# Equilibrium and Kinetic Adsorption of Hydrogen Fluoride onto Zeolite 3A

Authors: Shuo Duan; Ke Huang; Mengmeng Tao
Journal: Adsorption Science & Technology
 (2022)

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## Abstract

Equilibrium and kinetic adsorption behaviours of hydrogen fluoride (HF) onto zeolite 3A were investigated under different temperatures (298–338 K) and pressures (0.15–1.1 bar). The HF adsorption isotherms on zeolite 3A were well described by the Dubinin–Astakhov (DA) model. The isosteric heat of HF adsorption was calculated based on the DA model and Clausius–Clapeyron equation, and different kinetic models were used to analyze the HF adsorption kinetic. The results showed HF adsorption isotherms are type I of the IUPAC classification. The maximum adsorption capacities by the DA model are 0.443–0.5631 mg/g. TheHst values decrease with increasing surface loading indicating the surface energy heterogeneity of zeolite 3A. The HF adsorption kinetics on zeolite 3A follows simple first-order kinetics. The calculated film diffusion parameter Bt values show nonlinear characteristics with time. The order of magnitude of interparticle HF diffusion coefficient Dc is 10−9 m2/s. The higher pressure and temperature are in favour of HF diffusion. The intraparticle diffusion curves for HF adsorption on zeolite 3A show quart-linear characteristics, indicating the presence of four consecutive HF adsorption steps including film diffusion, interparticle diffusion, intraparticle diffusion, and surface adsorption. The intraparticle diffusion is a rate-controlling stage.


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## Body

## 1. Introduction

Fluorine-containing chemicals are widely used in atomic energy, metallurgy, machinery, chemical industry, and other industries because of their unique physical and chemical characteristics [1]. As a basic fluorine chemical product, hydrogen fluoride (HF) is widely used in producing refrigerants, fluorine resin, fluorine rubber, and fluorine-containing intermediate and fine chemicals [2]. HF is corrosive and toxic, and it poisons humans and animals through the food chain, destroys the normal metabolism of calcium and phosphorus, inhibits enzyme activity, and affects the nervous system [1]. In the use of fluorine (F2), e.g., uranium enrichment, optics, and material fluorination, HF is often accompanied by F2, which reduces the purity of fluorine [3–5]. Therefore, HF purification treatment and recovery are indispensable to save resources and protect the environment.The common methods of collecting and recovering HF are compression condensation, absorption, and adsorption [6]. The compression condensation method can purify HF gas well in theory, but this method needs low temperature and consumes more energy [7]. The HF amount treated by the absorption method is huge. However, absorption purification is wet with high requirements for equipment and chemical treatment problems [8]. Collecting HF by adsorption method cannot only remove HF gas but also reduce the emission of toxic gas HF and energy consumption. The adsorption method is mainly based on the HF adsorption performance. Thus, the basic HF adsorption data is required [9]. The frequently used adsorbents for HF adsorption are porous, e.g., sodium fluoride, activated alumina, activated carbon, and silica gel [2]. Zeolite is a commonly used adsorption material in gas separation and gas purification [6]. The application of zeolite can be extended to HF treatment.The studies on HF treatment by adsorption have been investigated by some scholars. Sodium fluoride (NaF) is a commonly used adsorption material for HF [10–12]. NaF reacts with HF to produce NaHF2. When the temperature is higher than 250°C, NaHF2 can be decomposed into NaF and HF. Afzal et al. conducted experiments on HF adsorption with NaF by the fixed bed, and the influence of concentration, temperature, and other parameters on the surface loading has been studied in detail [10–12]. The experimental results show that Langmuir and Temkin can better describe the HF adsorption isotherm than Freundlich [11]. Moreover, Liu et al. used NaF to adsorb and remove trace HF in the production of high-purity tungsten hexafluoride, and the HF adsorption by NaF under different temperatures, pressures, and gas flows was measured by orthogonal test [13]. The results showed the suitable adsorption temperature was 20–80°C, and the flow rate has a significant effect on adsorption efficiency. Activated alumina (Al2O3) is also used for HF adsorption. Activated alumina reacts with HF to produce AlF3 and H2O. In addition, Wu et al. studied the adsorption characteristics and influencing factors for HF adsorption by Al2O3, and the relationships between crystal structure, the specific surface area of Al2O3, and HF adsorption have been considered [14]. Sheng studied the HF adsorption behaviour on activated carbon, calcium oxide, activated alumina, iron oxide, and fly ash, and the Freundlich model described the adsorption isotherms well [15]. In addition to NaF and Al2O3, some other porous materials are also gradually applied to HF adsorption. Che et al. studied the HF adsorption behaviour on DB18C6/SiO2 composite [16]. Siahooe et al. studied the HF adsorption on carbon nanotubes and found that the HF adsorption density decreased with temperature increase [17]. Wang et al. investigated the HF adsorption behaviour on three metal–organic frameworks (MOFs) and found that MOFs had better HF adsorption performance than commercial Al2O3 and 13X zeolite [18]. Bahrami et al. investigated the HF gas adsorption by three kinds of activated carbon under vacuum and described the experimental data by isotherm adsorption models [19].Zeolite 3A is an excellent performance adsorbent for gas storage and separation [20]. However, the studies about HF adsorption on zeolite 3A are very lacking. Therefore, the study of the adsorption characteristics and influencing factors of HF on zeolite 3A is necessary. In this study, the equilibrium and kinetic adsorption curves of HF on zeolite 3A at different temperatures and pressures were measured. The HF adsorption isotherms on zeolite 3A were described by the three isotherms model. The DA model and the Clausius–Clapeyron equation were used to calculate the isosteric heat of HF adsorption, and different kinetic models were used to analyze the kinetic process for HF adsorption on zeolite 3A. The adsorption mechanism of HF onto zeolite 3A was evaluated based on kinetics and thermodynamics.


## 2. Materials and Methods

### 2.1. Materials

Zeolite 3A (8(K12[(AlO2)12(SiO2)12]·24H2O) used in this study was commercial zeolite manufactured by Lu Xinyuan Company (Henan, China). In this investigation, spherical 3A particles of 0.2 cm radius were studied. Hydrogen fluoride and helium with a purity of 99.99% were provided by China Shipbuilding (Handan) Perry Special Gas Co., Ltd.


### 2.2. Characterization of the Zeolite 3A

The compositions were measured by X-ray diffraction (XRD) using a Rigaku Smartlab 9kW with Cu Kα radiation (40 kV and 40 mA). The Fourier transform-infrared (FT-IR) of zeolite 3A spectra was obtained from an FT-IR spectrometer (Thermo Nicolet iS5, USA) using pellets of zeolite/KBr. The surface morphology was obtained by SEM (Zeiss sigma500) at an accelerating voltage of 10 kV. The pore structure distribution (PSD) of zeolite 3A was measured by the low-temperature CO2 adsorption method at 273 K using 3H-2000 PM.


### 2.3. Adsorption Isotherm and Kinetics Measurements

Equilibrium and kinetics measurements of HF adsorption on zeolite 3A were performed in a static volumetric instrument. The detailed composition of the experimental instrument is shown in Figure1. The pressures of the experimental system were recorded using a precision pressure sensor (Keller, Switzerland, ±0.01% precision). An automatic thermostatic oil bath with ±0.01 K accuracy was used to keep the system temperature constant.Figure 1
A schematic of experimental setup for HF adsorption.The main experimental procedures for equilibria and kinetics adsorption are:(1)
Sample pretreatment and filling. The 3A sample used in the adsorption experiment was first dried in the drying oven at 385 K for 24 h, weighed, and then quickly transferred to the sample cell. The constant temperature of the oil bath was set to 358 K and vacuumed for 12 h to remove the water and other impurities adsorbed in the sample transfer process(2)
Leakage test for adsorption system. After the sample pretreatment, the temperature of the oil bath was set to 338 K. After the system temperature is constant, helium (He) was fed into the reference and adsorption cells to a certain value (maximum pressure required for adsorption). The leakage testing time was 12 h. The system was heated and vacuumed for 4 h after the leakage test(3)
Measurement of void volume. The void volume of the adsorption cell filled with adsorbent was measured by the helium expansion method. The temperature for the helium expansion test was set to the adsorption experimental temperature. The helium density used in void volume measurement is calculated by the BWR equation [21]. Helium expansion tests were repeated at least four times and the values were averaged to minimize error(4)
Equilibrium adsorption experiment. A certain HF amount was injected into the reference cell when the temperature of the adsorption system was constant with the experimental setting value. The gas pressure for the reference cell was recorded until it is stable. The valve between the reference and sample cells was opened, the HF flowed into the sample cell from the reference cell and the adsorption began. The system pressure was recorded when the system pressure was constant for 5 h. The above operations were repeated until the maximum pressure point of the equilibrium adsorption is reached(5)
Adsorption kinetics experiment. HF was injected into the reference cell to a calculated pressure value when the temperature of the adsorption system was constant with the experimental set value. The valve between the reference and sample cells was then opened, the HF flowed into the adsorption cell, and the system pressure was recorded in real time by the high-precision pressure transmitter until the final system pressure was stabilized at the desired value. The kinetic experimental conditions were 0.15, 0.35, 0.5, 0.70, 0.95, and 1.10 bar at 298 K and 298, 308, 318, 328, and 338 K at 0.5 barDuring the experiment, the calculation process for HF adsorption capacity was based on the mass conservation under the ideal gas state, so the adsorption capacity is [19]:
(1)q=1RTp0VR−p1VR+Vv,where q is the adsorption capacity, p0 is the gas pressure in the reference cell before adsorption and p1 is the system gas pressure during the adsorption process. R and T are the ideal gas constant and the system temperature, respectively.


### 2.4. Adsorption Theory

#### 2.4.1. Isotherm Models

The relationship between adsorption capacity, temperature, and pressure in the adsorption process is usually described by the adsorption model. The Langmuir and Freundlich models had been successful in adapting the described HF adsorption process [11, 12]. The DA model is often used to describe the gas adsorption in micropores [22]. The DA model is expressed as follows:
(2)q=qmexp−RTElnp0pn,where q and qm are the adsorption capacity and saturated adsorption capacity of gas, p0 is the saturated vapor pressure of gas, and E is the adsorption characteristic energy.The saturated vapor pressurep0 of HF is calculated by the Antoine equation with extension [23]:
(3)log10p0=A+BT+Clog10T+DT+ET2,where the values of A, B, C, D, and E are 23.7347, −1799.6, −6.1764, 5.0046 × 10−10, and 6.15 × 10−6, respectively. The unit of p0 is mmHg in the calculation formula, which needs to be multiplied by 0.0013332 to convert to bar. The calculated saturated vapor pressures of 298, 308, 318, 328, and 338 K are 1.215, 1.678, 2.223, 3.130, and 4.149 bar, respectively.


#### 2.4.2. Heat of Adsorption

The isosteric heat of adsorption is an important thermodynamic parameter which indicates that heat released since the adsorbed state is more stable than the unadsorbed state for adsorbate molecule [24]. The Clausius–Clapeyron equation was used to calculate the isosteric heat at constant adsorption capacity, and its expression is as follows [24]:
(4)Hst=−R∂lnp∂1/Tq,where Hst is the calculated isosteric heat at the adsorption capacity q.The isosteric heat of adsorption (Hst) can be obtained by combining the DA model with the Clausius–Clapeyron equation [24]:
(5)Hst=E−lnθ1/n+αTn−lnθ1−n/n+hfg,where α is the thermal expansion coefficient of adsorbed phase and α is calculated by 1/T. hfg is the enthalpy of evaporation, which is expressed as follows:
(6)hfg=−R∂lnp0∂1/TC.


#### 2.4.3. Adsorption Kinetics

(1) Adsorption Rate Models. The pseudo first-order (PFO) model assumes that the adsorption rate is directly proportional to the number of active sites. The rate expression is given by [25, 26]:
(7)dq/dt=k1q1−q,where q1 and q represent the adsorption capacity at equilibrium and time t, respectively, and k1 is the first-order rate constant.After integrating Eq. (7) with the boundary conditions (t =0, q =0 and t=t∞, q=q1),
(8)q=q11−e−k1t.The pseudo second-order model (PSO) assumes the adsorption rate is proportional to the square of number of active sites; therefore, the rate model is given by [25, 26]:
(9)dq/dt=k2q2−q2,where q2 represents the equilibrium adsorption capacity, and k2 is the second-order rate constant.With the boundary conditions (t =0, q =0 and t=t∞, q=q2), the PSO is given by [25, 26]:
(10)q=k2q22t/1+k2q2t.(2) Diffusion Models.
(1)
Film diffusionBoyd’s film diffusion model assumes that the main diffusion resistance is boundary film around the adsorbent particles [26, 27]. Therefore, the model was used to distinguish whether the film diffusion was a rate-controlling step in HF adsorption on 3A. The expression of this model is given by [26]:
(11)F=1−6π2∑n=1∞1n2exp−n2Bt,whereF is the fraction at times t and can be expressed using adsorption capacity:
(12)F=qtqm.Bt can be expressed in F [28]:whenF>0.85,
(13)Bt=−0.4977−ln1−F,when F<0.85,
(14)Bt=π−π−π2F32.(2)
Interparticle diffusionThe model assumes interparticle diffusion control the adsorption rate, the model is given by the following expression [26, 27]:
(15)qtqe=1−6π2∑n=1∞1n2exp−n2π2Dctrp2,where qt is adsorption amount at time t, qe is adsorption amount at infinite time, Dc is interparticle diffusion coefficient, and rp is the radius of the particle. When qt/qe value is >70%, Eq. (15) can be simplified to [26]:
(16)qtqe=1−6π2exp−π2Dctrp2.By plottingln1−qt/qe versus t, the linear slope is −π2Dc/r2p and the intercept is ln6/π2.
(3)
Intraparticle diffusionIf the HF adsorption process on zeolite 3A is controlled by intraparticle diffusion, the HF adsorption (qt) should change linearly with time square root (t1/2) [26, 27]. The intraparticle diffusion model assumes three steps typically in adsorption: bulk or film diffusion, gradual adsorption, and the final adsorption equilibrium [26]. The intraparticle diffusion model can be used for determining the adsorption mechanism, and the model is given by [29]:
(17)qt=kit1/2+C,where ki is the intraparticle diffusion constant and C is the intercept. The intercept value is related to the film thickness. A large intercept value suggests a great film effect.


## 2.1. Materials

Zeolite 3A (8(K12[(AlO2)12(SiO2)12]·24H2O) used in this study was commercial zeolite manufactured by Lu Xinyuan Company (Henan, China). In this investigation, spherical 3A particles of 0.2 cm radius were studied. Hydrogen fluoride and helium with a purity of 99.99% were provided by China Shipbuilding (Handan) Perry Special Gas Co., Ltd.


## 2.2. Characterization of the Zeolite 3A

The compositions were measured by X-ray diffraction (XRD) using a Rigaku Smartlab 9kW with Cu Kα radiation (40 kV and 40 mA). The Fourier transform-infrared (FT-IR) of zeolite 3A spectra was obtained from an FT-IR spectrometer (Thermo Nicolet iS5, USA) using pellets of zeolite/KBr. The surface morphology was obtained by SEM (Zeiss sigma500) at an accelerating voltage of 10 kV. The pore structure distribution (PSD) of zeolite 3A was measured by the low-temperature CO2 adsorption method at 273 K using 3H-2000 PM.


## 2.3. Adsorption Isotherm and Kinetics Measurements

Equilibrium and kinetics measurements of HF adsorption on zeolite 3A were performed in a static volumetric instrument. The detailed composition of the experimental instrument is shown in Figure1. The pressures of the experimental system were recorded using a precision pressure sensor (Keller, Switzerland, ±0.01% precision). An automatic thermostatic oil bath with ±0.01 K accuracy was used to keep the system temperature constant.Figure 1
A schematic of experimental setup for HF adsorption.The main experimental procedures for equilibria and kinetics adsorption are:(1)
Sample pretreatment and filling. The 3A sample used in the adsorption experiment was first dried in the drying oven at 385 K for 24 h, weighed, and then quickly transferred to the sample cell. The constant temperature of the oil bath was set to 358 K and vacuumed for 12 h to remove the water and other impurities adsorbed in the sample transfer process(2)
Leakage test for adsorption system. After the sample pretreatment, the temperature of the oil bath was set to 338 K. After the system temperature is constant, helium (He) was fed into the reference and adsorption cells to a certain value (maximum pressure required for adsorption). The leakage testing time was 12 h. The system was heated and vacuumed for 4 h after the leakage test(3)
Measurement of void volume. The void volume of the adsorption cell filled with adsorbent was measured by the helium expansion method. The temperature for the helium expansion test was set to the adsorption experimental temperature. The helium density used in void volume measurement is calculated by the BWR equation [21]. Helium expansion tests were repeated at least four times and the values were averaged to minimize error(4)
Equilibrium adsorption experiment. A certain HF amount was injected into the reference cell when the temperature of the adsorption system was constant with the experimental setting value. The gas pressure for the reference cell was recorded until it is stable. The valve between the reference and sample cells was opened, the HF flowed into the sample cell from the reference cell and the adsorption began. The system pressure was recorded when the system pressure was constant for 5 h. The above operations were repeated until the maximum pressure point of the equilibrium adsorption is reached(5)
Adsorption kinetics experiment. HF was injected into the reference cell to a calculated pressure value when the temperature of the adsorption system was constant with the experimental set value. The valve between the reference and sample cells was then opened, the HF flowed into the adsorption cell, and the system pressure was recorded in real time by the high-precision pressure transmitter until the final system pressure was stabilized at the desired value. The kinetic experimental conditions were 0.15, 0.35, 0.5, 0.70, 0.95, and 1.10 bar at 298 K and 298, 308, 318, 328, and 338 K at 0.5 barDuring the experiment, the calculation process for HF adsorption capacity was based on the mass conservation under the ideal gas state, so the adsorption capacity is [19]:
(1)q=1RTp0VR−p1VR+Vv,where q is the adsorption capacity, p0 is the gas pressure in the reference cell before adsorption and p1 is the system gas pressure during the adsorption process. R and T are the ideal gas constant and the system temperature, respectively.


## 2.4. Adsorption Theory

### 2.4.1. Isotherm Models

The relationship between adsorption capacity, temperature, and pressure in the adsorption process is usually described by the adsorption model. The Langmuir and Freundlich models had been successful in adapting the described HF adsorption process [11, 12]. The DA model is often used to describe the gas adsorption in micropores [22]. The DA model is expressed as follows:
(2)q=qmexp−RTElnp0pn,where q and qm are the adsorption capacity and saturated adsorption capacity of gas, p0 is the saturated vapor pressure of gas, and E is the adsorption characteristic energy.The saturated vapor pressurep0 of HF is calculated by the Antoine equation with extension [23]:
(3)log10p0=A+BT+Clog10T+DT+ET2,where the values of A, B, C, D, and E are 23.7347, −1799.6, −6.1764, 5.0046 × 10−10, and 6.15 × 10−6, respectively. The unit of p0 is mmHg in the calculation formula, which needs to be multiplied by 0.0013332 to convert to bar. The calculated saturated vapor pressures of 298, 308, 318, 328, and 338 K are 1.215, 1.678, 2.223, 3.130, and 4.149 bar, respectively.


### 2.4.2. Heat of Adsorption

The isosteric heat of adsorption is an important thermodynamic parameter which indicates that heat released since the adsorbed state is more stable than the unadsorbed state for adsorbate molecule [24]. The Clausius–Clapeyron equation was used to calculate the isosteric heat at constant adsorption capacity, and its expression is as follows [24]:
(4)Hst=−R∂lnp∂1/Tq,where Hst is the calculated isosteric heat at the adsorption capacity q.The isosteric heat of adsorption (Hst) can be obtained by combining the DA model with the Clausius–Clapeyron equation [24]:
(5)Hst=E−lnθ1/n+αTn−lnθ1−n/n+hfg,where α is the thermal expansion coefficient of adsorbed phase and α is calculated by 1/T. hfg is the enthalpy of evaporation, which is expressed as follows:
(6)hfg=−R∂lnp0∂1/TC.


### 2.4.3. Adsorption Kinetics

(1) Adsorption Rate Models. The pseudo first-order (PFO) model assumes that the adsorption rate is directly proportional to the number of active sites. The rate expression is given by [25, 26]:
(7)dq/dt=k1q1−q,where q1 and q represent the adsorption capacity at equilibrium and time t, respectively, and k1 is the first-order rate constant.After integrating Eq. (7) with the boundary conditions (t =0, q =0 and t=t∞, q=q1),
(8)q=q11−e−k1t.The pseudo second-order model (PSO) assumes the adsorption rate is proportional to the square of number of active sites; therefore, the rate model is given by [25, 26]:
(9)dq/dt=k2q2−q2,where q2 represents the equilibrium adsorption capacity, and k2 is the second-order rate constant.With the boundary conditions (t =0, q =0 and t=t∞, q=q2), the PSO is given by [25, 26]:
(10)q=k2q22t/1+k2q2t.(2) Diffusion Models.
(1)
Film diffusionBoyd’s film diffusion model assumes that the main diffusion resistance is boundary film around the adsorbent particles [26, 27]. Therefore, the model was used to distinguish whether the film diffusion was a rate-controlling step in HF adsorption on 3A. The expression of this model is given by [26]:
(11)F=1−6π2∑n=1∞1n2exp−n2Bt,whereF is the fraction at times t and can be expressed using adsorption capacity:
(12)F=qtqm.Bt can be expressed in F [28]:whenF>0.85,
(13)Bt=−0.4977−ln1−F,when F<0.85,
(14)Bt=π−π−π2F32.(2)
Interparticle diffusionThe model assumes interparticle diffusion control the adsorption rate, the model is given by the following expression [26, 27]:
(15)qtqe=1−6π2∑n=1∞1n2exp−n2π2Dctrp2,where qt is adsorption amount at time t, qe is adsorption amount at infinite time, Dc is interparticle diffusion coefficient, and rp is the radius of the particle. When qt/qe value is >70%, Eq. (15) can be simplified to [26]:
(16)qtqe=1−6π2exp−π2Dctrp2.By plottingln1−qt/qe versus t, the linear slope is −π2Dc/r2p and the intercept is ln6/π2.
(3)
Intraparticle diffusionIf the HF adsorption process on zeolite 3A is controlled by intraparticle diffusion, the HF adsorption (qt) should change linearly with time square root (t1/2) [26, 27]. The intraparticle diffusion model assumes three steps typically in adsorption: bulk or film diffusion, gradual adsorption, and the final adsorption equilibrium [26]. The intraparticle diffusion model can be used for determining the adsorption mechanism, and the model is given by [29]:
(17)qt=kit1/2+C,where ki is the intraparticle diffusion constant and C is the intercept. The intercept value is related to the film thickness. A large intercept value suggests a great film effect.


## 2.4.1. Isotherm Models

The relationship between adsorption capacity, temperature, and pressure in the adsorption process is usually described by the adsorption model. The Langmuir and Freundlich models had been successful in adapting the described HF adsorption process [11, 12]. The DA model is often used to describe the gas adsorption in micropores [22]. The DA model is expressed as follows:
(2)q=qmexp−RTElnp0pn,where q and qm are the adsorption capacity and saturated adsorption capacity of gas, p0 is the saturated vapor pressure of gas, and E is the adsorption characteristic energy.The saturated vapor pressurep0 of HF is calculated by the Antoine equation with extension [23]:
(3)log10p0=A+BT+Clog10T+DT+ET2,where the values of A, B, C, D, and E are 23.7347, −1799.6, −6.1764, 5.0046 × 10−10, and 6.15 × 10−6, respectively. The unit of p0 is mmHg in the calculation formula, which needs to be multiplied by 0.0013332 to convert to bar. The calculated saturated vapor pressures of 298, 308, 318, 328, and 338 K are 1.215, 1.678, 2.223, 3.130, and 4.149 bar, respectively.


## 2.4.2. Heat of Adsorption

The isosteric heat of adsorption is an important thermodynamic parameter which indicates that heat released since the adsorbed state is more stable than the unadsorbed state for adsorbate molecule [24]. The Clausius–Clapeyron equation was used to calculate the isosteric heat at constant adsorption capacity, and its expression is as follows [24]:
(4)Hst=−R∂lnp∂1/Tq,where Hst is the calculated isosteric heat at the adsorption capacity q.The isosteric heat of adsorption (Hst) can be obtained by combining the DA model with the Clausius–Clapeyron equation [24]:
(5)Hst=E−lnθ1/n+αTn−lnθ1−n/n+hfg,where α is the thermal expansion coefficient of adsorbed phase and α is calculated by 1/T. hfg is the enthalpy of evaporation, which is expressed as follows:
(6)hfg=−R∂lnp0∂1/TC.


## 2.4.3. Adsorption Kinetics

(1) Adsorption Rate Models. The pseudo first-order (PFO) model assumes that the adsorption rate is directly proportional to the number of active sites. The rate expression is given by [25, 26]:
(7)dq/dt=k1q1−q,where q1 and q represent the adsorption capacity at equilibrium and time t, respectively, and k1 is the first-order rate constant.After integrating Eq. (7) with the boundary conditions (t =0, q =0 and t=t∞, q=q1),
(8)q=q11−e−k1t.The pseudo second-order model (PSO) assumes the adsorption rate is proportional to the square of number of active sites; therefore, the rate model is given by [25, 26]:
(9)dq/dt=k2q2−q2,where q2 represents the equilibrium adsorption capacity, and k2 is the second-order rate constant.With the boundary conditions (t =0, q =0 and t=t∞, q=q2), the PSO is given by [25, 26]:
(10)q=k2q22t/1+k2q2t.(2) Diffusion Models.
(1)
Film diffusionBoyd’s film diffusion model assumes that the main diffusion resistance is boundary film around the adsorbent particles [26, 27]. Therefore, the model was used to distinguish whether the film diffusion was a rate-controlling step in HF adsorption on 3A. The expression of this model is given by [26]:
(11)F=1−6π2∑n=1∞1n2exp−n2Bt,whereF is the fraction at times t and can be expressed using adsorption capacity:
(12)F=qtqm.Bt can be expressed in F [28]:whenF>0.85,
(13)Bt=−0.4977−ln1−F,when F<0.85,
(14)Bt=π−π−π2F32.(2)
Interparticle diffusionThe model assumes interparticle diffusion control the adsorption rate, the model is given by the following expression [26, 27]:
(15)qtqe=1−6π2∑n=1∞1n2exp−n2π2Dctrp2,where qt is adsorption amount at time t, qe is adsorption amount at infinite time, Dc is interparticle diffusion coefficient, and rp is the radius of the particle. When qt/qe value is >70%, Eq. (15) can be simplified to [26]:
(16)qtqe=1−6π2exp−π2Dctrp2.By plottingln1−qt/qe versus t, the linear slope is −π2Dc/r2p and the intercept is ln6/π2.
(3)
Intraparticle diffusionIf the HF adsorption process on zeolite 3A is controlled by intraparticle diffusion, the HF adsorption (qt) should change linearly with time square root (t1/2) [26, 27]. The intraparticle diffusion model assumes three steps typically in adsorption: bulk or film diffusion, gradual adsorption, and the final adsorption equilibrium [26]. The intraparticle diffusion model can be used for determining the adsorption mechanism, and the model is given by [29]:
(17)qt=kit1/2+C,where ki is the intraparticle diffusion constant and C is the intercept. The intercept value is related to the film thickness. A large intercept value suggests a great film effect.


## 3. Results and Discussion

### 3.1. Characterizations of the Zeolite 3A

The powder XRD pattern of zeolite 3A is shown in Figure2. The XRD characteristic diffraction peaks are in accordance with 3A crystals by Wang [30], indicating that the sample is a typical 3A zeolite. The FT-IR of zeolite 3A spectra is shown in Figure 3. The broad bands around 3,447.9 cm−1 belong to the stretching vibration of the O-H group. The bands at around 1,659.3 cm−1 belong to the bending and tensile vibrations of the O-H and Si-OH groups, respectively [31]. At about 1,005.5, 665.8, and 462.9 cm−1, three typical absorption peaks formed by amorphous aluminosilicate structure were observed, which belong to the asymmetric tensile vibration of the tetrahedron in the sample, the symmetric tensile vibration of the Si-O-Si bond, and the bending vibration of T-O (T is Si or Al) bond, respectively [31]. The same absorption peaks have also been found by Cao et al. [31]. The absorption peak at 554.6 cm−1 belongs to the vibration of double binary ring D4R, the main subunit structure unit of zeolite 3A.Figure 2
XRD pattern of zeolite 3A.Figure 3
IR spectra of zeolite 3A.The surface morphology of zeolite 3A is shown in Figure4, which indicates that the surfaces of the samples are not homogeneous. Zeolite 3A has a large grain size, good dispersibility, and many surface fractures, which has also been found in the literature [30]. The low-temperature CO2 isotherm and PSD of zeolite 3A are shown in Figure 5. The pore size of zeolite 3A is mainly concentrated at ~0.3 and 0.37 nm. The specific surface area of zeolite 3A and the pore volume are 402.81 m2/g and 0.1325 cm3/g, respectively.Figure 4
SEM images of zeolite 3A.Figure 5
(a) Low-temperature CO2 isotherm. (b) PSD of zeolite 3A.
(a)(b)


### 3.2. Adsorption Equilibrium

#### 3.2.1. Adsorption Isotherms

The HF adsorption isotherms on zeolite 3A at 298 to 338 K are shown in Figure6. All adsorption isotherms are type I according to the IUPAC classification. The adsorption amount of HF on zeolite 3A is close to that on activated carbon by Shen et al. [15] but less than that on activated carbon by Bahrami et al. [19] and MOF [18], which is mainly due to the pore characteristics and surface physicochemical properties of the adsorbent. The adsorption capacity increases with increasing pressure at the same temperature. The adsorption capacity decreases with the temperature increase because the binding strength of the zeolite 3A surface decreases with temperature, indicating that the HF adsorption on the zeolite 3A surface is exothermic. The Langmuir, Freundlich, and DA models were used to correlate the HF adsorption data using regression analysis [19]. Three statistical functions, including SSE, RMSE, and χ2, were used to estimate the goodness of fit [24].Figure 6
Adsorption isotherm and DA fitting of HF on zeolite 3A.The fitting parameter values for the three models are listed in Table1. The Langmuir parameters q0 and bL all decreased with the increasing temperature, which implied that the bonding of HF to zeolite decreased. The Freundlich parameter kF represents the adsorption capacity, and n shows the adsorption driving force and indicates the favourability of adsorption [10]. The kF values showed a negative correlation with temperature. The n values (1.271–1.368), determined from the Freundlich model suggested the moderately difficult nature of HF adsorption on zeolite 3A [10]. The same results for the Freundlich parameter n have been found in HF adsorption on produced NaF pellets and activated carbon [10–12].Table 1
Fitting results of the studied isotherm model.
ModelFitting parametersTemperature (K)298308318328338Langmuirq0/mg·g-11.0270.9880.9210.8750.827bL/bar-10.6180.5710.5540.5050.481SSE/×10-53.7534.3013.8624.1533.922RMSE/%0.3670.4350.3740.4320.389χ2/%0.0150.0270.0220.0190.023FreundlichkF/mg·g-10.3940.3590.3310.2920.270n1.3601.3681.3021.3731.271SSE/×10-54.2734.6814.3814.8724.396RMSE/%0.3740.4240.3950.4330.416χ2/%0.0170.0240.0230.0200.021DAqm/mg·g-10.43300.49130.52360.54520.5631E/J·mol-13472.043753.224146.694523.535005.89n1.19261.21861.24231.29471.3568SSE/×10-53.0852.7232.9512.8433.021RMSE/%0.3060.3550.3930.3470.316χ2/%0.0140.0170.0160.0140.014The values of SSE, RMSE, andχ2 in Table 1 for the DA model are the smallest among the three adsorption models, which indicates that the DA model predicted the adsorption data better than the other models. Figure 6 also shows the predicted HF adsorption data by the DA model. The DA model can describe well the HF adsorption curve, indicating that micropore filling existed in HF adsorption on zeolite 3A. Both characteristic energy E and DA parameter n increased with the increase of temperature. The DA parameter n can be used to describe the surface heterogeneity of the adsorbent [13, 24]. The study shows that the closer the n value is to 1, the higher the heterogeneity of the zeolite 3A surface, which is more related to the active adsorption site at low temperatures. The n value shows a positive correlation with the characteristics energy value E (Figure 7). The lower n value results in E value.Figure 7
Linear relationship between DA parametern and E.The regeneration of 3A zeolite affects the reuse of materials [18]. The adsorption capacity after regeneration was tested at 298 K. The zeolite 3A after HF adsorption was treated at 393 K in the muffle furnace for 12 h and then quickly transferred and sealed to the adsorption equipment (sample cell in Figure 5) and then vacuumed at 373 K for 10 h to reactivate its capacity. The HF repeatability experiments on zeolite 3A at 298 K are shown in Figure 8(a). The remaining HF capacity after regeneration was slightly reduced, which suggested the high stability of exposure to dry HF gas. The IR spectra of the zeolite 3A before and after HF adsorption are shown in Figure 8(b), suggesting no change in the surface functional group of the zeolite 3A molecular sieve after HF adsorption.Figure 8
(a) Repeatability experiments of HF on zeolite 3A at 298 K. (b) IR spectra of the zeolite 3A before and after HF adsorption.
(a)(b)


#### 3.2.2. Heat of Adsorption

The isosteric heat of adsorption (Hst) calculated using Eq. (5) is plotted with the HF surface load (q/qm), as shown in Figure 9. Hst values of HF on zeolite 3A decrease with the increase of surface loading, which indicates the surface energy heterogeneity of zeolite 3A. A large number of vacant adsorption sites exist on the zeolite 3A surface at the initial stage, which results in strong interaction between the HF molecules and zeolite 3A. Therefore, the Hst value is high at the initial adsorption stage. With further adsorption capacity increase, the adsorption sites are occupied, resulting in the weakening of the interaction between the HF molecules and zeolite 3A. Therefore, Hst decreases with the surface loading.Figure 9
The isosteric heat of adsorption (Hst) of HF.


### 3.3. Adsorption Kinetics

#### 3.3.1. Effect of Pressure on Adsorption Kinetic

The adsorption kinetic curve of HF on zeolite 3A at 298 K is shown in Figure10. The adsorption capacity continuously increases with the adsorption time. The adsorption capacity rapidly increases in the initial stage, which is mainly due to the high adsorption energy sites on the adsorbent surface and the rapid occupation of HF molecules onto the adsorption sites, so the adsorption rate is high. When large numbers of active adsorption sites are occupied, the adsorption sites available for HF molecules become less; hence, the adsorption rate becomes slow. When the active sites are almost occupied, HF molecules reach dynamic equilibrium on the surface of zeolite 3A. At this time, the number of HF molecules on the adsorbent surface will not increase; therefore, the total adsorption rate tends to zero and the adsorption capacity will not increase.Figure 10
Dynamic curves of HF under different pressures at 298 K.(1) Adsorption Rate. The HF adsorption kinetics curves and the corresponding curves predicted by the PFO model are shown in Figure 10. The kinetic constants calculated with the PFO and PSO models and the characteristic parameters of the kinetic model are listed in Table 2. The larger R2 of the PFO model indicates a better predictivity of the adsorption kinetic process over the whole pressure range well, so the adsorption of HF by zeolite 3A follows simple first-order kinetics. The calculated q1 values from the PFO model are more in accordance with the experimental data than the calculated q2 values by the PSO model.Table 2
The fitting kinetic parameters for PFO and PSO.
Pressure (bar)Pseudo first-orderPseudo second-orderq1/mg·g-1k1/min-1R2q2/mg·g-1k2/g mg-1.Min-1R20.150.07440.03950.99990.08440.63520.97830.350.17680.04720.99980.19660.34850.97260.500.25800.05340.99980.28320.28590.96850.700.31530.06160.99970.34260.28630.96380.950.37460.06870.99980.40370.28060.96021.100.42060.07430.99970.45100.27750.9576Bothq1 and q2 increase with pressure, which is consistent with the high pressure is conducive to HF adsorption. Meanwhile, the PFO and PSO model parameters (k1 and k2) increase with pressure because the velocity of the HF molecule will increase and the migration speed of HF molecules inside the pores will be faster at higher pressure, leading to an increase in the diffusion rate. The increased mass transfer coefficient makes the kinetic curve steeper. The k1 values (0.0395–0.0743 min−1) for HF on zeolite 3A are larger than that of H2S (0.00177 min−1) on zeolite 3A, which suggested that the HF adsorption rate is faster than that of H2S [6, 32].(2) Diffusion Mechanism. The HF adsorption process on zeolite 3A can be divided into five continuous processes, as shown in Figure 11: (a) HF molecules diffuse from free state to adsorbent gas film (bulk diffusion), (b) HF molecules diffuse in the film (film diffusion), (c) HF molecules diffuse in pores between particles (interparticle diffusion), (d) HF molecules diffuse in 3A crystal (intraparticle diffusion), and (e) surface adsorption. Generally, surface adsorption and bulk diffusion are very fast, so they are ignored in the analysis of the HF adsorption kinetic process, and the role of the other three processes in the adsorption process is mainly considered.
(1)
Film diffusionFigure 11
Adsorption mechanism of HF on 3A zeolite.Equations (11)–(14) can be used to predict HF adsorption control by particle or film diffusion [26, 27]. By plotting Bt vs. time, the mass transfer rate is controlled by pore diffusion if the plot is a straight line passing through the origin [26–28]. If the curve is nonlinear or does not pass through the origin, film diffusion can also be considered to affect the adsorption rate [26–28]. The calculated Bt values as a function of time are shown in Figure 12, and the curves are not entirely linear. The slopes and intercepts of the film diffusion model at all pressures are given in Table 3. The existence of intercept values suggests that the rate-controlling process for HF adsorption on zeolite 3A is mainly controlled by external mass transfer [26]. The intercept increases close to zero with increasing pressure, which indicates that pore diffusion appears to be more important at slightly higher pressures.
(2)
Interparticle diffusionFigure 12
Plots of Boyd’s film model for HF adsorption on 3A.Table 3
Kinetic parameters of linear fitting of film diffusion model.
Pressure (bar)SlopeInterceptR20.150.03954−0.429920.997650.350.04693−0.427810.998720.500.05256−0.405660.999260.700.06069−0.409490.999330.950.0678−0.410980.999361.100.07321−0.410120.99936The fitting results for the adsorption kinetics data with the interparticle diffusion linear form are shown in Figure13 and Table 4. A good correlation between ln1−qt/qe with t indicates that the experimental data can be well described by the model. The Dc/r2p and Dc values calculated by the slope of the linear fit increase continuously with increasing pressure, indicating that high pressure favours the HF gas diffusion in zeolite 3A, which is consistent with the previous calculation that high pressure favours the adsorption rate. The order of magnitude of interparticle diffusion coefficient Dc of HF is 10−9 m2/s. The intercept values obtained by linear fitting the experimental data are not close to −0.4977 (ln6/π2), which indicates that the HF adsorption rate on zeolite 3A is not completely controlled by the interparticle diffusion. The calculated interparticle diffusion coefficient Dc/r2p versus first-order rate constant k1 does not satisfy the 1/15 relationship and also reflects that the HF diffusion over zeolite 3A is not completely controlled by interparticle diffusion [26].
(3)
Intraparticle diffusionFigure 13
Linear fitting for experimental data with interparticle diffusion model.Table 4
The linear fitting results for interparticle diffusion model.
Pressure (bar)SlopeInterceptDc/r2p (10-3 s-1)Dc (10-9 s-1)0.15−0.040850.090714.1431.0360.35−0.048090.061034.8771.2190.50−0.053380.000015.4141.3540.70−0.061560.000036.2441.5610.95−0.068730.000036.9711.7431.10−0.074240.000027.5301.882The intraparticle diffusion curves for HF adsorption on zeolite 3A are shown in Figure14. The curves are observed to be nonlinear. According to the intraparticle diffusion model, the adsorption amount qt plot vs. t1/2 should be a straight line and pass through the origin of the mass transfer rate solely controlled by intraparticle diffusion [26]. Multilinearity can be observed when different processes are related to the adsorption mechanism. The slope of each linear portion represents the corresponding adsorption rate [27]. The curves in Figure 14 show quart-linear characteristics, indicating the presence of four consecutive HF adsorption steps on zeolite 3A. The initial part, region I, was ascribed to the HF diffusion from the free state to and through the gas film of zeolite 3A, and the initial stage was associated with the HF film diffusion. The second and third parts, regions II and III describe the adsorption-progressive stage where diffusion occurs within the particle. Regions II and III are related to interparticle and intraparticle adsorptions, respectively. The fourth part, region IV, is the final equilibrium adsorption stage where the diffusion becomes slower owing to the active adsorption site saturation. Figure 14 shows that the extended line for straight lines corresponding to regions II and III does not pass through the origin, which may result from the different diffusion rates for the first and other stages of HF adsorption.Figure 14
Prediction of intraparticle diffusion model for HF adsorption on 3A.The adsorption rate of each HF molecule is controlled by four processes at a certain pressure. In the first stage, the adsorption rate is controlled by the film diffusion, as shown in segment I of Figure14. The interparticle diffusion would be the rate-controlling process when the HF molecules diffuse into the particle pore. The intraparticle diffusion then controls the rate. Finally, the rate is governed by surface adsorption. The slope of each linear segment before region IV can be used to deduce which stage controls the whole HF adsorption rate [27]. Moreover, Figure 14 shows that the linear slope in region III is the smallest. The linear portion with the lowest slope is the rate-controlling step [27, 28]. This suggests that HF diffusion into the 3A particle is slower and the intraparticle diffusion stage is the rate-controlling stage. The linear slopes for regions II and III gradually increase with increasing pressure, which may be because the film thickness decreases as the pressure rises and the film diffusion rate will increase.


#### 3.3.2. Effect of Temperature

Kinetic experiments at 298–338 K and 0.50 bar were conducted to investigate the effect of temperature on the HF kinetic adsorption on zeolites 3A. The HF adsorption kinetics curves at five temperatures are shown in Figure15. The HF kinetic curves at five temperatures can be divided into three different stages: rapid adsorption, slow adsorption, and adsorption equilibrium stages. The HF adsorption capacity gradually decreases with increasing temperature, which is consistent with the discovery in literature [19]. High temperature enables the HF molecules to obtain more energy to overcome the intermolecular force and electrostatic interaction; thus, HF molecules remain in the free state. Simultaneously, the affinity between HF molecules and zeolite 3A surface will be weakened by the increasing temperature and will result in the decrease in adsorption capacity. In addition, high temperature is not conducive to the formation of a more orderly and stable configuration of adsorbed molecules, resulting in the reduction of adsorption capacity. Higher temperature is not conducive to improving HF adsorption recovery. It can also be found that the time to reach equilibrium decreases with the increasing temperature, which also shows that the temperature is conducive to the gas adsorption rate.Figure 15
Dynamic curves of HF under different temperature at 0.5 bar.(1) Adsorption Rate. The PFO and PSO models were used to predict the HF adsorption kinetic curves. The fitting results are shown in Figure 15 and Table 5. The adsorption rate constants k1 and k2 of HF increase with temperature, indicating that the HF adsorption rate shows a positive correlation with temperature, which is due to the acceleration of molecular motion caused by temperature increase. q1 and q2 decrease with increasing temperature, suggesting that higher temperature is conducive to gas diffusion; however, it will reduce the gas adsorption capacity.Table 5
The fitting kinetic parameters for PFO and PSO.
Temperature (K)Pseudo first-orderPseudo second-orderq1 (mg/g)k1R2q2 (mg/g)k2R22980.25800.05340.98980.28320.28590.96853080.22130.05920.98730.24110.38610.97263180.19900.06330.98670.21570.47150.97243280.18030.06810.98970.19440.57570.96753380.16010.07330.98370.17180.71660.9523(2) Diffusion Mechanism.
(1)
Film diffusionThe calculatedBt values are shown in Figure 16. Moreover, Bt is not completely linear. The slope and intercept of Boyd’s film diffusion model are listed in Table 6. The existence of intercept value shows that the HF adsorption rate on zeolite 3A was mainly controlled by external mass transfer. The intercept values decrease slightly with increasing temperature, suggesting that pore diffusion become more important at high temperature. The Bt values show a positive correlation with temperature, indicating that the film diffusion rate increases with temperature increase.
(2)
Interparticle diffusionFigure 16
Plots of Boyd’s film model for HF adsorption on 3A.Table 6
Kinetic parameters of linear fitting of film diffusion model.
Temperature (K)SlopeInterceptR22980.0526−0.40480.97923080.0583−0.40420.98723180.0623−0.40540.98933280.0670−0.40440.98923380.0721−0.40320.9867The linear fitting results for the HF adsorption kinetic curve using the interparticle diffusion model at five temperatures and 0.5 bar are shown in Figure17 and Table 7. A good correlation between ln1−qt/qe shows that t indicates that the experimental data can be well described by the model. In addition, Table 7 shows that Dc/r2p and Dc values increase with increasing temperature. Based on molecular dynamics theory, the essence of HF diffusion in zeolite 3A is due to the molecular irregular thermal movement. The average kinetic energy of HF molecules increases with temperature, which leads to an increase in amplitude and frequency of molecular vibration. The higher molecular irregular thermal movement intensity occurs at a higher temperature. Consequently, the HF diffusion rate in zeolite 3A becomes faster.
(3)
Intraparticle diffusionFigure 17
Linear fitting for experimental data with interparticle diffusion model.Table 7
The linear fitting results for interparticle diffusion model.
Temperature (K)SlopeInterceptDc/r2p (10-3 s-1)Dc (10-9 s-1)298−0.05340.000015.4161.354308−0.0592−0.000036.0041.501318−0.06330.000086.4201.605328−0.0681−0.000016.9071.727338−0.07330.000017.4341.859The quart-linear characteristics for intraparticle diffusion curves can be observed in Figure18, which indicated that three different processes are involved in the adsorption mechanism. The curves of the five temperatures in the first stage I are relatively close, indicating that the influence of temperature on the HF diffusion velocity from the free state to and through the gas film of zeolite 3A is little. In the second and third stages, the difference between the five curves increases with time. The linear slope for each stage decreases with increasing temperature, suggesting that the pore diffusion rate in the particles decreases slightly at this stage, which may be due to the impediment of diffusion by the interaction of HF molecules under high pressure. The same trend is also found in CO2 in porous MgO [27]. The extended line for straight lines corresponding to regions II and III does not pass through the origin. The linear portion for stage III with the lowest slope indicates that the diffusion rate is controlled by intraparticle diffusion.Figure 18
Prediction of intraparticle diffusion model for HF adsorption on 3A.


## 3.1. Characterizations of the Zeolite 3A

The powder XRD pattern of zeolite 3A is shown in Figure2. The XRD characteristic diffraction peaks are in accordance with 3A crystals by Wang [30], indicating that the sample is a typical 3A zeolite. The FT-IR of zeolite 3A spectra is shown in Figure 3. The broad bands around 3,447.9 cm−1 belong to the stretching vibration of the O-H group. The bands at around 1,659.3 cm−1 belong to the bending and tensile vibrations of the O-H and Si-OH groups, respectively [31]. At about 1,005.5, 665.8, and 462.9 cm−1, three typical absorption peaks formed by amorphous aluminosilicate structure were observed, which belong to the asymmetric tensile vibration of the tetrahedron in the sample, the symmetric tensile vibration of the Si-O-Si bond, and the bending vibration of T-O (T is Si or Al) bond, respectively [31]. The same absorption peaks have also been found by Cao et al. [31]. The absorption peak at 554.6 cm−1 belongs to the vibration of double binary ring D4R, the main subunit structure unit of zeolite 3A.Figure 2
XRD pattern of zeolite 3A.Figure 3
IR spectra of zeolite 3A.The surface morphology of zeolite 3A is shown in Figure4, which indicates that the surfaces of the samples are not homogeneous. Zeolite 3A has a large grain size, good dispersibility, and many surface fractures, which has also been found in the literature [30]. The low-temperature CO2 isotherm and PSD of zeolite 3A are shown in Figure 5. The pore size of zeolite 3A is mainly concentrated at ~0.3 and 0.37 nm. The specific surface area of zeolite 3A and the pore volume are 402.81 m2/g and 0.1325 cm3/g, respectively.Figure 4
SEM images of zeolite 3A.Figure 5
(a) Low-temperature CO2 isotherm. (b) PSD of zeolite 3A.
(a)(b)


## 3.2. Adsorption Equilibrium

### 3.2.1. Adsorption Isotherms

The HF adsorption isotherms on zeolite 3A at 298 to 338 K are shown in Figure6. All adsorption isotherms are type I according to the IUPAC classification. The adsorption amount of HF on zeolite 3A is close to that on activated carbon by Shen et al. [15] but less than that on activated carbon by Bahrami et al. [19] and MOF [18], which is mainly due to the pore characteristics and surface physicochemical properties of the adsorbent. The adsorption capacity increases with increasing pressure at the same temperature. The adsorption capacity decreases with the temperature increase because the binding strength of the zeolite 3A surface decreases with temperature, indicating that the HF adsorption on the zeolite 3A surface is exothermic. The Langmuir, Freundlich, and DA models were used to correlate the HF adsorption data using regression analysis [19]. Three statistical functions, including SSE, RMSE, and χ2, were used to estimate the goodness of fit [24].Figure 6
Adsorption isotherm and DA fitting of HF on zeolite 3A.The fitting parameter values for the three models are listed in Table1. The Langmuir parameters q0 and bL all decreased with the increasing temperature, which implied that the bonding of HF to zeolite decreased. The Freundlich parameter kF represents the adsorption capacity, and n shows the adsorption driving force and indicates the favourability of adsorption [10]. The kF values showed a negative correlation with temperature. The n values (1.271–1.368), determined from the Freundlich model suggested the moderately difficult nature of HF adsorption on zeolite 3A [10]. The same results for the Freundlich parameter n have been found in HF adsorption on produced NaF pellets and activated carbon [10–12].Table 1
Fitting results of the studied isotherm model.
ModelFitting parametersTemperature (K)298308318328338Langmuirq0/mg·g-11.0270.9880.9210.8750.827bL/bar-10.6180.5710.5540.5050.481SSE/×10-53.7534.3013.8624.1533.922RMSE/%0.3670.4350.3740.4320.389χ2/%0.0150.0270.0220.0190.023FreundlichkF/mg·g-10.3940.3590.3310.2920.270n1.3601.3681.3021.3731.271SSE/×10-54.2734.6814.3814.8724.396RMSE/%0.3740.4240.3950.4330.416χ2/%0.0170.0240.0230.0200.021DAqm/mg·g-10.43300.49130.52360.54520.5631E/J·mol-13472.043753.224146.694523.535005.89n1.19261.21861.24231.29471.3568SSE/×10-53.0852.7232.9512.8433.021RMSE/%0.3060.3550.3930.3470.316χ2/%0.0140.0170.0160.0140.014The values of SSE, RMSE, andχ2 in Table 1 for the DA model are the smallest among the three adsorption models, which indicates that the DA model predicted the adsorption data better than the other models. Figure 6 also shows the predicted HF adsorption data by the DA model. The DA model can describe well the HF adsorption curve, indicating that micropore filling existed in HF adsorption on zeolite 3A. Both characteristic energy E and DA parameter n increased with the increase of temperature. The DA parameter n can be used to describe the surface heterogeneity of the adsorbent [13, 24]. The study shows that the closer the n value is to 1, the higher the heterogeneity of the zeolite 3A surface, which is more related to the active adsorption site at low temperatures. The n value shows a positive correlation with the characteristics energy value E (Figure 7). The lower n value results in E value.Figure 7
Linear relationship between DA parametern and E.The regeneration of 3A zeolite affects the reuse of materials [18]. The adsorption capacity after regeneration was tested at 298 K. The zeolite 3A after HF adsorption was treated at 393 K in the muffle furnace for 12 h and then quickly transferred and sealed to the adsorption equipment (sample cell in Figure 5) and then vacuumed at 373 K for 10 h to reactivate its capacity. The HF repeatability experiments on zeolite 3A at 298 K are shown in Figure 8(a). The remaining HF capacity after regeneration was slightly reduced, which suggested the high stability of exposure to dry HF gas. The IR spectra of the zeolite 3A before and after HF adsorption are shown in Figure 8(b), suggesting no change in the surface functional group of the zeolite 3A molecular sieve after HF adsorption.Figure 8
(a) Repeatability experiments of HF on zeolite 3A at 298 K. (b) IR spectra of the zeolite 3A before and after HF adsorption.
(a)(b)


### 3.2.2. Heat of Adsorption

The isosteric heat of adsorption (Hst) calculated using Eq. (5) is plotted with the HF surface load (q/qm), as shown in Figure 9. Hst values of HF on zeolite 3A decrease with the increase of surface loading, which indicates the surface energy heterogeneity of zeolite 3A. A large number of vacant adsorption sites exist on the zeolite 3A surface at the initial stage, which results in strong interaction between the HF molecules and zeolite 3A. Therefore, the Hst value is high at the initial adsorption stage. With further adsorption capacity increase, the adsorption sites are occupied, resulting in the weakening of the interaction between the HF molecules and zeolite 3A. Therefore, Hst decreases with the surface loading.Figure 9
The isosteric heat of adsorption (Hst) of HF.


## 3.2.1. Adsorption Isotherms

The HF adsorption isotherms on zeolite 3A at 298 to 338 K are shown in Figure6. All adsorption isotherms are type I according to the IUPAC classification. The adsorption amount of HF on zeolite 3A is close to that on activated carbon by Shen et al. [15] but less than that on activated carbon by Bahrami et al. [19] and MOF [18], which is mainly due to the pore characteristics and surface physicochemical properties of the adsorbent. The adsorption capacity increases with increasing pressure at the same temperature. The adsorption capacity decreases with the temperature increase because the binding strength of the zeolite 3A surface decreases with temperature, indicating that the HF adsorption on the zeolite 3A surface is exothermic. The Langmuir, Freundlich, and DA models were used to correlate the HF adsorption data using regression analysis [19]. Three statistical functions, including SSE, RMSE, and χ2, were used to estimate the goodness of fit [24].Figure 6
Adsorption isotherm and DA fitting of HF on zeolite 3A.The fitting parameter values for the three models are listed in Table1. The Langmuir parameters q0 and bL all decreased with the increasing temperature, which implied that the bonding of HF to zeolite decreased. The Freundlich parameter kF represents the adsorption capacity, and n shows the adsorption driving force and indicates the favourability of adsorption [10]. The kF values showed a negative correlation with temperature. The n values (1.271–1.368), determined from the Freundlich model suggested the moderately difficult nature of HF adsorption on zeolite 3A [10]. The same results for the Freundlich parameter n have been found in HF adsorption on produced NaF pellets and activated carbon [10–12].Table 1
Fitting results of the studied isotherm model.
ModelFitting parametersTemperature (K)298308318328338Langmuirq0/mg·g-11.0270.9880.9210.8750.827bL/bar-10.6180.5710.5540.5050.481SSE/×10-53.7534.3013.8624.1533.922RMSE/%0.3670.4350.3740.4320.389χ2/%0.0150.0270.0220.0190.023FreundlichkF/mg·g-10.3940.3590.3310.2920.270n1.3601.3681.3021.3731.271SSE/×10-54.2734.6814.3814.8724.396RMSE/%0.3740.4240.3950.4330.416χ2/%0.0170.0240.0230.0200.021DAqm/mg·g-10.43300.49130.52360.54520.5631E/J·mol-13472.043753.224146.694523.535005.89n1.19261.21861.24231.29471.3568SSE/×10-53.0852.7232.9512.8433.021RMSE/%0.3060.3550.3930.3470.316χ2/%0.0140.0170.0160.0140.014The values of SSE, RMSE, andχ2 in Table 1 for the DA model are the smallest among the three adsorption models, which indicates that the DA model predicted the adsorption data better than the other models. Figure 6 also shows the predicted HF adsorption data by the DA model. The DA model can describe well the HF adsorption curve, indicating that micropore filling existed in HF adsorption on zeolite 3A. Both characteristic energy E and DA parameter n increased with the increase of temperature. The DA parameter n can be used to describe the surface heterogeneity of the adsorbent [13, 24]. The study shows that the closer the n value is to 1, the higher the heterogeneity of the zeolite 3A surface, which is more related to the active adsorption site at low temperatures. The n value shows a positive correlation with the characteristics energy value E (Figure 7). The lower n value results in E value.Figure 7
Linear relationship between DA parametern and E.The regeneration of 3A zeolite affects the reuse of materials [18]. The adsorption capacity after regeneration was tested at 298 K. The zeolite 3A after HF adsorption was treated at 393 K in the muffle furnace for 12 h and then quickly transferred and sealed to the adsorption equipment (sample cell in Figure 5) and then vacuumed at 373 K for 10 h to reactivate its capacity. The HF repeatability experiments on zeolite 3A at 298 K are shown in Figure 8(a). The remaining HF capacity after regeneration was slightly reduced, which suggested the high stability of exposure to dry HF gas. The IR spectra of the zeolite 3A before and after HF adsorption are shown in Figure 8(b), suggesting no change in the surface functional group of the zeolite 3A molecular sieve after HF adsorption.Figure 8
(a) Repeatability experiments of HF on zeolite 3A at 298 K. (b) IR spectra of the zeolite 3A before and after HF adsorption.
(a)(b)


## 3.2.2. Heat of Adsorption

The isosteric heat of adsorption (Hst) calculated using Eq. (5) is plotted with the HF surface load (q/qm), as shown in Figure 9. Hst values of HF on zeolite 3A decrease with the increase of surface loading, which indicates the surface energy heterogeneity of zeolite 3A. A large number of vacant adsorption sites exist on the zeolite 3A surface at the initial stage, which results in strong interaction between the HF molecules and zeolite 3A. Therefore, the Hst value is high at the initial adsorption stage. With further adsorption capacity increase, the adsorption sites are occupied, resulting in the weakening of the interaction between the HF molecules and zeolite 3A. Therefore, Hst decreases with the surface loading.Figure 9
The isosteric heat of adsorption (Hst) of HF.


## 3.3. Adsorption Kinetics

### 3.3.1. Effect of Pressure on Adsorption Kinetic

The adsorption kinetic curve of HF on zeolite 3A at 298 K is shown in Figure10. The adsorption capacity continuously increases with the adsorption time. The adsorption capacity rapidly increases in the initial stage, which is mainly due to the high adsorption energy sites on the adsorbent surface and the rapid occupation of HF molecules onto the adsorption sites, so the adsorption rate is high. When large numbers of active adsorption sites are occupied, the adsorption sites available for HF molecules become less; hence, the adsorption rate becomes slow. When the active sites are almost occupied, HF molecules reach dynamic equilibrium on the surface of zeolite 3A. At this time, the number of HF molecules on the adsorbent surface will not increase; therefore, the total adsorption rate tends to zero and the adsorption capacity will not increase.Figure 10
Dynamic curves of HF under different pressures at 298 K.(1) Adsorption Rate. The HF adsorption kinetics curves and the corresponding curves predicted by the PFO model are shown in Figure 10. The kinetic constants calculated with the PFO and PSO models and the characteristic parameters of the kinetic model are listed in Table 2. The larger R2 of the PFO model indicates a better predictivity of the adsorption kinetic process over the whole pressure range well, so the adsorption of HF by zeolite 3A follows simple first-order kinetics. The calculated q1 values from the PFO model are more in accordance with the experimental data than the calculated q2 values by the PSO model.Table 2
The fitting kinetic parameters for PFO and PSO.
Pressure (bar)Pseudo first-orderPseudo second-orderq1/mg·g-1k1/min-1R2q2/mg·g-1k2/g mg-1.Min-1R20.150.07440.03950.99990.08440.63520.97830.350.17680.04720.99980.19660.34850.97260.500.25800.05340.99980.28320.28590.96850.700.31530.06160.99970.34260.28630.96380.950.37460.06870.99980.40370.28060.96021.100.42060.07430.99970.45100.27750.9576Bothq1 and q2 increase with pressure, which is consistent with the high pressure is conducive to HF adsorption. Meanwhile, the PFO and PSO model parameters (k1 and k2) increase with pressure because the velocity of the HF molecule will increase and the migration speed of HF molecules inside the pores will be faster at higher pressure, leading to an increase in the diffusion rate. The increased mass transfer coefficient makes the kinetic curve steeper. The k1 values (0.0395–0.0743 min−1) for HF on zeolite 3A are larger than that of H2S (0.00177 min−1) on zeolite 3A, which suggested that the HF adsorption rate is faster than that of H2S [6, 32].(2) Diffusion Mechanism. The HF adsorption process on zeolite 3A can be divided into five continuous processes, as shown in Figure 11: (a) HF molecules diffuse from free state to adsorbent gas film (bulk diffusion), (b) HF molecules diffuse in the film (film diffusion), (c) HF molecules diffuse in pores between particles (interparticle diffusion), (d) HF molecules diffuse in 3A crystal (intraparticle diffusion), and (e) surface adsorption. Generally, surface adsorption and bulk diffusion are very fast, so they are ignored in the analysis of the HF adsorption kinetic process, and the role of the other three processes in the adsorption process is mainly considered.
(1)
Film diffusionFigure 11
Adsorption mechanism of HF on 3A zeolite.Equations (11)–(14) can be used to predict HF adsorption control by particle or film diffusion [26, 27]. By plotting Bt vs. time, the mass transfer rate is controlled by pore diffusion if the plot is a straight line passing through the origin [26–28]. If the curve is nonlinear or does not pass through the origin, film diffusion can also be considered to affect the adsorption rate [26–28]. The calculated Bt values as a function of time are shown in Figure 12, and the curves are not entirely linear. The slopes and intercepts of the film diffusion model at all pressures are given in Table 3. The existence of intercept values suggests that the rate-controlling process for HF adsorption on zeolite 3A is mainly controlled by external mass transfer [26]. The intercept increases close to zero with increasing pressure, which indicates that pore diffusion appears to be more important at slightly higher pressures.
(2)
Interparticle diffusionFigure 12
Plots of Boyd’s film model for HF adsorption on 3A.Table 3
Kinetic parameters of linear fitting of film diffusion model.
Pressure (bar)SlopeInterceptR20.150.03954−0.429920.997650.350.04693−0.427810.998720.500.05256−0.405660.999260.700.06069−0.409490.999330.950.0678−0.410980.999361.100.07321−0.410120.99936The fitting results for the adsorption kinetics data with the interparticle diffusion linear form are shown in Figure13 and Table 4. A good correlation between ln1−qt/qe with t indicates that the experimental data can be well described by the model. The Dc/r2p and Dc values calculated by the slope of the linear fit increase continuously with increasing pressure, indicating that high pressure favours the HF gas diffusion in zeolite 3A, which is consistent with the previous calculation that high pressure favours the adsorption rate. The order of magnitude of interparticle diffusion coefficient Dc of HF is 10−9 m2/s. The intercept values obtained by linear fitting the experimental data are not close to −0.4977 (ln6/π2), which indicates that the HF adsorption rate on zeolite 3A is not completely controlled by the interparticle diffusion. The calculated interparticle diffusion coefficient Dc/r2p versus first-order rate constant k1 does not satisfy the 1/15 relationship and also reflects that the HF diffusion over zeolite 3A is not completely controlled by interparticle diffusion [26].
(3)
Intraparticle diffusionFigure 13
Linear fitting for experimental data with interparticle diffusion model.Table 4
The linear fitting results for interparticle diffusion model.
Pressure (bar)SlopeInterceptDc/r2p (10-3 s-1)Dc (10-9 s-1)0.15−0.040850.090714.1431.0360.35−0.048090.061034.8771.2190.50−0.053380.000015.4141.3540.70−0.061560.000036.2441.5610.95−0.068730.000036.9711.7431.10−0.074240.000027.5301.882The intraparticle diffusion curves for HF adsorption on zeolite 3A are shown in Figure14. The curves are observed to be nonlinear. According to the intraparticle diffusion model, the adsorption amount qt plot vs. t1/2 should be a straight line and pass through the origin of the mass transfer rate solely controlled by intraparticle diffusion [26]. Multilinearity can be observed when different processes are related to the adsorption mechanism. The slope of each linear portion represents the corresponding adsorption rate [27]. The curves in Figure 14 show quart-linear characteristics, indicating the presence of four consecutive HF adsorption steps on zeolite 3A. The initial part, region I, was ascribed to the HF diffusion from the free state to and through the gas film of zeolite 3A, and the initial stage was associated with the HF film diffusion. The second and third parts, regions II and III describe the adsorption-progressive stage where diffusion occurs within the particle. Regions II and III are related to interparticle and intraparticle adsorptions, respectively. The fourth part, region IV, is the final equilibrium adsorption stage where the diffusion becomes slower owing to the active adsorption site saturation. Figure 14 shows that the extended line for straight lines corresponding to regions II and III does not pass through the origin, which may result from the different diffusion rates for the first and other stages of HF adsorption.Figure 14
Prediction of intraparticle diffusion model for HF adsorption on 3A.The adsorption rate of each HF molecule is controlled by four processes at a certain pressure. In the first stage, the adsorption rate is controlled by the film diffusion, as shown in segment I of Figure14. The interparticle diffusion would be the rate-controlling process when the HF molecules diffuse into the particle pore. The intraparticle diffusion then controls the rate. Finally, the rate is governed by surface adsorption. The slope of each linear segment before region IV can be used to deduce which stage controls the whole HF adsorption rate [27]. Moreover, Figure 14 shows that the linear slope in region III is the smallest. The linear portion with the lowest slope is the rate-controlling step [27, 28]. This suggests that HF diffusion into the 3A particle is slower and the intraparticle diffusion stage is the rate-controlling stage. The linear slopes for regions II and III gradually increase with increasing pressure, which may be because the film thickness decreases as the pressure rises and the film diffusion rate will increase.


### 3.3.2. Effect of Temperature

Kinetic experiments at 298–338 K and 0.50 bar were conducted to investigate the effect of temperature on the HF kinetic adsorption on zeolites 3A. The HF adsorption kinetics curves at five temperatures are shown in Figure15. The HF kinetic curves at five temperatures can be divided into three different stages: rapid adsorption, slow adsorption, and adsorption equilibrium stages. The HF adsorption capacity gradually decreases with increasing temperature, which is consistent with the discovery in literature [19]. High temperature enables the HF molecules to obtain more energy to overcome the intermolecular force and electrostatic interaction; thus, HF molecules remain in the free state. Simultaneously, the affinity between HF molecules and zeolite 3A surface will be weakened by the increasing temperature and will result in the decrease in adsorption capacity. In addition, high temperature is not conducive to the formation of a more orderly and stable configuration of adsorbed molecules, resulting in the reduction of adsorption capacity. Higher temperature is not conducive to improving HF adsorption recovery. It can also be found that the time to reach equilibrium decreases with the increasing temperature, which also shows that the temperature is conducive to the gas adsorption rate.Figure 15
Dynamic curves of HF under different temperature at 0.5 bar.(1) Adsorption Rate. The PFO and PSO models were used to predict the HF adsorption kinetic curves. The fitting results are shown in Figure 15 and Table 5. The adsorption rate constants k1 and k2 of HF increase with temperature, indicating that the HF adsorption rate shows a positive correlation with temperature, which is due to the acceleration of molecular motion caused by temperature increase. q1 and q2 decrease with increasing temperature, suggesting that higher temperature is conducive to gas diffusion; however, it will reduce the gas adsorption capacity.Table 5
The fitting kinetic parameters for PFO and PSO.
Temperature (K)Pseudo first-orderPseudo second-orderq1 (mg/g)k1R2q2 (mg/g)k2R22980.25800.05340.98980.28320.28590.96853080.22130.05920.98730.24110.38610.97263180.19900.06330.98670.21570.47150.97243280.18030.06810.98970.19440.57570.96753380.16010.07330.98370.17180.71660.9523(2) Diffusion Mechanism.
(1)
Film diffusionThe calculatedBt values are shown in Figure 16. Moreover, Bt is not completely linear. The slope and intercept of Boyd’s film diffusion model are listed in Table 6. The existence of intercept value shows that the HF adsorption rate on zeolite 3A was mainly controlled by external mass transfer. The intercept values decrease slightly with increasing temperature, suggesting that pore diffusion become more important at high temperature. The Bt values show a positive correlation with temperature, indicating that the film diffusion rate increases with temperature increase.
(2)
Interparticle diffusionFigure 16
Plots of Boyd’s film model for HF adsorption on 3A.Table 6
Kinetic parameters of linear fitting of film diffusion model.
Temperature (K)SlopeInterceptR22980.0526−0.40480.97923080.0583−0.40420.98723180.0623−0.40540.98933280.0670−0.40440.98923380.0721−0.40320.9867The linear fitting results for the HF adsorption kinetic curve using the interparticle diffusion model at five temperatures and 0.5 bar are shown in Figure17 and Table 7. A good correlation between ln1−qt/qe shows that t indicates that the experimental data can be well described by the model. In addition, Table 7 shows that Dc/r2p and Dc values increase with increasing temperature. Based on molecular dynamics theory, the essence of HF diffusion in zeolite 3A is due to the molecular irregular thermal movement. The average kinetic energy of HF molecules increases with temperature, which leads to an increase in amplitude and frequency of molecular vibration. The higher molecular irregular thermal movement intensity occurs at a higher temperature. Consequently, the HF diffusion rate in zeolite 3A becomes faster.
(3)
Intraparticle diffusionFigure 17
Linear fitting for experimental data with interparticle diffusion model.Table 7
The linear fitting results for interparticle diffusion model.
Temperature (K)SlopeInterceptDc/r2p (10-3 s-1)Dc (10-9 s-1)298−0.05340.000015.4161.354308−0.0592−0.000036.0041.501318−0.06330.000086.4201.605328−0.0681−0.000016.9071.727338−0.07330.000017.4341.859The quart-linear characteristics for intraparticle diffusion curves can be observed in Figure18, which indicated that three different processes are involved in the adsorption mechanism. The curves of the five temperatures in the first stage I are relatively close, indicating that the influence of temperature on the HF diffusion velocity from the free state to and through the gas film of zeolite 3A is little. In the second and third stages, the difference between the five curves increases with time. The linear slope for each stage decreases with increasing temperature, suggesting that the pore diffusion rate in the particles decreases slightly at this stage, which may be due to the impediment of diffusion by the interaction of HF molecules under high pressure. The same trend is also found in CO2 in porous MgO [27]. The extended line for straight lines corresponding to regions II and III does not pass through the origin. The linear portion for stage III with the lowest slope indicates that the diffusion rate is controlled by intraparticle diffusion.Figure 18
Prediction of intraparticle diffusion model for HF adsorption on 3A.


## 3.3.1. Effect of Pressure on Adsorption Kinetic

The adsorption kinetic curve of HF on zeolite 3A at 298 K is shown in Figure10. The adsorption capacity continuously increases with the adsorption time. The adsorption capacity rapidly increases in the initial stage, which is mainly due to the high adsorption energy sites on the adsorbent surface and the rapid occupation of HF molecules onto the adsorption sites, so the adsorption rate is high. When large numbers of active adsorption sites are occupied, the adsorption sites available for HF molecules become less; hence, the adsorption rate becomes slow. When the active sites are almost occupied, HF molecules reach dynamic equilibrium on the surface of zeolite 3A. At this time, the number of HF molecules on the adsorbent surface will not increase; therefore, the total adsorption rate tends to zero and the adsorption capacity will not increase.Figure 10
Dynamic curves of HF under different pressures at 298 K.(1) Adsorption Rate. The HF adsorption kinetics curves and the corresponding curves predicted by the PFO model are shown in Figure 10. The kinetic constants calculated with the PFO and PSO models and the characteristic parameters of the kinetic model are listed in Table 2. The larger R2 of the PFO model indicates a better predictivity of the adsorption kinetic process over the whole pressure range well, so the adsorption of HF by zeolite 3A follows simple first-order kinetics. The calculated q1 values from the PFO model are more in accordance with the experimental data than the calculated q2 values by the PSO model.Table 2
The fitting kinetic parameters for PFO and PSO.
Pressure (bar)Pseudo first-orderPseudo second-orderq1/mg·g-1k1/min-1R2q2/mg·g-1k2/g mg-1.Min-1R20.150.07440.03950.99990.08440.63520.97830.350.17680.04720.99980.19660.34850.97260.500.25800.05340.99980.28320.28590.96850.700.31530.06160.99970.34260.28630.96380.950.37460.06870.99980.40370.28060.96021.100.42060.07430.99970.45100.27750.9576Bothq1 and q2 increase with pressure, which is consistent with the high pressure is conducive to HF adsorption. Meanwhile, the PFO and PSO model parameters (k1 and k2) increase with pressure because the velocity of the HF molecule will increase and the migration speed of HF molecules inside the pores will be faster at higher pressure, leading to an increase in the diffusion rate. The increased mass transfer coefficient makes the kinetic curve steeper. The k1 values (0.0395–0.0743 min−1) for HF on zeolite 3A are larger than that of H2S (0.00177 min−1) on zeolite 3A, which suggested that the HF adsorption rate is faster than that of H2S [6, 32].(2) Diffusion Mechanism. The HF adsorption process on zeolite 3A can be divided into five continuous processes, as shown in Figure 11: (a) HF molecules diffuse from free state to adsorbent gas film (bulk diffusion), (b) HF molecules diffuse in the film (film diffusion), (c) HF molecules diffuse in pores between particles (interparticle diffusion), (d) HF molecules diffuse in 3A crystal (intraparticle diffusion), and (e) surface adsorption. Generally, surface adsorption and bulk diffusion are very fast, so they are ignored in the analysis of the HF adsorption kinetic process, and the role of the other three processes in the adsorption process is mainly considered.
(1)
Film diffusionFigure 11
Adsorption mechanism of HF on 3A zeolite.Equations (11)–(14) can be used to predict HF adsorption control by particle or film diffusion [26, 27]. By plotting Bt vs. time, the mass transfer rate is controlled by pore diffusion if the plot is a straight line passing through the origin [26–28]. If the curve is nonlinear or does not pass through the origin, film diffusion can also be considered to affect the adsorption rate [26–28]. The calculated Bt values as a function of time are shown in Figure 12, and the curves are not entirely linear. The slopes and intercepts of the film diffusion model at all pressures are given in Table 3. The existence of intercept values suggests that the rate-controlling process for HF adsorption on zeolite 3A is mainly controlled by external mass transfer [26]. The intercept increases close to zero with increasing pressure, which indicates that pore diffusion appears to be more important at slightly higher pressures.
(2)
Interparticle diffusionFigure 12
Plots of Boyd’s film model for HF adsorption on 3A.Table 3
Kinetic parameters of linear fitting of film diffusion model.
Pressure (bar)SlopeInterceptR20.150.03954−0.429920.997650.350.04693−0.427810.998720.500.05256−0.405660.999260.700.06069−0.409490.999330.950.0678−0.410980.999361.100.07321−0.410120.99936The fitting results for the adsorption kinetics data with the interparticle diffusion linear form are shown in Figure13 and Table 4. A good correlation between ln1−qt/qe with t indicates that the experimental data can be well described by the model. The Dc/r2p and Dc values calculated by the slope of the linear fit increase continuously with increasing pressure, indicating that high pressure favours the HF gas diffusion in zeolite 3A, which is consistent with the previous calculation that high pressure favours the adsorption rate. The order of magnitude of interparticle diffusion coefficient Dc of HF is 10−9 m2/s. The intercept values obtained by linear fitting the experimental data are not close to −0.4977 (ln6/π2), which indicates that the HF adsorption rate on zeolite 3A is not completely controlled by the interparticle diffusion. The calculated interparticle diffusion coefficient Dc/r2p versus first-order rate constant k1 does not satisfy the 1/15 relationship and also reflects that the HF diffusion over zeolite 3A is not completely controlled by interparticle diffusion [26].
(3)
Intraparticle diffusionFigure 13
Linear fitting for experimental data with interparticle diffusion model.Table 4
The linear fitting results for interparticle diffusion model.
Pressure (bar)SlopeInterceptDc/r2p (10-3 s-1)Dc (10-9 s-1)0.15−0.040850.090714.1431.0360.35−0.048090.061034.8771.2190.50−0.053380.000015.4141.3540.70−0.061560.000036.2441.5610.95−0.068730.000036.9711.7431.10−0.074240.000027.5301.882The intraparticle diffusion curves for HF adsorption on zeolite 3A are shown in Figure14. The curves are observed to be nonlinear. According to the intraparticle diffusion model, the adsorption amount qt plot vs. t1/2 should be a straight line and pass through the origin of the mass transfer rate solely controlled by intraparticle diffusion [26]. Multilinearity can be observed when different processes are related to the adsorption mechanism. The slope of each linear portion represents the corresponding adsorption rate [27]. The curves in Figure 14 show quart-linear characteristics, indicating the presence of four consecutive HF adsorption steps on zeolite 3A. The initial part, region I, was ascribed to the HF diffusion from the free state to and through the gas film of zeolite 3A, and the initial stage was associated with the HF film diffusion. The second and third parts, regions II and III describe the adsorption-progressive stage where diffusion occurs within the particle. Regions II and III are related to interparticle and intraparticle adsorptions, respectively. The fourth part, region IV, is the final equilibrium adsorption stage where the diffusion becomes slower owing to the active adsorption site saturation. Figure 14 shows that the extended line for straight lines corresponding to regions II and III does not pass through the origin, which may result from the different diffusion rates for the first and other stages of HF adsorption.Figure 14
Prediction of intraparticle diffusion model for HF adsorption on 3A.The adsorption rate of each HF molecule is controlled by four processes at a certain pressure. In the first stage, the adsorption rate is controlled by the film diffusion, as shown in segment I of Figure14. The interparticle diffusion would be the rate-controlling process when the HF molecules diffuse into the particle pore. The intraparticle diffusion then controls the rate. Finally, the rate is governed by surface adsorption. The slope of each linear segment before region IV can be used to deduce which stage controls the whole HF adsorption rate [27]. Moreover, Figure 14 shows that the linear slope in region III is the smallest. The linear portion with the lowest slope is the rate-controlling step [27, 28]. This suggests that HF diffusion into the 3A particle is slower and the intraparticle diffusion stage is the rate-controlling stage. The linear slopes for regions II and III gradually increase with increasing pressure, which may be because the film thickness decreases as the pressure rises and the film diffusion rate will increase.


## 3.3.2. Effect of Temperature

Kinetic experiments at 298–338 K and 0.50 bar were conducted to investigate the effect of temperature on the HF kinetic adsorption on zeolites 3A. The HF adsorption kinetics curves at five temperatures are shown in Figure15. The HF kinetic curves at five temperatures can be divided into three different stages: rapid adsorption, slow adsorption, and adsorption equilibrium stages. The HF adsorption capacity gradually decreases with increasing temperature, which is consistent with the discovery in literature [19]. High temperature enables the HF molecules to obtain more energy to overcome the intermolecular force and electrostatic interaction; thus, HF molecules remain in the free state. Simultaneously, the affinity between HF molecules and zeolite 3A surface will be weakened by the increasing temperature and will result in the decrease in adsorption capacity. In addition, high temperature is not conducive to the formation of a more orderly and stable configuration of adsorbed molecules, resulting in the reduction of adsorption capacity. Higher temperature is not conducive to improving HF adsorption recovery. It can also be found that the time to reach equilibrium decreases with the increasing temperature, which also shows that the temperature is conducive to the gas adsorption rate.Figure 15
Dynamic curves of HF under different temperature at 0.5 bar.(1) Adsorption Rate. The PFO and PSO models were used to predict the HF adsorption kinetic curves. The fitting results are shown in Figure 15 and Table 5. The adsorption rate constants k1 and k2 of HF increase with temperature, indicating that the HF adsorption rate shows a positive correlation with temperature, which is due to the acceleration of molecular motion caused by temperature increase. q1 and q2 decrease with increasing temperature, suggesting that higher temperature is conducive to gas diffusion; however, it will reduce the gas adsorption capacity.Table 5
The fitting kinetic parameters for PFO and PSO.
Temperature (K)Pseudo first-orderPseudo second-orderq1 (mg/g)k1R2q2 (mg/g)k2R22980.25800.05340.98980.28320.28590.96853080.22130.05920.98730.24110.38610.97263180.19900.06330.98670.21570.47150.97243280.18030.06810.98970.19440.57570.96753380.16010.07330.98370.17180.71660.9523(2) Diffusion Mechanism.
(1)
Film diffusionThe calculatedBt values are shown in Figure 16. Moreover, Bt is not completely linear. The slope and intercept of Boyd’s film diffusion model are listed in Table 6. The existence of intercept value shows that the HF adsorption rate on zeolite 3A was mainly controlled by external mass transfer. The intercept values decrease slightly with increasing temperature, suggesting that pore diffusion become more important at high temperature. The Bt values show a positive correlation with temperature, indicating that the film diffusion rate increases with temperature increase.
(2)
Interparticle diffusionFigure 16
Plots of Boyd’s film model for HF adsorption on 3A.Table 6
Kinetic parameters of linear fitting of film diffusion model.
Temperature (K)SlopeInterceptR22980.0526−0.40480.97923080.0583−0.40420.98723180.0623−0.40540.98933280.0670−0.40440.98923380.0721−0.40320.9867The linear fitting results for the HF adsorption kinetic curve using the interparticle diffusion model at five temperatures and 0.5 bar are shown in Figure17 and Table 7. A good correlation between ln1−qt/qe shows that t indicates that the experimental data can be well described by the model. In addition, Table 7 shows that Dc/r2p and Dc values increase with increasing temperature. Based on molecular dynamics theory, the essence of HF diffusion in zeolite 3A is due to the molecular irregular thermal movement. The average kinetic energy of HF molecules increases with temperature, which leads to an increase in amplitude and frequency of molecular vibration. The higher molecular irregular thermal movement intensity occurs at a higher temperature. Consequently, the HF diffusion rate in zeolite 3A becomes faster.
(3)
Intraparticle diffusionFigure 17
Linear fitting for experimental data with interparticle diffusion model.Table 7
The linear fitting results for interparticle diffusion model.
Temperature (K)SlopeInterceptDc/r2p (10-3 s-1)Dc (10-9 s-1)298−0.05340.000015.4161.354308−0.0592−0.000036.0041.501318−0.06330.000086.4201.605328−0.0681−0.000016.9071.727338−0.07330.000017.4341.859The quart-linear characteristics for intraparticle diffusion curves can be observed in Figure18, which indicated that three different processes are involved in the adsorption mechanism. The curves of the five temperatures in the first stage I are relatively close, indicating that the influence of temperature on the HF diffusion velocity from the free state to and through the gas film of zeolite 3A is little. In the second and third stages, the difference between the five curves increases with time. The linear slope for each stage decreases with increasing temperature, suggesting that the pore diffusion rate in the particles decreases slightly at this stage, which may be due to the impediment of diffusion by the interaction of HF molecules under high pressure. The same trend is also found in CO2 in porous MgO [27]. The extended line for straight lines corresponding to regions II and III does not pass through the origin. The linear portion for stage III with the lowest slope indicates that the diffusion rate is controlled by intraparticle diffusion.Figure 18
Prediction of intraparticle diffusion model for HF adsorption on 3A.


## 4. Conclusion

HF adsorption isotherms data on zeolite 3A at 298–338 K were type I. The adsorption capacity increased with increasing pressure and decreases with increasing temperature. HF adsorption isotherms data on zeolite 3A can be described well by the DA model. TheHst values of HF on zeolite 3A decreased with the increase of surface load, which suggested the surface energy heterogeneity of zeolite 3A.The HF adsorption by zeolite 3A at different adsorption conditions followed simple first-order kinetics. The first-order rate increased with pressure and temperature. The calculatedBt values showed nonlinear characteristics with time. Bt values increased with increasing pressure and temperature, indicating that high pressure and temperature favour film diffusion. The order of magnitude of the interparticle diffusion coefficient Dc of HF on zeolite 3A was 10−9 m2/s. The higher pressure and higher temperature favour the HF diffusion process. The intraparticle diffusion curves for HF adsorption on zeolite 3A showed quart-linear characteristics, indicating the presence of three consecutive HF adsorption steps on zeolite 3A. In the initial adsorption stage, the film diffusion controlled the adsorption rate. The intraparticle diffusion would be the rate-controlling process after HF molecules diffuse through the film. The intraparticle diffusion then controls the rate. Finally, the rate was governed by surface adsorption. HF diffusion into the particle of zeolite 3A was the slowest and therefore, the intraparticle diffusion is the rate-controlling stage.In this study, the HF adsorption mechanism onto zeolite 3A was evaluated based on kinetics and thermodynamics. However, only one adsorbent zeolite 3A was studied due to limited conditions, and other porous materials have not been analyzed in this paper. The adsorption kinetics and thermodynamics of HF on different materials will be compared in subsequent studies.



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