Transport in Porous Media最新文献

Packed beds with cylindrical particles of polymeric material are a better option for developing low-cost, durable thermal energy storage for higher temperature ranges and corrosive environments. In this work, the formulations for pressure drop and interfacial convective heat transfer coefficient in the packed bed system (PBS) filled with cylindrical particles are developed for a wide range of geometrical and operating parameters. Two experimental setups are developed to determine the effects of superficial velocity, porosity of PBS, and geometrical dimensions of cylindrical particles on pressure drop and interfacial convective heat transfer coefficient. A discrete element method-based numerical model of PBS is developed to obtain the effect of fluid properties. The machine learning regression is deployed on the experimental and numerical data set to obtain a pressure drop formulation. Further, an analytical expression based on the Ergun equation is developed to approximate the machine-learning-based pressure drop formulation. The interfacial heat transfer coefficient is estimated by solving the steady-state heat conduction equation using the experimentally measured particle surface and air temperatures. The developed pressure drop and interfacial heat transfer coefficient formulations show maximum mean absolute deviations of less than 10.1% and 5.5%, respectively, with the experimental results.

Graphical Abstract

Capillary rise experiments are conducted in a set of calcareous and siliceous rocks with varying mineralogy and petrophysical properties to understand the coupled impact of reactivity and spontaneous imbibition. A capillary rise experiment is performed in each sample: first with deionized water, then with a dilute acidic solution, and finally again with deionized water, and the capillary rise profile for each is recorded. Pre- and post-acid petrophysical properties such as porosity, permeability, pore size distribution, and contact angle are measured for each sample. The mineral makeup of the rocks significantly influences how the acidic fluids penetrate the samples. The primary reactions are the dissolution of Ca- and Mg-rich minerals which alter the pore network. The higher acid strength results in higher capillary rise in calcareous rocks and results in an increase in the average pore size. The same pH acid results in lower capillary rise in the siliceous rocks, and a general decrease in the average pore size is observed. Changes in contact angle indicate increased water affinity in carbonate and reduced affinity in sandstone. The link between capillary interactions and fluid reactivity is often overlooked in fluid flow studies, and this research sheds light on the importance of reactivity during spontaneous imbibition, offering insights into dissolution and precipitation processes during capillary flow.

Inertial permeability is a critical parameter that quantifies the pressure loss caused by inertia in fluid flow through rough-walled fractures, described by the Forchheimer equation. This study investigates the size effect on the inertial permeability of rough-walled fractures and establishes a characterization model for fractures of varying sizes. Numerical simulations are conducted on five large-scale fracture models (1 m × 1 m) by resolving the Navier–Stokes equations. Smaller models are extracted from these large-scale fracture models for detailed size-dependent analysis. The results show that the peak asperity height (ξ), asperity height variation coefficient (η), and the fitting coefficient of the aperture cumulative distribution curve (C) significantly affect inertial permeability. Specifically, as ξ increases, the fluid flow experiences greater resistance, resulting in a reduction of inertial permeability. Similarly, a larger η corresponds to more variable asperity heights, further decreasing permeability. In contrast, a higher C value, indicating a more uniform aperture distribution, increases inertial permeability by facilitating smoother fluid flow. Quantitatively, the relationship between inertial permeability and fracture size follows a power law, with the sensitivity to roughness parameters diminishing as fracture size increases. This characterization model provides a method for scaling from laboratory-scale to field-scale fractures, offering practical implications for hydraulic engineering and subsurface fluid flow management.

Four types of voids exist in shale, including inorganic pores, organic pores, natural fractures, and hydraulic fractures, where the gas flow within is affected by voids sizes, shapes, and the mineral composition surrounding them. It is still a challenge to build an effective multi-scale model for shale by now. A model classifying organic pores and inorganic pores with and without clay was proposed in our previous work by incorporating various testing methods. However, some improvements can be made, including wider the pore size of the model to full-scale and adding the fractures without being considered previously. Therefore, a new model is proposed by integrating an improved full-scale matrix pore network model (PNM) with fractures. That is, the effects of four types of voids, including organic pores, inorganic pores containing clay, inorganic pores without clay, and fractures, on gas flow are all considered in the model. Then, the factors affecting the permeability of the matrix (i.e., without fractures) and the whole model (i.e., with fractures) were analyzed. The results show that connectivity both in small- and large-scale PNM and total organic content facilitate the flow, while clay content and water film thickness hinder the flow, especially within small pores. Fractures along the pressure drop accelerate gas flow, and the fractures perpendicular to the pressure drop only channel the pressure when the fractures along the pressure drop both exist. The model can be applied to other mudstones and shales and studies the fluid migration within them through proper parameters adjustment.

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.