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.