(32e) Multi-Scale CO2 Conversion Modelling on Cu-Based Catalysts

Background. Increasing
concentrations of carbon dioxide in the atmosphere, although not toxic per se, are problematic due to their
link to global warming. To fight climate change, several methods have been
proposed. Carbon dioxide utilization through catalytic reduction to methanol is
one of the most promising avenues to alleviate this problem. In this way,
carbon dioxide can be captured directly at high-concentration sources (such as
thermal power stations) and transformed into a useful chemical and an
easy-to-handle energy source. Industrially, copper-zinc-alumina (CZA) catalysts
are most commonly used because of their high conversions, selectivities
towards methanol and resistance against deactivation. Although their operations
is empirically understood well enough for engineering purposes, there is much
debate about the exact mechanism and kinetics. Such knowledge is essential if
one aims to systematically improve the catalysts.

We synthesised
two catalysts (Cu/ZnO/alumina and Cu/MgO/alumina), experimentally tested them and performed ab initio multi-scale modelling,
employing density functional theory (DFT), kinetic Monte Carlo (kMC), and micro-kinetic modelling (MK). Although no empirical
assumptions were made in the process, results from theoretical modelling follow
experiments nicely. Catalysts were synthesised in-house in such a way as to
mimic the industrial catalysts as closely as possible but to avoid any spurious
effects from impurities that are found in industrial catalysts (binders,
stabilizers, intellectual property related compounds etc.).

Experimental. Experimentally,
we aimed to discover the influence of MgO and ZnO on the characteristics of Cu-based catalysts. The
Cu/M/Al catalysts (Cu:M: Al
= 50:30:20 and M = Zn or Mg) were prepared by co-precipitation method at a
constant pH = 8.  Catalysts were
characterized by BET, XRD, TPR, N₂O-titration, CO₂-TPD,
XPS and micrographic techniques. Then, their catalytic activity for CO₂
hydrogenation to methanol was evaluated. The catalytic activity was assessed in
relation to the physicochemical properties of the catalysts together with the
copper surface area, the reducibility of CuO and the
catalyst basicity.

Ab initio calculations. DFT simulations were
carried out in plane-wave formalism with exchange-correlation Perdew-Burke-Ernzerhof (PBE)
functional within generalized gradient approximation (GGA). To take Cu-ZnO or Cu-MgO interface effect into
account, which is the actual active site, into account, catalysts were modelled
as follows. Cu sites were modelled as a Cu(111)
surface. On top of the surface, a ZnO or MgO cluster, consisting of six atoms, was placed in the energetically
most favourable orientation. The contact of ZnO or MgO clusters with Cu(111) was
active site where the reaction took place.

A complex
reaction pathway consisting of all possible intermediates and their
interconversions was constructed. In total, 26 species and 33 reversible reaction
steps were taken into account. To account for the hydrogen spill-over effect, which
play a prominent role in catalyst performance, surface diffusion of hydrogen
was explicitly included. Adsorption energy for each species was calculated,
from which adsorption and desorption kinetics as functions of temperature and
partial pressure were obtained from collision theory. For all elementary
reaction steps, transition states were found and vibrational analysis was
performed. This enabled us to use the transition state theory to obtain the first-principles-derived
reaction rates as functions of temperature, which were used in kMC and MK modelling.

Modelling KMC. Kinetic Monte Carlo (kMC) simulations represent one of the pillars of
multi-scale modelling approach, linking the atomistic-scale DFT computations
with mesoscopic-scale kinetics. Recently, kMC has
been gaining importance in the heterogeneous catalysis field to describe the
performance (e.g. selectivity,
conversion, surface kinetics) of a catalyst under operating conditions. Using
DFT-obtained results of methanol synthesis reactions from carbon dioxide and
hydrogen on two types of catalysts (metal-oxide alloys of Cu/Zn or Cu/Mg), we
simulated the reaction pathway using kMC software
package Zacros.

The methanol
synthesis model consists of overall 19 lattice and 7 gas species, and 33
reversible reaction steps. For both catalysts, we simulated the reaction
pathway at various temperatures (ranging from T = 480 K to T = 600
K) and pressures (ranging from P = 20 bar
to P = 60 bar). We studied how
selectivity, reaction steps frequencies, and lattice coverage change over time,
temperature, and pressure.

We found that selectivities towards methanol are in general reasonably
high at low temperatures but tumble with increasing temperature for all four
catalysts (i.e. 80 % at T = 600
K for Cu/Mg catalyst). In line with other theoretical and experimental studies,
we also observed an increase in selectivity with increasing pressure. By
analysing the event frequency distribution, we studied the relative importance
of certain reaction step for each of the two catalysts, confirming that the
reaction pathway towards methanol production is slightly different for each of
them and also dependent on the operating conditions. Similar conclusions were
obtained also by our microkinetic modelling studies,
as well as experiments.

Microkinetics. Using microkinetic modelling (MK), a CSTR
reactor was simulated. The surface reaction rates were defined as:

r_i is the rate of i-th reaction (in s^-1), where k_i and k_-i
are forward and backward constants, respectively. Θ denotes the surface coverage of species. Mass balances for
surface species were defined as:

Where n is the number of reactions and S_ij is
the “stoichiometric coefficient”, which denotes how many times the species in
question occurs in the reaction and whether it is produced or consumed. For the
bulk species (gas phase concentrations), the mass balances were:

C_j is the concentration of the species in the bulk phase, M_sites
is the total concentration of catalysts sites in the reactor volume, ε is the void fraction of the
catalyst bed, F is the total
volumetric flow through the reactor, V_R
is the reactor volume and C_j,inlet is the inlet
concentration of the bulk species.

Using the
systematic approach described above, a system of 33 non-linear ordinary
differential equations was obtained. Starting with an empty catalyst, the
system was solved until a steady state was reached.

Results. Microkinetic modelling showed high selectivities towards methanol at low temperatures (between
95 and 100 %). Selectivities decreased with
increasing temperature for both catalysts, although the magnitude of the change
was somewhat smaller than in the experiment and kMC. As
in kMC, Cu/Mg catalyst was observed to have a little
higher selectivity than Cu/Zn, but the latter nevertheless performs better on
account of great conversion, especially at lower temperatures. Above
650 K, the conversion for both catalysts is the same. As for pressure
dependence, the conversions and selectivities
increase with increasing pressure. This effect is more pronounced on Cu/Zn
catalyst.

Figure 1: Temperature dependence of
selectivity towards CH₃OH and conversion of CO₂ for the investigated
catalysts from microkinetic modelling at p = 40 bar and GHSV = 6000 h⁻¹.

Conclusion. We have synthesised Cu/Zn and Cu/Mg catalysts for catalytic
hydrogenation of carbon dioxide into methanol. Experimental results showed high
selectivities (above 90 %) at industrially
relevant temperatures (200-250 °C) and pressure (20-40 bar) and good
conversions. As the temperature increases, selectivity is lowered but the
conversion is increased. The main side product is carbon monoxide, which is
formed through reverse water-gas shift (RWGS) reaction because it is favoured
at higher temperatures and pressures. Cu/Zn catalyst had much higher
conversion, while Cu/Mg exhibited marginally better selectivity towards
methanol. Results from kMC and MK modelling were in
good agreement with these experimental results, proving that out model is sound
and veracious for describing catalytic methanol synthesis.

DFT results
prove that the reaction proceeds via formate pathway,
i.e. through HCOO, H₂COO,
H₂COOH, H₂CO, H₃CO to
CH₃OH. On Cu/Zn catalyst, formation of H₂COO has the
highest activation energy along the aforementioned reaction path and is
probably the rate-determining step. On Cu/Mg, the rate-determining step is the
same, but H₂COOH is never formed as H₂COO decomposes into
H₂COO directly. Insights from kMC reveal
the temporal evolution of the lattice coverage and frequency of each reaction
step. Lattice is first quickly saturated with hydrogen. As the reaction
proceeds, other intermediates are gradually formed until the steady state is
reached. Interestingly, H₂COO hydrogenation into H₂COOH
is decisively the most frequent reaction step (the opposite of rate-determining
step) on Cu/Zn , while on Cu/Mg RWGS pathway
contributes non-negligibly.

Our results
offer novel insights into the hydrogenation of carbon dioxide to methanol.
Exact elucidation of the pathway, including energetics and kinetics of every
reaction step, allows for calculation of catalyst performance across a wide
range of operating conditions. This approach can be extended to other catalyst
combinations, revealing promising catalysts in hope of improving the industrial
grade CZA catalyst.