Mathematical Modeling of a Microfluidic for the Reduction of Carbon Dioxide.

[NNadir]

The paper I'll discuss in this post is this one: Correlating Uncertainties of a CO2 to CO Microfluidic Electrochemical Reactor: A Monte Carlo Simulation (Raman et al, Ind. Eng. Chem. Res.2019, 58. 42, 19361-19376) It's in the current issue of this journal as of this writing.

The paper's introductory graphic is a cartoon evoking an Ishikawa "fish plot" diagram:



Removal of the dangerous fossil fuel waste carbon dioxide, which is killing the planet, from the atmosphere is only possible if future generations have something to do with it. Although our current practice is to burn a dangerous greenhouse gas, dangerous natural gas; a liquid, dangerous petroleum; or a solid, dangerous coal, to produce this dangerous fossil fuel waste, with sufficient energy, the combustion of these dangerous fossil fuels is reversible, via a reaction known as the Boudouard Reaction.

I've written at length in various places about this reaction.

Here, from another paper about adjusting the thermal equilibrium the reaction describes, is a graphic that describes the Boudouard reaction:



Source: Microwave-Specific Enhancement of the Carbon–Carbon Dioxide (Boudouard) Reaction

The reaction is shown at the top of this graphic. The equilibrium lines in this graphic, one is thermal and the other driven by microwave radiation, shows that one can make carbon - which under the right conditions can be processed into useful materials - from carbon monoxide if one removes one of the reactants, which would be carbon dioxide.

A great deal has been written in the scientific literature about reducing carbon dioxide to carbon monoxide, and this paper is just one example. Microfluidic devices are just what they sound like, devices with small channels that are designed to maximize surface area by forcing a fluid - in this case as gas, the dangerous fossil fuel waste carbon dioxide - through tiny channels. Although the technology for making these devices has advanced to a high level only in recent times, these types of devices have long been known: A well understood microfluidic device, in this case for fluid exchange, is a human lung.

There are many variations on the Boudouard reaction, some of my personal favorites being "dry reforming" of waste organic materials, municipal and industrial carbon based wastes for example, or the dry reforming of biomass. The method described here is electrochemical. Although electricity is a thermodynamically questionable approach to energy storage or materials processing, there are certain conditions where grid and load balancing make waste electricity available for electrochemical processes, for example in the case of a plant designed for continuous operation that runs during low load periods.

From the paper's introduction:

Climate change and global warming are among the major present-day concerns due to increasing CO2 emissions across the world.(1) Following several global initiatives to address these concerns, such as the Paris Agreement and the Kyoto Protocol, CO2 reduction and CO2 utilization technologies have attracted increased attention.(2?7) Utilizing captured CO2through electrochemical methods not only serves as an alternative to carbon sequestration but also helps toward achieving a carbon neutral energy cycle when operated by renewable sources such as solar, wind, and so forth.(8?12)These electrochemical reactors convert the feedstock, CO2, to useful chemicals such as formic acid and formates,(13,14) alcohols,(15,16) carbon monoxide (CO),(17,18) ethylene,(19,20) and methane.(21) The selectivity of the electrochemical conversion depends on three major factors: (1) the reaction mechanism, in the form of a cathode side catalyst, (2) the ion-adsorbate interaction, in the form of the electrolyte species, and (3) the electrochemical activation energy, in the form of the applied potential.

Typically, the selectivity toward one or more of the above-mentioned products is controlled by the choice of the cathode side catalyst including metal surfaces,(21) metal nanoparticles,(22) metal oxides,(23) organometallic molecules,(24) and metal and covalent organic frameworks.(25,26) Several recent reviews outline the recent trends in the selectivity-based electrocatalyst development.(27?30) These electrocatalysts are usually studied and screened in a three-electrode setup or an H-cell. However, these reactor configurations can be mass-transport-limited.(31,32) In addition, these systems are batch reactors and are not scalable, making them less relevant for commercialization.

To overcome mass transport limitations and to achieve scalability, flow cell architectures were investigated. These flow cell reactors are of different types, viz., solid oxide electrolysis cells,(33,34) membrane-based electrolytic cell,s(32,35) and microfluidic flow cells (MFCs).(36,37) Berlinguette and co-workers(38) present a detailed account on the development of flow cells for the electroreduction of CO2. Bevilacqua et al.(39) discuss the efforts to scale up these flow cells. Despite a large number of such studies being experimental, there has also been recent interest toward the mathematical modeling of such systems.(6,40?43) These mathematical models, depending on their complexity, can shed light on the intricate interplay between gas transport and electrochemistry. Along with suitable experiments, through these models, we can delve deeply into the effects of various design, physical, material, operating, and electrochemical parameters on the functioning of the reactor...

...during the large-scale fabrication of these microfluidic reactors, the properties may deviate from the values specified for a desired output. Therefore, in practical applications, it is difficult to identify these uncertainties and estimate their influence on the conversion efficiency, reactor performance, and selectivity.
To capture this random yet probabilistic nature of variation of the input parameters, a stochastic method such as Monte Carlo simulations (MCS) is necessary. Through MCS, we can identify not only the most critical input parameter in a given range of operating parameters but also uncover the effects of the simultaneous variation of different input parameters on the system. Following this stochastic approach, deterministic analyses such as identifying optimal regions of operation, different choices of materials, and robust control strategies, diagnoses, and prognoses can be carried out...

...In light of the lack of a stochastic technique that can record the probabilistic nature of the input parameters and their relative impact on the current density and the trade-off between cell performance and conversion efficiency and the Faradaic efficiency of an MFC reactor, first we conduct MCS of a 2D mechanistic model of the MFC reactor. To achieve this, we generate a large random population of input parameters and simulate a detailed mechanistic model of the MFC reactor across the parameter space. A fish-bone diagram relating these stochastic input parameters to the response variables is illustrated in Figure 1. The varied stochastic parameters can be classified as (a) geometric/design, consisting of the thickness of each functional layer and the cell length and width; (b) physical, involving the porosity of the functional layers and the dynamic viscosity of the feed gas; (c) material, consisting of the electrical conductivity of the different functional layers and the ionic conductivity of the electrolyte; (d) operating, including the applied cell potential, temperature, feed gas flow rates, and inlet feed mole fractions; and (e) electrochemical parameters, including the exchange current densities and charge transfer coefficients...

Figure 1:



The caption:

Figure 1. Cause and effect “fish-bone” diagram illustrating the varied stochastic parameters influencing the MFC CO2 converter.

After some following discussion the authors write this to describe their approach to modeling putative electrochemical devices for reducing carbon dioxide to carbon monoxide:

Microfluidic Cell Model. We consider an MFC consisting of several functional layers: cathode and anode current collectors, cathode and anode gas flow fields, cathode and anode gas diffusion electrodes, and an electrolyte channel. An aqueous electrolyte solution flows between the cathode and the anode gas diffusion electrodes. The cathode and anode gas diffusion electrodes are coated with the catalyst at the interface with the electrolyte, giving rise to a gas diffusion layer and a catalyst layer. A detailed schematic of the MFC along with the computational domain is presented in Figure 2.

Figure 2:



The caption:

Figure 2. Overall 2D schematic of the microfluidic CO2 converter presenting different functional layers and the computational domain with boundaries marked with Roman numerals: (I) cathode feed inlet; (II) cathode and anode outlets; (III) anode feed inlet; (IV) insulated vertical walls; (V) cathode current collector horizontal wall; (VI) gas flow field?current collector interface; (VII) gas diffusion layer?gas flow field interface; (VIII) catalyst layer?gas diffusion layer interface; (IX) electrolyte?catalyst layer interface; (X) anode current collector horizontal wall.

The reactions considered here by the authors involve a hydrogen side product. There are examples of such reactions which do not involve hydrogen, although in the electrical case, the reduced carbon dioxide is made into hydrocarbons and/or alcohols.

From the text:

The electrochemical reduction of CO2 to CO takes place in the cathode catalyst layer. Along with this reaction, when a sufficiently large overpotential is applied, the water diffused out of the electrolyte also undergoes reduction to produce H2 gas. On the cathode side, the production of CO and the hydrogen evolution reaction (HER) can be summarized as



The oxygen evolution reaction (OER) on the anode side is given as

The latter reaction, the oxygen evolution reaction at an electrode is the subject of much discussion in the scientific literature, because of its nature as a 4 electron reaction. Although electrolysis is well known and often practiced, although most of the world's hydrogen is made by reforming dangerous natural gas, it places limits on the energy efficiency of electrochemical water splitting and is thus open to improvement.

A table of the variables considered.



Some other graphics from the the paper which may or may not mean much:




The caption:



Figure 3. (a) Polarization curve and (b) conversion efficiency (—) and Faradaic efficiency (---) as a function of the applied cell potential, corresponding to the mean values of input parameters.



The caption:

Figure 4. Sample distribution of the inlet CO2 mole fraction, xCO2in (bars), and the fitted normal distribution functions (lines) for different sample sizes: (a) 170 and (b) 103.

The caption:


Figure 5. Ranking of stochastic parameters under the IND scenario at Ecell = ?2.7 V (black), ?2.8 V (blue), ?2.9 V (green), ?3.0 V (gray), and ?3.1 V (violet) for (a) cell performance, (b) conversion efficiency, and (c) Faradaic efficiency.



The caption:

Figure 6. Ranking of stochastic parameters under the SIM scenario at Ecell = ?2.7 (black), ?2.8 (blue), ?2.9 (green), ?3.0 (gray), and ?3.1 V (violet) for (a) cell performance, (b) conversion efficiency, and (c) Faradaic efficiency.

The caption:

Figure 7. Scatter plots of the cell performance against ?CO, xCO2in, and L in (a–c) the IND scenario (circles) and (d–f) the SIM scenario (circles). The triangle represents the cell performance corresponding to the mean values of input parameters.

The caption:

Figure 8. Comparison of the REG model (circles) and GPR model (dots) for the SIM scenario at Ecell = (a) ?2.7, (b) ?2.8, (c) ?2.9, (d) ?3.0, and (e) ?3.1 V.

The caption:

Figure 9. Probability distribution of cell performance for the SIM scenario at Ecell = (a) ?2.7, (b) ?2.8, (c) ?2.9, (d) ?3.0, and (e) ?3.1 V.

In the above, SIM, IND, and REG refer to manner the Monte Carlo Simulation is run, i.e. the process and sequence by which the variables are subject to perturbations.

This kind of research can be obscure and arcane, but it is very, very, very important nonetheless.

A word we hear too much is could, but I'll use it anyway. Properly focused we could do so much with the power of our scientific tools, but regrettably we are doing very little.

Have a nice weekend.