Prediction for the Adsorption of Low-Concentration Toluene by Activated Carbon

Abstract

Activated carbon filters are widely used to remove gaseous pollutants in order to guarantee a healthy living environment. The standard method for evaluating the adsorption performance of filters is conducted at ~100 ppm. Although this accelerates the test and avoids the high requirements of the test device, it is still far from the contaminant concentration in the indoor environment, and adsorbents in practical application may show different capabilities. Therefore, this study compared several methods for predicting the adsorption performance of activated carbon and recommended a procedure based on the Wheeler–Jonas model to estimate the breakthrough curve at low concentrations using experimental data at high concentrations. The results showed that the Langmuir model and Wood–Lodewyckx correlation were the most suitable for obtaining the equilibrium adsorption capacity and mass transfer coefficient, which are critical parameters in the Wheeler–Jonas model. The predicted service life was derived from the breakthrough curve. A modification method based on a relationship with inlet gas concentration was proposed to reduce the prediction deviation of the service life. After modification, the maximum deviation was within two hours and the relative deviation was no more than 7%.

1. Introduction

Volatile organic compounds (VOCs) are primary pollutants contributing to the deterioration of indoor air quality [1]. According to the chemical structure, VOCs can be divided into alkanes, aromatic hydrocarbons, alkenes, halogen hydrocarbons, esters, aldehydes, etc. They are mainly released from decoration materials, various furniture in buildings, and human activities, and are transmitted from the outdoors. Long-time exposure to formaldehyde and highly hazardous VOCs, such as benzene and toluene, harms human health, inducing various diseases such as Sick Building Syndrome (SBS), respiratory diseases, cardiovascular diseases, and even leukemia and cancer [2]. It is reported that indoor VOC pollution is severe in China. Zhou et al., tested 436 air samples in residential buildings from 6 cities, indicating that the over-standard rates of formaldehyde and TVOC were 70% and 50%, respectively. The concentrations of benzene, toluene, and xylene were also over the limits by varying degrees [3]. Therefore, removing VOCs is essential for improving indoor air quality and protecting the occupants’ health.

Adsorption is considered one of the most promising VOC removal strategies due to its low cost, easy operation, and lack of by-products [4,5]. Among numerous adsorbents, granular activated carbon (GAC) is the most popular because of its large specific surface area, well-developed pore structure, strong adsorption capacity, stable chemical properties, and reusability [6,7]. The concentration of indoor VOCs is only at the ppb~ppm level. To acquire the adsorption performance of activated carbon at low concentrations, some researchers attempted to test the gas-phase filters at the ppb~ppm level [8,9,10]. However, the test duration needed to be shorter, yet was sometimes as long as hundreds of hours. It also had high demands for experimental instruments. Therefore, it is infeasible to test the gas-phase filters with low-concentration pollutants considering the test duration and economic cost. To limit the measurement effort, ISO 10121-2 was set to assess the performance of gas-phase air cleaning media, in which toluene was recommended as a representative substance for VOCs at concentrations of 9 or 90 ppm [11]. In another standard of ASHRAE 145.1, the concentration of toluene in the accelerated test was 100 ppm [12]. However, the concentration in the standard methods is still significantly higher than that in the actual buildings, and adsorbents may show different capabilities in practical application, so the standard test methods did not seem suitable for evaluating the long-term performance of the air cleaning media under realistic conditions.

In contrast, there is a quick and effective method to build a model that can predict low-concentration adsorption of VOCs by fitting the measurement data at higher concentrations. The differential equations based on the adsorption kinetics mechanism describe the breakthrough adsorption capacity of the gas-phase filters. Vizhemehr et al. [13] studied three typical models based on the absorption process in activated carbon, namely the homogeneous surface diffusion model (HSDM), the pore diffusion model (PDM), and the pore surface diffusion model (PSDM). The finite difference method was used to discretize the space of the adsorption bed, and the adsorption process was regarded as a series of nodes. The concentration of pollutants was obtained by time integration using the Matlab software. Many parameters involved in the models were estimated from empirical or semi-empirical formulas, which led to the prediction from the models being inconsistent with the experimental data at higher concentrations of 15~150 ppm but disagreeing with those at a lower concentration. From the perspective of service life, the deviation of predicted and measured values at 15 ppm was over 5 h. Subsequently, Shaverdi et al. [14] used the differential equation in place of the mass balance equation to simplify the calculation process of the iterative algorithm in the Matlab software. They made the predicted results closer to the adsorption data of methyl ethyl ketone, at 15~100 ppm, and n-hexane, at 18~100 ppm. In the study of Ligoski et al. [15], the breakthrough curves of toluene at concentrations of 0.09 or 0.9 ppm were predicted using the experimental data at 9~90 ppm. However, the predicted curves were only in good agreement with the S-shaped breakthrough curve. The experiment at 0.09 ppm still needed to be completed, and the accuracy of the service life still needed to be determined. Yao et al. [16] summarized the dynamic models for predicting the breakthrough curves, including the Yoon–Nelson model, Adams–Bohart model, Wolborska model, Thomas model, Boltzmann distribution function, etc. It was concluded that the Yoon–Nelson model was widely used in various adsorption systems because the input parameters were easily obtained. The breakthrough curve predicted by Shiue et al. [17], based on the D–R equation and modified Yoon–Nelson model, could estimate the service life of chemical filters at different VOC concentrations (10~70 ppm) and different filtration speeds (0.076, 0.114, and 0.152 m/s). Nevertheless, since the critical parameters for the modeling were determined under the low face velocities deviated from the realistic operating conditions, the feasibility of this method needed to be verified by the experimental data when the face velocity was above 1 m/s.

As previously mentioned, a variety of prediction models were proposed. Due to the complicated calculation process [13,14] for differential equations, it is more efficient to predict chemical filters’ adsorption performance and service life using a breakthrough model [15,17]. With the problems of the limited range of applications [15] and insufficient experimental verification [17], it is necessary to verify the prediction method further to accurately evaluate the adsorption performance and the service life of the gas-phase air cleaning medium in a realistic operation environment. In this paper, a test on activated carbon for toluene adsorption at low concentrations was conducted. Then, we compared four prediction methods based on the Wheeler–Jonas model to predict the toluene adsorption in the activated carbon at the ppm level. To accomplish this, we used the experimental data from relatively high concentrations and further optimized the prediction method to obtain the accurate service life of the adsorbent.

2. Experimental Section

2.1. Characteristics of Activated Carbon

Activated carbon made from coconut shells was chosen for the experiments and named granular activated carbon (GAC). The structural parameters through BET characterization are summarized in

Table 1. Structural parameters of activated carbon sample.

Sample	BET-Specific Surface Area (m2/g)	Average Pore Size (nm)	Total Pore Volume (cm3/g)	Microporous Volume (cm3/g)	Mesoporous Volume (cm3/g)
GAC	1143.9	1.79	0.1020	0.0356	0.0665

. The adsorption and desorption curves of activated carbon in nitrogen, as well as the pore distribution, are shown in Figure 1 and Figure 2. The BET-specific surface area of GAC was 1143.9 m²/g. The GAC was dominated by mesoporosity with a proportion of 65.2%, and its average pore size was 1.79 nm. The total pore volume of GAC was 0.1020 cm³/g. To eliminate the influence of the size of the granular activated carbon on the adsorption, the activated carbon sample was uniformly ground to 20~30 meshes (0.6~0.9 mm).

The breakthrough curves of toluene with different inlet concentrations were measured in the experiments. The prediction methods were compared based on the measurement data of GAC, and then the accuracy and feasibility of the methods were analyzed.

2.2. Experimental Facility

The experimental system is shown in Figure 3 with the functions of challenge gas generation and adsorption in the activated carbon. The pressurized air successively passed through a silica gel drying column and a high-efficiency particulate air (HEPA) filter to become dry and clean carrier gas. The toluene with a high concentration of 100 ppm in the cylinder was mixed with carrier gas to reach the desired concentration. The flow rate of clean gas was controlled by mass flow controller 1, with a range of 0~10 L/min, and the flow rate of toluene was controlled by mass flow controller 2, with a range of 0~2 L/min. The accuracy of each controller was 1% of the full range. The flow rate of the adsorption column was 2.5 L/min, controlled by a rotameter, and the excess gas was bypassed and discharged into the atmosphere after treatment. Before the experiment, the concentration of toluene was tested to ensure a constant concentration upstream of the adsorption column by using a blank column. The fluctuation was within 5% of the desired concentration. The activated carbon sample was fixed by metal mesh in the adsorption column. The adsorption column had an inner diameter of 10 mm and a filling height of 3 mm. The ppbRAE 3000 device was used to continuously monitor the concentration of toluene downstream of the adsorption column, and the data were recorded at an interval of 1 min. The ppbRAE 3000 is a device to measure the concentration of organic gaseous pollutants, with a wide detection range from 1 ppb to 10,000 ppm. It uses a third-generation photoionization detector (PID) to improve detection accuracy and reach a resolution of 1 ppb.

Chen et al. [18] tested the newly renovated houses and found that the TVOC reached 9.22 mg/m³ (2.41 ppm). During the decoration period, the highest TVOC concentration in the office building reached 11 mg/m³ (2.87 ppm) [19]. Then, for indoor TVOC pollution, we selected 6 desired concentrations of 0.5, 1.0, 2.0, 3.0, 4.0 and 5.0 ppm.

3. Prediction Method

With the simple formulas and easily available parameters, the Wheeler–Jonas model was popular for predicting the breakthrough curve. The Wheeler–Jonas model was initially derived from the mass balance of gases entering and passing through the adsorption bed, and was then modified [20]. The model is expressed as follows:

$$t_b=\frac{q_e{m}_{GAC}}{C_{i}Q}+\frac{q_e{\rho }_b}{K_v{C}_i}\ln (\frac{C_b}{C_i-C_b})$$

(1)

where $t_b$ is the breakthrough time, h; $K_v$ is the mass transfer coefficient, 1/h; $q_e$ is the equilibrium adsorption capacity at the concentration of $C_i$, mg/g; $C_b$ is the breakthrough concentration of adsorbate, ppm; $C_i$ is the initial concentration of adsorbate, ppm; ${\rho }_b$ is the bulk density of activated carbon, g/m³; $Q$ is the carrier gas flow rate through the adsorption column, m³/min.

The advantage of the Wheeler–Jonas model was considering the characteristics of fixed bed and operation conditions. It was easily noted that it was essential to acquire the equilibrium adsorption capacity and the mass transfer coefficient for the prediction. Then, the appropriate methods for obtaining the two critical parameters were presented.

3.1. Isotherms

3.1.1. Langmuir Model

The Langmuir model was the theoretical model for monolayer adsorption, and it was widely used to describe the VOCs adsorption in the adsorbents [21]. It is expressed as:

$$\frac{q_e}{q_m}=\frac{K_l{C}_i}{1+K_l{C}_i}$$

(2)

where $C_i$ is the inlet concentration, mg/m³; $q_e$ is the equilibrium adsorption capacity at the concentration of $C_i$, mg/g; $q_m$ is the maximum adsorption capacity in theory, mg/g; and $K_l$ is the equilibrium adsorption constant, m³/mg, which is related to the nature of adsorbate.

The equilibrium adsorption capacity $q_e$ can also be calculated by Equation (3) using numerical integration:

$$q_e=\frac{Q(C_i{t}_f-{\displaystyle {\int }_0^{t_f}{C}_{b}dt)}}{m_{GAC}}$$

(3)

where $Q$ is the flow rate of carrier gas through the adsorption column, m³/min; $C_b$ is the breakthrough concentration, mg/m³; $t_f$ is the time at 95% breakthrough fraction, min; $m_{GAC}$ is the quality of absorbent, g.

3.1.2. Freundlich Model

The Freundlich model is an empirical model based on experimental results without theoretical derivation [22]. The expression of the Freundlich model is:

$$q_e=K_f{C}_i^{1/n}$$

(4)

where $K_f$ is the equilibrium adsorption constant describing how strong the absorbate is attached to the surface of the adsorbent. $1/n$ represents the difficulty in the adsorption process. The value of $1/n$ is between 0 and 1 in most cases. A smaller value of $1/n$ indicates that the adsorption occurs more easily. Once the value reaches more than 2, it indicates that the it is challenging for adsorption to occur.

3.1.3. Dubinin–Radushkevich (D–R) Model

The D–R model is a semi-empirical equation based on adsorption potential theory and micropore filling theory [23]. The expression of the D–R model is:

$$W_{\mathrm{e}}=W_0\exp \{-{(\frac{1}{E})}^2{\left[RT\ln (\frac{p_0}{p})\right]}^2\}$$

(5)

where $W_e$ is the pore volume occupied by the adsorbate, cm³/g; $W_0$ is the limiting pore volume of adsorption, cm³/g; $E$ is the adsorption free energy of the adsorbate, J/mol; $RT\ln (p_0/p)$ is the adsorption potential; $R$ is the gas constant, 8.314 J/mol·K; $T$ is absolute temperature, K; $p_0/p$ is the relative pressure of the adsorbate; $p_0$ is the saturation pressure of the adsorbate at the adsorption temperature, Pa; and $p$ is the pressure of the adsorbate vapor, Pa.

Since the pore volume occupied by the adsorbate is challenging to obtain, the D–R model isotherm can be rewritten by the expression of adsorption capacity as Equation (5) [24]:

$$q_{\mathrm{e}}=q_m\exp \{-\frac{1}{2E^2}{\left[RT\ln (1+\frac{1}{C_i})\right]}^2\}$$

(6)

The calculation of equilibrium adsorption capacity is generally performed with the Langmuir, Freundlich, and D–R models. To determine the applicability of the three isotherms for different concentration ranges, the application of isotherms for toluene adsorption in the previous studies is shown in Figure 4. The results showed that three isotherms could fit toluene adsorption without a strict adsorbate concentration requirement. Particularly, the Langmuir model was widely used at the ppm level [25,26], which was applicable at concentrations close to the indoor environment. In the study conducted by Seo et al. [26], the value of R² of the Langmuir model was 0.9956, which could fit the adsorption of toluene by activated carbon at 0.4–1.6 ppm. Mobasser et al. [27] conducted adsorption tests on activated carbon, zeolite, and organosilica with a toluene concentration of 0.02–1 ppm and found that the Freundlich model fitted well. The D–R model was less frequently used than the Langmuir and Freundlich models because of its complex form and the greater number of parameters involved. The Langmuir and Freundlich models were used to describe the adsorption of toluene at the ppm level, whereas it should still be verified which isotherm was the most suitable.

3.2. Breakthrough Models

The critical parameter of the mass transfer coefficient can be obtained by breakthrough models describing the dynamic breakthrough curves of adsorption. With a simple form and easily available parameters, the Yoon–Nelson model was widely used. The application of this model was not restricted to the absorbent’s physical and chemical properties [33]. The expression of the Yoon–Nelson model is:

$$t_b=\tau +\frac{1}{K_v}\ln (\frac{C_b}{C_i-C_b})$$

(7)

where $K_v$ is the mass transfer coefficient, 1/h; $t_b$ is the breakthrough time, h; $\tau$ is the breakthrough time required for 50% breakthrough, h; $C_b$ is the breakthrough concentration of adsorbate, ppm; and $C_i$ is the initial concentration of adsorbate, ppm.

The mass transfer coefficient was calculated by the Wheeler–Jonas model expressed in Equation (1). The expression was similar to the Yoon–Nelson model, and could be regarded as a complex expression of the Yoon–Nelson model.

3.3. Prediction Procedure

Step 1: The equilibrium adsorption capacity was predicted at low concentrations (0.5 and 1.0 ppm or lower) by fitting adsorption isotherms and experimental data. The actual adsorption capacity was calculated by integrating the breakthrough curve using Equation (3). We compared different fitting results by isotherms and chose the one with the highest accuracy in predicting adsorption capacity.

Step 2: The mass transfer coefficient at low concentrations was obtained in several ways. The critical parameter was usually obtained by the breakthrough model describing the dynamic adsorption properties in Section 3.2. We were also able to obtain it from another empirical formula. Wood and Lodewyckx [34] proposed an equation to calculate the mass transfer coefficient $K_v$:

$$K_v=\alpha {\beta }^{0.33}{v}_L^{0.75}{d}_p^{-1.5}{(\frac{q_e}{M})}^n$$

(8)

where $\alpha$ is the overall correlation coefficient; $\beta$ is the affinity coefficient; $v_L$ is the linear flow rate through the adsorption column, cm/s; $d_p$ is the diameter of activated carbon; $M$ is the molecular weight; and $n$ is the adjustable exponent.

Compared with the model mentioned in Section 3.2, the Wood–Lodewyckx equation took into account not only the parameters of the adsorption bed ($d_p$) and adsorption conditions ($v_L$), but also the parameters of the adsorbate properties ($\beta$, $M$).

Then, we summarized four methods for obtaining the mass transfer coefficient:

-

Method 1: $K_v$ was calculated by fitting experimental data and the Yoon–Nelson model at high concentrations (2.0–5.0 ppm). The linear function relationship of $K_v$ and $C_i$ was established to predict $K_v$ at low concentrations (0.5 and 1.0 ppm or lower).

-

Method 2: The procedure was similar to method 1, but contrastingly, the influence of the quadratic function relationship of $K_v$ and $C_i$ on the prediction was studied.

-

Method 3: Considering the impact of adsorbent characteristics and adsorption conditions, we used the Wheeler–Jonas model to obtain the mass transfer coefficient at high concentrations (2.0–5.0 ppm). The linear function relationships of $K_v$ and $C_i$ were used to obtain the predicted $K_v$ at low concentrations.

-

Method 4: The transfer coefficient was calculated by the Wheeler–Jonas model at high concentrations (2.0–5.0 ppm). The Wood–Lodewyckx correlation, which took into account the properties of the adsorbate, was used to obtain the predicted values at low concentrations.

Step 3: After obtaining the two key parameters and inputting the other parameters into Equation (1), we were able to obtain the corresponding breakthrough concentration at different moments as well as the prediction curves at low concentrations.

4. Results

4.1. Validation of Adsorption Isotherms

The breakthrough curves of toluene in the GAC with inlet concentrations of 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0 ppm are shown in Figure 5. The breakthrough curves show S-shapes. In theory, the mass transfer of toluene into the activated carbon follows three steps [35]: (1) Film diffusion: toluene molecules pass through a layer of gas film on the absorbent surface before being adsorbed. Contaminant flux through the film is directly proportional to the linear concentration gradient across the film. (2) Pore diffusion: this occurs within the interior of activated carbon; toluene molecules diffuse within the pore space from the surface of activated carbon. The pore diffusion rate is influenced by the gas-phase concentration of toluene [36]. For small pores, the number of molecule–wall collisions exceeds that of intermolecular collisions, and the Knudsen diffusion dominates. For large pores, more intermolecular collisions occur, and the viscous flow dominates [37]. (3) Surface diffusion: the toluene molecules are adsorbed on the active sites on the inner surface of the pores of the activated carbon, and they continue to diffuse along the adsorbent surface within the pores. Mass transfer resistances at the three stages are different, resulting in different diffusion rates. The stage with the slowest diffusion rate significantly affects the mass transfer process. Kim et al. [38] indicated that the rate of gas adsorption by activated carbon was determined by pore diffusion. Therefore, as the inlet concentration of toluene was increased, the diffusion rate of toluene in the activated carbon was increased, and the physical adsorption was accelerated in order to shorten the time necessary to reach the adsorption equilibrium.

The equilibrium adsorption capacities of toluene at 0.5, 1.0, 2.0, 3.0, 4.0, and 5.0 ppm on the GAC were 69.00, 102.08, 134.26, 150.03, 159.38, and 165.58 mg/g, respectively. These values were calculated by the numerical integration method, as in Equation (3), and are shown in

Table 2. Equilibrium adsorption capacities (mg/g).

Sample	0.5 ppm	1.0 ppm	2.0 ppm	3.0 ppm	4.0 ppm	5.0 ppm
GAC	69.00	102.08	134.26	150.03	159.38	165.58

. The isotherms for the Langmuir, Freundlich, and D–R models were obtained by fitting the experimental data for toluene adsorption on the GAC using the least-square method (Figure 6).

Table 3. Regression results using three isotherms.

Sample	Model	Equation	R2
GAC	Langmuir	$q_e=0.0051C_i+0.018$	0.9899
	Freundlich	$q_e=61.64C_i^{0.3489}$	0.9591
	D–R	$q_{\mathrm{e}}=151.33\exp \left[-4.435\ln (1+1/C_i)\right]$	0.9223

summarizes the results of the regression. It can be seen that both the Langmuir and Freundlich models fit with the experimental data of GAC. The R² of the Langmuir model was as high as ~0.99. It can be speculated that the adsorption of toluene molecules on the surface of activated carbon was monolayer adsorption. The R² of the D–R model was 0.9223 for GAC, which indicated that micropore filling might not occur during the adsorption process.

4.2. Validation of Breakthrough Models and Predicted Models

Method 1: The prediction curve was established based on the Wheeler–Jonas equation, expressed as Equation (1), in which the value of equilibrium adsorption capacity $q_e$ could be obtained from the Langmuir equation in Section 4.1. Next, it was essential to calculate the mass transfer coefficient $K_v$. This method used the Yoon–Nelson model to predict $K_v$ at low concentrations.

The calculation of $K_v$ was based on the least-square technique. The Yoon–Nelson equation yielded linear curves using the Levenberg–Marquardt algorithm. The breakthrough time $t_b$ was the abscissa, the logarithmic concentration was the ordinate, and the slope of the curve was $K_v$. The relationship between $K_v$ and $C_i$ was determined by linear function based on the results at 2.0, 3.0, 4.0, and 5.0 ppm. The linear function could be expressed as $K_v=0.0016C_i+0.0045$ (Figure 7). The excellent fit found that the R² was 0.9107. The linear relationship between $K_v$ and $C_i$ was also obtained at concentrations of 9, 40, and 90 ppm in the study of Ligotski et al. [15]. It seemed that the relationship for $K_v$ was suitable, since it was obtained based on the experimental data at the concentration of the ppm level and the excellent fit.

Then, the structural parameters of activated carbon, such as $m_{GAC}$ and ${\rho }_b$, the inlet concentration of toluene $C_i$, the equilibrium capacity $q_e$, and the mass transfer coefficient $K_v$ were input into the Wheeler–Jonas equation (Equation (1)) to generate the predicted breakthrough curve (Figure 8).

According to Figure 8, the deviation between the prediction and the measured data was significant. Especially when the toluene concentration was at 0.5 and 1.0 ppm, the predicted breakthrough time significantly exceeded the tested value. This equation, expressed as $K_v=0.0016C_i+0.0045$ in Step 2, was indicated to be unsuitable for predicting the mass transfer coefficient.

Method 2: Observing the prediction results in Figure 8, it could be speculated that the linear expression could not accurately reveal the relationship between $K_v$ and $C_i$. Then, determination of the quadratic function relationship was attempted using Method 2. The equation was $K_v=-0.0006C_i^2+0.0055C_i-0.0016$ and the R² was 0.9997 (Figure 9). Then, $K_v$ could be calculated by this equation at 0.5 and 1.0 ppm. The other steps were the same as those in Method 1. It was found that the predicted curves were still far from the measured data in Figure 10, especially when the toluene concentration was 0.5 and 1.0 ppm. It could be speculated that the Yoon–Nelson model was not appropriate for the prediction.

Method 3: The Wheeler–Jonas model was used to calculate the mass transfer coefficient $K_v$ at 0.5 and 1.0 ppm. By fitting the experimental data and Equation (1), the equation between $K_v$ and $C_i$ was expressed as $K_v=-0.0004C_i+0.0072$, and the values are shown in

Table 4. Results of the predicted mass transfer coefficient K_v in Method 3.

Toluene Concentration (ppm)	0.5	1.0	2.0	3.0	4.0	5.0
$K_v$ (1/min)	0.0070	0.0068	0.0064	0.0060	0.0056	0.0052

.

Then, the calculated $q_e$ in Step 1 and $K_v$ in Table 4 were input into the Wheeler–Jonas model, and the predicted curves are shown in Figure 11. Compared with the previous two methods, this method was able to reflect the adsorption process more accurately. Due to the Wheeler–Jonas model considering detailed parameters, such as the characteristics of the adsorption bed ($m_{GAC}$, ${\rho }_b$), adsorption condition ($C_i$, $Q$), and equilibrium adsorption capacity, it is more widely applicable. The breakthrough curves of activated carbon and the breakthrough time under different experimental conditions can be obtained by changing the different parameters of the equation.

Method 4: Step 1 was to calculate $q_e$ by the Langmuir model, and Step 2 was to calculate $K_v$ by Equation (8). $K_v$ could be calculated by fitting experimental data and the Wheeler–Jonas model, and the equilibrium adsorption capacities were obtained by the Langmuir model at 2.0, 3.0, 4.0, and 5.0 ppm. The relationship was built between $K_v$ and $q_e$, and the predicted values were obtained (

Table 5. Results of the predicted mass transfer coefficient in Method 4.

Toluene Concentration (ppm)	0.5	1.0	2.0	3.0	4.0	5.0
$K_v$ (1/min)	0.0055	0.0057	0.0060	0.0065	0.0080	0.0109

). Step 3 was to input $K_v$ and $q_e$ into Equation (1) and obtain the predicted curves (Figure 12).

The predicted curves in Method 4 also achieved good results. From the user’s point of view, people are more concerned about the service life of the filter. The service life was derived from the breakthrough curves. The predicted and actual service lives are listed in

Table 6. Measured and predicted service life.

Toluene Concentration (ppm)	Measured Service Life (min)	Predicted Time in Method 3 (min)	Predicted Time in Method 4 (min)
5.0	904	931	901
4.0	950	1076	1067
3.0	1094	1302	1307
2.0	1452	1690	1678
1.0	1869	2495	2308
0.5	2487	3326	2754

to more effectively compare the accuracy of the two methods. Regarding the aspect of service life, the predicted value in method 4 was closer to the measured data. When the toluene concentration was 0.5 ppm, the service life was improved by 572 min. At 1.0 ppm, the predicted service life was improved by 187 min. However, on the whole, the deviation between the measured and the predicted values was large at the beginning and the end of adsorption, which were the sources of the deviation in the prediction. In the early adsorption stage, there were many unoccupied adsorption sites on the surface of the activated carbon, and the toluene molecules had a higher probability of contacting and being adsorbed on the surface. Therefore, the actual breakthrough time was later than the predicted value. At the end of adsorption, numerous toluene molecules were adsorbed, and there were few empty adsorption sites on the surface of the activated carbon. Therefore, the toluene molecules would directly penetrate the adsorption column, so the activated carbon would quickly reach saturation and adsorption would no longer occur. As a result, the actual service life was significantly shorter than the predicted value.

4.3. Modification of Prediction Method

Although the predicted values in Method 4 showed good agreement with the measured data, a deviation still existed in predicted service life. To improve the prediction accuracy, a relationship was built between the predicted deviation and toluene concentration (Figure 13), and the expression was $\Delta t=-13.197C_i^2-3.1937C_i+339.6$ (R² = 0.8093). The predicted value in Method 4 minus the deviation $\Delta t$ computed by the equation was the modified value. The modified predicted values are shown in

Table 7. Results of improved predicted service life.

Toluene Concentration (ppm)	Measured Service Life (min)	Modified Value (min)	Deviation (min)	Relative Deviation (%)
5.0	904	907	3	0.36
4.0	950	951	1	0.14
3.0	1094	1096	2	0.16
2.0	1452	1398	−54	−3.75
1.0	1869	1985	116	6.20
0.5	2487	2419	−68	−2.72

. After modification, the precision of prediction was improved and the relative deviation was no more than 7%. When the concentration was 0.5 and 1.0 ppm, the accuracy was improved by 8.01% and 17.29%, respectively.

5. Conclusions

In this paper, the toluene adsorption by granular activated carbon at the ppm level was tested. The methods of toluene adsorption prediction in activated carbon, based on the Wheeler–Jonas model, were compared and modified using the experimental data. Some conclusions can be drawn as follows:

• The Langmuir and Freundlich models were both suitable for predicting the equilibrium adsorption capacity, and the Langmuir model was preferred under the considered conditions.
• Using the equilibrium adsorption capacity obtained from the Langmuir model and the mass transfer coefficient from the Wood–Lodewyckx correlation was the most accurate method for the prediction of the breakthrough curve based on the Wheeler–Jonas model.
• The service life was obtained based on the predicted breakthrough curve, which could be significantly improved using the relationship with the inlet concentration of the adsorbate to obtain a value close to the actual service life.

Usually, the adsorption of gaseous filters is conducted under complex conditions. The methodology presented in this study requires more validation regarding different adsorbents and operating conditions.