Catalytic Gasification – A Critical Analysis of Carbon Dioxide Methanation on a Ru/Al2O3 Catalyst

Eric M. Lange; Brianne DeMattia; Jorge E. Gatica

doi:10.1515/ijcre-2018-0008

Article

Catalytic Gasification – A Critical Analysis of Carbon Dioxide Methanation on a Ru/Al₂O₃ Catalyst

Eric M. Lange , Brianne DeMattia and Jorge E. Gatica

Published/Copyright: May 25, 2018

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From the journal International Journal of Chemical Reactor Engineering Volume 16 Issue 7

Abstract

This paper proposes a corrected kinetic model for the Sabatier (CO₂ Methanation) reaction. Several other kinetic studies have been performed on the Sabatier reaction to date; however, many of these studies contain simplifications. Data available from one of the first studies (Lunde, P.J., and F.L. Kester. 1974. “Carbon Dioxide Methanation on a Ruthenium Catalyst.” Industrial & Engineering Chemistry Process Design and Development 13 (1): 27–33) was utilized to perform a new analysis of the kinetics of CO₂ Methanation. This work examined two models for the Sabatier reaction, the Perfect Mixing assumption and the differential (conversion) reactor assumption. After available data was screened for the occurrence of the Reverse Water Gas Shift reaction, the differential (conversion) reactor assumption was validated. A critical comparison to similar models available in literature is also presented.

Keywords: Sabatier; CO2 Methanation; Kinetics; Trash to Supply Gas Technology

Acknowledgements

These authors would like to acknowledge the Ohio Space Grant Consortium, the National Aeronautics and Space Administration, the Ohio Department of Education Chose Ohio First Program, as well as the Washkewicz College of Engineering and the Jack, Joseph and Morton Mandel Honors College at Cleveland State University for providing support and resources for this research.

Appendix

Kinetic models from literature

Table 4:

Sabatier power law kinetic models from literature for ruthenium catalysts.

−rCO2=1RT5b Ae−EART MCO2MH24−MCH4MH2O2KMn

Metal Support	Temperature Range (K)	A	EAkJmol	n	b	M	−rCO2 Units
Ru/TiO₂	524–675	7.75 × 10³m1.5mol0.5∗s	69	0.30	N/A	C	molm3∗s	Arena et al. (2011)
Ru/Al₂O₃	480–719	4.91 × 10⁵1atm3.25∗s	69	0.85	1	p	molm3∗s	De Filippis et al. (2004)
Ru/Al₂O₃	477–644	4.92 × 10 1atm0.15∗s	68	0.23	0	p	atms	Brooks et al. (2007)
Ru/Al₂O₃	477–644	2.31 × 10² m2.7∗mol0.1kg∗s	67	0.20	0.20	p	molkg∗s	[This Study]

Table 5:

Sabatier intrinsic kinetic models for ruthenium catalysts.

−rCO2=kpCO20.5pH2O−0.5pH21.51+K1pH20.5+K2pCO20.5pH2O−0.5pH20.53

Metal Support	Temperature Range (K)	kmolkg∗kPa1.5∗s	K1kPa−0.5	K2kPa−0.5
Ru/TiO₂	426–483	6.32 × 10^–5 – 1.11 × 10^–3	0.411 – 0.474	0.057 – 0.123	Environmental Protection Agency (2016)

Table 6:

Sabatier intrinsic kinetic models for nickel catalysts Part 1.

rCH4=kpCO20.5pH20.51+K1pCO2pH20.5+K2pCO20.5pH20.5+K3pCO+K4pH2O2

Metal/ Support	Temperature Range (K)	kmolkg∗ kPa∗s	K1dimensionless	K2kPa−1	K3kPa−1	K4kPa−1
Ni/SiO₂	500–600	535–15,900	0.156 – 0.998	0.01 – 0.07	22.8 – 0.91	-	He et al. (2009)
Ni/γ-Al₂O₃	443–483	5.9 × 10^–6 – 4.8 × 10^–5	0.039 – 0.110	1.6 × 10^–3	-	2.3 × 10^–3 – 1.1 × 10^–3	Hintze et al. (2012)

Table 7:

Sabatier intrinsic kinetic models for nickel catalysts Part 2.

rCH4=kpH2apCO2b1−pCH4pH2O2pCO2pH24Keq1+K1pH2OpH20.5+K2pH20.5+K3pCO20.52						k=krefexpEAR1Tref−1T,
						Ki=KirefexpΔHiR1Tref−1T

Metal Support	Temperature Range (K)	a	b	k		K1		K2		K3
Metal Support	Temperature Range (K)	a	b	EAkJmol	k1555(molkg∗kPa0.54∗s)	ΔH1kJmol	K1555kPa−0.5	ΔH2kJmol	K2555kPa−0.5	ΔH3kJmol	K3555kPa−0.5
Ni/Al(O)_x	453–613	0.31	0.16	93.6	5.33 × 10^–3	64.3	0.062	-	-	-	-	Aznar et al. (2006)
Ni/Al(O)_x	453–613	0.5	0.5	77.5	2.88 × 10^–2	22.4	0.050	−6.2	0.044	−10.0	0.088	Aznar et al. (2006)

Table 8:

Sabatier intrinsic kinetic models for nickel catalysts Part 3.

−rCO2=ke−EARTpCO21+K1pCO2

Metal Support	Temperature Range (K)	kmolkg∗kPa∗s	EAkJmol	K1kPa−1
Ni/γ-Al₂O₃	500–600	3.73 × 10⁹	105,855	12.53	Ewert et al. (2013)

Deriving Lunde and Kester’s design equation from a general mole balance

Lunde and Kester (1974) originally proposed that the reaction rate for the Sabatier reaction was equivalent to the change in partial pressure of CO₂ over the change in time.

(26)−dpAdt=Ae−EARTpApB4−pCpD2KPn

Presented here is the derivation of the above expression starting from the fundamental general mole balance for a packed bed reactor, i. e.

(27)dFAdW=rA′

The mole flow rate of species A (CO₂) and the catalyst mass are rewritten as follows

(28)FA=FAo1−XA

(29)W=ρbV

Differentiation of eqs. (28) and (29) leads to the following expressions

(30)dFA=−FAodXA

(31)dW=ρbdV

Substituting the differential flow rate of A and the differential catalyst mass leads to the general mole balance in terms of conversion and volume, i. e.

(32)−dXAdV=ρbFAorA′

Next, the design equation may be expressed in terms of conversion and time. Time may be described as

(33)t=VQ

Differentiating eq. (33) and substituting the differential volume into eq. (32) leads to the general mole balance in terms of conversion and time, i. e.

(34)dt=dVQ

(35)−dXAdt=ρb∗QFAorA′

The last step is to express the general mole balance in terms of pressure of CO₂. The relationship between pressure and conversion of CO₂ can be found from the definition of conversion

(36)XA=1−FAFAo=1−yAyAoFTFTo,where FTFTo=1+εXA, and ε=yAoδ

The inlet and outlet mole fraction of CO₂ can be described using Dalton’s Law

(37)yAo=pAoPTOTAL

(38)yA=pAPTOTAL

Assuming ideal gas relations and substituting the inlet and outlet mole fractions into the definition of conversion leads to the following expression for the pressure of CO₂

(39)pA=pAo1−XA1−2yAoXA

Differentiating the above with respect to conversion yields the following relationship

(40)dpA=pAodXA2yAo−11−2yAoXA2

Substituting into eq. (35) expresses the general mole balance in term of partial pressure of CO₂ and time, i. e.

(41)−dpAdt=ρb∗QFA∘∗pA∘∗2yA∘−11−2yA∘∗XA2∗r′A,where CA∘=FA∘Q, and pA∘=CA∘RT

Rearranging the expression and inserting the reaction rate leads to

(42)−dpAdt=ρbRT1−2yAo1−2yAoXA21RT5nAe−EARTpApB4−pCpD2KPn

One can clearly see that the authors’ proposed model lacks the temperature and compressibility terms. In addition, these authors neglected to correct concentrations when expressing the reaction rate as a function of partial pressures.

Converting design equations for kinetic parameter comparisons

Converting Lunde and Kester’s proposed design equation

Lunde and Kester (1974) originally proposed that the reaction rate for the Sabatier reaction was equivalent to the change in partial pressure of CO₂ over time.

(43)−dpAdt=Ae−EARTpApB4−pCpD2KPn=−rA′

The model used in this paper solves the design equation of a packed bed reactor. These authors’ design equation must be adapted to allow for a proper comparison with the parameters determined by this study. Presented here are the steps to modify the design equation originally proposed by Lunde and Kester such that the change in partial pressure of CO₂ with time is expressed in terms of conversion of CO₂ as a function of the mass of catalyst

First, the design equation is expressed in terms of pressure of CO₂ and catalyst mass. The residence time can be described as a function of the mass of catalyst as follows

(44)t=VQ=WQρb, where V=Wρb

Differentiating with respect to the catalyst mass leads to

(45)dt=dVQ=dWQρb, where dV=dWρb

Substituting into Lunde and Kester’s design equation leads to the design equation in terms of partial pressure of CO₂ and catalyst mass, i. e.

(46)−dpAdt=1Qρb−rA′

Next, the differential pressure of CO₂ must be expressed in terms of conversion of CO₂. The partial pressure of CO₂ can be described as

(47)pA=pAo1−XA1−2yAoXA

Differentiating leads to the partial pressure of CO₂ expressed as a function of the differential conversion, i. e.

(48)dpA=pAodXA2yAo−11−2yAoXA2

Substituting the above into eq. (46) and rearranging leads to the following expression

(49)dXAdW=1−2yAoXA22yAo−11pAo1QρbAe−EARTpApB4−pCpD2Kpn

Equation (49) can then be utilized in the model when predicting the conversion profiles with Lunde and Kester’s kinetic parameters A, E_A, and n.

Converting Ohya and coworkers’ proposed design equation

Ohya et al. (1997) reported an equivalent rate of reaction expression for the Sabatier reaction, i. e.

(50)dfAdL=rA

It should be noted that the above reaction rate is on a volume basis. In eq. (50), f_A and L represent the mole flow of CO₂ per unit area and the length of the reactor, respectively. According to Ohya and collaborators, the reaction rate of the Sabatier reaction can then be described as follows

(51)−rA=1RT−dpAdt

where the change in partial pressure of CO₂ over the change in time function is expressed as

(52)−dpAdt=Ae−EARTpApB4−pCpD2KPn

The model used in this paper solves the design equation of a packed bed reactor. To make a proper comparison between Ohya and colleagues’ kinetic parameters and the parameters determined by this work, the design equation proposed by Ohya et al. (1997) must be expressed in terms of of the change of conversion as a function of the mass of catalyst. Presented here are the steps to modify design equation originally presented by Ohya and coworkers. First, the reactor length can be defined as

(53)L=Vπ∗r2=Wπ∗r2∗ρb, where V=Wρb

Differentiating the reactor length leads to

(54)dL=dVπ∗r2=dWπ∗r2∗ρb, where dV=dWρb

Substituting the differential length into eq. (50) leads to Ohya and coworkers’ design equation expressed in terms of mole flow rate of CO₂ per unit area and catalyst mass, i. e.

(55)dfAdW=1πr2ρbrA

Next, the mole flow rate of CO₂ per unit area must be expressed in terms of the conversion of CO₂.

(56)fA=FAoA1−XA

Differentiating the mole flow of CO₂ per unit area leads to

(57)dfA=−FAoAdXA

Substituting into eq. (55) leads to the design equation expressed in terms of conversion and catalyst mass, i. e.

(58)dXAdW=AFAo1πr2ρb−rA

Recalling the relationship between the reaction rate and the change in partial pressure over time, the design equation simplifies to

(59)dXAdW=AFAo1πr2ρb1RTAe−EARTpApB4−pCpD2KPn

Equation (59) can then be utilized in the model to predict conversion profiles along the reactor length using Ohya and colleagues’ kinetic parameters A, E_A, and n.

Nomenclature

Variable: Description
A: Arrhenius Pre–exponential
AR: Cross Sectional Area of Reactor
b: Empirical Constant
CAo: Inlet Concentration of CO₂
EA: Activation Energy
FA: Molar Flow Rate of CO₂
FAO: Inlet Molar Flow Rate of CO₂
fA: Molar Flow Rate of CO₂ per Unit Area
fpi: Pressure Function of Sabatier Rate Law
fpiOUT: Pressure Function as Function of Outlet Partial Pressures
f〈pi〉: Pressure Function as Function of Avg.Partial Pressures
i: Species of CO₂,H₂,CH₂,H₂ O,or O₂/N₂
k+: Arrhenius Forward Rate Constant
Kp: Pressure Equilibrium Constant
L: Reactor Length
n: Catalyst Coefficient
pAo: Inlet Partial Pressure of CO₂
pA: Partial Pressure of CO₂
pi: Partial Pressure of Species i
piOUT: Outlet Partial Pressure of Species i
〈pi〉: Average Partial Pressure of Species i
Q: Volumetric Flow Rate
r: Reactor Radius
R: Ideal Gas Constant
R2: Coefficient of Determination
rCO2or rA: Reaction Rate of CO₂
〈rA′〉: Average Reaction Rate of CO₂
t: Time
T: Temperature
yAo: Inlet Mole Fraction of CO₂
yAVERAGE: Average of Experimental Value used to Calculate R₂
yEXPERIMENTAL: Experimental Value used to Calculate R₂
yPREDICTED: Predicted (Model) Value used to Calculate R₂
XA: Conversion of CO₂
W: Mass of Catalyst
ρb: Catalyst Bulk Density
ε: Compressibility
δ: Change in the Number of Moles

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Received: 2018-01-14

Accepted: 2018-03-21

Published Online: 2018-05-25

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Articles in the same Issue

https://doi.org/10.1515/ijcre-2018-0008

Keywords for this article

Sabatier; CO2 Methanation; Kinetics; Trash to Supply Gas Technology