Continuum Modeling of Porous Electrodes for Electrochemical Synthesis.

Electrochemical synthesis possesses substantial promise to utilize renewable energy sources to power the conversion of abundant feedstocks to value-added commodity chemicals and fuels. Of the potential system architectures for these processes, only systems employing 3-D structured porous electrodes have the capacity to achieve the high rates of conversion necessary for industrial scale. However, the phenomena and environments in these systems are not well understood and are challenging to probe experimentally. Fortunately, continuum modeling is well-suited to rationalize the observed behavior in electrochemical synthesis, as well as to ultimately provide recommendations for guiding the design of next-generation devices and components. In this review, we begin by presenting an historical review of modeling of porous electrode systems, with the aim of showing how past knowledge of macroscale modeling can contribute to the rising challenge of electrochemical synthesis. We then present a detailed overview of the governing physics and assumptions required to simulate porous electrode systems for electrochemical synthesis. Leveraging the developed understanding of porous-electrode theory, we survey and discuss the present literature reports on simulating multiscale phenomena in porous electrodes in order to demonstrate their relevance to understanding and improving the performance of devices for electrochemical synthesis. Lastly, we provide our perspectives regarding future directions in the development of models that can most accurately describe and predict the performance of such devices and discuss the best potential applications of future models.

Multigrid hierarchical simulated annealing method for reconstructing heterogeneous media.

A reconstruction methodology based on different-phase-neighbor (DPN) pixel swapping and multigrid hierarchical annealing is presented. The method performs reconstructions by starting at a coarse image and successively refining it. The DPN information is used at each refinement stage to freeze interior pixels of preformed structures. This preserves the large-scale structures in refined images and also reduces the number of pixels to be swapped, thereby resulting in a decrease in the necessary computational time to reach a solution. Compared to conventional single-grid simulated annealing, this method was found to reduce the required computation time to achieve a reconstruction by around a factor of 70-90, with the potential of even higher speedups for larger reconstructions. The method is able to perform medium sized (up to 300(3) voxels) three-dimensional reconstructions with multiple correlation functions in 36-47 h.

Stochastic reconstruction using multiple correlation functions with different-phase-neighbor-based pixel selection.

A reconstruction methodology based on threshold energy based energy minimization (TA) and different-phase-neighbor (DPN)-based pixel swapping is presented. The TA method uses an energy threshold rather than probabilities as an acceptance criteria for annealing steps. The DPN-based pixel selection method gives priority to pixels which are segregated from clusters instead of random selection. An in-house solver has been developed to obtain two-dimensional reconstructions of heterogeneous two-phase mediums. Compared to conventional simulated annealing with random pixel swapping, the proposed method was found to achieve an optimal structure with up to an order of magnitude reduction in energy. When selecting a threshold tolerance value, the proposed method showed a 50% improvement in convergence time compared to conventional simulated annealing with random pixel swapping. The improved algorithm is used to study the effect of multiple correlation functions during the reconstruction. It was found that a combination of two-point correlation function and lineal path function for both phases results in most accurate reconstructions.