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CHEE 321 — Chemical Reaction Engineering Project

Fall 2022

1 Presentation

The object of this project is to study CO2 capture via catalytic hydrogenation of

methanol, modelled through the following system of reactions:

CO2 + 3 H2 CO2 + H2 CO + 2 H2

CH3OH + H2O

H2O + CO

CH3OH

(1)

(2)

(3)

The ﬁrst 2 reactions are the ”Reverse Water-Gas shift reaction”, while the last reaction is the ”dry reaction” . The objective is to maximize the production of methanol in a Packed Bed Reactor (PBR). The catalysis suggested is a commercially available Cu–Zn–Al catalyst.

In general, the reaction scheme is limited, mainly from a thermodynamic stand- point, and the outside a few speciﬁc industrial sectors, the overall process is of limited economic interest. Recent progresses, including some pointers on ﬁxed-bed reactor operation, are given in (Fornero et al., 2011) and (Park et al., 2014).

The project consists in four (4) parts, detailed below:

• 1. Thermodynamic analysis;

• 2. Kinetics analysis;

• 3. Effects of parameters; and,

• 4. Design considerations.

References are given at the end of this document. When possible, the teams are encouraged to consult these references and critically assess the choice of some of the values/relations proposed.

2 Phase 1: Thermodynamic Analysis

The ﬁrst part of the project consists in studying the system of reactions, follow- ing what was covered in the class:

CO2 + 3 H2 r1 CH3OH + H2O

CO2 + H2 r2 H2O + CO

CO + 2 H2 r3 CH3OH

The heat of reaction, at T = 298K are (Rahmatmand et al., 2018):

HR,1 = ←49.5 kJ/mol CO2

HR,2 = 41.2 kJ/mol CO2

HR,3 = ←90.7 kJ/mol CO.

In the main text of your report, present:

• The expressions for the equilibrium constant Keq,i for each reaction as a function of the molar fractions yj and the pressure P .

You are also asked to:

• Discuss if high pressure or low pressure favor the production of methanol, from an equilibrium standpoint.

Steps leading to these results can be reported in the Appendix for Part I.

Bonus work, to be reported in the main text, could include:

• Verify the conservation of mass for each reaction.

• Compute the values of ∆gR using Gibbs free energy of formation. (In this case, provide the reference(s) for the data).

• Compute the value of ∆hR using enthalpies of formation and dis- cuss, using the van’t Hoff equation, if low temperature of high tem- perature favor the production of methanol, from an equilibrium stand- point.

3 Phase 2: Kinetics

The reaction rates for the three reactions considered are taken directly from (Graaf et al., 1988). One can also consult (Graaf et al., 1990) for some discus- sion points. A cleaner discussion can be found in (Rahmatmand et al., 2018) (be careful about the numbering of the reactions if you consult any source — we used a different numbering system than in the references). The rates are given as follows:

r1 = ╱PCO2P ← \

r2 = ╱PCO2PH2 ← 、

r3 = ╱PCOP ← \

where the denominator term is given by:

den = (1 + KCOPCO + KCO2PCO2) ╱P + PH2O\

Rate constants are given as follows:

k1 = 1.09E05 exp ╱ 、

k2 = 9.64E11 exp ╱ 、

k3 = 4.89E07 exp ╱ 、

Equilibrium constants are given as follows:

Keq,1 = 10()

Keq,2 = 10( )

Keq,3 = 10( )

Adsorption Equilibrium constants are given as follows:

KCO2

KCO

KH2O

1/2 K

= 7.05E ← 07 exp ╱ 、

= 2.16E ← 05 exp ╱ 、

= 6.37E ← 09 exp ╱ 、

In the main text of your report, present:

• Report the expression of the production rates Rj for the reaction scheme considered.

• (Graphically) The reaction rates as function of temperature, for ﬁxed molar compositions (here you can consider the rates at V = 0, i . e ., reporting of the rates at the inlet of the ﬁxed-bed reactor).

You are also asked to:

• Discuss if high temperature or low temperature favor the production of methanol, from a kinetic standpoint.

Steps leading to these results can be reported in the Appendix for Part II.

Bonus work, to be reported in the main text, could include:

• Derive the expression of selectivity SCH3OH/H2O and discuss how you would maximize it (this can include qualitative explanations rather than ”optimization” arguments).

• Discuss how you could consider catalyst deactivation in the model, following the discussion from (Fichtl et al., 2015) and (Liang et al., 2019).

• Report other kinetic studies for the reaction scheme, including the po- tential merit of using different catalysts, see for example (Bustamante et al., 2004).

• Discuss critically the derivation of the Langmuir– Hinshelwood rates in (Graaf et al., 1988).

4 Phase 3: Effects of Parameters

For this part of the report, we are interested in the effect of the bed parameters on effectiveness. Remember that the Thiele modulus Φ is deﬁned as the ratio of the reaction rate over the diffusion rate. (When Φ is small, diffusion in the pellet dominates over reaction at the surface, while when Φ is large, reaction at the surface dominates over the diffusion in the pellet.) From the Thiele modulus, we derive the expression of the effectiveness η for spherical catalyst pellets:

η = ╱ ← 、 .