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The paper presents a workflow for fast pore-scale simulation of single-phase flow in tight reservoirs typically characterized by low, multiscale porosity. Multiscale porosity implies that the computational domain contains porous voxels…

This study presents a novel workflow for constructing hybrid macropore-Darcy models from micro-CT images of microporous rocks. In our approach, macropore networks are extracted using established methods, while the microporosity is…

Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic…

Numerical Analysis · Mathematics 2023-12-27 Mina Karimi , Kaushik Bhattacharya

We introduce a Darcy-scale model to describe compressible multi-component flow in a fully saturated porous medium. In order to capture cross-diffusive effects between the different species correctly, we make use of the Maxwell--Stefan…

Analysis of PDEs · Mathematics 2020-12-02 Lukas Ostrowski , Christian Rohde

An open-sourced multiphase Darcy-Brinkman approach is proposed to simulate two-phase flow in hybrid systems containing both solid-free regions and porous matrices. This micro-continuum model is rooted in elementary physics and volume…

Computational Physics · Physics 2021-03-15 Francisco J. Carrillo , Ian C. Bourg , Cyprien Soulaine

In this work we examine the dispersion of conservative tracers (bromide and fluorescein) in an experimentally-constructed three-dimensional dual-porosity porous medium. The medium is highly heterogeneous ($\sigma_Y^2=5.7$), and consists of…

Fluid Dynamics · Physics 2018-03-14 Daniel Vogler , Sassan Ostvar , Rebecca Paustian , Brian Wood

This paper deals with simulation of flow and transport in porous media such as transport of groundwater contaminants. We first discuss how macro scale equations are derived and which terms have to be closed by models. The transport of…

Numerical Analysis · Mathematics 2018-07-03 Quanji Cai , Sheema Kooshapur , Michael Manhart , Ralf-Peter Mundani , Ernst Rank , Andreas Springer , Boris Vexler

Transport of viscous fluid through porous media is a direct consequence of the pore structure. Here we investigate transport through a specific class of two-dimensional porous geometries, namely those formed by fluid-mechanical erosion. We…

Fluid Dynamics · Physics 2020-05-20 Shang-Huan Chiu , M. N. J. Moore , Bryan D. Quaife

The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…

Numerical Analysis · Mathematics 2025-05-06 Surendra Nepal , Vishnu Raveendran , Michael Eden , Rainey Lyons , Adrian Muntean

This work presents a data-driven framework for multi-scale parametrization of velocity-dependent dispersive transport in porous media. Pore-scale flow and transport simulations are conducted on periodic pore geometries, and volume-averaging…

Numerical Analysis · Mathematics 2024-10-21 Edward Coltman , Martin Schneider , Rainer Helmig

We perform direct numerical simulations (DNS) of a turbulent channel flow over porous walls. In the fluid region the flow is governed by the incompressible Navier--Stokes (NS) equations, while in the porous layers the Volume-Averaged…

Fluid Dynamics · Physics 2023-07-19 Marco E. Rosti , Luca Cortelezzi , Maurizio Quadrio

The accurate description of fluid flow and transport in fractured porous media is of paramount importance to capture the macroscopic behaviour of an oil reservoir, a geothermal system, or a CO2 sequestration site, to name few applications.…

Numerical Analysis · Mathematics 2019-08-01 Alessio Fumagalli , Eirik Keilegavlen

This work presents a unified numerical framework for simulating incompressible flows within the coupled fluid-porous-medium system and involving heat and solute transport and phase-changing process. A complete set of governing equations is…

Fluid Dynamics · Physics 2026-01-28 Rongfu Guo , Yantao Yang

In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…

Numerical Analysis · Mathematics 2020-08-24 Junlong Lyu , Zhongjian Wang , Jack Xin , Zhiwen Zhang

This dissertation resolves a longstanding discussion of a mathematical problem important in contaminant hydrogeology and chemical-reaction engineering, the proper mathematical description for a miscible solute undergoing longitudinal…

Analysis of PDEs · Mathematics 2007-05-23 W. J. Golz

The effective diffusivity of Brownian tracer particles confined in periodic micro-channels is smaller than the microscopic diffusivity due to entropic trapping. Here, we study diffusion in two-dimensional periodic channels whose…

Statistical Mechanics · Physics 2019-05-29 M. Mangeat , T. Guérin , D. S. Dean

When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…

Fluid Dynamics · Physics 2024-10-16 Lucy C Auton , Mohit P. Dalwadi , Ian M. Griffiths

This paper studies the mechanisms of dispersion in the laminar flow through the pore space of a $3$-dimensional porous medium. We focus on pre-asymptotic transport prior to the asymptotic hydrodynamic dispersion regime, in which solute…

Fluid Dynamics · Physics 2018-03-05 Marco Dentz , Matteo Icardi , Juan J. Hidalgo

We analyse the process of convective mixing in two-dimensional, homogeneous and isotropic porous media with dispersion. We considered a Rayleigh-Taylor instability in which the presence of a solute produces density differences driving the…

Fluid Dynamics · Physics 2025-10-08 Marco De Paoli , Guru Sreevanshu Yerragolam , Roberto Verzicco , Detlef Lohse

3D bicontinuous two-phase materials are increasingly gaining interest because of their unique multifunctional characteristics and advancements in techniques to fabricate them. Due to their complex topological and structural properties, it…

Materials Science · Physics 2024-07-09 Salvatore Torquato , Jaeuk Kim
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