1、 Lumeng Liu is a PhD candidate in the School of Environmental Science and Engineering, Tianjin University, Tianjin, China. Junjie Liu is a professor in the School of Environmental Science and Engineering, Tianjin University, Tianjin, China. Jingjing Pei is an associate professor in the School of Env
2、ironmental Science and Engineering, Tianjin University, Tianjin, China. Is the Wheeler-Jonas Equation Applicable to Describe the Breakthrough Curve of an Oxidizing Gas: Ozone? Lumeng Liu Junjie Liu, PhD Jingjing Pei, PhD Student Member ASHRAE Fellow ASHRAE Fellow ASHRAE ABSTRACT Ozone is the criteri
3、a pollutant with respect to oxidizing gases to be tested in ASHRAE Standard 145.2-2011. In non-industrial buildings, ozone is normally removed by activated carbon (AC). In practice, how often the filters should be replaced is a key question. The Wheeler-Jonas equation (WJE) is widely used for descri
4、bing breakthrough curves of organic vapours removal by AC. Some studies reported the WJE is also applicable of some inorganic gases including the acid gas - chlorine and the basic gas - ammonia. This paper firstly investigated applicability of the WJE of an oxidizing gas - ozone. The experiments wer
5、e conducted on a well-designed bench-scale test rig. The results indicated that the WJE does not work for ozone. There are two assumptions associating with the WJE, constant adsorption kinetics and neglecting axial diffusion. Multiple ozone-AC reaction mechanisms combined with different reactivities
6、 were confirmed from the literature review, which indicate the assumed constant adsorption kinetics is improper for ozone-AC reacitons. Finally, a new mass balance model described by a partial differential equation (PDE) which introduces the axial diffusion term and first order kinetics accompanied
7、by exponential deactivation was proposed. The PDE solution is in good agreement with the experimental data. The Pclet number was calculated with the estimated axial diffusion coefficient from the PDE model. The large value indicates the axial diffusion is not significant. Therefore, the constant ads
8、orption kinetics assumed in the WJE is considered to be the major reason of its inapplicability of ozone. INTRODUCTION Many studies reported association between ground-level ozone and various adverse health effects, including increased morbidity and mortality of respiratory and cardiovascular diseas
9、es (Anderson et al., 2004; Silva et al. 2013). Overall the current ozone levels have doubled over last century due to fossil fuel and bio-mass burning (Gauss et al. 2006). The increase is expected to continue in twenty-first century, particularly in developing countries (Gauss et al. 2003). As a pow
10、erful oxidant, ozone is also a significant initiator of indoor chemistry by driving various oxidative processes specifically with unsaturated organic compounds (e.g., terpenoids, unsaturated fatty acids) (Weschler et al. 2006). Ozone-initiated products include gaseous organic compounds (aldehydes, k
11、etones, carboxylic acids and hydroper-oxides), short-lived intermediates, radicals and secondary organic aerosols (SOAs) (Weschler 2004). Estimation by Weschler (2006) indicated average daily indoor intakes of ozone oxidation products accounts for one-third to twice the indoor intakes of ozone alone
12、. Consequently, ASHRAE (2011a) also suggests that indoor ozone level be “as low as reasonably achievable“. Ozone is also the criteria challenge gas with respect to oxidizing gases to be tested in ASHRAE Standard 145.2-2011 (ASHRAE 2011b). In non-industrial buildings, ozone is normally removed by act
13、ivated carbon (AC, Dusenbury and Cannon 1996; Lee and Davidson 1999). In practice, how often the filters should be changed on specific operation condition is a key question. The Wheeler-Jonas equation (WJE) is most widely used for describing breakthrough curves of organic vapours adsorption by AC (L
14、odewyckx et al. 2004). Lodewyckx et al. (2004) reviewed the recent developments of the WJE. They concluded the equation is extendedly applicable to chemisorption and other environment circumstances (e.g., presence of water and non-linear flow) due to its simplicity: “the combination of a single capa
15、city term and an overall kinetic effect“. The applicabilities of the WJE of inorganic gases including the acid gas - chlorine (Lodewyckx and Verhoeven 2003) and the basic gas ammonia (Verhoeven and Lodewyckx 2001) have been confirmed. This paper will investigate the applicability of the WJE of an ox
16、idizing gas - ozone. METHODS Theoretical The WJE was proposed by Wheeler and Robell (1969) and modified by Jonas et al. (Jonas and Rehrmann 1972; Wood and Moyer 1989) to its current form, as shown in Equation 1: (1) Where, tb the breakthrough time, min, M the weight of carbon bed, gcarbon, We the eq
17、uilibrium adsorption capacity, g gcarbon-1, Q the volumetric flow rate, cm3 min-1, cin the inlet contamination concentration, g cm-3, cout the chosen breakthrough concentration, g cm-3, b the bulk density of carbon bed, gcarbon cm-3, and kv the overall adsorption rate coefficient, min-1. Among all t
18、he parameters, the equilibrium capacity We and overall rate coefficient kv need further calculation. While We is normally determined by the DubininRadushkevich equation (Dubinin 1989), the determination of kv is relatively complicated. Wu et al. (2005) discussed the problems of the existing models o
19、f kv and proposed a new systematic method based on multivariate data analysis (MVDA) to estimate kv. However, all the models used to determine We and kv were derived from investigations of physical adsorption of organic vapours. It should be cautious to use them in the chemisorption cases. To invest
20、igate the applicability of WJE of ozone, experiments with different weights of AC (a.k.a. M) were conducted. Obviously, We is independent of M. The review of existing models of kv by Wu et al. (2005) indicates kv is also independent of M. If the WJE works for ozone: 1. Plotting the breakthrough time
21、 versus varying M should yield a straight line. 2. Using the We and kv calculated from slope and intercept of the straight line, the equation should also be able to predict the breakthrough time with respect to different outlet concentration (at least) on the same operating conditions. Experimental
22、The experiments were carried out on a bench-scale test rig of which the schematic diagram is shown in Figure 1. The airflow was provided by an air compressor and purified by a filtration unit consisting of a HEPA filter and a packed AC bed. Ozone was generated by a UV ozone generator (UVP, Upland, U
23、S) and controlled by a mass flow controller (MC-5SLPM-D, Alicat, US). To eliminate the effect of water vapour, a drying colume filled with silica-gel desiccant was connected to the upstream of ozone generator. The AC holder was made of quartz column with i.d. of 0.4 in (1.0 cm) in which commercially
24、 derived granular activated carbon was packed. Ozone concentration was measured with a photometric ozone analyzer (T400, API, US). The upstream and downstream ozone concentration can be measured alternatively. Figure 1 Schematic diagram of the bench-scale test rig. RESULTS The 10% breakthrough time
25、with respect to varying AC weights are shown in Figure 2. For each AC weight three independent sets of measurements were conducted. The error bars display the standard error of the mean (SEM). Applying linear least squares fitting, the good agreement (R2=0.9833) indicates the first prerequisite fore
26、mentioned is met. The slope and intercept were also obtained from the fitting. Figure 2 Breakthrough time versus different AC weights. To further test applicability of the WJE, one should compare the predicted breakthrough time with experimental breakthrough time. Here another ten breakthrough time
27、with respect to ten outlet concentrations and a single 3.5 ct (0.7 g) AC were calculated according to the WJE. The results were compared with the corresponding experimental data, as shown in Figure 3. Since the variance of the three measurements of the 3.5 ct (0.7 g) AC is small (see in Figure 2), t
28、he propagation of errors was not shown in this comparison. The discrepancy indicates the WJE cannot predict the breakthrough time of ozone, even with the same flowrate and inlet concentration. Figure 3 Experimental breakthrough time versus calculated breakthrough time from WJE. DISCUSSION The WJE wa
29、s originally derived from mass balance with two major assumptions: constant adsorption kinetics and neglecting axial diffusion (Wheeler and Robell 1969; Bohart and Adams 1920). The rate of change in vapor concentration is asummed to be first order in vapor concentration and first order in remaining
30、reactive sites (Bohart and Adams 1920). It stands to reason that one or both the assumptions being improper for ozone interaction with AC may be the reason of the inapplicability of ozone. Reaction Mechanisms of Ozone and AC Compared with physisorption of organic vapours or chemisorption of some ino
31、rganic gases, ozone-AC interactions involve chemical reactions and catalytical decomposition (Dusenbury and Cannon 1996; Lee and Davidson 1999; Subrahmanyam et al. 2005; Takeuchi and Itoh 1993). Ozone reacts with the C=C bonds and produces ozonide, epoxide with oxygen, and molozonide. These intermed
32、iates will further transform to oxygen functional groups (OFGs), such as -COOH, -OH and -C=O. The OFGs then transform to CO and CO2 through dehydration condensation between themselves or ozonization by ozone. Unpaired electrons on AC also react with ozone and produce oxygen. Besides chemical reactio
33、ns, ozone also decomposes to oxygen catalytically on the active sites of AC. The reaction mechanisms of ozone and AC are summarized in Figure 4. Figure 4 The reaction mechanisms of ozone and AC. As shown in Figure 4, there are at least three ways in which ozone reacts with AC. At early stage , ozone
34、 reacts with the C=C bonds and unpaired electrons chemically in higher reactivity (Subrahmanyam et al. 2005). When the C=C bonds and unpaired electrons are “exhausted”, the conversion turns to catalytic decomposition of ozone on the active sites in lower reactivity (Subrahmanyam et al. 2005). The mu
35、ltiple reaction mechanisms combined with different reactivities indicate the assumed constant adsorption kinetics is improper for ozone-AC reacitons. Essentially, the WJE is an idealized (constant adsorption kinetics) and simplified (neglecting axial diffusion) mass balance formulation of gas-surfac
36、e interacitions. The discrepancy between the WJE and experiment data was also observed in physisorption of organic vapors (Wood 2002). In fact, the heterogeneity of AC surface intrinsically contradicts the constant adsorption kinetics. When it comes to the adsorption process without extra reactions,
37、 the variance between the WJE and reality is usually acceptable. However, the chemical and catalytic reactions besides adsorption between ozone and AC can magnify the variance and thus go beyond the scope of the WJE. Comparison of the WJE and PDE Model To further investigate the effects of ozone-AC
38、reaction mechanisms and the axial diffusion, a one-dimentional (neglecting radial dispersion) mass balance model described by a partial differential equation (PDE) was formulated, as shown in Equation 2. t)(z ,Ckez t)(z ,Cuz t)(z ,CDt t)C( z, Ctk22L d (2) With the initial and boundary conditions of
39、C(z, 0) = 0, C(0, t) = Cin, 0z t)C(L, In this model, the term on the left corresponds to the change rate of ozone concentration in the void fractions of the AC bed. The axial diffusion (first term on the right) was characterized by a diffusion coefficient. The second term on the right reflects the a
40、dvective transport of ozone in the axial direction. An irreversible first-order reaction accompanied by deactivation (third term on the right) was proposed to characterize the inconstant reaction kinetics. The deactivation of AC can be considered to be resulted from the poisoning of ozone. According
41、ly, the exponential decay funcition (first order decay) was adopted (Fogler 2005). The unknown parameters were derived from literature (lvarez et al. 2008) or estimated by data fitting using EASY-FITModelDesign (Schittkowski 2013), as shown in Table 1. The parameters were fitted with the measurement
42、s of another three independent sets of experiments of which the operation conditions are the same as those in Figure 3. Finally the PDE was numerically solved using the pdepe solver of the Matlab (The MathWorks, Inc.). Table 1. Modeling Parameters Paramters values Bed porosity, 0.26 Axial diffusion
43、coefficienta, DL 0.0042 ft2/s 0.00039 m2/s Superficial air velocity, u 4.9 ft/s (1.5 m/s) Deactivation rate constanta, kd 0.000152 s-1 Removal rate constanta, k 1524 s-1 Internal effectiveness factorb, 0.23 External effectiveness factorb, 1 Bed length, L 0.79 in (0.02 m) a Estimated by EASY-FITModel
44、Design b Derived from literature To better contrast the PDE model with the WJE, rearrange the WJE and let outlet concentration be the dependent variable. As shown in Figure 5 (a), the experimental data are in good agreement with the PDE model. In contrast, the Wheeler-Jonas curve deviates the experi
45、mental data after 1.5 h since the mearsurements began. The experimental data in this comparison are the same as those used in Figure 3. Calculated breakthrough time against experimental time in Figure 5 (b) also exhibite similar contrast between the PDE model and the WJE. Figure 5 (a) Comparison of
46、outlet concentration between the PDE model and experimental data and (b) comparison of breakthrough time among the PDE model, the WJE, and experimental data The effect of axial diffusion can be measured by the Pclet number (Huysmans and Dassargues 2005). Its the ratio of advective transport rate to
47、the diffusive transport rate, as shown in Equation 3. LDuLPe (3) When the Pclet number is much larger than 1, the advection dominates and the diffusion can be neglected. Using the estimated axial diffusion coefficient DL (in Table 1), the Pclet number is 77, which implies effect of axial diffusion i
48、s not significant. CONCLUSION This paper firstly investigated applicability of the WJE of an oxidizing gas - ozone. The experiments were conducted on a well-designed bench-scale test rig. The results indicated that the WJE does not work for ozone. There are two assumptions associating with the WJE,
49、constant adsorption kinetics and neglecting axial diffusion. Multiple ozone-AC reaction mechanisms combined with different reactivities were confirmed from the literature review, which indicate the assumed constant adsorption kinetics is improper for ozone-AC reacitons. Finally, a new mass balance model described by a partial differential equation (PDE) which introduces the axial diffusion term and first order kinetics accompanied by exponential deactivation was proposed. The PDE solution is in good
