Transport in Porous Media最新文献

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.

This study aims to investigate forced convection and heat transfer in a two-dimensional channel featuring a backward-facing step, a stationary adiabatic porous cylinder, and a deformable upper wall. The research addresses the complex coupling of fluid–structure interaction and porous media effects, a novel configuration not extensively explored in the existing literature. A numerical approach based on the finite element method within an arbitrary Lagrangian–Eulerian (ALE) framework is employed to simulate laminar flow and heat transfer over ranges of Reynolds (10 ≤ Re ≤ 200), Darcy (10⁻⁶ ≤ Da ≤ 10⁻¹), and Cauchy (10⁻⁷ ≤ Ca ≤ 10⁻⁴) numbers. The results, illustrated through isotherms, streamline patterns, and both local and average Nusselt number distributions, demonstrate that increasing the Reynolds number significantly enhances convective heat transfer. A decrease in the cylinder’s porosity strengthens vortex formation and thermal gradients, leading to a 36.4% increase in the average Nusselt number. Moreover, greater wall elasticity yields a modest 2.3% improvement in heat transfer. Regarding fluid–structure interaction, the maximum deformation of the upper elastic wall increases markedly with the Cauchy number, decreases by approximately 52.6% as the Reynolds number increases from 10 to 200, and reaches a peak at an intermediate Darcy number (Da = 10⁻³), highlighting the coupled influence of flow inertia and porous permeability. These findings provide quantitative insights into the interplay between structural deformation and porous media, contributing to the optimization of thermal management strategies in deformable thermo-fluidic systems.

Flow through the configuration of a three-layer channel containing a transition porous layer of variable permeability is revisited in this work to illustrate how Brinkman’s equation, which governs the flow in the transition layer, is reduced to the classic inhomogeneous differential equations of Airy and Weber, with constant forcing terms. Solutions to the homogeneous parts of these equations are given in terms of Airy’s and Weber’s special functions. Particular solutions to the resulting inhomogeneous equations give rise to three Nield-Kuznetsov functions of the first kind, which are analyzed in this work and extended to obtain general solutions to equations with variable forcing terms whose general solutions are expressed in terms of three Nield-Kuznetsov functions of the second kind. Methods of evaluation of all resulting special functions are presented.

Current underground nuclear explosion (UNE) detection strategies rely heavily on atmospheric noble gas sampling of radioxenon. However, discriminating nuclear weapons testing programs from civilian sources is difficult due to highly variable atmospheric radioxenon backgrounds and processes affecting subsurface transport of parent radionuclides. We aim to study the transport of gases produced by subsurface explosions as novel stable signatures for underground nuclear explosion (UNE) monitoring. These gases may be produced in large quantities with distinct molecular ratios, which will be impacted by subsurface transport processes. To demonstrate how ratios of gases produced by explosions can change during transport in geomaterials, we conducted laboratory benchtop experiments on the transport of carbon dioxide (CO₂) and hydrogen (H₂) gases through variably saturated zeolitic tuff, which is abundant at the historic US testing site. We observed that zeolitic tuff sorbs substantial quantities of CO₂ while allowing H₂ to transport more freely, leading to changes in the molecular ratios of the two gases along the transport pathway. Gas uptake in the dry zeolitic tuff core was 72.3% for CO₂, compared with 53.4% for xenon and 7.6% for H₂. The presence of 20% water saturation disrupted the CO₂ sorption process, though to a lesser extent than observed for noble gases, with a 36.7% drop in xenon sorption compared with a 21.9% drop for CO₂. These results represent the first observations of zeolite sorption altering explosive gas ratios during transport through geomedia relevant to nuclear proliferation monitoring.

Convolution neural networks (CNNs) are well-suited to model the nonlinear relationship between the microscale geometry of porous media and the corresponding flow distribution, thereby accurately and efficiently coupling the flow behavior at the micro- and macroscale levels. In this paper, we have identified the challenges involved in implementing CNNs for macroscale model closure in the turbulent flow regime, particularly in the prediction of the drag force components arising from the microscale level. We report that significant error is incurred in the crucial data preparation step when the Reynolds averaged pressure and velocity distributions are interpolated from unstructured stretched grids used for large eddy simulation (LES) to the structured uniform grids used by the CNN model. We show that the range of the microscale velocity values is 10 times larger than the range of the pressure values. This invalidates the use of the mean squared error loss function to train the CNN model for multivariate prediction. We have developed a CNN model framework that addresses these challenges by proposing a conservative interpolation method and a normalized mean squared error loss function. We simulated a model dataset to train the CNN for turbulent flow prediction in periodic porous media composed of cylindrical solid obstacles with square cross-section by varying the porosity in the range 0.3 to 0.88. We demonstrate that the resulting CNN model predicts the pressure and viscous drag forces with less than 10% mean absolute error when compared to LES while offering a speedup of O(10⁶).

To characterize turbulence over porous media with porosities (varphi <0.5), three types of packed-beds were manufactured: cubically packed spheres (case S), randomly packed rice-grain-shaped pellets (case E), and crushed stones (case C), with measured porosities of (varphi =0.45), 0.37, and 0.30, respectively. After measuring their permeabilities, particle image velocimetry (PIV) measurements were conducted for flows under conditions characterized by the permeability Reynolds number ((Re_K)) ranging from 2.1 to 18.3. The results were then compared with previous data on turbulent flows over foamed ceramics with a porosity of (varphi simeq 0.8), reported by Suga et al. (Int J Heat Fluid Flow 31(6), 974–984, 2010). The measured turbulence characteristics were analyzed to examine their correlation with (Re_K) and to evaluate the applicability of a unified scaling approach across a wide range of porous beds. The findings suggest that while some distribution profiles generally follow (Re_K), this parameter alone is insufficient as a universal scaling factor for turbulence over packed-beds, as the roughness scale also exhibits significant dependence on surface shape rather than the porosity.

A bounded porous domain saturated with a Newtonian fluid and subjected to time-dependent temperature variation has various practical applications, such as in solar energy storage, nuclear reactors, food processing industry, and agricultural science. In the current work, we study Darcy–Bénard convection in a horizontal fluid-saturated porous layer that is heated from below and confined in all directions. We look into an intricate form of the modulated Darcy–Bénard problem, where the temperatures at the bottom and top boundaries undergo sinusoidal temporal modulation about their mean values. We perform linear stability analysis to understand the onset of convection using a two-phase heat model based on the assumption that the solid and fluid phases of the system are not in local thermal equilibrium. The time-periodic eigenvalue problem obtained here is solved using the Floquet theory to find the onset threshold value of critical Rayleigh number. Our results suggest that the convection through subharmonic modes is preferable for either small ((text {H} < 4.3)) or large (H (> 175)) interphase heat transfer coefficient, while for the moderate values of H, convection takes place through harmonic mode only. In the paper, we discuss the results in detail and present a comparison with those from previous studies.

Mathematical modelling of coupled flow systems containing a free-flow region in contact with a porous medium is challenging, especially for arbitrary flow directions to the fluid–porous interface. Transport processes in the free flow and porous medium are typically described by distinct equations: the Stokes equations and Darcy’s law, respectively, with an appropriate set of coupling conditions at the common interface. Classical interface conditions based on the Beavers–Joseph condition are not accurate for general flows. Several generalisations are recently developed for arbitrary flows at the interface; some of them are however only theoretically formulated and still need to be validated. In this manuscript, we propose an alternative to couple free flow and porous-medium flow, namely the hybrid-dimensional Stokes–Brinkman–Darcy model. Such formulation incorporates the averaged Brinkman equations within a complex interface between the free-flow and porous-medium regions. The complex interface acts as a buffer zone facilitating storage and transport of mass and momentum and the model is applicable for arbitrary flow directions. We validate the proposed hybrid-dimensional model against the pore-scale resolved model in multiple examples and compare numerical simulation results also with the classical and generalised coupling conditions from the literature. The proposed hybrid-dimensional model demonstrates its applicability to describe arbitrary coupled flows and shows its advantages in comparison to other generalised coupling conditions.