Transport in Porous Media最新文献

As more and more promising applications of magnetic nanoparticles in complicated environments are explored, their flow properties in porous media are of increasing interest. We here propose a hybrid approach based on the multiparticle collision dynamics method extended to porous media via friction forces and coupled with Brownian dynamics simulations of the rotational motion of magnetic nanoparticles’ magnetic moment. We simulate flow in planar channels homogeneously filled with a porous medium and verify our implementation by reproducing the analytical velocity profile of the Darcy–Brinkman model in the non-magnetic case. In the presence of an externally applied magnetic field, the non-equilibrium magnetization and friction forces lead to field-dependent velocity profiles that result in effective, field-dependent permeabilities. We provide a theoretical expression for this magneto-permeability effect in analogy with the magneto-viscous effect. Finally, we study the flow through planar channels, where only the walls are covered with a porous medium. We find a smooth crossover from the Poiseuille profile in the center of the channel to Brinkman–Darcy flow in the porous layers. We propose a simple estimate of the thickness of the porous layer based on the flow rate and maximum flow velocity.

The title problem which has recently been addressed in this journal is revisited in the present paper under a new point of view. It is shown that the joint effect of the Berman suction or injection normal to the boundaries and the velocity slip along the boundaries is equivalent to the sole effect of an oblique suction or injection of the fluid. The solution of the corresponding boundary value problem is given by a Maclaurin series expansion of the similar stream function to powers of the scaled transverse coordinate y/h. Compared to the classical Berman problem, the existence of several new solution branches of the oblique suction/injection problem is reported. Subsequently, the physical and mathematical aspects of the mentioned equivalence are discussed in the paper in some detail. It is pointed out that the vanishing midplane velocity represents the crossover from the physically feasible unidirectional flows to the unfeasible bidirectional flow configurations, where in the neighborhood of the midplane of the channel reverse flows occur.

Abstract

The fluid flow dynamics on the porous scaffolds and their static responses on the adjacent bone are very crucial parameters for bone adaptation. Researchers are trying to develop different algorithms to design biomimetic porous scaffolds incorporating bone tissue engineering. In this present work, three types of biomimetic heterogeneous porous scaffolds (HPS) were designed with the help of the Voronoi tessellation method and Swarm Intelligence and those were analysed under fluid perfusion as well as under static loading conditions. In computational fluid dynamics (CFD) analysis, the wall shear stress (WSS) and the permeability of the porous scaffolds were compared to the natural trabecular bone to understand their hydrodynamic responses. In static analysis, the von Mises stresses of the Ti₆Al₄V scaffolds were checked to ensure no-yield condition. The strain energy density (SED) distributions were also studied on the neighbouring bone region of the femur greater trochanter to obtain stress shielding (SS) patterns and these findings were then compared with the natural trabecular bone at the same anatomical region. The outcome parameters, viz. the induced WSS, von Mises stress, the permeability, and SS of the scaffold, are found to be independent of the scaffold architecture. The von Mises stress and permeability increased with an increase in porosities, while the induced WSS and SS nature of the scaffolds showed the reverse trend. The results showed that the HPS designed based on the Swarm Intelligence incorporating Physarum Polycephalum algorithm offered the least SS level of 41.096 for 75% porous HPS, which may be considered the most promising result. Considering all the parameters, the novel designed scaffold based on Swarm Intelligence showed the most trabecular bone mimicking nature compared to the other scaffolds.

The adequate management of the damage caused by effective permeability loss in stress-sensitive reservoirs becomes essential to productivity maintenance. This paper proposes a new unsteady-state poroelastic solution for the nonlinear hydraulic diffusivity equation in Biot’s effective stress-sensitive reservoirs fully penetrated by fractured oil wells. The hydraulic fracture in the proposed mathematical modeling is finite with tip effects and crosses the whole reservoir net pay. The NHDE is expanded in a first-order asymptotic series, and a poroelastic integro-differential solution coupled with a Green’s function (GF) is used to represent the source/sink term. A set of pore pressure and permeability data is used from geomechanical literature and transformed into effective stress through Biot’s equation. The effect of the Biot’s coefficient, overburden stress, oil flow rate, fracture’s tip, and proppant porosity arrangements is simulated. The results show that these parameters are essential to minimize formation damage. The accuracy, ease of implementation, and low computational costs constitute the main advantages of the model addressed in this paper. Hence, it may be a valuable and attractive mathematical tool to identify flow regimes, providing permeability loss control and supporting well–reservoir management. Hence, the proposed modeling becomes a useful and attractive tool for forecasting and monitoring permeability loss, oil flow rate specification, and reservoir history matching.

Abstract

We consider steady-state immiscible and incompressible two-phase flow in porous media. It is becoming increasingly clear that there is a flow regime where the volumetric flow rate depends on the pressure gradient as a power law with an exponent larger than one. This occurs when the capillary forces and viscous forces compete. At higher flow rates, where the viscous forces dominate, the volumetric flow rate depends linearly on the pressure gradient. This means that there is a crossover pressure gradient that separates these two flow regimes. At small enough pressure gradient, the capillary forces dominate. If one or both of the immiscible fluids percolate, the volumetric flow rate will then depend linearly on the pressure gradient as the interfaces will not move. If none of the fluids percolate, there will be a minimum pressure gradient threshold to mobilize the interfaces and thereby get the fluids moving. We now imagine a core sample of a given size. The question we pose is what happens to the crossover pressure gradient that separates the power-law regime from the high-flow rate linear regime and the threshold pressure gradient that blocks the flow at low pressure gradients when the size of the core sample is increased. Based on analytical calculations using the capillary bundle model and on numerical simulations using a dynamical pore-network model, we find that the crossover pressure gradient and the threshold pressure gradient decrease with two distinct power laws in the size. This means that the power-law regime disappears in the continuum limit where the pores are infinitely small compared to the sample size.

Abstract

Plurigaussian simulation is a method of discrete random field generation that can be used to generate many complex geometries depicting real world structures. Whilst it is commonly applied at larger scales to represent geological phenomena, the highly flexible approach is suitable for generating structures at all scales. Here, an extension of plurigaussian simulation to periodic plurigaussian simulation (P-PGS) is presented, such that the resulting fields are periodic in nature. By using periodic Gaussian random fields as components of the method, periodicity is enforced in the generated structures. To substantiate the use of P-PGS in capturing complex heterogeneities in a physically meaningful way, the pore-scale microstructure of cement paste was represented such that its effective properties can be calculated through a computational homogenisation approach. The finite element method is employed to model the diffusion of heat through the medium under dry and saturated pore conditions, where numerical homogenisation is conducted to calculate the effective thermal conductivity of the medium. Comparison of the calculated values with experimental observations indicated that the generated microstructures are suitable for pore-scale representation, given their close match. A maximal error of 1.38% was observed in relation to the numerically determined effective thermal conductivity of mortar paste with air filled pores, and 0.41% when considering water filled pores. As the assumption of a periodic domain is often an underlying feature of numerical homogenisation, this extension of plurigaussian simulation enables a path for its integration into such computational schemes.

Article Highlights

• Integrating P-PGS into numerical homogenisation frameworks enhances complex heterogeneous material representation

• The flexibility of P-PGS enables a wide range of material microstructures to be represented accurately

• Use of the generated structures allows material properties to be estimated accurately through numerical homogenisation

Using extensive numerical simulation of the Navier–Stokes equations, we study the transition from the Darcy’s law for slow flow of fluids through a disordered porous medium to the nonlinear flow regime in which the effect of inertia cannot be neglected. The porous medium is represented by two-dimensional slices of a three-dimensional image of a sandstone. We study the problem over wide ranges of porosity and the Reynolds number, as well as two types of boundary conditions, and compute essential features of fluid flow, namely, the strength of the vorticity, the effective permeability of the pore space, the frictional drag, and the relationship between the macroscopic pressure gradient ({varvec{nabla }}P) and the fluid velocity v. The results indicate that when the Reynolds number Re is low enough that the Darcy’s law holds, the magnitude (omega _z) of the vorticity is nearly zero. As Re increases, however, so also does (omega _z), and its rise from nearly zero begins at the same Re at which the Darcy’s law breaks down. We also show that a nonlinear relation between the macroscopic pressure gradient and the fluid velocity v, given by, (-{varvec{nabla }}P=(mu /K_e)textbf{v}+beta _nrho |textbf{v}|^2textbf{v}), provides accurate representation of the numerical data, where (mu) and (rho) are the fluid’s viscosity and density, (K_e) is the effective Darcy permeability in the linear regime, and (beta _n) is a generalized nonlinear resistance. Theoretical justification for the relation is presented, and its predictions are also compared with those of the Forchheimer’s equation.

Colloidal transport and clogging in porous media is a phenomenon of critical importance in many branches of applied sciences and engineering. It involves multiple types of interactions that span from the sub-colloid scale (electrochemical interactions) up to the pore-scale (bridging), thus challenging the development of representative modelling. So far published simulation results of colloidal or particulate transport are based on either reduced set of forces or spatial dimensions. Here we present an approach enabling to overcome both computational and physical limitations posed by a problem of 3D colloidal transport in porous media. An adaptive octree mesh is introduced to a coupled CFD and DEM method while enabling tracking of individual colloids. Flow fields are calculated at a coarser scale throughout the domain, and at fine-scale around colloids. The approach accounts for all major interactions in such a system: elastic, electrostatic, and hydrodynamic forces acting between colloids, as well as colloids and the collector surface. The method is demonstrated for a single throat model made of four spherical segments, and the impact of clogging is reported in terms of the evolution of the critical path diameter for percolation and permeability. We identified four stages of clogging development depending on position and time of individual colloid entrapment, which in turn correlates to a cluster evolution and local transport.

Internal insulation of the building envelope is a prime topic in building physics, due to the risk of moisture problems that this technique entails. As a remedy to these problems, the application of a water-repellent agent, which reduces the amount of absorbed wind-driven rain, has become popular in recent years. When such an agent is applied on a building material, it penetrates the pore network of the material, hereby attaching itself to the pore surfaces and rendering them hydrophobic. It is generally believed that some smaller pores can remain hydrophilic due to the inability of the agent to enter. An in-depth microscopic investigation towards these hydrophilic pores, however, has never been performed. Since direct visualisation of the polymer chains was proven impossible, this paper locates the hydrophilic (parts of) pores in a material, hydrophobised with 3 different water-repellent agents, by imaging the moisture storage at pore level using X-ray computed tomography images at different stages of the desaturation process. While completely hydrophilic pore bodies and throats are not found in the studied material, water storage remains possible in hydrophilic corners of hydrophobised pore bodies and throats. These corner islands are less present than in hydrophilic media and do not form a continuous liquid flow path. Therefore, they provide possible locations for little moisture storage but do not contribute notably to moisture flow.

To meet the extensive demand for lithium (Li) for rechargeable batteries, it is crucial to enhance Li production by diversifying its resources. Recent studies have found that produced water from shale reservoirs contains various organic and inorganic components, including a significant amount of Li. In this study, findings from hydrothermal reaction experiments were analyzed to fully understand the release of Li from organic-rich shale rock. Subsequently, numerical algorithms were developed for both pore-scale and continuum-scale models to simulate the long-term behavior of Li in shale brines. The experimental conditions considered four different hydrothermal solutions, including the solutions of KCl, MgCl₂, CaCl₂, and NaCl with various concentrations under the temperature of 130 °C, 165 °C, and 200 °C. The release of Li from shale rock into fluid was regarded as a chemical interaction of cation exchange between rock and fluid. The reactive transport pore-scale and upscaled continuum-scale models were developed by coupling the chemical reaction model of Li interaction between rock and fluid. The model was first implemented to investigate the release and transport of Li in the pore scale. Continuum-scale properties, such as effective diffusivity coefficients and Li release rate, were obtained as the field-averaged pore-scale modeling results. These properties were used as the input data for the upscaled continuum-scale simulation. The findings of this study are expected to provide new insight into the production of Li from shale brines by elucidating the release, fate, and transport of Li in subsurface formations.