Transport in Porous Media最新文献

Relative permeability and capillary pressure are key parameters in multiphase flow modelling. In heterogeneous porous media, flow direction- and flow-rate dependence result from non-uniform saturation distributions that vary with the balance between viscous, gravitational, and capillary forces. Typically, relative permeability is measured using constant inlet fractional-flow—constant outlet fluid pressure conditions on samples mounted between permeable porous plates to avoid capillary end-effects. This setup is replicated in numeric experiments but ignores the extended geologic context beyond the sample size, impacting the saturation distribution and, consequently, the upscaled parameters. Here, we introduce a new workflow for measuring effective relative permeability and capillary pressure at the bedform scale while considering heterogeneities at the lamina scale. We harness the flexibility of numeric modelling to simulate continuum-REV-scale saturation distributions in heterogeneous rocks eliminating boundary artefacts. Periodic fluid flux boundary conditions are applied in combination with arbitrarily oriented, variable-strength pressure gradient fields. The approach is illustrated on a periodic model of cross-bedded sandstone. Stepping saturation while applying variable-strength pressure-gradient fields with different orientations, we cover the capillary-viscous force balance spectrum of interest. The obtained relative permeability and capillary pressure curves differ from ones obtained with traditional approaches highlighting that the definition of force balances needs consideration of flow direction as an additional degree of freedom. In addition, we discuss when the common viscous and the capillary limits are applicable and how they vary with flow direction in the presence of capillary interfaces.

We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore scale is modeled using a diffuse interface approach in the form of a coupled Allen–Cahn Navier–Stokes system with an additional momentum flux due to surface tension forces. Using periodic homogenization and formal asymptotic expansions, a two-scale model with cell problems for phase evolution and velocity contributions is derived. We investigate the computed effective parameters and their relation to the saturation for different fluid distributions, in comparison to commonly used relative permeability saturation curves. The two-scale model yields non-monotone relations for relative permeability and saturation. The strong dependence on local fluid distribution and effects captured by the cell problems highlights the importance of incorporating pore-scale information into the macro-scale equations.

This study examines the simultaneous impact of temperature-dependent viscosity and Robin boundary conditions on velocity, focusing on analyzing the stability of buoyant parallel flow in a differentially heated vertical porous layer. The neutral stability condition and the instability thresholds are determined numerically for various values of governing parameters. The onset of instability of the base flow is accurately analyzed by introducing a non-negative parameter that measures the extent of departure of boundaries from impermeable to permeable. It is established that the base flow becomes unstable when this parameter exceeds a threshold value, which significantly depends on the variable viscosity parameter. This work demonstrates a clear bridge between impermeable and permeable boundaries in the context of a variable viscosity fluid.

Polymer silica nanocomposites are advanced materials with unique properties combining the advantages of an inorganic nanofiller and the organic polymer matrix, which attracted considerable interest for applications in energy conversion and storage, drug delivery, environmental remediation, and many more. However, the dispersion of the nanofiller in the polymer matrix leads to complexified nanocomposite materials whose barrier properties are altered resulting in a tortuous pathway for the transport of current, matter, and velocity. The tortuosity of these nanocomposite materials, which depends on their porosity organization, is a parameter usually challenging to quantify accurately. Therefore, the objective of this study was to develop a method to quantify the electrical tortuosity and to develop a theoretical model to accurately predict electrical tortuosity in these in-house prepared silica powder and nanocomposite membrane materials at different porosity ranges. The SBA-15 silica powder and nanocomposite membranes’ conductivity was measured with the help of impedance spectroscopy in a 1 M sodium chloride electrolyte solution from which the electrical tortuosity is quantified. The calculated tortuosity of SBA-15 silica powder was found to be well correlated to the entire range of its porosity. The plots of the tortuosity versus porosity from the Maxwell and the modified Maxwell models showed a well-fitted curve to the entire range of porosity. These theoretical models will help to give a perfect prediction of the electrical tortuosity of materials from porosity measurements, which would be a vital technique to characterize materials used in electrochemical devices and battery technology.

Migration of variably sized fines or geogenic colloids is a significant concern for the long-term efficiency of aquifer management and reservoir injection and extraction operations. Characterizing the migration of colloids in porous media has been widely studied; however, few studies have quantified sub-core colloidal transport behavior and related this to bulk sample observations under transient conditions. In this study, the transport of colloidal kaolinite through sand packs is analyzed using UV–Vis spectrophotometry and positron emission tomography (PET). PET imaging was completed by imaging an aqueous pulse of suspended radiolabeled kaolinite under single-phase flow conditions. The experimental PET imaging approach allows for the accurate 4-D quantification of changes in colloidal kaolinite transport, attachment, and detachment properties at the sub-centimeter scale. This study provides a novel approach for the quantification of inorganic colloid transport in geologic porous media, providing a foundation for future work to be done on more complex and heterogeneous systems under transient flow and fluid chemistry conditions.

Reliable reactive transport models require careful separation of mixing and dispersion processes. Here we treat displacing and displaced fluids as two separate fluid phases and invoke Whitman’s classical two-film theory to model mass transfer between the two phases. We use experimental data from Gramling’s bimolecular reaction experiment to assess model performance. Gramling’s original model involved just three coupled PDEs. In this context, our new formulation leads to a set of seven coupled PDEs but only requires the specification of two extra parameters, associated with the mass transfer coefficient and its dependence on time. The two film mass transfer model provides a simple and theoretically based method for separating mixing from dispersion in Eulerian continuum-scale methods. The advantage of this approach over existing methods is that it enables the simulation of equilibrium chemical reactions without having to invoke unrealistically small reaction rate coefficients. The comparison with Gramling’s experimental data confirms that our proposed method is suitable for simulating realistic and complicated bimolecular reaction behaviour. However, further work is needed to explore alternative methods for avoiding the need of a time-dependent mass transfer rate coefficient.

Fluid injection can induce mechanical deformation in granular porous media due to the elevation of internal pore fluid pressure. This gains more significance when more than two immiscible fluids are involved, attributable to capillary and viscous drag forces. Such a coupled hydromechanical behavior associated with immiscible fluid flows plays an important role in injection, storage, and recovery of fluids in deformable porous media. This study presents a dimensionless map with newly proposed dimensionless parameters to predict deformation occurrence due to an immiscible fluid flow in deformable porous media. A series of hydromechanically coupled pore network simulations are first performed while varying the capillary number, mobility ratio, medium stiffness, and effective confining stress over orders of magnitudes. The compilation of simulation results with previously published Hele–Shaw experiment results is analyzed with the dimensionless parameters, such as the capillary number, mobility ratio, particle-level force ratios, and particle-level pressure ratios. Particularly, the particle-level pressure ratios include the capillary pressure ratio, defined as the ratio of capillary pressure to fracture pressure, and the viscous drag pressure, defined as the ratio of viscous drag pressure to fracture pressure. The dimensionless map based on the particle-level pressure ratios, where the capillary pressure ratio and viscous drag pressure ratio are defined as the ratios of capillary pressure and viscous drag pressure to fracture pressure, effectively delineates four deformation regimes—no deformation, capillary-induced deformation, drag-driven deformation, and mixed-mode deformation. The results demonstrate that capillary-induced deformation occurs when the capillary pressure ratio is greater than 10⁻¹, while drag-driven deformation is observed when the viscous drag pressure ratio exceeds 10⁻². The presented dimensionless map and dimensionless parameters are expected to be applicable for geological subsurface processes, including geological storage of carbon dioxide and hydrogen, and enhanced oil recovery.

Visualising fluid flow in porous media using optical techniques is challenging due to the inability to see through the medium. Here, we present an experimental methodology based on shadowgraphy to investigate the dynamic spreading of convective plumes in saturated transparent porous media made of glass beads. The saturated porous medium can be tuned transparent by matching the refractive index of the solid glass beads to that of the saturating fluid mixture. The proposed technique allows to investigate the essential elements of convective mixing within a porous medium using miscible fluids. We also describe a method to determine the velocity of convective plumes as they propagate. Our experimental results show that the density difference achieved during convection significantly affects the convective front velocity of the plumes. This is significant because it allows to quantitatively predict the intensity of convective mixing in porous media from the speed of the convective front.

Additive manufacturing (AM) allows the production of the internal structure of porous media (PM) with porosity and permeability tailored for a specific application. Material extrusion (MEX) AM enables the fabrication of a lattice-type porous structure by varying process parameters, usually applying the zigzag raster filling strategy. In a recent study, a Variable Bead Width Porous Filling (VBWPF) strategy was proposed, which generates pores by changing the printing speed during filament deposition and resulting in a unique porous structure with less pore interconnectivity. Specific pores’ dimensions and distribution on the layer can be obtained with the strategy’s parameters. In this work, different configurations of the VBWPF strategy were produced, and their porosity and permeability were measured experimentally. A PM with traditional raster filling (lattice structure) was also printed and measured for comparison. The porous structures of different VBWPF configurations were analyzed with micro-computed tomography (µCT). The results showed that VBWPF parameters were able to modify the porous structure obtained, changing the porosity and permeability of the PM. The PM produced exhibited 27% lower porosity and 55% lower permeability than the traditional raster filling PM with similar pore widths. These unique characteristics open up the field for applications of PM obtained through AM.