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Nuclear magnetic resonance (NMR) techniques are key in the study of porous reservoir rocks. They can provide valuable insight into the pore size distribution of the pore space of a given rock sample due to its dependence on the magnetic fluid/matrix interaction. The pore space is often studied at the μm scale through the use of micro-CT images, which are often composed of hundreds of millions of voxels, posing significant challenges to numerical simulations. In this paper, we present an image-based, fully explicit, and matrix-free finite element implementation for the simulation of NMR relaxation process that is capable of handling such large 3D problems in single GPUs. The chosen explicit time-integration scheme uses a lumped capacitance formulation and stabilization via hyperbolization, and it is capable of handling arbitrary time-step sizes with controllable error levels. The image-based representation of the pore space is used for a memory-efficient, matrix-free formulation of the time integration using massively parallel processes on a single GPU. In addition, we propose the substitution of a global digital roughness correction factor that depends on the porous space's geometry for a problem-independent local correction factor, based on nodal neighborhoods. We show that the numerical scheme converges with successive refinements as expected and that our local correction coefficient is capable of estimating the correct S/V parameter of several different classical geometries. We tested our formulation against an image-based Random Walk simulation of four digital rock core samples, achieving good agreement between them. We manage to simulate a giga-voxel image-based model on a personal use GPU (less than 10GB of memory use) in 33 min with our FEM implementation. [ABSTRACT FROM AUTHOR]

NMR techniques are key in the study of porous reservoir rock, both experimentally and numerically. The T 2 relaxation process, the most common application of NMR, measures the loss of coherence of transversal magnetization and strongly depends on the fluid/matrix interaction—thus providing useful insights into the pore size distribution of a rock sample. The pore space is often studied at the μm scale through the use of micro-CT images, which are formed by stacks of images with hundreds of thousands of pixels each, posing significant challenges to numerical simulations. In this paper, we present an image-based, fully explicit, and matrix-free finite element implementation for the simulation of the T 2 relaxation process that is capable of handling such large problems. The utilized mathematical model considers relaxation due to bulk effects and surface relaxivity, not taking into account the effects of magnetic field gradients. We propose the usage of stable time marching schemes that use hyperbolization as means of acquiring stability with large time-steps. We compare the numerical performance of different time-marching schemes, showing that the application of the Leap-Frog method in a hyperbolized form of the equation can give the best trade-off between memory use and numerical convergence. Additionally, we show that the use of a lumped mass matrix allows for a fully explicit and simpler implementation while adding negligible amounts of numerical error. Article Highlights: A novel image-based and matrix-free methodology combined with explicit stable methods permits the solution of large problems with low time and low memory consumption. Performance of three explicit time-integration schemes is studied numerically with different coefficients, grid sizes, and time-step sizes. The lumping of the mass matrix allows the implementation of a fully explicit scheme while adding negligible amounts of numerical error. [ABSTRACT FROM AUTHOR]

Textile supercapacitors (TESCs) are an emerging energy storage solution to power smart gadgets integrated on clothes. Herein, efficient solid-state TESCs with different active areas (2–8 cm2) were produced based on cotton fabrics coated with industrial grade multi-walled carbon nanotubes (MWCNTs) as electrodes and a safe polyelectrolyte. The textile electrodes were fabricated by an optimized eco-friendly scalable dip-pad-dry process. The lowest electrical resistance (2.62 Ω cm−2) and most uniform coating of the electrodes were achieved using 10 mg mL−1 CNTs dispersion and 8 dip-pad-dry steps. The TESCs exhibited a specific capacitance of 8.01 F g−1 (9.18 F cm−2) and high cyclability (5000 cycles). The energy and power densities were tuned by changing the electrode area: the largest TESC presented the highest energy density of 6.30 Wh kg−1, which was 14× higher than those of other EDLC-type carbon-based TESCs reported in the literature; the smallest TESC presented the highest power density of 2.72 kW kg−1, being 49× higher than the values reported for comparable systems. Finally, a sensor was powered for 47 min by coupling two TESCs in series (14 cm2). This work demonstrated the ability to produce efficient TESCs using industrial grade MWCNTs by processes implemented in the Textile Industry, boosting technological transfer for high-tech applications. [ABSTRACT FROM AUTHOR]