381824 Analytical Model for the Electrochemical Reduction of CO2 in a Microfluidic Cell
Globally, CO2 emission through the combustion of fossil fuels has increased by about 1.6 times between 1990 (the Kyoto Protocol reference year) and 2013, with approximately 9.9 GtC added to the atmosphere in 2013.1 To limit the potential effect of climate change caused by carbon emission, many strategies are being explored, including carbon capture and sequestration (CCS) and increasing the use of carbon-neutral energy sources such as nuclear, wind, solar and hydroelectricity. When it is powered by the carbon-neutral electricity source, electrochemical conversion of CO2 not only provides an economic way of utilizing the CO2 captured, but also can serve as a storage mechanism for storing excess energy from intermittent renewable sources into fuels.2
Many early studies on electrochemical conversion of CO2 are experimental in nature, focusing on the possible mechanisms for the various products of CO2 electro-reduction, or exploring different types of electrodes and catalysts to improve performance3. As an alternative approach to the laborious experiments, first-principles modeling of electrochemical reactors can complement the current experimental work by elucidating the complex transport and electrochemistry particularly in porous electrodes, and help in designing and optimizing such reactors. Currently, there is a lack of detailed full cell model and no analytical model for the aqueous electrochemical reduction of CO2 in a microfluidic cell, which has been demonstrated to be an effective reactor and a versatile analytical tool4.
Here, we will present a full steady-state isothermal model and the approximate analytical solutions for an electrochemical microfluidic cell that reduces CO2 to CO. Conversion of CO2 into CO is attractive due to the versatility of CO (with H2) as a feedstock in Fischer-Tropsch synthesis to a variety of products including liquid hydrocarbon fuels. We will begin our analysis with a full model that takes into account all the significant physics and electrochemistry in the cell, such as the transport of species and charges, momentum and mass conservations, and electrochemical reactions. The full model consists of partial differential equations (PDEs) is solved using finite element method. It is calibrated and validated using experimental data obtained for various inlet flow rates and compositions. A narrow-gap approximation and scale arguments allow for a significant reduction in the mathematical complexity of the full model; that is, the PDEs reduce to a set of ordinary differential equations and Poisson’s equations. Integration, Taylor-series expansions, homogenization and separation of variables then allow for approximate analytical solutions. The approximate analytical solutions are verified with the numerical results obtained from the full model; good agreement is found. As the approximate analytical solutions are more computational efficient, it can be suitably extended for stack design and optimization.
1. T. A. Boden, G. Marland and R. J. Andres, ed. O. R. N. L. Carbon Dioxide Information Analysis Center, Oak Ridge, Tenn., U.S.A., 2010.
2. D. T. Whipple and P. J. A. Kenis, The Journal of Physical Chemistry Letters, 2010, 1, 3451-3458.
3. H.-R. M. Jhong, S. Ma and P. J. A. Kenis, Current Opinion in Chemical Engineering, 2013, 2, 191-199.
4. D. T. Whipple, E. C. Finke and P. J. A. Kenis, Electrochemical and Solid-State Letters, 2010, 13, B109.
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