The transition from fossil fuels to renewable energy has brought + about a rapid increase in the availability of clean electricity. + However, electricity generated from sources such as wind and solar are + limited to intermittent operation due to daily and seasonal variation. + One solution is to utilize electrochemical devices in energy storage + and electrochemical manufacturing applications, where they can harness + surplus energy and decarbonize chemical industries traditionally + reliant on petrochemical feedstocks. Managing the growing prevalence + of renewable energy underscores the importance of developing and + scaling up these technologies, which can in turn facilitate the + achievement of carbon emission reduction commitments of companies and + developed economies. Likewise, the electrification of transport + creates an increasing need for energy-dense electrochemical energy + storage devices such as batteries and supercapacitors. Naturally, + simulation tools are required to assist in the design of efficient and + industrial-scale electrochemical devices.
+Modeling and simulation are used extensively to describe the + physics of the electrochemical and transport mechanisms in + electrochemical devices. These devices have many applications, from + miniaturized lithium-ion batteries for medical devices up to + industrial-scale hydrogen fuel cells for backup power generation. + Energy storage devices include batteries and supercapacitors, as well + as flow batteries, which utilize a flowing electrolyte instead of a + stationary liquid or polymer electrolyte. Electrolyzers are devices + that use electrical energy to perform electrochemical reactions. Some + current industrial applications for electrolysis include the + chlor-alkali process for the production of chlorine gas and the + Hall-Héroult process for aluminum production. Active areas of research + include the development of electrolyzers that transform carbon dioxide + into useful chemicals such as base molecules for sustainable aviation + fuels or the chemical industry, as well as electrolyzers that create + hydrogen from water. In the reverse process, fuel cells use fuels such + as hydrogen to generate electricity. While electrochemical devices + span many scales and industries, the governing equations and + underlying physical phenomena remain similar.
+The transport of charged chemical species in a fluid is often
+ modeled using the Nernst-Planck equation, which includes the usual
+ advection and diffusion transport as well as
+
EchemFEM provides a high-level user interface for a finite element
+ implementation of the Nernst-Planck equation. The user is simply
+ required to provide physical parameters as well as functions
+ describing the chemical reactions (charge-transfer or bulk reactions).
+ The mesh can be defined using either built-in functions for simple
+ geometries, or imported from external packages, such as Gmsh
+ (
EchemFEM is based on Firedrake
+ (
The repository includes several examples of electrochemical devices + such as flow reactors, flow batteries, and CO2 electrolyzers.
+Electrochemical phenomena are highly complex, making + characterization of electrochemical devices through in-operando + experiments challenging. Simulation is an important tool for + predicting the performance of electrochemical devices, as well as + assisting in their design. As technologies get scaled up from the + laboratory scale to industrial scale, experiments become less + tractable and therefore simulation increasingly important. Naturally, + the scalability of simulators is crucial. Furthermore, many existing + models and codes are just one dimensional. To capture the effects of + fluid flow and non-monolithic, architected electrodes, + higher-dimensional effects do matter. For three-dimensional systems, + iterative methods and appropriate preconditioners are required to + maintain scalability.
+Currently, commercial software are the most commonly used codes for + electrochemistry simulations. COMSOL Multiphysics®, with its detailed + electrochemistry module, is the most popular, while Simcenter™ + STAR-CCM+™ is also used commonly for flowing systems. These programs + provide simple graphical user interfaces (GUI), which allow users to + quickly set up new simulations. Additionally, other physics modules + such as fluid dynamics are available and can usually be coupled with + the electrochemistry simulation. However, there are several drawbacks + to using such commercial software. For instance, license fees can be + prohibitively expensive, therefore limiting collaboration. + Furthermore, the closed nature of the source code limits the + flexibility of the software. Indeed, it is not possible to implement + new discretization schemes and preconditioning approaches that may be + required for numerical stability or scalability, respectively. + Finally, since everything needs to be set up through the GUI, + scripting and coupling to other software are difficult tasks.
+There is a growing number of open-source software for
+ electrochemistry, especially Python-based packages
+ (
EchemFEM provides a general framework for simulating + electrochemical transport: it is not specific to an application. Since + it is based on Firedrake, any additional physics that can be + implemented in a finite element framework can be coupled to EchemFEM. + In one of the demos, the incompressible Navier-Stokes equations are + solved in a reactor with an irregular surface, providing a velocity + field for the transport equations. Similarly, in a flow battery + example, the Navier-Stokes-Brinkman equations are solved.
+In some cases, for example for fast flows, stabilization schemes
+ that are not offered in other software may be required. For continuous
+ Galerkin (CG) elements, a streamline-upwind Petrov-Galerkin (SUPG)
+ method for the Nernst-Planck equation is provided. For discontinuous
+ Galerkin (DG), a custom upwind scheme for the Nernst-Planck equation
+ is used
+ (
As opposed to commercial software, custom scalable solvers are
+ available in Firedrake. A plethora of solver options are available
+ through simple PETSc keywords and custom operators for preconditioning
+ can be defined using Firedrake
+ (
Combining EchemFEM with other Python packages is rather simple. In
+ Govindarajan et al.
+ (
Firedrake’s automatic adjoint capabilities facilitate the
+ straightforward solution of PDE-constrained optimization problems
+ (
This work was performed under the auspices of the U.S. Department + of Energy by Lawrence Livermore National Laboratory (LLNL) under + Contract DE-AC52-07NA27344, and was partially supported by a + Cooperative Research and Development Agreement (CRADA) between LLNL + and TotalEnergies American Services, Inc. (affiliate of TotalEnergies + SE) under agreement number TC02307 and Laboratory Directed Research + and Development (LDRD) funding under projects 19-ERD-035 and + 22-SI-006. LLNL Release Number LLNL-JRNL-860653.
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