Indoor and Built Environment

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How to Select Adsorption Material for Removing Gas Phase Indoor Air Pollutants: A New Parameter and Approach Qiujian Xu, Yinping Zhang, Jinhan Mo and Xinxiao Li Indoor and Built Environment 2013 22: 30 DOI: 10.1177/1420326X12470301 The online version of this article can be found at: http://ibe.sagepub.com/content/22/1/30

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Original Paper

Indoor and Built Environment

Indoor Built Environ 2013;22;1:30–38

Accepted: November 12, 2012

How to Select Adsorption Material for Removing Gas Phase Indoor Air Pollutants: A New Parameter and Approach Qiujian Xua,b Yinping Zhanga

Jinhan Moa Xinxiao Lia

a

Department of Building Science, Tsinghua University, Beijing, P.R. China Department of Engineering Physics, Tsinghua University, Beijing, P.R. China

b

Key Words Indoor air quality E Adsorbent E Air cleaning E Formaldehyde E Exposure

Abstract Adsorption material is widely used to remove gas phase indoor air pollutants such as volatile organic compounds. The commonly used parameter, the adsorption capacity, is not sufficient to determine how much of a gas phase pollutant can be removed in a given time period. In this study, we put forward a new parameter (Va,c , the normalised volume of air cleaned) and an approach to select the most suitable adsorption material for given conditions. We find that Va,c of a single adsorbent pellet is the function of the Biot number for mass transfer (Bim), the air–adsorbent interface partition coefficient (K) and the Fourier number (Fom). The correlation between them is derived, which enables us to determine the most suitable adsorption material under given conditions. The Va,c of a fixed-bed air filter is also presented, from which the required quantity of material or the filter size can be determined too. Some examples illustrating how to use the parameter and the approach are presented. ß The Author(s), 2012. Reprints and permissions: http://www.sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/1420326X12470301 Accessible online at http://ibe.sagepub.com Figures 1, 2 and 4–6 appear in colour online

This new parameter and approach are very helpful for selecting adsorption materials and developing adsorption filters for removing gas phase indoor air pollutants.

Nomenclature Bim ¼ Biot number, Bim ¼ hm r0 =D C ¼ local gas pollutant concentration in air phase (mg m3) Cad ¼ local equivalent concentration in the pellet (mg m3) (adsorbent volume) Cg ¼ gas pollutant concentration in the gaps of fixed bed (mg m3) C1 ¼ gas pollutant concentration in bulk air (mg m3) D ¼ gas pollutant diffusion coefficient in the pellet (m2 s1) Dab ¼ gas pollutant diffusion coefficient in air (m2 s1) DL ¼ gas pollutant longitudinal dispersion coefficient (m2 s1) Fom ¼ Fourier number, Fom ¼ Dt=r20

Yinping Zhang, Department of Building Science, Tsinghua University, Beijing, P.R. China. Tel. þ86 10 62772518, Fax þ86 10 6277 3461, E-Mail [email protected] Downloaded from ibe.sagepub.com at Tsinghua University on February 25, 2013

G ¼ flow rate of air cleaner (m3 h1) K ¼ partition coefficient Va,c ¼ normalised volume of air cleaned in a given time Vad ¼ volume of adsorption material (m3) b ¼ adsorption constant (m3 mg) hm ¼ external mass transfer coefficient (m s1) qeq ¼ local adsorbed mass at equilibrium (mg) qmax ¼ maximal local adsorbed mass (mg) q(t) ¼ adsorbed mass over time 0–t (mg) r ¼ radial distance (m) r0 ¼ radius of the pellet (m) t ¼ adsorption time (h) u ¼ average linear velocity in the gaps of pellets (m s1) un ¼ positive root of the transcendental equation z ¼ distance in flow direction (m) e ¼ once-through efficiency of air cleaner eb ¼ bulk porosity ep ¼ pellet porosity u ¼ kinematic viscosity (m2 s1)

Introduction Removing gas phase indoor air pollutants such as formaldehyde, volatile organic compounds (VOCs) indoors is important for improving indoor air quality (IAQ). Many ‘‘modern’’ buildings are designed to be airtight to save energy. Lack of adequate ventilation in these buildings could cause an accumulation of harmful indoor air pollutants such as VOCs and formaldehyde, which are emitted from various building materials, furniture, etc. [1–3]. Some experimental chamber studies such as Mølhave et al. [4] and epidemiological studies such as Apter et al. [5] have shown that exposure to excessive levels of VOCs in indoor air may cause sick building syndrome (SBS). And some of these pollutants such as formaldehyde and benzene are carcinogenic [6,7]. Ventilation is an important mean to dilute the concentrations of these compounds by supplying clean air. However, since in many buildings the ventilation is inadequate, and the outdoor environment is bad due to traffics or factory emissions, purification of indoor air by air cleaners or passive purification materials is required to re-generate clean air by removing target indoor air pollutants. Although there are more and more new indoor air cleaning technologies, such as photocatalytic oxidation (PCO) [8], plasma catalytic oxidation [9], and thermal

Adsorption Material for Removing Gas Phase IAP

catalytic oxidation [10], adsorption is still most widely used for its distinctive advantages: it is cheap, simple, highly efficient and safe (no harmful by-products) [11]. Many studies have been done on various adsorbents for VOC removal [12–14]. However, as far as we know, existing parameters and approaches are not sufficient to select the most suitable adsorption material for a given operational condition. The common parameter used for adsorbent evaluation is the equilibrium adsorption capacity [15]. However, as defined, it is the capacity at static equilibrium, and no transport properties would be taken into account. The purification rate and time period of adsorbent before saturation may be very different when the mass-transfer related physical properties are different, even though the equilibrium capacities are the same. So the purification performance cannot be determined only by this parameter. Another parameter is the breakthrough time of the adsorption material [16], which is obtained by a breakthrough experiment on the adsorbent fixed-bed. It has been used for adsorbent evaluation in many studies [17,18]. However, this parameter depends on the experimental conditions, such as the air flow rate and filling density [19]. When these conditions changed, it is hard to estimate the adsorbent’s performance without a new experiment. In practice, it is desirable to know which adsorbent can adsorb most target pollutant(s) for a given time period and conditions. However, it is impossible to solve the problem by using the aforementioned two parameters, i.e. the equilibrium adsorption capacity and breakthrough time. The objectives of this paper are: (1) to address the problem by developing a parameter and an approach; (2) to show their application in adsorption material selection and filter development with some illustrative examples.

Problem Description and the New Parameter Adsorption air cleaners are often of fixed-bed form [20–22], which tend to be composed of adsorption pellets of similar sizes. Therefore, their removal performance can be estimated based upon the adsorption performance of the pellets. One adsorbent pellet can be regarded as a representative element of this type of adsorption device (Figure 1). The adsorption process includes external diffusion, inner diffusion and inner surface sorption, which were influenced by the external mass transfer coefficient (hm), the diffusion coefficient of target VOC

Indoor Built Environ 2013;22:30–38


31

As q(t) with a constant Cin can be estimated by knowing the material and operation parameters, the volume of air cleaned can be obtained by: Va,c ¼

Fig. 1. The schematic of air pollutant adsorption on an adsorbent pellet and a fixed-bed.

in the pellet (D), and the partition coefficient (K), respectively. For air cleaners with a constant once-through efficiency to target pollutant, such as VOC removal by catalytic oxidation, the clean air delivery rate (CADR) is an appropriate parameter for evaluating the performance, defined by [23]: CADR ¼ "G

ð1Þ

where e is the once-through efficiency of the air cleaner, and G is the flow rate of the air cleaner (m3 h1). For an adsorption device, the once-through efficiency is not a constant due to the decreasing adsorption rate, as the device approaches saturation. This causes a problem that it is hard to compare the performance of such device with catalytic oxidation devices. Since the practical effectiveness of such device is reflected on the mass of the target pollutant removed by the device in a given time period, it is possible to define a new parameter for the comparison of different types of air cleaners, as Equation (2). In a given time period 0–t, the quantity of the target pollutant removed by an air cleaner is: Zt qðtÞ ¼ "GCin dt ð2Þ 0

where Cin is the inlet target pollutant concentration (mg m3). To compare air cleaners within a same pollutant condition, assume that the inlet target pollutant concentration is a constant. A new parameter, the volume of air cleaned, which reflects the VOC removal ability of air cleaner, is defined as: Va,c ¼ "Gt

ð3Þ

the average where Va,c is the volume of air cleaned, and ", once-through efficiency over time 0–t.

32

qðtÞ Cin

ð4Þ

By using the above parameter, the target pollutant removal performance of air cleaners can be designed and compared. For an air cleaner composed of adsorption materials, Va,c can be normalised by dividing by the volume of the adsorption material as represented by: Va,c ¼

Va,c Vad

ð5Þ

where Va,c is a new parameter put forward by us, representing the normalised volume of air cleaned in given time, and Vad , the volume of the adsorption material (m3). The physical meaning of Va,c is the volume of air cleaned supplied by per volume of adsorption material in given time. By modelling, the function of Va,c and the physical properties of the adsorption material can be obtained. The adsorbent with maximum Va,c can be regarded as most suitable one for removing the target pollutant for a given time and conditions.

Model Development and Solution Model of Single Pellet Adsorption A mass transfer model was developed to analyse the given period that adsorbed mass in a porous pellet is a representative element of an air cleaning device. The adsorption pellet with spherical shape is considered in this study for adsorbent selection. For adsorbents with other shapes, a modified shape factor may be applied to use the following results, which needs further study. At low concentration range, the partition of pollutant between the adsorbed phase and the air phase in the pellet was found to obey the Langmuir isotherm model as represented by [24]: qeq ¼ qmax

bC 1 þ bC

ð6Þ

where C is the local air phase concentration (mg m3), b, the adsorption constant (m3 mg1), qeq, the local adsorbed mass at equilibrium (mg) and qmax, the local maximal adsorbed mass (mg). When the concentration is very low, that is the value of bC lower than 0.05, the adsorbed mass is almost linear to the concentration (Henry’s law), qeq ¼ qmaxbC, especially at typical levels of indoor air, from several ppbv (parts per billion in volume)



Xu et al.

to several hundred ppbv. A recent study about formaldehyde adsorption on activated carbon also showed the linearity at low concentration range [25]. The partition coefficient in Henry’s law, K, is defined as the ratio between the local equivalent concentration in the pellet and the local air concentration as represented by: K¼

Cad C

ð7Þ

where Cad is the local pollutant concentration in the pellet (mg m3) (adsorbent volume). By theoretical analysis and modelling (See the Appendix for details), equation (8) is derived for the normalised volume of air cleaned Va,c : 2 3 !1 1 2 X 2 K K 2 2 u Fo un þ1 un e n m 5 Va,c ¼ K41 6 Bim Bi2m n¼1 ð8Þ where un is the positive root of the equation: un ctgun ¼ 1 BiKm (n ¼ 1, 2, 3 . . . ); Fom ¼ Dt=r20 is the Fourier number of mass transfer representing the dimensionless time; and Bim ¼ hm r0 =D is the Biot number of mass transfer representing the resistance ratio of mass transfer. Obviously, Va,c is in the range of [0, K], and Va,c /K is in the range of [0,1] which represents the degree of adsorption from beginning to the equilibrium point. Model of Pellets in a Fixed-bed Structure Similarly, for a fixed-bed structure, the normalised volume of air cleaned Va,c is determined by (See the Appendix for details): Z Fom Cg ðL,tÞ r20 u "b Va,c ¼ 1 ð9Þ dFom C1 D L 1 "b 0 where Cg(L,t) is the outlet concentration of the fixed-bed (see the Appendix for details), L, the depth, u, the linear velocity and eb the bulk porosity. So, for a fixed-bed adsorption filter, by knowing the parameters of a single pellet (D, K, hm and r0), and the parameters of the fixed-bed (L, eb and u), the Va,c can be determined.

Method to Determine K and D of Adsorbents The data of K and D were determined using a breakthrough curve fitting method. The adsorbents were grinded and screened into small pellets with certain size range. They were filled into a tube and fixed. The inlet of the tube supplies certain air pollutant with a stable test condition. The test condition was 258C, 16% relative humidity, with a stable inlet concentration range of 50–300 ppbv. The outlet concentration was measured online by proton transfer reaction mass spectrometer (PTR-MS). By integration of outlet concentration from start to equilibrium, K can be obtained. And D was determined by the regression of the outlet curve (Use equation (S12) in Appendix).

Application of Vac in Selecting Suitable Adsorption Material and Developing a Filter-principle and Illustrative Examples Determine the Suitable Adsorption Material and the Operative Conditions In order to conveniently determine the most suitable adsorbent and optimised condition, curves of Va,c /K (representing the degree of adsorption to the equilibrium) varying with Fom and Bim/K are presented in Figure 2. For a given condition and known material parameters, the performance of different adsorption materials can be easily compared by comparing their Va,c values using this figure. Figure 2 can also be used to optimise the working conditions of the adsorption material. The adsorption process accelerates when Bim/K increases – the upper limit of the adsorption curve corresponds to infinite Bim/K value. It means that for a given adsorption material, increasing the external air flow rate will decrease the external mass transfer resistance so that the adsorption rate will be increased. However, when Bim/K 4 20, the influence of Bim/K on Va,c =K is less than 0.05 after Fom 4 0.1, which indicates that the pursuit of higher air flow rate is not economical under these conditions.

Numerical Method By Equations (8) and (9), Va,c of both single pellet and fixed-bed can be obtained by numerical method. The integration was examined by reducing its increment size 5 times. The integration result showed that it was independent of the increment size.

Development of a Fixed-bed Filter To develop a fixed-bed filter with a required removal performance of the target VOC, the following two steps should be taken: (1) select the most suitable material (using Figure 2); (2) determine the filter parameters in Equation (9) by using Va,c as an indicator of its effectiveness. Figure 3 shows the flow diagram for selecting the suitable adsorption material and developing the fixed-bed filter.




33

1.0

formaldehyde removal, the suitable adsorption material can be selected. In this example, formaldehyde removal ranks are mixed metal oxide, activated alumina, silicon gel, zeolite 13X and activated carbon. Therefore, the mixed metal oxide is selected as a formaldehyde removal adsorbent. In the first hour, per litre such adsorbent can supply 641 m3 ‘‘cleaned air’’ by active adsorption or 157 m3 ‘‘cleaned air’’ by passive adsorption.

0.8 V*a,c / K

0.2 0.1 0.05 0.02

0.6

Bim/K=

10 5 2 1 0.5 0.3 1111111111111111

1 ∞20

0.4 0.2 0.0 0.01

0.1

1 Fom

10

100

Fig. 2. The chart of Va,c /K and Fom with different Bim/K.

Illustrative Examples There are three typical ways of using adsorption material in indoor air purification: (1) directly and passively exposed to the air; (2) filled in a fixed-bed filter and driven by a fan; (3) filled in a fixed-bed filter and passively exposed to the air. Different adsorption materials and different ways of using them can be chosen for removing different air pollutants. For the purpose of illustrating the application of the parameter and the approach in selecting the adsorbents and developing the fixed-bed, three examples are presented. Example 1: Select the adsorption material for indoor formaldehyde removal. Five commercial adsorbents, activated carbon (AC), silica gel (SG), activated alumina (AA), mixed metal oxide (MMO) and zeolite 13X (13X) are alternatives for indoor formaldehyde removal. The most suitable material can be selected by comparing the parameters of Va,c of formaldehyde removal. The K and D parameters of these adsorbents are obtained by the regression of breakthrough curves (See the Appendix for details) and are listed in Table 1. The hm parameter is determined by the correlation expressed in Equation (10) [24]: 2hm r0 2r0 u 0:6 0:33 ¼ 2 þ 1:1 ð10Þ Dab Dab where Dab is the diffusion coefficient in air (m2 s1), and u, the kinematic viscosity (m2 s1). By using Va,c , the formaldehyde removal performance of the adsorbents were evaluated and compared. Figure 4 shows the result of their performance in 1 h and 24 h with the external air velocity 0.02 m s1 (passive purification) and 10.0 m s1 (active purification). By the rank of Va,c of

34

Example 2: Design the fixed-bed filter driven by a fan for formaldehyde removal. Fixed-bed filters are used in air ducts or air cleaners for gaseous pollutants removal. A fixed-bed filter filled with MMO 3.0 mm diameter pellets is designed for formaldehyde removal. In this case, the cross-sectional area of the filter is 0.2 m 0.2 m, and bulk porosity is 0.286. The air flow rate across the filter is 412 m3 h1, and the required average clean air delivery rate is 200 m3 h1. By using the parameters of Va,c , the required filter depth can be determined. The average clean air delivery rate for a given time period is calculated by: CADR ¼

Va,c Vad t

ð11Þ

Figure 5 shows the influence of filter depth on average clean air delivery rate in time periods of 1 h, 6 h, 1 day and 7 days. From the results, the required filter depths for the CADR are 0.016 m, 0.035 m, 0.072 m and 0.267 m, respectively, corresponding to the four working time periods. Example 3: Design the shape of a passive fixed-bed filter with certain adsorption material quantity. Passive fixed-bed filters can be hung on the wall or put on the table or floor to adsorb gaseous pollutants. A passive fixed-bed filter filled with MMO 3.0 mm diameter pellets is designed for formaldehyde removal. The pellet density is 564 kgm3 and the bulk porosity of the fixed-bed is 0.286. It is assumed that only one side of the filter is exposed to the air, and the velocity in the bed gaps is 0.02 m s1. In this case, the total mass of the adsorbent is 0.4 kg, and the cross-sectional area can be designed using the parameters of Va,c . The required ‘‘cleaned air’’ volume in given time of each room may be different according to the condition of ventilation rate of the room and emission rate of the pollutant. When the required ‘‘cleaned air’’ volume is determined, the required filter can be designed. Figure 6 shows the supplied ‘‘cleaned air’’ volume when filling the



Xu et al.

Fig. 3. The diagram for adsorption material selecting and filter development.

Table 1. Pellet parameters of five adsorption materials Adsorbent

Abbreviation

Activated carbon Silica gel Activated alumina Mixed metal oxide Zeolite 13X

AC SG AA MMO 13X

K

D (m2 s1)

r0 (m)

1.65 104 6.56 104 5.94 105 5.07 106 5.06 104

2.16 1010 3.77 1011 1.09 1011 1.21 1012 2.18 1011

1.5 103 1.5 103 1.5 103 1.5 103 1.5 103

100

Average clean air delivery rate (m3/h)

Volume-of-air cleaned in given time (104 air vol./sorbent vol.)

AC: activated carbon; SG: silica gel; AA: activated alumina; 13X: zeolite 13X; MMO: mixed metal oxide.

AC SG AA MMO 13X

10

1 PP-1h

AP-1h

PP-24h

AP-24h

500 400 300 200 1-hour 6-hour 1-day 7-day

100 0 0.0

0.1 0.2 0.3 Fixed-bed depth (m)

0.4

Fig. 4. Volume-of-air cleaned by 5 adsorbents for removing formaldehyde. PP: passive purification, external velocity 0.02 m s1; AP: active purification, external velocity 10.0 m s1.

Fig. 5. The influence of fixed-bed depth on the average clean air delivery rate of filter.




35

Volume of air cleaned (m3)

4000

3000

2000

considered in the present study. However, using the normalised volume-of-air cleaned is a good method to sort adsorbents for target pollutants, to estimate their performance and design fixed-bed parameters and to achieve the required performance.

A=0.2 m2 A=0.1 m2 A=0.05 m2 A=0.02 m2 A=0.01 m2

1000

Conclusions 0 101

102

103 Time (hour)

104

Fig. 6. The supplied ‘‘cleaned air’’ volume when using different cross-section areas of a fixed-bed filter with 0.4 kg MMO pellet.

adsorbent with different cross-sectional areas. By using these results, the filter area can be determined for a required valid time period and required ‘‘cleaned air’’ volume.

A new dimensionless parameter representing the dimensionless volume-of-air cleaned was put forward as an evaluation indicator of adsorption material performance. By using this parameter and the approach presented in this paper, the most suitable adsorption material, filter size, etc. can be conveniently determined.

Acknowledgement Discussion In practice, the concentration variation in a room would change the adsorption process, which is not

We gratefully acknowledge the support of National Nature Science Foundation of China (grant nos. 51136002, 51006057), and project of State Key Laboratory of Subtropical Building Science (grant no. 2008KA08).

References 1 Salthammer T, Mentese S, Marutzky R: Formaldehyde in the indoor environment: Chem Rev 2010;110(4):2536–2572. 2 Weschler CJ: Changes in indoor pollutants since the 1950s: Atmos Environ 2009; 43(1):153–169. 3 Yu CWF, Kim JT: Building pathology, investigation of sick buildings – VOC emissions: Indoor Built Environ 2010;19(1):30–39. 4 Mølhave L, Bach B, Pedersen OF: Human reactions to low concentrations of volatile organic compounds: Environ Int 1986; 12(1–4):167–175. 5 Apter A, Bracker A, Hodgson M, Sidman J, Leung WY: Epidemiology of the sick building syndrome: J Allergy Clin Immunol 1994;94(2):277–288. 6 International Agency for Research on Cancer (IARC): Formaldehyde, 2-butoxyethanol and 1tert-butoxy-2-propanol. IARC monographs of the evaluation of carcinogenic risks to humans, Vol 88. Lyon, France, World Health Organization (WHO), 2006. 7 McMichael AJ: Carcinogenicity of benzene, toluene and xylene: epidemiological and experimental evidence: IARC Sci Publ 1988;85:3–18.

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8 Mo JH, Zhang YP, Xu QJ, Lamson JJ, Zhao RY: Photocatalytic purification of volatile organic compounds in indoor air: a literature review: Atmos Environ 2009;43(14):2229– 2246. 9 Ding HX, Zhu AM, Yang XF, Li CH, Xu Y: Removal of formaldehyde from gas streams via packed-bed dielectric barrier discharge plasmas: J Phys D Appl Phys 2005; 38(23):4160–4167. 10 Xu QJ, Zhang YP, Mo JH, Li XX: Indoor formaldehyde removal by thermal catalyst: kinetic characteristics, key parameters, and temperature influence: Environ Sci Technol 2011;45(13):5754–5760. 11 Zhang Y, Mo J, Li Y, Sundell J, Wargocki P, Zhang J, Little JC, Corsi R, Deng Q, Leung MHK, Fang L, Chen W, Li J, Sun Y: Can commonly-used fan-driven air cleaning technologies improve indoor air quality? A literature review: Atmos Environ 2011; 45(26):4329–4343. 12 Zaitan H, Bianchi D, Achak O, Chafik T: A comparative study of the adsorption and desorption of o-xylene onto bentonite clay and alumina: J Hazard Mater 2008;153(1–2): 852–859.



13 Tsai J-H, Chiang H-M C, Huang G-Y, Chiang H-L: Adsorption characteristics of acetone, chloroform and acetonitrile on sludge-derived adsorbent, commercial granular activated carbon and activated carbon fibers: J Hazard Mater 2008;154(1–3):1183–1191. 14 Qu F, Zhu L, Yang K: Adsorption behaviors of volatile organic compounds (VOCs) on porous clay heterostructures (PCH): J Hazard Mater 2009;170(1):7–12. 15 Wood GO: Activated carbon adsorption capacities for vapors: Carbon 1992;30(4):593–599. 16 VanOsdell DW: Evaluation of test methods for determining the effectiveness and capacity of gas-phase air filtration equipment for indoor air applications-phase1: literature review and test recommendations: ASHRAE J;94(2):511–523. 17 VanOsdell DW, Owen MK, Jaffe LB, Sparks LE: VOC removal at low contaminant concentrations using granular activated carbon: J Air Waste Manage Assoc 1996; 46(9):883–890. 18 Guo B, Zhang JS, Nair S, Chen W, Smith J: VOC removal performance of pellet/granulartype sorbent media – Experimental results: ASHRAE Trans 2006;112(2):430–440.

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19 Scahill J, Wolfrum EJ, Michener WE, Bergmann M, Blake DM, Watt AS: A new method for the rapid determination of volatile organic compound breakthrough times for a sorbent at concentrations relevant to indoor air quality: J Air Waste Manage Assoc 2004;54(1):105–110. 20 Rasmuson A, Neretnieks I: Exact solution of a model for diffusion in particles and longitudinal dispersion in packed-beds: AlChE J 1980;26(4):686–690.

21 Pei JJ, Zhang JS, Nair S, Chen WH, Guo B, Wong J: VOC removal performance of pellet/ granular type sorbent media-from testing to predictions: ASHRAE Trans 2008;114: 462–471. 22 Pei J, Zhang J: Modeling of sorbent-based gas filters: development, verification and experimental validation: Build Simul 2010;3(1):75–86. 23 ANSI/AHAM AC-1988: Portable Household Electric Cord-connected Room Air Cleaners.

Appendix A: Supplementary Data

By substituting Equation (S5) into Equation (S6), Equation (S7) is obtained:

Mass Transfer Process of a Single Porous Pellet The mass transfer process of a single porous pellet adsorption is described by Equation (S1): !

@Cad @2 Cad 2 @Cad ¼D þ , at 0 r r0 , t40 r @r @t @r2

ðS1Þ

where D is the target VOC diffusion coefficient in the pellet (m2 s1), and r0 the radius of the pellet (m). The initial condition and boundary conditions are as described by Equations (S2), (S3) and (S4): Cad ¼ 0, at 0 r r0 , t ¼ 0,

hm ðC1 CÞ ¼ D

D

@Cad , at r ¼ r0 , t40, @r

@Cad ¼ 0, at r ¼ 0, t40: @r

Cad ¼ 1 2

1 X

e

u2n Dt=r20

n¼1

qðtÞ ¼

8r40 C1

" # 1 hm X u2n Dt=r20 ðsin un =un cos un Þ sin un ð1 e Þ D n¼1 u2n ðun sin un cos un Þ

ðS7Þ From Equation (S7), the adsorbed mass in a given time is obtained. By using the adsorbed mass, the normalised volume of air cleaned Va,c can be calculated by Equation (S8): " # 1 6hm r0 X u2n Dt=r20 ðsin un =un cos un Þ sin un Va,c ¼ ð1 e Þ D u2n ðun sin un cos un Þ n¼1 ðS8Þ

ðS2Þ

ðS3Þ

ðS4Þ

where hm is the external mass transfer coefficient (m s1). By solving Equations (S1) to (S4), the local pollutant concentration (Equation (S5)) in the pellet can be obtained: "

Chicago, Association of Home Appliance Manufacturers, 1988. 24 Ruthven DM: Principles of Adsorption and Adsorption Processes. New York, WileyInterscience Publication, 1984, pp. 68–69. 25 Carter EM, Katz LE, Speitel GE, Ramirez D: Gas-phase formaldehyde adsorption isotherm studies on activated carbon: correlations of adsorption capacity to surface functional group density: Environ Sci Technol 2011;45(15):6498–6503.

# ðsin un =un cos un Þ sinðun r=r0 Þ ðun sin un cos un Þr=r0

KC1 ,

This parameter can be used to select adsorption materials by comparing the adsorption performance of them over a given time period, with given pellet parameters, and external flow conditions. In order to understand the general characteristics of adsorption performance and to make the application of the result easier, it is helpful to normalise the equations above to get the result expressed as a function of dimensionless parameters. The following two commonly used dimensionless parameters in mass transfer analysis are used for the normalisation: Fom ¼ Dt=r20 , Bim ¼ hm r0 =D. By substituting the dimensionless parameters into Equation (S8), the Va,c can be written as a function of three dimensionless parameters (K, Bim/K and Fom) as Equation (8) in the main text.

ðS5Þ where un is the positive root of the equation: m R0 un ctg un ¼ 1 hDK (n ¼ 1, 2, 3 . . . ). The given period adsorbed mass in the pellet q(t) can be calculated by Equation (S6): Z qðtÞ ¼ 0

t

4r20 hm C1 Cjr¼r0 dt


ðS6Þ

Mass Transfer Process of Fixed-bed In a fixed-bed, the mass balance of VOC in gas phase is show in Equation (S9): @Cg @Cg @2 Cg 1 " @q þu DL 2 ¼ "b Vad @t @t @z @z

ðS9Þ

where Cg is the local gas phase concentration in the fixed bed (mg m3), u, the average linear velocity in the gaps of



37

pellets (m s1), DL the longitudinal dispersion coefficient (m2 s1), "b the bulk porosity and z the distance in flow direction (m). The boundary condition and initial condition of the fixed-bed are as described by Equations (S10) and (S11): Cg ¼ C1 , at z¼0, t40

ðS10Þ

Cg ¼ 0, at 0 z L, t ¼ 0

ðS11Þ

The mass transfer equations from bulk air into the pellet are the same as Equations (S1)–(S4). The exact solution of above equations was solved by Rasmuson and Neretnieks [20]. Cg at z ¼ L is a function of pellet parameters, fixed-bed parameters and time, as Equation (S12):

L 1"b residence time, ¼ 3DK "b , H1 and H2 are intermedir20 u ate calculation variables, formed by parameters of Bim/K and . The calculation of intermediate valuables of H1 and H2 in Equation (S12) are as follows: HD1 þ ðH2D1 þ H2D2 ÞK=Bim , ð1 þ HD1 K=Bim Þ2 þ ðHD2 K=Bim Þ2 HD2 H2 ¼ , ð1 þ HD1 K=Bim Þ2 þ ðHD2 K=Bim Þ2 sinh 2þsin 2 sinh 2sin 2 where HD1 ¼ cosh 2cos 2 1, HD2 ¼ cosh 2cos 2 . H1 ¼

The normalised volume of air cleaned Va,c can be calculated by Equation (S13): Z t Cg ðL,tÞ u "b 1 dt ðS13Þ Va,c ¼ C1 L 1 "b 0

2 0 31=2 9 !2 11=2 > 2 = 2 Cg ðL,tÞ 1 2 1 1 2 1 1 ¼ þ exp Pe 4 @Pe2 Pe þ H1 þ2 Pe2 þ H2 A þ Pe Pe þ H1 5 > > C1 2 0 2 4 3 RK 2 4 ; :2 8 2 0 31=2 9 !2 11=2 > > 2 = d > u 2 4 3 RK 2 4 ; : r0 Z

1

8 >