Engineering Calculations for Catalytic Hydrolysis of CF₄

Abstract

Tetrafluoromethane (CF₄) is the simplest perfluorocarbon, a class of compounds with very high greenhouse gas potential. Catalytic hydrolysis offers an opportunity to convert these compounds to manageable CO₂ and HF. Recently published data showed the effectiveness of Ga-doping to overcome the fluorine poisoning of various Al₂O₃ catalysts at relatively modest temperatures. This prior work offered a partial catalytic mechanism together with kinetic and conversion data. The current paper completes the catalytic mechanism, and then analyzes it using the Langmuir–Hinshelwood algorithm for both the initial CF₄ conversion, and the catalyst site regeneration. The resulting derived rate expression, together with a catalyst activity coefficient expression, are then used in flow reactor configurations to simulate both relatively short exposure time runs with little loss of activity, as well as longer runs with severe activity loss. The reasonable agreement with the published laboratory data suggests that these expressions can be used for a larger-scale practical reactor design.

1. Introduction

Perfluorocarbons (PFCs) contain only carbon and fluorine atoms. These compounds are non-flammable, chemically inert, and stable. They are even used in medical theranostics [1]. Despite their unique properties, PFCs are under growing scrutiny as “forever chemicals”—species that, due to their chemical stability, tend to linger and accumulate in the environment and the body. The US Environmental Protection Agency recently issued a drinking water national standard [2] for polyfluoroalkyl substances.

A potentially more concerning environmental consequence is the high greenhouse gas potential of PFCs, especially CF₄ [3]. The symmetry and high C-F bond strength of CF₄ preclude easy decomposition. The key is the activation of the strong C-F bond [4]. Catalytic hydrolysis, especially using alumina-based catalysts, offers a viable pathway to the conversion of CF₄ to stable products that can be captured easily. The overall desired hydrolysis reaction is $C{F}_4+2H_{2}O\to C{O}_2+4HF$, $∆H_r^o=$ −70.06 kJ/mole.

Thermal decomposition of CF₄ has been demonstrated with many different catalysts [5,6]. Transition metal-doped alumina is widely considered to be a useful catalyst for organic reactions [7] and the degradation and adsorption of organic dyes [8]. The often-cited catalyst for the hydrolysis of CF₄ is a Lewis acid-based metal oxide, for example, alumina [9]. The active site for CF₄ bond activation has been identified as the Al site [10]. The efficiency and resilience of θ-${\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$ over other alumina forms has been established [11].

However, even at temperatures as high as 973 K, these catalysts suffer rapid F-poisoning [3]. Alumina with a metal dopant offers poisoning resistance [3,12]. Doping θ-${\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$ with Ga resulted in a strong, sustained activity for CF₄ hydrolysis at a reduced temperature (773 K) compared to the undoped case [3]. Switching to ZrO₂ doped with -HSO₄ is another option [13]. Similar results have been obtained with H₂SO₄-treated ZnAl₂O₄ [4].

In this paper, the mechanism and kinetic work in [3] is expanded into an engineering application. Additional details for the initial CF₄ conversion steps within the catalytic cycle are proposed to complete the catalytic cycle. A rate expression for CF₄ hydration based on the whole cycle is developed with the Langmuir–Hinshelwood algorithm. The rate expression includes the catalyst activity, which is modeled quantitatively. This kinetic model is tested against CF₄ conversion data [3] for θ-${\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$ and γ-${\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$ catalysts that poison relatively easily. The rate expression is then tested against CF₄ conversion data [3] for a Ga/θ-${\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$ catalyst. The purpose of these derivations and calibrations is to facilitate a future engineering scaleup design.

2. Development of Kinetic Rate Expressions

This section shows the development of a working kinetic rate expression that can be used for a future CF₄ catalytic hydrolysis reactor design. Including the activity offers the chance to guide important reactor planning such as parallel trains and catalyst regeneration. Subsections cover an expanded mechanism cycle, the derivation of a working rate expression including catalyst activity, a facilitated unsteady packed bed reactor description, and finally preparation for the activity calibration.

2.1. Mechanism

Figure 5 in Reference [3] proposes a catalytic cycle for the CF₄ hydrolysis on Al₂O₃. The cycle illustrates the relevant catalytic sites, and can be divided into two portions:

$$\mathrm{Portion} \mathrm{I}: C{F}_4+regenerated site\to C{O}_2+2HF+poisoned\left(fluorinated\right)site$$

$$\mathrm{Portion} \mathrm{II}: poisoned site+2H_{2}O\to 2HF+regenerated site$$

The analysis below builds on the partial catalytic cycle shown in [3]. While much detail is provided in [3] for Portion II, no details are shown for Portion I. Below is a proposed detailed mechanism for each portion, including likely transition states. For clarity, the mechanism is presented in a linear (not cyclic) way. Stable catalyst sites are S*, while transition states are TS*. The mechanism is shown with a Ga replacing an Al but is valid for the non-doped case. Approaching reactant and departing product molecules are also shown. Bond breaking and formation are shown as dashed lines. Portion I reactions are graphically shown in Figure 1 and Figure 2. Portion II reactions are shown in Figure 3 and Figure 4.

2.1.1. Portion I Mechanism

The elementary reactions (steps) in Portion 1 are the following:

$$1. C{F}_4+S1=HF+S2$$

$$2. S2=HF+S3$$

$$3. S3=C{O}_2+S4$$

The CF₄ conversion cycle begins with the removal of the first F by the reaction of a H from the OH group on either Ga or Al. The adsorption energy is greater for F than for OH on Al, while the bond length is shorter. These data indicate the stronger bond of F to Al, thus resulting in the poisoning [3]. The case is less severe for a Ga site than an Al site.

Zhang et al. [3] show conclusively that the poisoned S4 can be more easily regenerated due to the reduced Lewis acidity of the Ga dopant. In the absence of Ga-doping, the rate of removal of the F atoms from S4 in Portion 2 is very much diminished due to the stronger adsorption of F atoms to the Al site (higher Lewis acidity). The Ga-doped site has a weaker adsorption to F atoms (lower Lewis acidity), thus making the F atom removal by subsequent hydrolysis (Step 6 below) more favorable.

2.1.2. Portion II Mechanism

The elementary reactions (steps) in Portion II are the following:

$$4. S4+H_{2}O=S5+HF$$

$$5. S5=HF+S6$$

$$6. S6+H_{2}O=S1$$

The Ga-F bond is weaker than the Al-F bond [3]. This facilitates the start of the poisoned site regeneration in Portion II.

2.2. Langmuir–Hinshelwood Analysis

The classical Langmuir–Hinshelwood (L-H) analysis of the above mechanism begins with the assumption of a slow or rate-determining-step (RDS). The other steps are assumed to be quasi-equilibrated (pseudo-equilibrium). The validity of the overall kinetic rate expression, derived from the subsequent algebraic analysis, is judged by comparison to the observed rates or conversions obtained under specific experimental conditions. If the derived rate expression is not consistent with observed data, then another step should be selected as the RDS, and the derivation is repeated.

The L-H analysis here assumes that Step 1 is the RDS. The six steps can now be presented as follows:

$$1. C{F}_4+S1\to HF+S2$$

$$2.S2\approx HF+S3$$

$$3.S3\approx C{O}_2+S4$$

$$4. S_4+H_{2}O\approx S_5+HF$$

$$5.S5\approx HF+S6$$

$$6. S6+H_{2}O\approx S1$$

The overall rate expression is:

$$r\equiv r_1=k_1{y}_{{CF}_4}{C}_{S1}$$

(1)

where r_i = rate of Step i, k_i = forward rate constant for Step i, y_j = species j mole fraction, and C_Si = surface concentration of catalyst site i. To estimate C_S1, total site balance is used:

$$C_t=C_{S1}+C_{S2}+C_{S3}+C_{S4}+C_{S5}+C_{S6}$$

(2)

where C_t = total surface concentration of all catalytic sites, which is taken as constant. The remaining mechanism steps are now used to estimate the remaining site concentrations.

For C_S2, as an example for other site concentrations, consider the net rate of Step 2:

$$r_2=k_2{C}_{S2}-k_{-2}{y}_{HF}{C}_{S3}$$

(3)

where k_−i = reverse rate constant for Step i. Rearrangement of Step 3 yields:

$$r_2/k_2=\left[C_{S2}-y_{HF}{C}_{S3}/\left(k_2/k_{-2}\right)\right]$$

(4)

Step 2 is elementary, so its rate constant ratio is equal to its equilibrium constant:

$$k_2/k_{-2}=K_2$$

(5)

where K_i = equilibrium constant for Step i. Step 2 is assumed to be in a quasi-equilibrium condition, which is represented by:

$$0\approx r_2/k_2=\left[C_{S2}-y_{HF}{C}_{S3}/K_2\right]$$

(6)

The rate r₂ is finite non-zero, while k₂ is assumed to be large (fast). C_S2 is estimated as:

$$C_{S2}\approx y_{HF}{C}_{S3}/K_2$$

(7)

The pattern used in Equations (3)–(7) is repeated for estimates of C_S3 through C_S6:

$$C_{S3}\approx y_{C{O}_2}{C}_{S4}/K_3 C_{S4}\approx y_{HF}{C}_{S5}/\left(K_4{y}_{H_{2}O}\right)$$

(8)

$$C_{S5}\approx y_{HF}{C}_{S6}/K_5 C_{S6}\approx C_{S1}/\left(K_6{y}_{H_{2}O}\right)$$

(9)

Successive substitutions result in all expressions for C_Si in terms of C_S1. All of these are, in turn, substituted into the Equation (2) site balance. The result in an estimate for C_S1:

$$C_{S1}={\displaystyle \frac{C_t}{1+\frac{y_{HF}^3{y}_{C{O}_2}}{K_2{K}_3{K}_4{K}_5{K}_6{y}_{H_{2}O}^2}+\frac{y_{HF}^2{y}_{C{O}_2}}{K_3{K}_4{K}_5{K}_6{y}_{H_{2}O}^2}+\frac{y_{HF}^2}{K_4{K}_5{K}_6{y}_{H_{2}O}^2}+\frac{y_{HF}}{K_5{K}_6{y}_{H_{2}O}}+\frac{1}{K_6{y}_{H_{2}O}}}}$$

(10)

Combining Equations (1) and (10) yields an expression for the overall rate:

$$r={\displaystyle \frac{k_1{C}_t{y}_{C{F}_4}}{1+\frac{y_{HF}^3{y}_{C{O}_2}}{K_2{K}_3{K}_4{K}_5{K}_6{y}_{H_{2}O}^2}+\frac{y_{HF}^2{y}_{C{O}_2}}{K_3{K}_4{K}_5{K}_6{y}_{H_{2}O}^2}+\frac{y_{HF}^2}{K_4{K}_5{K}_6{y}_{H_{2}O}^2}+\frac{y_{HF}}{K_5{K}_6{y}_{H_{2}O}}+\frac{1}{K_6{y}_{H_{2}O}}}}$$

(11)

2.3. Reconciliation of Derived L-H Rate Expression with Experimental Conditions

Figure 1c in Reference [3] presents an Arrhenius plot of experimental rate constants k obtained for three catalysts: Ga-doped θ-${\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$, θ-${\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$, and γ-${\mathrm{A}\mathrm{l}}_2{\mathrm{O}}_3$. Direct communication with the corresponding author of Reference [3] confirmed that the assumed rate expression used for their kinetic analysis was first order in the mole fraction of CF₄.

To simplify the derived rate expression (Equation (11)) to first order in CF₄, consider the reactor experimental conditions reported in Figure 1 of Reference [3]: feed gas (vapor) was 0.96 mole% CF₄, 19.68% H₂O, and a balance of Ar. Under these conditions, it is easily argued that $y_{C{F}_4}\ll y_{H_{2}O}$, $y_{C{O}_2}\ll y_{H_{2}O}$, $y_{HF}\ll y_{H_{2}O}$, and $y_{H_{2}O}\approx$ constant. Under these conditions, the non-unity terms in the Equations (10) and (11) denominators fall out. The derived rate expression can be simplified to:

$$r\equiv {k_1{C}_{S1}{y}_{C{F}_4}\approx k}_1{C}_t{y}_{C{F}_4}\equiv k{y}_{C{F}_4}$$

(12)

where $k\equiv k_1{C}_t$.

2.4. Impact of F-Poisoning on Rate Expression

Equation (12) suggests that the impacts of F-poisoning and Ga-doping might be expressed through the total site concentration C_t. Figure 1b in Reference [3] shows that the Ga-doped catalyst activity is effectively exposure-time independent. With Ga-doping and excess H₂O, the first-order dependence also suggests that Steps 2–6 are favorable; i.e., K₂ through K₆ are “large”. This all results in $C_t\approx C_{S1}$. However, the authors show that the regeneration of fluorinated site S4 effectively stalls if Ga-doping is not used. Therefore, site concentration C_S4 builds up since Step 4 becomes unfavorable, i.e., K₄ is “small”. All terms containing K₄ in the denominator of Equation (10) are now “large”, thus causing $C_{S1}\ll C_t$, with a subsequent large decline in CF₄ conversion.

The rapid termination of CF₄ decomposition using the undoped catalysts suggests a time (exposure)-dependent expression for C_t. This time dependence for C_t can be indirectly expressed through the catalytic activity a:

$$a\equiv r_{obs}/r_o$$

(13)

where r_o = catalytic rate without poisoning (with Ga-doping or a fresh catalyst) and r_obs = observed rate. Combining Equations (12) and (13) gives the working rate expression:

$$r_{obs}={ak}_1{C}_t{y}_{C{F}_4}\equiv ak{y}_{C{F}_4}$$

(14)

For a given catalyst, k is taken as a constant corresponding to no poisoning. The activity accounts for the poisoning ultimately due to exposure to CF₄.

There are several expressions for activity a, depending on the situation [14]. A potential candidate here is a first-order dependence:

$$da/dt=-k_{p}a{y}_p$$

(15)

where k_p = rate constant for catalyst poisoning, and y_p = mole fraction of the poisoning agent. Since CF₄ is the source of the poison (i.e., F atoms), we can take $y_p\equiv y_{CF4}$.

2.5. Catalytic Reactor Modeling

The catalytic reactor used in [3] is taken to be a packed bed reactor (PBR), with observed CF₄ conversions exceeding the 10% cutoff for a differential reactor, as confirmed by the corresponding author. The steady-state PBR model, with CF₄ given as A, is:

$$d{F}_A/dW=r_A^{\prime }$$

(16)

where F_A = molar flow rate of A within the reactor, W = catalyst mass, and $r_A^{\prime }$ = molar reaction rate based on catalyst mass. Applying the same composition argument used for Equation (12) above, and including Equation (14), Equation (16) can be written as:

$$d{y}_A/dW=-k{y}_A/F_T$$

(17)

where the total molar flow rate $F_T\approx$ constant. Equation (17) is good for either very little or no poisoning (i.e., $a\approx 1$). For poisoning, Equation (17) must include the activity a. But, poisoning here is a time-dependent phenomenon. The poisoned PBR model is:

$$\partial y_A/\partial W=-ka{y}_A/F_T\partial a/\partial t=-k_{p}a{y}_A$$

(18)

The Equation (18) partial differential equation (PDE) problem can be handled more easily by approximating the PBR as several unsteady, equal-sized, continuous stirred tank reactors (CSTRs)-in-series [14], as seen in Figure 5. For this problem, five CSTRs are used. The total catalyst mass W is divided equally (W_i) between the five. This approach changes the PDE problem to a simultaneous ordinary differential equations (ODEs) problem.

For this application, the unsteady ith CSTR species balance is:

$$F_{A,i-1}-F_{A,i}+r_{A,i}^{\prime }{W}_i=d{N}_{A,i}/dt$$

(19)

where N_A,i = moles of A within the catalyst void space, and is approximated by:

$$N_{A,i}=y_{A,i}{N}_{T,i}=y_{A,i}{C}_{T,i}{V}_{g,i}\approx y_{A,i}\left[P/\left(RT\right)\right]\varphi V_{c,i}$$

(20)

where N_T,i = total moles of gas within reactor i, C_T,I = total molar gas concentration, P = pressure, T = temperature, $\varphi$ = catalyst “bed” porosity, and V_c,i = catalyst “bed” volume.

The PDE problem (Equation (18)) is now approximated as:

$$d{y}_{A,i}/dt=\left[RT/\left(P\varphi V_{c,i}\right)\right]\left[F_T\left(y_{A,i-1}-y_{A,i}\right)-k{a}_i{y}_{A,i}{W}_i\right]$$

(21)

The two ODEs for each CSTR (total of ten) are executed simultaneously using the Polymath^® software (v. 6.10) package [15]. The initial conditions (at t = 0) for the activities a_i are 1.0, and 0.0 for the mole fractions y_A,i. For the first CSTR, y_A,o = CF₄ feed mole fraction. This model is comparable to a reactor startup. For no-poisoning cases (a_i = 1 constant since k_p = 0), the transient solution rapidly reaches a steady-state which will be shown to be comparable to the algebraic solution for five CSTRs-in-series. For poisoning cases $\left(k_p\ne 0\right)$, results below show that the CSTR-in-series reaches a relatively quick solution then shows a slower degradation over time.

2.6. Preparation of Data for Simulations

2.6.1. Pre-Exponentials for Rate Constants

Figure 1c of Reference [3] offers an Arrhenius plot for the CF₄ hydration using the three catalysts. Activation energies (E_act) are provided, but no pre-exponentials (A_f). For each catalyst, the A_f values were estimated at four temperatures covering the presented range and then averaged. The results are shown in

Table 1. Arrhenius parameters for CF₄ hydration.

Catalyst	Af (Mole/g-min) *	Ea (Joule/Mole) #
Ga/θ-Al2O3	231	83,900
θ-Al2O3	32,613	122,000
γ-Al2O3	779,907	144,700

* This work, # Reference [3].

. It is assumed that the k value data shown in Table 1 of Reference [3] were collected before any significant catalyst poisoning occurred. The rising values of the A_f, E_a pairs is consistent with the increased difficulty of overcoming the impact of F-poisoning due to the increases in Lewis acidity.

2.6.2. Estimation of ϕ and V_c,i

Solving Equation (21) requires values for the catalyst “bed” porosity ϕ and the volume of catalyst “bed” V_c,i. Figure 1 of [3] reports a total gas feed of 41.46 cm³/min (STP) with a gas hourly space velocity (GHSV) of 1000/h. This gives an estimate of the total catalyst bed volume at 2.49 cm³. With five CSTRs-in-series, each bulk volume of the catalyst “bed” V_c,i is 0.498 cm³. With a total catalyst mass of 2 g, the bulk density of the catalyst bed is 0.803 g/cm³. The bed porosity ϕ values were then estimated using the catalyst mass densities ρ_cat. The ρ_cat value for the Ga/θ-Al₂O₃ was interpolated from the values for Al₂O₃ and Ga₂O₃. The catalyst mass in each of the five CSTRs-in-series W_i is 0.4 g. The values for ρ_cat and ϕ are presented in

Table 2. Physical properties of catalyst and catalyst bed.

Catalyst	ρcat (g/cm3)	ϕ (est)
Ga/θ-Al2O3	4.23 (est)	0.811
θ-Al2O3	3.69	0.779
γ-Al2O3	3.65	0.783

.

3. Results and Discussion

3.1. Short-Term Catalytic Runs

Figure 1a of Reference [3] presents CF₄ conversion data for each of the catalysts at various temperatures. The exposure times are fairly short so that catalyst activities do not appear to be affected, though there is a fair amount of fluctuation. These runs were simulated using both a steady-state PBR model (Equation (17)) and five CSTRs-in-series. The results are shown in Figure 6. Uncertainty bars have been estimated and included.

Figure 6 shows that the predicted X_A values from the five CSTRs-in-series model are consistently slightly lower than the PBR model, which is no surprise since an infinite number of CSTRs-in-series is required to exactly [14] model a plug flow reactor (PBR in this case). This difference is less than any model deviations from the observed data. It is noted that the transient CSTRs-in-series model showed the exact same numerical results as the steady-state version. Therefore, the use of the transient five CSTRs-in-series model with time-dependent activities (Equation (21)) over the PDE problem is justified.

Figure 6 shows that the PBR model fits to the experimental data trend are reasonable. The deviations might be attributed to experimental uncertainty (not quantified in Reference [3]) and non-PBR behavior in the reactor. Insufficient detail was provided to judge whether or not plug flow conditions existed in the experimental reactors used in Reference [3]. Since their conversions exceeded 10%, a differential reactor assumption was not justified. Nonetheless, the agreements are good enough to justify using Equation (21) to simulate the long-term transient runs in Figure 1b of Reference [3].

3.2. Long-Term Catalytic Runs

With the Arrhenius parameters for the CF₄ hydration for each catalyst (Table 1) and the unsteady CSTRs-in-series with the activities reactor model (Equation (21)) in hand, the long exposure time experiments shown in Figure 1b of Reference [3] were modeled. The values used for the poisoning rate constant k_p are shown in

Table 3. Activity loss rate constant k_p as used in the Figure 7 simulations.

Catalyst	kp (min−1)
Ga/θ-Al2O3	0
θ-Al2O3	0.035
γ-Al2O3	0.080

. They are adjusted to provide a reasonable fit to the data trends. The results are shown in Figure 7.

Figure 6 shows that the five CSTRs-in-series model (Equation (21)) slightly underpredicts the PBR model. A correction for this underprediction has been applied to the model curves shown in Figure 7. In addition, estimates were made for the uncertainty in the experimental data as suggested by a close examination of Figure 1b of Reference [3]. The resulting uncertainty bars are applied in Figure 7.

The model curves shown in Figure 7 begin a short time past zero. This is more of an artifact of the solution method. The solution of the five CSTRs-in-series (Equation (21)) very quickly reaches an early pseudo steady-state before any significant poisoning occurs. The declining conversion trends after the initial drops are due to real activity losses over time observed for the θ-Al₂O₃ and γ-Al₂O₃ catalysts. The model fit to the γ-Al₂O₃ data is remarkably good. The model fits for the θ-Al₂O₃ and Ga/θ-Al₂O₃ cases fall within the estimated experimental X_A uncertainties. These results demonstrate the ability of the reactor model to acceptably predict CF₄ conversion over time with or without poisoning.

4. Conclusions

The mechanism cycle proposed by Zhang et al. [3] on the alumina-catalyzed hydration of CF₄ has been expanded to show details for the hydration up to the point of potential F-poisoning. The expanded cycle is analyzed with the Langmuir–Hinshelwood algorithm to give a kinetic rate expression. Consideration of the reported experimental conditions in [3] results is a first-order expression for which Arrhenius parameters are completed based on data in [3]. The rate expression is combined with an unsteady catalyst activity expression, and then applied in simulations of experimental reactor runs shown in [3]. The results show reasonable simulations of the observed constant activity of Ga/θ-Al₂O₃ and the declining activities for the θ-Al₂O₃ and γ-Al₂O₃ catalysts due to F-poisoning. The kinetic rate expression and accompanying activity coefficient offer the opportunity to design future larger-scale hydration reactors.