed by a Matlab program to obtain the diameter of each droplet in the image.

There w ere totally six packing combinationsin thisw ork(Fig.3),including P-1(single packing ring betw een rotor 1 and rotor 2),P-2(single packing ring betw een rotor 2 and rotor 3),P-3(single packing ring betw een rotor 3 and rotor 4),P-12(double packing rings betw een rotor 1 and rotor 3),P-13(double packing rings betw een rotor 1&2 and rotor 3&4),P-123(triple packing rings betw een rotor 1 and rotor 4).These combinations can be classi fi ed into three groups based on different characters,including the radius of the packing ring(P-1,P-2,P-3),the numbers of the packing ring(P-1,P-13),and the radius of the packing(P-1,P-12,P-123).

2.2.Mass transfer experiments

The chemical absorption of CO2into the aqueous NaOH(Fig.1)w as conducted to measure the total mass transfer area in HSD reactor.During normal operation,CO2-N2stream fl owed inwardsfrom agasinlet on the w all of HSD reactor,and the diameter of the gas inlet is 52 mm.Meanwhile,the NaOHsolution wasintroduced via the liquid distributor and fl ow ed outw ards radially.Thus,CO2-N2stream and NaOH solution contacted and reacted w ithin and outside the packing.Finally,the gas with low CO2concentration left the HSD reactor from the gas outlet and then w as analyzed by a CO2analyzer,w hile the solution w as expelled from the liquid outlet of the HSD reactor and w as analyzed by the acid-base titration.The parameters of HSD reactor are listed in Table 1.

Fig.1.(a)Schematic of experimental apparatus(1)storage tank(2)pump(3)fl ow meter(4)light(5)high-speed disperser(6)motor(7)high-speed camera(8)CO2 analyzer(9)gas cylinder;(b)rotor.

Fig.2.(a)Structure of HSD rotor w ith packing and(b)the camera position.

In general,the HSD rotor w as operated under the rotational speed betw een 400 r·min-1and 1400 r·min-1.During the operation,the gas fl ow rate w asvaried from 400 L·h-1to 1000 L·h-1w hile the liquid fl ow rate wasbetween 20 L·h-1and 60 L·h-1.The CO2concentration in the inlet CO2-N2stream w as maintained at 10%(in volume)and the NaOH concentration in the inlet liquid stream w as set at 1.0 mol·L-1.CO2concentration in the inlet and outlet gas stream w ere measured by an infrared(IR)CO2analyzer(GXH-3010E1,Huayun,China).The experiments w ere conducted at 25°C.Asteady state w asachieved w ithin 2 min,and the experiment w as repeated three times under each set of condition.

2.3.Data processing

2.3.1.Mean diameter droplet

More than 1000 droplets in the cavity zone were analyzed under each set of condition in the calculation of the mean droplet diameter.Fig.4 shows a typical droplet in the shape of ellipse,and its diameter can be calculated by the length of major and minor axis.w here d1and d2are the major and minor axis lengths of the droplet in pixels,and s is the calibrated spatial resolution of the droplet image(0.025 mm·pixel-1).

Fig.3.Structure of six packing combinations(packing ring is marked in shadow).

2.3.2.Total mass transfer area

Based on the titration results of bicarbonate solution and CO2absorption rate,the total mass transfer area of HSDreactor can be calculated by the chemical absorption method[16].The chemical absorption process mainly consisted of reaction(3)and reaction(4).The CO2gas fi rstly w ill be dissolved in the w ater

Then the CO2in the aqueous solution reacts w ith NaOH

The rate of Reaction(4)is much higher than that of Reaction(3).

Theequilibrium constant of Reaction(3)isbetw een 3006 m3·kmol-1and 15893 m3·kmol-1[32],hence Reaction(3)can be treated as irreversible.

As to H2O-CO2system,w hen the gas-side masstransfer resistance is ignored,the mass transfer rate can be expressed as

w here kLis the liquid fi lm mass transfer coef fi cient(m·s-1),Ciis the CO2concentration at the gas-liquid interface(kmol·m-3),Niis the absorption rate of CO2(kmol·s-1),A is the total mass transfer area(m2).

Table 1 The parameters of HSD reactor in experiment

Fig.4.The typical image of a droplet(Q L=30 L·h-1,N=1400 r·min-1).

Asthereaction rateof Reaction(3)ishigh enough,equilibrium at theinterface of the droplets can be described by Henry's law.

w here H is the equilibrium solubility of CO2in the solution.The solubility coef fi cient of CO2in the solution can be calculated by

hi,hgare the solute constants of the corresponding ion and gas.The solute constant of ions Na+,OH-and CO32-are 0.117,0.756 and 0.166,and the solute constant of gas is-0.0183[33].

The solubility coef fi cient of CO2,H0,in the pure w ater can be applied w hen the temperature is in the range of 293 K-303 K.

w here PCO2is the partial pressure of CO2and it can be w ritten as

The mass transfer rate is enhanced w hen NaOH is added,and the process can be expressed by the chemical reaction enhancement factor E.The mass transfer rate can be expressed as

E is the chemical reaction enhancement factor.

According to the surface renew al model of mass transfer,the chemical reaction enhancement factor is

w here Ha isthe Hatta number.When Ha＞2,k1isthe pseudo-fi rst-order rapid reaction rate constant and D is the solute diffusivity

Nican begot from thetitration results,and theabsorption rateof CO2equalsto the formation rate of the Na2CO3.

V2is the volume of HCl consumed in the second titration end-point,and V0is the volume of the sample.

The diffusivity of CO2D0in the pure w ater is

The diffusion coef fi cient of gases into the aqueous electrolyte solutionscan be estimated by

k1istherate constant of the pseudo-fi rst-order reaction and k2isthe rate constant of the second order reaction of CO2and OH-.

The formula for the ionic strength is as follow s

Cjis the concentration of ions in the solution(kmol·m-3),and it can be obtained in the titration,and Ziis the valence of the ion.

Combining the equations(Eqs.5 to 20),the total mass transfer area in the HSDreactor is

2.4.Mass transfer area model in the cavity zone

According to study of Burns et al.[34],the liquid holdup in the RPBs in the cavity zone is

w here udis the super fi cial liquid fl ow velocity in the cavity zone,a0is the characteristic centrifugal acceleration(100 m·s-2),and u0is the characteristic liquid fl ow velocity(1 m·s-1).

where acisthecentrifugalacceleration of the rotor and h istheheight of the rotor.QLis the liquid fl ow rate andωis the angular velocity of the rotors.Ri(i=1,2,3,4,5)is the radius of the rotor or reactor wall.Hence the liquid holdup in the cavity zone can be w ritten as

A correlation betw een the interfacial area ad,mass transfer area in the cavity zone Ac,and liquid holdupεdis given by[35].

The mass transfer area in the cavity zone is

The total mass transfer area in HSD reactor contains tw o parts,the mass transfer area in the cavity zone and in the packing zone.Because thetotal masstransfer areaisevaluated in the NaOH-CO2absorption experiment,the mass transfer area in the packing zone can be calculated by

3.Results and Discussion

3.1.Total mass transfer area and the absorption quality

Fig.5 show sthe relationship betw een the total masstransfer area as well as the absorption quality and the rotational speed.The absorption qualityηis de fi ned as:

As show n in Fig.5,the total mass transfer area and absorption quality both increases w ith the increasing rotational speed.Results indicate that the larger rotational speed isbene fi cial to the generation of thinner liquid fi lms in the packing zone and smaller droplets in the cavity zone,leading to a larger mass transfer area.Moreover,from the point of total mass transfer area and absorption quality,the mass transfer performance of packing P-13 and packing P-3 are apparently better than that of other packing combinations.

3.2.Effect of packing combination on the mean droplet diameter

3.2.1.Radius of packing ring

Fig.6 shows that the mean droplet diameter decreases with the increase of packing ring radius and rotational speed(P-3＞P-2＞P-1 in theradiusof packing ring).Asthe droplet isstabilized by thecentrifugal force and the surface tension[35].

Fig.5.Effect of rotational speed on the total mass transfer area and absorption quality.

Fig.6.Effect of packing ring radius on the mean droplet diameter.

w hereωisthe angular velocity of therotor and R istheradiusof packing ring.The increase in rotational speed and packing ring radius both contribute to the increase of centrifugal force,and the stronger centrifugal force disperses the liquid into smaller droplets,resulting that the droplet generated from packing P-3 is smaller than that in the cases P-2 and P-1.

Previousstudieshave shown that the end effect zone in RPBsranges radially in 10 mm to 20 mm from the inner side of the packing[36].The w idths of the packing ring in present experiments are all in this range(see Table 1),so all the three packing rings(P-1,P-2,P-3)can be regarded as three end effect zones,and it also indicates that the mean droplet diameter decreases when increasing the radius of end effect zone.

3.2.2.Number of packing ring

Fig.7.Effect of packing ring number on the mean droplet diameter.

Fig.3 show s that there are two concentric rings in the packing P-13,and the liquid experiences rapid changes twice in the velocity in these tw o packing rings.Fig.7 show s that in the cavity zonethe mean droplet diameter under packing P-13 is generally half of that w ith packing P-1,indicating that the mean droplet diameter decreases w ith increasing number of end effect zone.Compared w ith packing P-1,packing P-13 dispersesliquid violently in tw o end effect zones.And the stronger centrifugalforcein thesecond end effect zoneenhancestheshear effect and generates smaller droplets.

3.2.3.Radius of packing

Fig.8 shows that the mean droplet diameter decreases with the increasing packing radius under various rotational speeds.Due to the stronger centrifugal force in the larger radius packing,more energy is imposed on the liquid by the rotating packing and it results in smaller dropletsunder packing P-123.Besides,the gap on mean droplet diameter betw een packing P-123 and packing P-12 is averagely 1.71 times of the gap betw een P-12 and P-1,indicating that the effect of packing radius on mean droplet diameter can be enhanced by increasing the radius of packing.

Fig.8.Effect of packing radius on the mean droplet diameter.

3.3.Mass transfer area in the packing zone

3.3.1.Mass transfer area contribution of packing zone

Since the mass transfer area in the cavity zone can be calculated by Eq.(26),the contribution of mass transfer area in the packing zone to the total mass transfer area can be calculated by Eq.(30).

w hereφis the mass transfer area contribution of the packing zone,ACand A are the masstransfer areain cavity zoneand the total masstransfer area in the reactor.

Fig.9(a)shows that the contribution of mass transfer area in the packing zone increases from 61%to 82%,w hen the rotational speed ranges from 400 r·min-1to 1400 r·min-1.The increasing rotational speed leads to the increase of centrifugal force and enhances the shear of multi-layer packing,resulting in the increase in mass transfer area.However,the increase of masstransfer area in thecavity zone issmaller in theabsenceof packing.Consequently,asshow n in Fig.9(b),the mass transfer areain packing zoneis larger than that in the cavity zoneunder the same conditions,and thegap on the masstransfer area betw een the packing zone and cavity zone increases,w hen the rotational speed increases.This result agrees with the work of Guo et al.[18],in w hich they reported that the contribution of mass transfer area in the cavity zone is around 70%.

3.3.2.Dimensionless mass transfer area in packing zone

Asthemasstransfer areain thepacking zoneis affected by the operating condition and packing combination,the function about the dimensionlessmass transfer area in packing zone can be:

The fundamental dimension of the mass transfer area function includes time(T),length(L)and mass(M),and the relevant dimensionless parameter are de fi ned as follow s,based on packing P-1 to represent the mass transfer area in other fi ve packing combinations.

Fig.9.(a)Mass transfer area contribution of packing zone(b)mass transfer area in cavity zone and packing zone.

where the Weber number(We)is the ratio of inertia force to the surface tension of droplets,and the Reynolds number(Re)is the ratio of inertia force to viscous force of droplets.The dimensionless liquid fl ow velocity(q)isthe ratio of liquid fl ow velocity to the maximum tangential velocity of liquid in thepacking,and thedimensionlessmasstransfer areain packing zone(a)is the ratio of mass transfer area in packing zone to the surface area of the cylinder packing.AR,P-iis the surface area of the cylinder packing combination,and it can be calculated by the height and radius of each packing.As the thickness of each packing is known(Fig.2),the number and radius of each packing in the packing combination are know n,thus the surface area of packing combination can be calculated by Eq.(36).

where the R1and Rnrepresent the inner and outer radius of the packing,and h is the height of the packing,and n is the number of packing in the packing combination.Therefore,the surface area AR,P-iof packing combinations P-1,P-2,P-3,P-12,P-13,P-123 are 0.0499 m2,0.055 m2,0.0744 m2,0.105 m2,0.124 m2,0.155 m2,respectively.

The correlation about the dimensionless mass transfer area of packing zone is

w here the dimensionless parameters ranges in 2145＜We＜149844,82906＜Re＜926127,0.05＜q＜0.356.Fig.10 show sthat thecorrelation could beused to predict the dimensionlessmasstransfer areaof packing zone with a deviation of±20%.

3.4.Mass transfer area enhancement factor

In order to evaluate the effect of packing combination on the mass transfer area in the packing zone,w e de fi ne an enhancement factor

Fig.10.Comparison of the dimensionless mass transfer area between the evaluation and correlation values.

Where AP-1is the packing zone mass transfer area in packing P-1,and AP-i(i can be 1,2,3,12,13,123)isthe packing zone mass transfer area in various packing combinations.

3.4.1.Radius of packing ring

Fig.11 show sthat the enhancement factorsof packing P-3 and packing P-2 are about 1.8 and 1.1,indicating that the mass transfer area in packing zone increases w ith the increasing packing ring radius.With the larger packing ring radius,the relative velocity betw een droplets and packing becomes higher in the end effect zone,resulting in a larger masstransfer area.Thus,the mass transfer area in the packing zone increases w ith the increasing end effect zone radius.

Fig.11.Effect of packing ring radius on the enhancement factor.

Moreover,results show that the enhancement factor of packing P-2 decreasesw ith the increasing rotational speed,indicating that the effect of rotational speed on themasstransfer areain packing P-2 islesssignificant than that in packing P-1.As shown in Fig.3,the liquid dispersion process in packing P-2 is disturbed by the blades on rotor 1 and rotor 4,thustheeffect of rotational speed on themasstransfer areain packing P-2 is inhibited,resulting in the decrease of enhancement factor.

3.4.2.Number of packing ring

Fig.12 show s that the enhancement factor in packing P-13 is larger than that in packing P-1 under the same conditions,meaning that the mass transfer area in packing zone is proportional to the packing ring numberswhen the rotational speed issmaller than 800 rpm.Asthe relative velocity increases w ith the increasing end effect zone radius,the shear effect of packing P-13 is stronger than that of packing P-1,resultingin theincrease of masstransfer areain the packing zone.In addition,the enhancement factor of packing P-13 increasesfrom 1.3 to 2.8 when therotational speed isfrom 400 r·min-1to 1400 r·min-1,which is result of thedual effect of theincreasing rotational speed and theend effect zone number.

3.4.3.Radiusof packing

Fig.12.Effect of packing ring number on the enhancement factor.

Fig.13 show s that the enhancement factors of packing P-123 and packing P-12 are averagely 1.2 and 1.1.It is evident that the end effect zone in these packing combinations only exists in the fi rst packing ring,while the second and third packing rings mainly act as the bulk zone.Thus it means that the mass transfer area contribution of packing P-2 and P-3 is about only one-tenth of that of packing P-1,w hich is in accordance w ith Chu et al.'s w ork[27],w here they found the mass transfer in the end effect zone is one magnitude higher than that in bulk zone.Because the relative velocity in the bulk zone is smaller than that in the end effect zone,the shear effect of packing is going to be weaker and the mass transfer area contribution of bulk zone is smaller.

Additionally,the resultsalso indicatethat theenhancement factor of packing P-123 and P-12 increases with the increasing packing radius at low rotational speed.How ever,w hen the rotational speed exceeds 1000 rpm,the enhancement factor of packing P-12 is close to 1 while that of packing-123 is even smaller than 1.These results suggest that the bulk zone has a negative effect on the mass transfer at high rotational speed w hen comparing w ith packing P-1.As the packing radius and rotational speed increase,the relative velocity in the bulk zone of packing P-123 becomes smaller than that in the rotors of packing P-1,resulting in the limited contribution of bulk zone.Therefore,the mass transfer contribution of bulk zone decreases w ith the increasing rotational speed.In such a high-speed rotating device w ith the purpose of excellent mass transfer,only by enlarging the size of the packing or increasing the rotational speed is not a universal way.

Fig.13.Effect of packing radius on the enhancement factor.

4.Conclusions

In this w ork,the mean droplet diameter and the total mass transfer area in an HSD reactor w ith different packing combinations were measured and evaluated by visual study and NaOH-CO2absorption experiment.Results show that the mean droplet diameter in the cavity zone generally decreases when increasing the rotational speed of the rotor,radiusand numbers of the packing ring,asw ell asthe radiusof packing.

The contribution of packing zone to the total mass transfer area ranges from 61%to 82%.Acorrelation wasregressed by the dimensionless analysis to predict the mass transfer area in the packing zone.An enhancement factor w as proposed to evaluate the impact of packing combination on the mass transfer area in the packing zone.Results show that the enhancement factor increases w ith the increasing packing ring radius and numbers,and it increases w ith the increasing packing radius at low rotational speed.

When the HSD reactor is equipped w ith at least one packing ring w ith large radius(P-3),increasing the rotational speed w ould be benefi cial to the masstransfer.However,in the case of a small packing ring(P-12),increasing the rotational speed has marginal effect on the enhancement of mass transfer area.

Considering the mean droplet diameter,the optimum combinations should be packing P-3,packing P-13,and packing P-123.When taking the masstransfer area into consideration,P-3 and P-13 are prior.Therefore,the optimum combinationsshould be the large radiuspacking ring P-3 and the split packing rings P-13.Split packing is an effective w ay to improve the mass transfer performance in the packed high-speed disperser reactor,rather than simply increasing the volume of the packing.

Nomenclature

A total mass transfer area,m2

ACmass transfer area in the cavity zone,m2

APmass transfer area in the packing zone,m2

ARPsurface area of the cylinder packing,m2

a dimensionless mass transfer area in the packing zone,m3·m-3

accentrifugal acceleration,m2·s-1

a0characteristic centrifugal acceleration,100 m2·s-1

adgas-liquid interfacial area,m2·m-3

Ciconcentration of CO2at the gas-liquid interface,kmol·m-3

Cjconcentration of ions in the solution,kmol·m-3

COH- concentration of OH-ion in the solution,kmol·m-3

CHClconcentration of hydrochloric acid in the solution,kmol·m-3

CCO23- concentration of CO32-ion in the solution,kmol·m-3

D diffusivity of CO2in solution,m2·s-1

E chemical reaction enhancement factor

H solubility coef fi cient of CO2in the electrolyte solution,kmol·m-3·Pa-1

Hithickness of the packing ring,m

H0solubility coef fi cient of CO2in the puri fi ed w ater,kmol·m-3·Pa-1

h height of the rotor,m

hGconstant of the vapor solute,-0.0183 m3·kmol-1

h+solute constant of Na+,0.117 m3·kmol-1

h-solute constant of OH-and CO32-,0.756 m3·kmol-1and 0.166 m3·kmol-1

I ionic strength,kmol·m-3

k'Lliquid mass transfer coef fi cient when concentration difference is impetus,m·s-1

kLliquid mass transfer coef fi cient,m·s-1

k1pseudo-fi rst-order rate constant,s-1

k2reaction rate constant,m3·kmol-1·s-1

k2∞reaction rate constant in in fi nitely dilute NaOH solution,m3·kmol-1·s-1

N rotational speed of the rotor,r·min-1

Niabsorption rate of CO2,kmol·s-1

n number of packing in the packing combination

pCO2partial pressure of CO2in the gas phase,Pa

pipartial pressure of CO2in equilibrium at the interface of gas and liquid,Pa

p0standard atmospheric pressure,105Pa

QGgas fl ow rate,L·h-1

QLliquid fl ow rate,L·h-1

q dimensionless liquid fl ow velocity

Re Reynolds number in the packing zone

Riradius of rotor,packing and reactor wall,m

T absolute temperature of the liquid,K

u liquid fl ow velocity at the liquid inlet,m·s-1

udsuper fi cial liquid fl ow velocity in the rotor,m·s-1

u0characteristic liquid fl ow velocity,1 m·s-1

V volume of the rotor,m3

V0volume of titration sample,L

V1volume of hydrochloric acid consumed at the fi rst titration end-point,L

V2volume of hydrochloric acid consumed at thesecond titration end-point,L

We Weber number in the packing zone

yCiOinlet mole fraction of CO2in gas phase

o2

yCO2outlet mole fraction of CO2in gas phase

yCO2molefraction of CO2in gasphasein the packing areaand shell zone interface

Zivalence of ion

β mass transfer area enhancement factor

η absorption quality

ε liquid holdup in the reactor

μ kinematic viscosity of liquid,Pa·s

ρ liquid density,kg·m-3

σ surface tension,N·m-1

ω angular velocity,rad·s-1