Transport in Porous Media最新文献

Foam flow in porous media increased the scientific community’s attention due to several potential industrial applications, including remediation of contaminated aquifers, soil remediation, acid diversion, and hydrocarbon recovery. Natural reservoirs typically have fractured and multi-layered structures. We investigate an immiscible incompressible two-phase foam flow in an internally homogeneous two-layered porous medium with different porosities and absolute permeabilities. For our analysis, we extended the previous result, evidencing that the presence of foam induces the existence of a single flow front in both layers. Using the traveling wave solution, we classify the foam flow depending on the absolute permeability and the porosity ratio between layers. We show that the mass crossflow between layers is connected to the relative position of the flow front in these layers and that the porosity difference between layers impacts the mass crossflow. All analytical estimates were supported by direct numerical simulations.

X-ray micro-computed tomography (X-ray micro-CT) is widely employed to investigate flow phenomena in porous media, providing a powerful alternative to core-scale experiments for estimating traditional petrophysical properties such as porosity, single-phase permeability or fluid connectivity. However, the segmentation process, critical for deriving these properties from greyscale images, varies significantly between studies due to the absence of a standardized workflow or any ground truth data. This introduces challenges in comparing results across different studies, especially for properties sensitive to segmentation. To address this, we present a fully open-source, automated workflow for the segmentation of a Bentheimer sandstone filled with nitrogen and brine. The workflow incorporates a traditional image processing pipeline, including non-local means filtering, image registration, watershed segmentation of grains, and a combination of differential imaging and thresholding for segmentation of the fluid phases. Our workflow enhances reproducibility by enabling other research groups to easily replicate and validate findings, fostering consistency in petrophysical property estimation. Moreover, its modular structure facilitates integration into modeling frameworks, allowing for forward-backward communication and parameter sensitivity analyses. We apply the workflow to exploring the sensitivity of the non-wetting phase volume, surface area, and connectivity to image processing. This adaptable tool paves the way for future advancements in X-ray micro-CT analysis of porous media.

Transport equations are widely used to describe the evolution of scalar quantities subject to advection, dispersion and, possibly, reactions. Numerical methods are required to solve these equations in applications, adopting either the advective or conservative formulations. Conservative formulations are usually preferred in practice because they conserve mass. Advective formulations do not, but have received more mathematical attention and are required for Lagrangian solution methods. To obtain an advective formulation that conserves mass, we subtract the discretized fluid flow equation, multiplied by concentration, from the conservative form of the transport equation. The resulting scheme not only conserves mass, but is also elegant in that it can be interpreted as averaging the advective term at cell interfaces, instead of approximating it at cell centers as in traditional centered schemes. The two schemes are identical when fluid velocity is constant, and both have second-order convergence, but the truncation errors are slightly different. We argue that the error terms appearing in the proposed scheme actually imply an improved representation of subgrid spreading/contraction and acceleration/deceleration caused by variable velocity. We compare the proposed and traditional schemes on several problems with variable velocity caused by recharge, discharge or evaporation, including two newly developed analytical solutions. The proposed method yields results that are slightly, but consistently, better than the traditional scheme, while always conserving mass (i.e., mass at the end equals mass at the beginning plus inputs minus outputs), which the traditional centered finite differences scheme does not. We conclude that this scheme should be preferred in finite difference solutions of transport.

We derive an analytical solution to a Darcy flow problem in a discrete 1D fracture coupled to a 2D continuum matrix. Separate unknowns for the fracture and matrix domain are considered, coupled by a Robin-type condition. The solution, in the form of a Fourier series, applies to a wide range of problem parameters, covering both conductive and barrier fracture cases. The evaluation procedure and convergence properties are discussed. To validate the solution, we compare it against a numerical solution using second-order finite differences in a parametric study. Our results demonstrate the accuracy and effectiveness of the analytical solution, making it a valuable tool for testing numerical schemes for discrete fracture-matrix models.

Evaporation of droplets formed at the interface of a coupled free-flow–porous medium system enormously affects the exchange of mass, momentum, and energy between the two domains. In this work, we develop a model to describe multiple droplets’ evaporation at the interface, in which new sets of coupling conditions including the evaporating droplets are developed to describe the interactions between the free flow and the porous medium. Employing pore-network modeling to describe the porous medium, we take the exchanges occurring on the droplet–pore and droplet–free-flow interfaces into account. In this model, we describe the droplet evaporation as a diffusion-driven process, where vapor from the droplet surface diffuses into the surrounding free flow due to the concentration gradient. To validate the model, we compare the simulation results for the evaporation of a single droplet in a channel with experimental data, demonstrating that our model accurately describes the evaporation process. Then, we examine the impact of free-flow and porous medium properties on droplet evaporation. The results show that, among other factors, velocity and relative humidity in the free-flow domain, as well as pore temperature in the porous medium, play key roles in the droplet evaporation process.

Counter-current imbibition can improve the recovery efficiency of complex fractured reservoirs, but there are few studies on the pore-scale mechanism and the factors affecting the recovery efficiency. This paper attempts to track the microscopic oil–water imbibition process through phase field method simulation, revealing the distribution characteristics of oil and water phases at different stages, as well as the sudden change characteristics of pressure and velocity at the instant of oil film rupture. Then, the influence of fracture aperture, capillary number and viscosity ratio on oil recovery efficiency is discussed. Results indicate that the microscopic imbibition process can be divided into 4 stages: the oil film forms after oil–water contact, then the oil film ruptures to form oil droplets, then the oil–water line moves outward from the large pore, and finally the oil droplets gather to discharge from the fracture. It is also found that there will be sudden changes at the moment of oil film rupture, the pressure drops sharply and the velocity increases sharply. Moreover, there exists a critical fracture aperture which is approximately 10 times the average pore size, and if the fracture is smaller than the critical fracture aperture, a dead oil zone occurs, which affects recovery. Additionally, LogM-LogCa stability diagram is constructed which is mainly dominated by viscous forces, capillary forces. As the capillary number increases, the recovery efficiency shows an overall decreasing trend. When the viscosity ratio was greater than 10, there was no significant change in the recovery efficiency, influenced by the weakening of the dominant role of viscous forces. New findings are beneficial to enhancing the recovery efficiency of low permeability reservoirs.

The development of reliable mathematical models and numerical discretization methods is important for the understanding of salt precipitation in porous media, which is relevant for environmental problems like soil salinization. Models on the pore scale are necessary to represent local heterogeneities in precipitation and to include the influence of solution-air-solid interfaces. A pore-network model for saturated flow, which includes the precipitation reaction of salt, is presented. It is implemented in the open-source simulator DuMu(^{textrm{X}}). In this paper, we restrict ourselves to one-phase flow as a first step. Since the throat transmissibilities determine the flow behaviour in the pore network, different concepts for the decreasing throat transmissibility due to precipitation are investigated. We consider four concepts for the amount of precipitation in the throats. Three concepts use information from the adjacent pore bodies, and one employs a pore-throat model obtained by averaging the resolved pore-scale model in a thin-tube. They lead to different permeability developments, which are caused by the different distribution of the precipitate between the pore bodies and throats. We additionally apply two different concepts for the calculation of the transmissibility. One obtains the precipitate distribution from analytical assumptions, the other from a geometric minimization principle using a phase-field evolution equation. The two concepts do not show substantial differences for the permeability development as long as simple pore-throat geometries are used. Finally, advantages and disadvantages of the concepts are discussed in the context of the considered physical problem and a reasonable effort for the implementation and computational costs.

We consider heat transport within a discontinuous domain by relying on the modeling approach proposed by Baioni et al. Such approach has been specifically designed to address diffusive processes in media with discontinuous physical properties and generalized boundary conditions at the discontinuities. Three algorithms are here applied to estimate the conductive heat transport in a bimaterial medium. The algorithms undergo testing using two test cases that share the same computational domain but differ in terms of their initial conditions. According to the numerical results all the algorithms ensure the conservation of thermal energy and preserve thermal equilibrium under steady state conditions. The Generalized Uffink Method (GUM) and Generalized HYMLA demonstrate sensitivity to the choice of the time step, whereas the Generalized Skew Brownian Motion appears to be unaffected by the value of (Delta t). The GUM algorithm presents an optimal trade-off between accuracy and computational time.

Fluctuations in the production of renewable-based electricity have to be compensated by converting and storing the energy for later use. Underground methanation reactors (UMR) are a promising technology to address this issue. The idea is to create a controlled bio-reactor system in a porous underground formation, where hydrogen obtained from renewable energy sources by electrolysis and carbon dioxide from industrial sources are fed into the reactor and converted into methane. Microorganisms, known as methanogenic archaea, catalyze the chemical reaction by using the two non-organic substrates as nutrients for their growth and for their respiratory metabolism. The generated synthetic methane is renewable and capable to compete with the fossil methane. Mathematical models play an important role in the design and planning of such systems. Usually, a numerical solution of the model is required since complex initial-boundary problems cannot be solved analytically. In this paper, an existing bio-reactive transport model for UMR is simplified to such an extent that an analytical solution of the advection-dispersion-reaction equation can be applied. A second analytical solution is used for the case without dispersion. The analytical solutions are shown for both the educt (hydrogen) and the reaction product (methane). In order to examine the applicability of the analytical models, they are compared with the significantly more complex numerical model for a 1D case and a 3D case. It was shown that there is an acceptable agreement between the two analytical solutions and the numerical solution in different spatial plots of hydrogen and methane concentration and in the methane concentration in the withdrawn gas. The mean absolute error in the mole fraction is well below 0.015 in most cases. The spatial distribution of the hydrogen concentration in the comparison to the 3D case shows a higher deviation with a mean absolute error of approx. 0.023. As expected, the model with dispersion shows a slightly lower error in all cases, as only here the gas mixing resulting in smeared displacement fronts can be represented. It is shown that analytical modeling is a good tool to get a first estimation of the behavior of an UMR. It allows to help in the design of well spacing in combination with the injection rate and injected gas composition. Nevertheless, it is recommended to use more complex models for the later detailed analysis, which require a numerical solution.