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Reservoir simulation computational costs have been continuously growing due to high-resolution reservoir characterization, increasing model complexity, and uncertainty analysis workflows. Reducing simulation costs by upscaling is often necessary for operational requirements. Fast evolving High-Performance-Computing (HPC) technologies offer opportunities to reduce cost without compromising fidelity. This work presents a novel in-house massively parallel full-physics reservoir simulator running on the emerging graphics processing unit (GPU) architecture. Almost all the simulation kernels have been designed and implemented to honor the GPU single insruction, multiple data (SIMD) programming paradigm. These kernels include physical property calculations, phase equilibrium computations, Jacobian construction, linear and nonlinear solvers, and wells. Novel techniques are devised in various kernels to expose enough parallelism to ensure that the control and data-flow patterns are well suited for the GPU environment. Mixed-precision computation is also employed when appropriate (e.g., in derivative calculation) to reduce computational costs without compromising the solution accuracy. The GPU implementation of the simulator is tested and benchmarked using various reservoir models, ranging from the synthetic SPE10 Benchmark (Christie & Blunt, 2001) to several industrial-scale models. These real field models range in size from tens of millions to hundreds of millions of cells with black-oil and multicomponent compositional fluid. The GPU simulator is benchmarked on the IBM AC922 massively parallel architecture having tens of Nvidia Volta V100 GPUs. To compare performance with CPU architectures, an optimized CPU implementation of the simulator is benchmarked on the IBM AC922 CPUs and on a cluster consisting of thousands of Intel Haswell-EP Xeon® CPU E5-2680 v3. Detailed analysis of several numerical experiments comparing the simulator performance on the GPU and the CPU architectures is presented. In almost all of the cases, the analysis shows that the use of hardware acceleration offers substantial benefits in terms of wall time and power consumption. This novel in-house full-physics, black-oil and compositional reservoir simulator employs several novel techniques in various simulation kernels to ensure full utilization of the GPU resources. Detailed analysis is presented to highlight the simulator performance in terms of runtime reduction, parallel scalability and power savings.

Traditional models of electrokinetic transport in porous media are based on homogenized material properties, which neglect any macroscopic effects of microscopic fluctuations. This perspective is taken not only for convenience, but also motivated by the expectation of irrotational electro-osmotic flow, proportional to the electric field, for uniformly charged surfaces (or constant zeta potential) in the limit of thin double layers. Here, we show that the inherent heterogeneity of porous media generally leads to macroscopic vortex patterns, which have important implications for convective transport and mixing. These vortical flows originate due to competition between pressure-driven and electro-osmotic flows, and their size are characterized by the correlation length of heterogeneity in permeability or surface charge. The appearance of vortices is controlled by a single dimensionless control parameter, defined as the ratio of a typical electro-osmotic velocity to the total mean velocity.

Many battery electrodes contain ensembles of nanoparticles that phase-separate on (de)intercalation. In such electrodes, the fraction of actively intercalating particles directly impacts cycle life: a vanishing population concentrates the current in a small number of particles, leading to current hotspots. Reports of the active particle population in the phase-separating electrode lithium iron phosphate (LiFePO4; LFP) vary widely, ranging from near 0% (particle-by-particle) to 100% (concurrent intercalation). Using synchrotron-based X-ray microscopy, we probed the individual state-of-charge for over 3,000 LFP particles. We observed that the active population depends strongly on the cycling current, exhibiting particle-by-particle-like behaviour at low rates and increasingly concurrent behaviour at high rates, consistent with our phase-field porous electrode simulations. Contrary to intuition, the current density, or current per active internal surface area, is nearly invariant with the global electrode cycling rate. Rather, the electrode accommodates higher current by increasing the active particle population. This behaviour results from thermodynamic transformation barriers in LFP, and such a phenomenon probably extends to other phase-separating battery materials. We propose that modifying the transformation barrier and exchange current density can increase the active population and thus the current homogeneity. This could introduce new paradigms to enhance the cycle life of phase-separating battery electrodes.

We reformulate and extend porous electrode theory for non-ideal active materials, including those capable of phase transformations. Using principles of non-equilibrium thermodynamics, we relate the cell voltage, ionic fluxes, and Faradaic charge-transfer kinetics to the variational electrochemical potentials of ions and electrons. The Butler-Volmer exchange current is consistently expressed in terms of the activities of the reduced, oxidized and transition states, and the activation overpotential is defined relative to the local Nernst potential. We also apply mathematical bounds on effective diffusivity to estimate porosity and tortuosity corrections. The theory is illustrated for a Li-ion battery with active solid particles described by a Cahn-Hilliard phase-field model. Depending on the applied current and porous electrode properties, the dynamics can be limited by electrolyte transport, solid diffusion and phase separation, or intercalation kinetics. In phase-separating porous electrodes, the model predicts narrow reaction fronts, mosaic instabilities and voltage fluctuations at low current, consistent with recent experiments, which could not be described by existing porous electrode models.

Porous electrodes composed of multiphase active materials are widely used in Li-ion batteries, but their dynamics are poorly understood. Two-phase models are largely empirical, and no models exist for three or more phases. Using a modified porous electrode theory based on non-equilibrium thermodynamics, we show that experimental phase behavior can be accurately predicted from free energy models, without artificially placing phase boundaries or fitting the open circuit voltage. First, we simulate lithium intercalation in porous iron phosphate, a popular two-phase cathode, and show that the zero-current voltage gap, sloping voltage plateau and under-estimated exchange currents all result from size-dependent nucleation and mosaic instability. Next, we simulate porous graphite, the standard anode with three stable phases, and reproduce experimentally observed fronts of color-changing phase transformations. These results provide a framework for physics-based design and control for electrochemical systems with complex thermodynamics., National Science Foundation (U.S.) (Contract DMS-0948071), Samsung-MIT Alliance

In nanoparticulate phase-separating electrodes, phase separation inside the particles can be hindered during their charge/discharge cycles even when a thermodynamic driving force for phase separation exists. In such cases, particles may (de)lithiate discretely in a process referred to as mosaic instability. This instability could be the key to elucidating the complex charge/discharge dynamics in nanoparticulate phase-separating electrodes. In this paper, the dynamics of the mosaic instability is studied using Smoothed Boundary Method simulations at the particle level, where the concentration and electrostatic potential fields are spatially resolved around individual particles. Two sets of configurations consisting of spherical particles with an identical radius are employed to study the instability in detail. The effect of an activity-dependent exchange current density on the mosaic instability, which leads to asymmetric charge/discharge, is also studied. While we show that our model reproduces the results of a porous-electrode model for the simple setup studied here, it is a powerful framework with the capability to predict the detailed dynamics in three-dimensional complex electrodes and provides further insights into the complex dynamics that result from the coupling of electrochemistry, thermodynamics, and transport kinetics., National Science Foundation (U.S.) (Contract No. DMS-0842504), National Science Foundation (U.S.) (grant number OCI-1053575, under allocation No. TG-DMR110007), National Science Foundation (U.S.) (Contract No. DMS-0948071), Samsung (Firm) (Samsung-MIT Program for Materials Design and Energy Applications)