A simplified adsorption model for water vapor adsorption on activated carbon

J. Cent. South Univ. (2014)21: 1434- 1440包SpringerDOI: 10. 1007/511771-014-2082-5.A simplifed adsorption model for water vapor adsorption on activated carbonYAO Xiao-long(姚小龙)，LI Li-qing(李立清)，LI Hai-long(李海龙), MA Wei- wu(马卫武)School of Energy Science and Engineering, Central South University, Changsha 410083, ChinaC Central South University Press and Springer-Verlag Berlin Heidelberg 2014Abstract: A simplified model was developed to describe the water vapor adsorption on activated carbon. The development of thesimplified model was started from the original model proposed by DO and his co-workers. Two different kinds of carbon materialswere prepared for water vapor adsorption, and the adsorption experiments were conducted at different temperatures (20- -50 °C) andrelative humidities (5%- 99%) to test the model. It is shown that the amount of adsorbed water vapor in micropore decreases with thetemperature increasing, and the water molecules form larger water clusters around the functional group as the temperature is up to ahigher value. The simplified model describes reasonably well for all the experimental data. According to the ftted values, theparameters of simplified model were represented by the temperature and then the model was used to calculate the water vaporadsorption amount at 25 °C and 35。C. The results show that the model can get relatively accurate values to calculate the water vaporadsorption on activated carbon.Key words: water vapor; adsorption; activated carbon; modeland provides a good fit of the adsorption branch of type1 IntroductionV isotherms near room temperature, but it can notexplain the specific mechanism of water vaporadsorption. MULLER et al [8] reported a moleculesbeen one of the important problems in gas separation andmodel of water vapor on activated carbon pores builtpurification, such as hydrogen gas from steam methanewith grand canonical Monte Carlo simulation method.reforming and volatile organic compounds (VOCs)The simulation results at low pressures have goodremoval from air [1- -4]. Despite the hydrophobicity of agreement with experiment data, but those at moderateactivated carbon, the presence of water vapor affects thepressures have relatively large errors. Besides, TALUseparation of hydrogen and methane and adsorption of and MEUNIER [9] presented another equation basicallyVOCs, especially in high relative humidity conditions,involving the clustering of water molecules aroundwhere the water vapor adsorption has very high capacitychemisorption sites. However, it does not explain the roleand competes well with organic gas adsorption. Becauseof the microscopic structure of activated carbon in theof the importance of these problems, the water vaporadsorption of water vapor.adsorption on activated carbon from both theoretical andDO et al [10] developed a new model based orexperimental points of view has been an attractive issuecluster formation and penetration of clusters into theto study.micropore. This model accounts for the microporeSeveral researchers attempted to analyze the waterstructure of activated carbon, with functional groupsvapor adsorption through theoretical method. DUBININpresent at the edges of the basal planes of the graphiticet al [5-6] studied this issue based on a kinetic theory ofunits, and the hysteresis in the adsorption- desorptionwater sorption onto sorption sites， and the obtainedisotherm lies on the relaxation of water clusters insideequation can be applied in describing some experimentalthe micropore. It can describe different shapes of waterdata. However, due to the high concentration ofvapor adsorption isotherm for carbonaceous materials,functional groups existing on activated carbon surface, it and can present the mechanism of water vaporcan not describe water vapor adsorption on activatedadsorption on activated carbon. Water molecules arecarbon. STOECKLI et al [7] studied water vaporadsorbed around the functional groups in the form ofadsorption on activated carbons using DUBININ-cluster and when this water cluster is large enough theyASTAKHOV (DA) equation. They found that thewill enter the micropores, Based on the DO model,equation becomes S-shaped in medium relative pressuresvarious modifica中国煤化工HORIKAWAFoundation item: Projects(2 1376274, 51206192) supported by the National Natural Science FoundatiMHCNMH GReceived date: 2013- -04- 17; Accepted date: 2013- -07- -11Corresponding author: LI Liqing, Professor, PhD; Tel: +86-13807483619; E-mail: liqingli@hotmail.conJ. Cent. South Univ. (2014)21: 1434- 14401435et al [11] extended previous model by adding anequilibrium constant for adsorption and desorption peradditional term to the original equation to account forunit functional group, kp is the equilibrium constant foradsorption in mesopores. NEITSCH et al [12] proposed aadsorption and desorption on the water adsorbed oImodification to the DO model, which assumes that thefunctional group, andx is the relative pressure of watercluster size is variable. FUEMANIAK et al [13vapor. Using the summation rule of geometricdeveloped an heterogeneous DO model to account forprogression, the two different polynomials in Eq. (1) can .the ditribution of adsorption energy of the functionalbe replaced by exponential terms, respectively:group. COSSARUTTO et al [14] modified the DO modelby using a Langmuir equation to describe adsorption ons x"_x-x*(3)functional groups.1-xAlthough DO model can well describe differentshapes of water vapor adsorption isotherm on activated(4)1-x.carbon, many physical parameters in the model, such asn=a-equilibrium constant for micropore adsorption, and theThus, Eq. (1) can be rearranged assize of water clusters, can not be detected directly.Besides，this model can only fit the water vapor9u=9u,s'k(1-x*)kqxadsorption data on activated carbon, and can nok(1-x9)+(x-"-x)(1-x)[1+(kp-1)x]calculate water vapor adsorption capacity in different(5)conditions. Thus, it is necessary to develop a newIntroducing equilibrium adsorption amount of wateradsorption model that can be represented withvapor on activated carbon (qo) into Eq. (5), and Eq. (5) ismeasureable parameters, and can calculate water vaporrearranged asadsorption capacity under different environments.In this work, based on the theoretical system of DO9u=90| qus.k(1-x°)model, a simplified model for adsorption of water vapor9o k(1-x°)+(x-“-x)data in two different kinds of activated carbon were fitedAs..(6)with the simplified model, and all the parameters 0qo (1-x)[1+(kp -1)x]]simplified model were represented with measureableAccording to the DO model, the equilibriumparameters. At last, the simplified model was used tocalculate the water vapor adsorption at differentadsorption amount of water vapor on activated carbon istemperatures. The accuracy of numerical simulation wasthe sum of 9qus and qs. Thus, the deformation formula isshown as follows:studied as well.lus.2 Theoretical basis9o k(1-x°)+(x-"-x)The development of the simplified model is startedkpx_9ufrom the original model proposed by DO et al [10]. The(1-x)[1+(kp-1)x] 9o (1-x)[1+(k -1)x]assumptions of the simplified model are the same with(7)those of the DO model. The DO equation describing theIn most cases, the value of qus is far greater thanadsorption isthat of qs [10, 15- 16], and the value of 9u,s is almostkZx"rEx"equal to the value of 90. Thus, Eq. (7) can be simplifiedn=a+1and the final adsorption model is described as9u = 9us"Zx"+Zx"as (1-x)[1+(kq-1)x]n=a+1 n=a+1(1)9u=9o.k(1-x°)+(x~a-x)(8)kr=k(23 Experimentwhere qu is the adsorption amount of water vapor on3.1 Material preparationactivated carbon, 9us is the equilibrium adsorptionA commercial granular activated carbon, purchasedamount of water vapor in the micropore， qs is thefrom Shanxi中国煤化工Co.，, Ltd.concentration of the functional groups on the surface, a(KZ15-2), was uIYHCNMH G Prior to use,is the water cluster size inside the micropore, ku is theit was washed bydeionzea water tO remove impuritiesequilibrium constant for micropore adsorption, k is the .and was kept in a drying vacuum oven at 573 K for more1436J. Cent. South Univ. (2014) 21: 1434- 1440than 24 h to remove functional groups. This sample was(Center Technology Corp., Taipei). The relative pressuresdenoted as RAC. A portion of RAC was furtherat the inlet and outlet of column were calculated with RH,immersed into 1 mol/L calcium acetate ((CH3COO)2Ca)which were equal to RH/100. The RH at outlet of columnsolution at room temperature for 72 h. Then, it was putincreased gradually until the adsorption process reachedinto drying vacuum oven once again, and was kept atits equilibrium, which was defined as the variation of RH393 K for 24 h. The activated carbon obtained in this at outlet of column was less than 3% for more than 1 h.way was denoted as MAC.All experiments were conducted in the RH range from5% to 9%.3.2 Adsorption experimentsThe configuration of the experimental apparatus4 Results and discussionused in fixed-bed adsorption experiments is shown inFig. 1. Dry compressed air flowed through an electronic4.1 Water vapor adsorptionmass flow controller (MFC， Qixin HuachuangConsidering the measurability of the parameters, itInstruments, Beijing, China) to regulate air flow throughis assumed qo values detected at 99% relative humidity asthe system. Then, it was divided into two parts. One wasequilibrium adsorption, which are given in Table 1. Thebubbled into saturated water to obtain moist air. Theexperimental and simulation results of water vaporother was connected with mixing tank to dilute the moistadsorption on RAC and MAC are shown in Fig. 2. It isair. In order to obtain the moist air with high relativeseen that the model describes the adsorption isothermhumidity, the saturated water was firstly heated with awell. According to the classification of IUPAC, thethermostatic water bath (TWB， Tiandi Instruments,isotherms of both RAC and MAC are close to Type V,Henan, China), and then the superheated vapor waswhich is a typical isotherm for water vapor adsorption oncondensed with a graham condenser (GC) beforeactivated carbon [17]. In the temperature range of 20-entering the mixing tank. The mixed air was held at 2.030 °C, the amount of adsorbed water vapor on RAC isL/min by means of flow meter. The relative humidityless than that on MAC in low relative pressure range.(RH) in the system was adjusted by flow meters (FM,This is probably attributed to the fact that theSuzhou Beida Instruments, Jiangsu, China) which were concentration of hydrophilic functional on RAC surfaceinstalled at the upstream of the mixing tank. Theis less than that on MAC surface [18]. However, there isadsorption column was composed of glass pipe (innern opposite phenomenon presenting in high relativediameter of 0.8 cm) and the temperature was controlledpressure range that RAC exhibits better adsorptionin the range from 293 K to 323 K during the adsorptioncapacity than MAC, which is mainly due to blocking ofprocess. The RH values at the inlet and outlet of columnsome micropore of MAC by the added functional groupswere measured by a moisture monitor Center 310[19]. Besides, the amounts of adsorbed water vapor onValveThermal insulationOutlctTWBMFC|ValveX kMoiture monitor- tx-不Adsorption columnInletFM{M_Mixing.tankCondenserDry air。中国煤化工PumpTWB .MYHCNMH GFig. 1 Configuration of experimental apparatusJ. Cent. South Univ. (2014)21: 1434- 14401437Table 1 Equilibrium adsorption amount of water vapor in RACreside in the micropore as the temperature is up to aand MAChigher value, which needs to form larger water clustersqo/(mgg )around the functional group. Besides, the parametersTemperature/9CRACMACdifference existing between RAC and MAC is probablyattributed to the different concentrations of functional20322.5groups on their surfaces. DO et al [10] considered that3(204.7192.8the presence of pores with high concentration of40109.4110.3functional groups, can stabilize smaller clusters, allowing11.5534.66them to be confined within the pore.both RAC and MAC decrease with temperature4.2 Comparison with results of DO modelincreasing, and MAC exhibits better adsorption capacityThe water vapor adsorption on RAC and MAC waswithin the whole relative pressure range when thecalculated with DO model as well, and the values oftemperature is above 40 °C. It is indicated that theparameters are given in Table 3. The surface functionalthermal stability of water adsorbed in the micropore ofgroups on RAC and MAC were measured by Boehmactivated carbon is worse than that connected withtitration [20]. The comparison results for both simplifiedfunctional group as hydrogen bonding.The ftting values of simplified model parametersmodel (qesim) and DO model (qe,Do) are given in Table 4.for RAC and MAC are given in Table 2. Both the valuesIt is clearly shown that both of them describe theof ku and a increase with temperature, but the values forexperimental data of water vapor adsorption on RACRAC are greater than those for MAC. This may bereasonably well. To MAC, the relative error of twobecause the amount of adsorbed water vapor indifferent models is slightly higher than that to RAC,micropore decreases with temperature increasing, whichwhich is due to the pore blockage by the functionalinduces the water vapor adsorption in micropore togroup. From the analysis above, it is considered that theachieve equilibrium faster. On the other hand, the watersimplified model can describe the experimental data ofmolecules must acquire larger sufficient potential towater vapor adsorption on RAC and MAC reasonably.400(a)Experimental, RAC00 t”)■ Experimental, RAC●Experimental, MACExperimental, MAC"300F-Calculated, RAC::Calculated, RAC--- Calculated, MAC150- --- Calculated, MAC200 I0010050-).6.0Relative pressure4C| (C)(d)?0 100 F“30-一Calculated, RAC75! 2050一25景10+十:中国煤化工.20.YHCNMH GFig. 2 Effects of termperature on water vapor adsorption isotherm of RAC and MAC: (a) 20 °C; (b) 30 °C; (c) 40。C; (d) 50 °C1438J. Cent. South Univ. (2014) 21: 1434- 14404.3 Representation simplified model with macro-Table 3 Fitting values of DO model parameters for water vaporscopical parametersadsorption on RAC and MACIn the simplified model, both ku and a for RAC andTemperature/ quqsMAC increase with temperature. In order to obtain theSample(mgg ) (mg:g )kpaku20374.80.035 2000 12 102.3Table 2 Fitting values of simplified model parameters for watervapor adsorption isotherm of RAC and MAC3(203.90.035 12000 14 118.7RACMAC40108.80.035 55095 19 175.1Temperature/9Ckkua5(11.10.035 127300 31 350.2100.130.32(321.90.072 1560 9 30.130119.8140.1192.10.072 8540 10 39.8175.2108.50.072 33500 12 59.90349.93140.4225033.0.072 92350 22 141.1Table 4 Simulation results of simplified model and DO model for water vapor adsorption on RAC and MACSample Temperature/9Cqe.exp(mgg) 9ge.o/(mgg )__ qe sim/(mgg )0po/%8m/%0.400.69 .0.638.508.450.509.598.94 .8.946.816.760.6055.8067.0467.0220.1420.120.70218.33217.71217.420.280.420.80 .321.22327.36326.861.911.760.95374.91368. 19367.901.791.871.211.481.4922.5923.0816.31 .17.5317.607.487.8886.7291.5391.775.555.820.80151.89171.50171.8412.9113.13202.66200.57201.071.030.780.921.15 .1.1625.2125.7722.3518.1318.2018.8918.5777.8978.0578.270.210.48107.38107.37107.670.010.272.762.832.982.597.8010.7110.8511.391.296.3421.6918.5517.5114.4819.2850.3375.6073.8050.2146.63163.56177.24174.768.366.85260.50258.72256.370.681.59319.35306.47_304.914.034.520.40 .1.220.7421.3139.3411.847.8733.5342.510.60 .39.5537.9536.044.058.870.70 .90.13102.3613.5711.18156.44156.36155.000.05187.65185.06184.441.381.712.312.251.372.6040.6411.3813.20 .11.5215.991047.5549.8847.764.900.44101.5687.9987.60 .13.3613.74108.18105.94106.752.071.323.592.47中国煤化工56.6315.3517.99TCHCNMHG 9.2433.7433.870.39J. Cent. South Univ. (2014)21: 1434- 14401439relationship between the two parameters and temperature,they are correlated with temperature, and the results are70shown in Fig. 3 and Fig. 4, respectively. The polynomial: RAC60fitting parameters of a. and ku for RAC and MAC areCalculated, RACCalculated. MACshown in Table 5.50It is seen that the relationships between temperatureand a. and ku are well ftted by the polynomials. As aresult, all of parameters in Eq. (8) are represented by the30measurable parameters， which indicate that thesimplified model may be used to directly calculate thewater vapor adsorption amount in different experimental10conditions.5350Fig. 4 a values of simplified model for water vapor adsorptionRACMAC00 t4.4 Verification--- Calculated, MAC506In order to validate the accuracy of the simplifiedmodel represented by the measurable parameters, themodel was tested with adsorption data of water vapor on50 tRAC and MAC at 25 °C and 35。C, respectively. Theexperimental and calculation results are shown in Fig. 5.It is seen that the model describes the data in adsorption5(process very well, which indicates that the simplifiedmodel can get relatively accurate values to describe the20water vapor adsorption on activated carbon. This mayTemperature/PCprovide a new feasible method to calculate water vaporFig. 3 k values of simplified model for water vapor adsorptionadsorption on activated carbon.Table 5 Polynomial fting formulas of a and k represented with termperature for RAC and MACSample Parameter4oA2 AsFormulaRAC _a1.18333-0.045 0.000667a-=10000+1.183337- 0.0450072 +6.66667*10413k-17530.0833-1.10.01417k=- 175+30.083337-1.17+0.01417730182.88333-0.10.00117--82.83337-0.17+0.00117720. 1667-0.70.00833k=- 16020.6667-0.7*+0.008337*300175: Experimental, RACExperimental, RAC20 250 t●Experimental, MAC。150Caiculated, RAC-Calculated, RAC-- Calculated, MAC125100150-75100 |9o.RAc=158.24 mg/g90.RAc-281.82 mg/gGo.MAc=151.29 mgg90.MAC -265.33 mg/g250.20.40.0.81.0中国煤化工Relative pressureYYHCNMH GFig. 5 Water vapor adsorption on RAC and MAC at 25。C (a) and 35。C (b)1440J. Cent. South Univ. (2014) 21: 1434- 1440[6] DUBININ M M, ZAVERINA E, VV s. The sorption of water vapour5 Conclusionsby active carbon []. 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