EDF Renewables

This article provides a derivation of the averaged equations governing the motion of dispersed two-phase flows with interfacial transport. We begin by revisiting the two-fluid formulation, as well as the distributional form of the interfacial transport equation which holds on the entire domain. Following this, a general Lagrangian model is introduced, which accounts for the effects of both internal and interfacial properties of the dispersed inclusions (bubbles, droplets, or particles) within a continuous phase. This is achieved by derivation of conservation laws for particle surface and volume-integrated properties. By summing the internal and interfacial conservation laws, we derive a conservation equation for an arbitrary Lagrangian property associated with the inclusion. We then proceed by deriving the lesser-known conservation equations for the moments of the volume and surface distribution of an arbitrary Lagrangian property. Next, the averaged equations for the dispersed phase are derived through two distinct approaches: the particle-averaged (or Lagrangian-based) formalism, and the phase-averaged method. One important conclusion of this work is the demonstration of the relationship between the particle-averaged and phase-averaged equations. We show that the dispersed phase-averaged equations can be interpreted as a series expansion of the particle-averaged moment equations. We then present a "hybrid" set of equations, consisting of phase-averaged equations for the continuous fluid phase, complemented by an arbitrary number of moment conservation equations for the dispersed phase. To further illustrate the methodology, we derive the mass, momentum, second moment of mass and first moment of momentum equations for droplets or bubbles suspended in a Newtonian fluid. In particular, we highlight the role of the second-order moment of mass equation and first-order moment of momentum equation, which link droplet deformation to the stresslet. We then derive closure laws in the dilute, viscous-dominated regime, with particular emphasis on the effects of surface tension gradients. Additionally, we discuss several covariance closure terms that emerge in the averaged equations. Finally we demonstrate how the leading order deformation of the droplets can be obtained thanks to the second-order mass moment and first moment of momentum equation.

Ab initio molecular dynamics (AIMD) calculations were performed to study isomerization (I1), synchronous dehydration and isomerization (DHI1) and dehydration (DH1) reactions of isobutanol over acid chabazite leading to formation of branched products, i.e., tert-butanol, tert-butyl cation, and isobutene, respectively. Reactions I1 and DHI1 were shown to be variants of the same transformation, differing only in the relative position of water with respect to the carbenium cation formed after passing through a common transition state. The Bennett-Chandler approach predicted that DHI1 is strongly favored over variant I1, mainly due to stability of the tert-butyl intermediate interacting with water, which is further enhanced by the entropic effect. The relative importance of this class of transformations compared to the I2 and DHI2 reactions leading to the formation of linear products (n-butanol, n-butyl cation, n-butenes) was assessed. At the experimentally relevant temperature of 500 K, reactions ultimately yielding isobutene (DHI1 and I1) were found to be dominant, in line with experimental observations made for large pore zeolites. Although the transformations leading to linear butenes (DHI2, I2) are slower, with rate constants 1-2 orders of magnitude lower than those of DHI1/I1, they are still competitive. The importance of dynamic effects was underlined by comparison with a static approach, which strongly underrated importance of synchronous dehydration and isomerization reaction channels.

A novel combination of experimental characterization techniques has been used to assess the impact of the controlled addition of macroporosity to mesoporous catalyst supports for use with diffusion-limited, gas-phase reactions. This is the first study to 2D-map the gas-phase uptake across different internal regions within individual mesoporous pellets (or any other inorganic mesoporous media) using hyperpolarized xenon MRI. A porogen-templating method aimed to control the gas-phase mass transport properties of disordered alumina pellets. The degree of success of the pore structure design was examined using electron microscopy and gas sorption, and, for the resultant mass transport properties, using gas-phase PFG NMR and hyperpolarized xenon MRI. TEM showed that the macropore templating led to the creation of a corona of parallel-aligned alumina platelets around the macropore boundaries. The particular impact of this corona on mass transport was studied using PFG NMR, and found to be significant. The MRI showed that individual pellets had very large length-scale heterogeneities in the macroscopic spatial distribution of gas uptake rates. The data from the pore structural characterization, along with percolation theory, was used to develop a structural model to predict the impact of creating additional macroporosity by the particular fabrication method employed, and was successfully validated using the PFG NMR data for gas self-diffusion and MRI mapping of gas uptake rates across individual pellets.

Deep learning methods are now achieving strong results for segmentation tasks, and the standard metric for evaluating methods is the Intersection over Union (IOU). However, we show in this paper that IOU is not efficient in evaluating the quality of segmentation for electron tomography (ET) images of zeolites. We perform a physics-oriented evaluation to ensure that the segmentation results yield coherent physical measures. We also formalize Mixed Supervised / Self-Supervised Contrastive Learning Segmentation (M3S-CLS), a semi-supervised approach using a contrastive learning approach that uses expert annotations to train the neural network model. A detailed comparison of this method with a standard cross-entropy-based model is provided. In addition, we publish a database of five fully segmented ET volumes along with corresponding baseline results. The code and the database is available at http://gitlab.univ-st-etienne.fr/labhc-iscv/M3S-CLS.

We studied a rock sample belonging to the Mid-Continent Rift in Kansas (USA) that is partially hydrated with the formation of serpentine and amphibole. At the mineral scale, the original mineral assemblage of olivine and orthopyroxene (+ plagioclase + alkali feldspar) is partially replaced by serpentine, magnetite, biotite, amphibole, with locally some apatite and quartz. The replacement tends to preserve the shape of the original olivine and orthopyroxene, supporting a pseudomorphic replacement. Scanning Electron Microscopy (SEM), Electron Probe Micro-Analyzer (EPMA) mineral compositional map, and mass balance equations were used to quantify the transfers of mass during fluid infiltration. Here, the hydration reactions involve the decrease of rock density and, under the assumption of volume preservation, require a significant loss of mass through the fluid phase. Indeed, this study demonstrates that the formation of the newly formed hydrated minerals results from similar mass transfers between parent mineral, fluid, and product minerals. This study also demonstrates that the redox conditions are similar during the formation of all of these hydrated minerals. These observations confirm the close relationship between local stress generated by hydration reactions, mass transfers, and the scale over which the system is open.