Transport in Porous Media最新文献

The steady free convection and entropy generation in a differentially heated square inclined enclosure filled with a saturated bidisperse porous medium (BDPM) is analysed. The governing equations of the model, consisted by the continuity equation, Darcy equation and energy for both phases, containing interphase transfer terms, are transformed in terms of non-dimension variables. The numerical solution of both phases of flow and heat transfer is achieved through the utilisation of a modified finite difference technique. After the process of discretisation, the algebraic system is solved using the successive over relaxation method. The influence of the involved parameters on the flow and heat transfer characteristics (stream functions, isotherms, and Nusselt numbers) is observed as well as the entropy generation for monodisperse and bidisperse porous medium cases. The results are focused on the behaviour of the flow at different angles of the inclination of the cavity. A strong correlation was observed between the present findings and previously published results in the open literature, for a vertical cavity.

The water–gas dispersion system, in which gas is stabilized as microsized bubbles within a liquid phase, constitutes a stable two-phase system with a uniform spatial distribution. This method has proven effective for enhancing oil recovery in low-permeability reservoirs, demonstrating notable success in field trials. This study investigated the pore-scale mechanism of microbubble-induced vortex dynamics on residual oil mobilization through integrated microscopic visualization experiments and numerical simulations. Key findings reveal three critical phenomena: (1) Microbubble coalescence generates microscale vortices at merged interfaces through surface energy release; (2) these vortices enhance multiphase transport via three coupled mechanisms, intensifying interfacial energy–momentum transfer to modify oil film flow regimes, amplifying shear stress for oil film detachment, and accelerating mass transfer to reduce crude oil viscosity through oil–water–gas mixing; (3) dynamic pressure fluctuations associated with vortex formation–dissipation cycles exhibit a maximum pressure differential of 29.56 kPa, synergistically mobilizing residual oil trapped in isobaric pore throats and blind-end structures—the primary reservoirs of post waterflood residual oil. The interaction between microscale vortices and pore-scale turbulence promotes mutual amplification, increasing the pressure fluctuation intensity while increasing the fluid sweep efficiency. These insights establish a theoretical foundation for optimizing microbubble systems through controlled vortex dynamics, offering strategic implications for improving capillary-trapped oil recovery in complex porous media.

This paper presents a comprehensive modeling framework for turbulent flow and phase-change phenomena in porous media. The study revisits the double-decomposition concept for macroscopic turbulence modeling, where instantaneous variables are averaged in both time and space, leading to distinct forms of the governing equations. The model extends the “One-Energy Equation Model” to simulate melting and solidification of pure substances and alloys, treating the solid phase as a porous medium with low porosity and permeability. During phase transition, thermal equilibrium is assumed in the mushy zone, while viscous and form drag effects are adjusted based on temperature. The latent heat is treated implicitly in the energy equation, and the liquid fraction is updated iteratively. Numerical solutions employ the SIMPLE algorithm with the Strong Implicit Procedure for inner iterations. Validation against existing literature demonstrates the model’s accuracy for pure substances.

We introduce a framework for analysing thermosolutal convection within a Kelvin–Voigt fluid of first order using a Brinkman–Darcy porous medium. This setup involves heating and salting from below, leading to a scenario where the thermal and solutal gradients compete: Thermal gradients tend to destabilise the system, whereas solutal gradients have a stabilising effect. Additionally, we explore scenarios where heating occurs from below while salting is introduced from above. This study examines how couple stresses affect the dynamics. We calculate the threshold at which instability occurs, noting the complexity of the instability surface’s shape. Factors such as the Kelvin–Voigt property, couple stresses, Brinkman, and Prandtl numbers are significant, stabilising forces, especially when the convection exhibits oscillatory behaviour. Details on the instability surface’s quantitative aspects are provided. Furthermore, we touch upon the issue of nonlinear stability in this context.

Permeability is an important parameter characterizing ablative thermal protection system (TPS) materials as it impacts the internal pressure that builds within the material during the production of pyrolysis gas. Experiments to measure permeability must provide good sealing to ensure that the measured flow is only through the sample of interest; however, for TPS materials that have been partially charred, the sample geometry can complicate this measurement. Prior measurement techniques were found to be inadequate for such charred samples. A new method was developed which can robustly and repeatably mount and seal irregularly shaped centimeter scale samples of porous media such that their Darcy permeabilities and Klinkenberg molecular slip coefficients can be measured. Such measurements were achieved using steady flows of nitrogen at absolute pressures up to 1000 Torr. Two techniques were devised for processing test articles to be compatible with the experiment. The first of these methods involves the direct casting of porous media into thermoset resin and can accommodate uneven or irregularly shaped test articles as occur for charred TPS. The second method involves the mounting of porous media into a constrictive sleeve lined with thermoplastic adhesive. This second method better preserves the two outer surfaces of the TPS sample. A commercially available porous TPS material, Zuram, was subjected to partial thermal decomposition in nitrogen and then studied using the developed techniques. The method for sealing the samples was found to enable measurements on these charred samples and showed the permeability increases by a factor of 4 in a nonlinear manner during the early stages of mass loss.

The Connectedness Theory is a mathematical approach to understanding the interactions between any number of phases in a complex medium that have different physical properties. It arose from the development of an Archie’s Law for n-phases when it is applied to fluid permeability. We have shown that Connectedness Theory allows for relative permeabilities to be expressed as ratios of connectednesses. This approach demonstrates why the sum of the non-wetting phase and wetting phase relative permeabilities is always less than unity. In its most general form the Connectedness Theory for two-phase relative permeabilities has eight independent parameters and allows both the fractions of immobile and mobile wetting phase and non-wetting phase, and the phase exponents to vary as a function of wetting phase and non-wetting phase saturation. However, if we make the common assumption that the irreducible wetting phase saturation and residual non-wetting phase saturation are constant and that the phase exponents are also constant, we can use the Connectedness Theory to prove the Brooks and Corey approach to relative permeability modelling and to relate its lambda parameters to phase exponents. In doing so, we also show that the wetting phase relative permeability endpoint is not an independent parameter but arises from variability of phase exponents and hence connectednesses as a function of fluid saturations, and that the two Brooks and Corey coefficients are interdependent. Finally, the Connectedness Theory also predicts that in principle one relative permeability curve can be calculated from the other. Since the theory upon which it is based is valid for any number of different phases, the two-phase scenario followed by most of this work is easily extended to three-phase relative permeabilities.

Super-resolution imaging techniques use deep learning to create large-scale, high-resolution images by combining a low-resolution image encompassing a large volume with high-resolution images on a smaller volume; however, applications to date have been limited to determining the pore structure only. We have successfully applied an enhanced deep super-resolution (EDSR) method to three-dimensional X-ray images of two fluid phases in the pore space of water-wet and mixed-wet Bentheimer sandstone, producing high-resolution results that capture both the pore space and two fluid phases within it, while expanding the field of view. We calculated and compared the geometrical and physical properties, including porosity, permeability, saturation, interfacial area, interfacial curvature, and contact angle derived from high-resolution, super-resolution, and low-resolution images. This comparison confirms that our super-resolution outcomes are consistent with the ground truth and far superior to low-resolution results.

In this work, we study immiscible two-phase flow in porous media through the upscaled model derived by Whitaker in 1994. This model contains two momentum equations for each fluid, which are coupled through four effective tensors, one for each phase and two crossed tensors between phases. Two tensors correspond to the effective permeability of phases, and the other two are named as viscous drag tensors. The four tensors are determined by solving associated tensorial closure problems in representative geometries of the porous medium. We have numerically solved the integro-differential equations composing the closure problems in a 2D cavity (unit cell) undergoing imbibition and drainage processes, as a first approximation. Thus, we have estimated the main directions of the effective tensors as functions of the wetting-phase saturation. The effective permeabilities follow trends similar to experimentally measured permeability relative curves, showing hysteresis for drainage and imbibition, although with some deviations from the experimental values. Meanwhile, the viscous drag tensors exhibit estimations of order 1, which are in agreement with the analytical predictions of Whitaker. The findings of this work are promising, as in future works, more realistic cells as: thin sections of rocks, SEM images, or 3D tomography of rocks, can be used to improve the numerical predictions of the effective tensors and elucidate thus the effect of microscale phenomena on the two-phase flow at larger scales.

Air and water flows occurring in a porous material modify its mechanical properties. Evolution of the interface between saturated and partially saturated layers of a soil is of concern in this paper. In particular, the description of a drainage/imbibition front is developed gathering the two classical saturated and partially saturated poromechanical problems, with pressures of both fluids and solid displacement as unknowns. The presented model enables saturated and partially saturated layers to coexist without considering gaseous air dissolving into liquid water. Nucleation or collapse of the drainage/imbibition front moving from or reaching an air connected boundary is characterised considering the Signorini contact conditions on the liquid phase. The model abilities are confirmed numerically, via finite element simulations, showing among other that this new description of interface motion does not imply hysteresis phenomena. Parametric investigation developed with respect to drainage kinetics and thickness of the layer which regularises the interface between the saturated and the partially saturated domain are also provided.

This study explores the onset of thermal instability within a bidisperse porous medium saturated with a homogeneous, incompressible fluid, subjected to a non-uniform internal heat generation and constant temperature gradient due to heating from below. The fluid motion is modelled with the Darcy’s law in micropores, while the Brinkman’s law is employed in macropores to ensure a more accurate representation of momentum transfer across different scales. The system is modelled under the Oberbeck–Boussinesq approximation, where density variations are incorporated solely in the buoyancy term, with the fluid density being temperature-dependent. Linear and nonlinear stability analyses are performed and different profiles of depth-dependent heat source are considered to investigate its effect in various physical scenarios. Both analyses lead to a generalized eigenvalue problem that is solved numerically by means of the Chebyshev-(tau) method. The nonlinear stability analysis is carried out in the context of the energy theory by means of the differential constraints method. A golden section algorithm is implemented to determine the critical thresholds for linear and nonlinear stability analyses and discuss their proximity.