In the simulations of enhanced oil recovery by polymer flooding, it is widely acknowledged that the inaccessible pore volume (IPV) must be properly accounted for. The effect of IPV is to make the interstitial velocity of polymer molecules higher than that of water molecules. This acceleration is traditionally modeled by a velocity enhancement factor. The difficulty, however, lies in finding a relevant closure law for this factor that preserves well-posedness of the overall flow model. Previous works by Bartelds et al. (Transp. Porous Med. 26, 75-88, 1997) and Hilden et al. (Transp. Porous Med. 114, 65-86, 2016) have demonstrated that ill-posedness occurs for the popular constant enhancement factor and they proposed some alternative physical IPV laws that partially addressed the question of stability. This paper is aimed at bringing new mathematical insights into the design of IPV laws that ensure weak hyperbolicity for a Buckley-Leverett type two-phase polymer flow model. To begin with, we show that by switching to Lagrangian coordinates, it is possible to derive several practical and meaningful sufficient conditions for weak hyperbolicity. Next, special solutions to some of these sufficient conditions are shown to coincide with well-known IPV laws in the literature and then investigated more thoroughly. Finally, by patching together these piecewise sufficient conditions, we are in a position to develop original IPV laws that guarantee weak hyperbolicity for the flow model.
This work presents a novel framework for approximating multiphase chemical equilibrium in porous media flow simulations. This framework facilitates the development of approximation schemes that, by leveraging equilibrium data from previous time steps, significantly reduce computational costs when integrated within a global mass conservation formulation of reactive transport in porous media. The formulation ensures the conservation of mass for an arbitrary number of chemical species distributed across multiple fluid and solid phases, while rigorously enforcing chemical equilibrium and pore volume conservation, and being compatible with the incorporation of additional kinetic reactions when needed. Comparative tests between the approximate schemes and a fully implicit reference version across three test configurations with increasing complexity demonstrates good performance. Additionally, a criterion is introduced to assess the validity of the proposed approximations, enabling adaptive switching to higher-fidelity equilibrium models when required. This adaptive methodology achieves results comparable to the fully implicit scheme while minimizing computational demands.
Bismuth oxyfluoride films were successfully deposited by reactive magnetron sputtering using different Ar/O2/CF4 gas mixtures. For a reactive gas ratio (Rf), defined as the O2/(O2 + CF4) flow rate ratio, ranging from 0 to 0.6, the films consist of two phase-system composed of BiO0.5F2 and metallic bismuth (Bi0); whereas for Rf = 0, a single phase BiF3 is observed when Rf > 0.5. The amount of metallic Bismuth within the oxyfluoride matrix can be tuned not only by Rf, but also by adjusting the target power or by varying a single reactive gas flow rate. Increasing the film thickness does not significantly affect the composition but enhances crystallization of the phases. Hence, we succeed in forming one-step Bi/BiO0.5F2 heterojunctions, where the metal presence improves the light absorption, the photogenerated carrier separation, and thus the photocatalytic efficiency for Methylene Orange, MO, degradation in water. Among all the conditions investigated, the film obtained with Rf = 0.3 and a deposition time, td = 20 min exhibits the best overall performance. Indeed, 90 % of MO is degraded after 2 hours of irradiation, and the catalyst remains stable over 3 photocatalytic cycles (approximately 9 hours of total use). Moreover, this material selectively photoconverts CO2 in CO, with a higher efficiency to create useful electrons (rē ≈ 29 mmol/molcata) than pure BiO0.5F2 thin film, and even nanostructured TiO2 P25 (rē ≈ 11 mmol/molcata).
A major challenge of poly(vinyl chloride) (PVC) recycling is the prevalence of "legacy" additives, such as certain phthalate plasticizers. Deformulation seeks the separation of these additives using solvent-based technologies to obtain materials more suitable for reincorporation in the value chain. In this scope, this work explores the potential of accelerated solvent extraction (ASE) for the separation of phthalate plasticizers from PVC. Several model and real-world PVC feedstocks underwent ASE experiments, using mass balance and gas chromatography using flame ionization detection to determine how ASE and extraction profiles can be affected by factors such as temperature, solvent composition, and plastic formulation. A Fickian model was fitted to each kinetic extraction profile to estimate the diffusivity of the phthalate plasticizers across PVC and the partition coefficient across the solvent-PVC interface. Distinct kinetic profiles highlight the influence of plasticizer side-chain structure and initial concentration for ASE yield and the benefits of adding a swelling agent as cosolvent. These results benefit the knowledge of plastic-related ASE applications and demonstrate that ASE could be an asset as a part of the PVC deformulation recycling processes.
