Transport in Porous Media最新文献

The main theme of this article is to find analytically the solution of an irreversible reaction of two components in liquid chromatography. The two-dimensional flow is considered in a closed channel, namely, the chromatographic column. The mathematical model, known as the equilibrium dispersive model (EDM), comprises two partial differential equations. Chemical reaction, dispersion in both radial and axial directions, and convection occur and are reflected in the model. A linear Langmuir adsorption isotherm is used for continuous flow and rectangular pulse injection. Application of Laplace and Hankel transformations is used as a basic tool for the solution. Hankel transformation is useful to tackle the radial effect of the flow, and Laplace transformed solution is important in very important for moment analysis in chromatography. The analytical solution, if possible, is verified using the high-resolution finite volume scheme. In case where no exact analytical solution is possible, we used the numerical Laplace inversion for the solution. Two well-known boundary conditions Dirichlet and Danckwert’s are used at inlet of the flow channel in combination with Neumann condition at outlet of the flow channel. The effects of key parameters ((mu), (D_z), and v) involved in our model on the behavior of the solution concentration of the components, such as peak sharpness and retention time, have been discussed. This physically validates the transport mechanism involved in the process.

Foam is often used to displace liquid from porous media, as it produces more stable displacements than using solely gas as a displacing fluid. A model is considered for the foam displacement process in geological applications. The liquid saturation field is divided into an outer region (in which capillary suction effects can be neglected) and an inner region (in which capillary suction effects are retained). The outer region solution exhibits a discontinuous jump in liquid saturation, sometimes referred to as a shock. The inner region solution is a travelling wave that is superposed across that jump. The focus here is upon the inner region. The liquid saturation profile across the inner region is shown to be asymmetric, with abrupt changes for high liquid saturations but gradual changes for lower liquid saturations. These gradual changes should be taken into account when matching onto the outer region. The inner region is predicted to be of small extent, but also accesses fluid mobilities which are much lower than those in the outer region. However, the very lowest mobilities are only attained within a tiny part of the inner region in which saturation is still changing abruptly. In much of the inner region, mobility is only marginally less than in the outer region. Hence, the presence of the inner region does not significantly enhance flow resistance of the foam displacement process. Consequently, the inner region should have little impact on the ability of foam to produce stable displacement processes in porous media.

Understanding imbibition in multiscale porous carbonates is essential for predicting fluid distribution in subsurface applications. We measured the capillary pressure for spontaneous imbibition and forced water injection in a mixed-wet multiscale oolitic limestone with distinct macro-, intermediate-size-, and micropore structure using the differential imaging-based porous plate (DIPP) technique. Spontaneous imbibition was found to occur through water-wet micropore channels, whereas forced water injection was dominated by the flow in mixed-wet and oil-wet macro-pores with residual oil found in pores of intermediate size. The analysis of contact angle, curvature, macro-pore occupancy, and overall water Amott index demonstrated mixed-wet-to-oil-wet conditions, resulting in a percolation-like advance during forced water injection. The water Amott index calculated on each pore size classification indicated water-wet micropores and oil-wet intermediate-size- and macro-pores. Our results highlight the role of micropores in sustaining water flow at low saturation and the role of intermediate-size-pores in retaining residual oil, advancing the predictive understanding of fluid behavior in carbonate reservoirs.

The tortuosity of a porous medium has a significant effect on heat transfer through it, but this effect is difficult to quantify. In this study, we have developed the concept of applied thermal tortuosity and the thermal tortuosity function which characterizes the effect of porous medium geometry and the thermal conductivity ratio on the averaged path length of heat conduction in a porous medium. We have also proposed new macroscopic geometric parameters of porous media that can better describe the complexity of the porous media geometry. The relationship between the macroscopic geometric parameters and the developed thermal tortuosity function was established by using a neural network model. We used the developed thermal tortuosity function to calculate effective thermal conductivity, which can be applied in the thermal energy equation. Computations were performed for arbitrary two-dimensional porous media. Despite the model’s uncertainties, the developed neural network model is significantly more accurate than empirical correlations for determining the effective thermal conductivity. Optimization of the neural network architecture can further improve the accuracy of the model, but the problem of uncertainty cannot be completely solved. The study shows the importance of embedding the established knowledge of transport in porous media into the neural network model to improve its accuracy.

We consider the effect of viscous dissipation on the onset and nonlinear development of two-dimensional convection in a unit enclosure heated from below. First, we show that the linear theory is unchanged from that which arises when viscous dissipation is absent. Second, a weakly nonlinear analysis shows that convection becomes weaker with increasing values of ({widetilde{textrm{Ge}}}), a modified Gebhart number. In addition, the rate of heat transfer at the lower and upper sufaces differ from one another. Third, nonlinear convection is found to lose both up/down and left/right symmetry as both ({widetilde{textrm{Ge}}}) and (textrm{Ra}) (the Darcy–Rayleigh number) increase. It is also found that once viscous dissipation increases in strength to unphysically large amounts, then the maximum temperature migrates from the lower boundary to the interior of the enclosure.

The study presented in this paper is devoted to the laminar forced convection heat transfer in a porous microduct with a circular cross section. At small cross-section scales, the effects of roughness at the duct walls may be important for the evaluation of the heat transfer rate. The analysis aims to provide the Nusselt number as a quantity dependent on the boundary shape uncertainty by averaging over statistical samples of microducts having different roughness distributions generated randomly. Each statistical sample refers to a prescribed ratio between the maximum size of the wall roughness and the microduct nominal radius, and to a prescribed number of nodes employed to draw the boundary shape. Boundary conditions of either uniform wall temperature (T condition) or wall heating (H1 or H2 conditions) are considered. The results show that both the roughness and the number of nodes defining the microduct cross-sectional shape tend to inhibit the heat transfer: a sufficiently high value of the roughness amplitude may halve the Nusselt number relative to the smooth case. The Nusselt number obtained for the H2 condition decreases faster with the roughness amplitude compared with the Nusselt number obtained for the T and H1 conditions.

This study extends the classical Darcy–Bénard convection problem for isoflux thermal conditions in a horizontal porous layer with basic cellular flow and Hadley circulation to incorporate the Forchheimer effect taking care of inertial effects at medium/high flow rates. The traditional Darcy–Bénard problem can be considered a limiting case of this extension, omitting the circulation in an infinitely wide single cell. Three key parameters govern the basic circulation and temperature fields in this isoflux Darcy–Forchheimer–Bénard problem: the Forchheimer resistance number, the Rayleigh number, and the horizontal temperature gradient parameter. Although solutions are unique in the classical Darcy flow, dual Hadley solutions are detected in the Forchheimer extended Darcy flow valid for certain limited Forchheimer resistance number. Despite the fact that these solutions are asymmetric themselves, unlike the symmetric structure in the classical Hadley cell, dual solutions are formed as the symmetric part of each other with respect to a movable point. While the temperature gradient parameter enhances and readjusts the temperature distribution through the porous layer, the Forchheimer resistive force is shown to conversely reduce the magnitude of the cellular circulation and lower the overall temperature of the porous media in one instance, it increases in the other, exhibiting contrasting thermal behavior.

This study presents advanced numerical simulation of thermotaxis behavior in thermotactic microorganisms suspended within a fluid-saturated porous medium. Based on our previously established linear stability analysis framework, we extend the investigation to supercritical regimes, where thermotactic bioconvection patterns emerge due to the dynamic coupling between microorganism motility, thermal diffusion, and induced fluid flow. The mathematical formulation employs volume-averaged governing equations incorporating Darcy’s law and the Boussinesq approximation, with a focus on key dimensionless parameters including the Peclet number (Pe), Lewis number (Le), thermal Rayleigh number (Ra_T), and bioconvection Rayleigh number (Ra_N).The simulation explores various heating configurations—namely heated-from-below and heated-from-above—demonstrating how Pe modulates the onset of pattern formation, while Le exerts a stabilizing influence. This research provides the first numerical evidence of thermotactic bioconvection beyond critical thresholds in porous media. The findings elucidate fundamental mechanisms governing microorganism gradient-based motion and have potential applications in biosystems modeling, including thermally guided sperm migration, and explanations for Harmful Algal Bloom formation on water surfaces. The interplay between parameters offers a comprehensive insight into the regulation of bioconvection regimes, contributing to broader understanding in biological transport phenomena, microfluidics, and environmental modeling.

Enhanced geothermal system (EGS), typically designed as a doublet of injection and production wells, is a promising approach to exploit hot dry rock (HDR) resources. However, modeling fluid flow and heat transfer in fractured reservoirs remains challenging due to multi-scale fracture heterogeneities and coupled interactions. This study develops a three-dimensional discrete fracture network (DFN)-based thermal-hydraulic coupling model solved by the finite element method (FEM) to efficiently evaluate the heat extraction performance of fractured HDR reservoirs. The developed modeling scheme is validated against analytical and numerical benchmarks, and then applied to a large-scale fractured geothermal reservoir. Results show that the heterogeneity of the fracture network leads to a highly uneven temperature distribution, with the cold front advancing along the primary percolating fracture network pathways. Higher injection temperature and larger fracture aperture accelerate the geothermal reservoir cooling, while the increased well spacing extends EGS lifetime and reduce the electricity cost. This research provides deeper insights into the development of 3D EGS and supports the optimization of operational parameters and economic feasibility.

The usability of enzymatically induced calcium carbonate precipitation (EICP) as a method for altering porous media properties, soil stabilization, or biocementation depends on our ability to predict the spatial distribution of the precipitated calcium carbonate in porous media. While current REV-scale models can reproduce the main features of laboratory experiments, they neglect effects like the formation of preferential flow paths and the appearance of multiple polymorphs of calcium carbonate with differing properties. We show that extending an existing EICP model by the conceptual assumption of a mobile precipitate, amorphous calcium carbonate (ACC), allows for the formation of preferential flow paths when the initial porosity is heterogeneous. We apply sensitivity analysis to understand the influence of characteristic parameters of ACC that are uncertain or unknown, and compare two model variations based on different formulations of the ACC detachment term to analyze the plausibility of our hypothesis. An arbitrary polynomial chaos (aPC) surrogate model is trained based on the full model and used to reduce the computational cost of this study.