High Performance Computing for Pore Scale Design of Flow-Through Electrodes: A Water Desalination Application

Abstract

A growing population and environmental changes continue to threaten human development and supply of water and energy resources. Electrochemical devices are well positioned to solve many of these challenges due to their ability to store or use energy from renewable sources. Capacitive Deionization (CDI) is an example of such a device that uses electricity to desalinate water. It works by storing ions such as sodium and chloride from brackish water inside the electrical double layers of microporous carbon.

Electrochemical devices such as CDI come in a variety of different architectures or flow configurations. Flow-through CDI is one example where water flows through the macropores of the activated carbon or other electrode. The advantage is the fast salt adsorption rates, but the disadvantage is the pumping power required to force fluid through the electrode’s pores. To mitigate pressure losses, hierarchical design of the pore space must be considered carefully. Pore scale models are an excellent route to study and optimize microstructure for flow-through electrodes. One of the challenges with optimization, however, is how computationally demanding it can be. Therefore, much of this thesis is focused on laying the foundation for optimization by applying high-performance computing to the pore scale including GPU accelerated solvers, JIT compilation, and automatic differentiation. The first two works are focused on efficient construction of pore networks from images or experimental data while the final work applies GPU and JIT accelerated solvers to better understand transport around engineered channels for flow-through CDI.

This thesis explores two different methods for constructing pore networks that reliably characterize properties important for flow-through electrodes. In the first method, a modern and open-source implementation of the classic medial axis network extraction was written. It featured finding pores along long throats, a parallelized skeleton by chunking, and a fast walker method finding equivalent throat diameter. The new network extraction was tested on a 400³ image of Berea sandstone and the permeability predicted was within 5% of the lattice Boltzmann permeability. A speed-up of 4.2× compared to the watershed segmentation was observed. The second method calibrates a pore network to experimental data using gradient-descent optimization. The accessibility of automatic differentiation in increasingly popular machine learning packages was leveraged to write a fully differentiable pore network, suitable for gradient descent. This approach was used to match porosimetry and permeability data of a Berea sandstone in which a final combined loss of 9.7 × 10⁻⁴ was achieved. The optimization took roughly 20 minutes for a 10³ network of pores.

Finally, both methods for constructing a pore network were evaluated and the second method was chosen to construct a pore network of a porous activated carbon electrode because no volumetric image was available. A pair of pore networks were fit to the available experimental data representing the entire range of pore sizes from 50 nm to 10 μm. The pore network was used to simulate ion transport in the pore space surrounding channels engineered for flow-through CDI. The pore network model was written entirely in JAX to access GPU-accelerated and JIT-compiled solvers for electrochemical simulation in pore networks. The computation time of JAX’s iterative implicit solvers were compared to PyPardiso’s direct solvers (after factorization) and results showed a speedup of 23× and 14× for mass and charge transport respectively. The effect of hole size on CDI cell performance was studied and a final recommendation for smaller holes (~30 μm) spaced 100 μm apart was modelled and 17× faster salt adsorption was observed.