In the upscaling from pore- to continuum (Darcy) scale, reaction and deposition phenomena at the solid-liquid interface of a porous medium have to be represented by macroscopic reaction source terms. The effective rates can be computed, in the case of periodic media, from three-dimensional microscopic simulations of the periodic cell. Several computational and semi-analytical models have been studied in the field of colloid filtration to describe this problem. They often rely on effective deposition rates defined by simple linear reaction ODEs, neglecting the advection-diffusion interplay, and assuming slow reactions. Therefore, when these rates are inserted into general macroscopic transport equations, they can lead to conceptual inconsistencies and, therefore, often qualitatively wrong results. In this work, we study the upscaling of Brownian deposition on face-centred spherical arrangements using a linear effective reaction rate, defined by volume averaging, and a macroscopic advection-diffusion-reaction equation. The case of partial deposition, defined by an attachment probability, is studied and the limit of ideal deposition is retrieved as a particular case. We make use of a particularly convenient computational setup that allows the direct computation of the asymptotic stationary value of effective rates. This allows to drastically reduce the computational domain down to the scale of the single repeating periodic unit: the savings are ever more noticeable in the case of higher Peclet numbers, when larger physical times are needed to reach the asymptotic regime, and thus, equivalently, a much larger computational domain and simulation time would be needed in a traditional setup. We show how this new definition of deposition rate is more robust and extendable to the whole range of Péclet numbers; it also is consistent with the classical heat and mass transfer literature.
Upscaling the effect of heterogeneities in porous media is crucial for macroscopic flow predictions, with widespread applications in energy and environmental settings. In this study, we derive expressions for the upscaled flow properties of a porous medium with a vertical heterogeneity, using a combination of asymptotic analysis and numerical simulations. Then, we use these upscaled expressions to describe the dynamic flooding of an aquifer, where the classic Buckley-Leverett formulation is modified to account for heterogeneities. In particular, we show that heterogeneities can modify flooding…
We present a model for upscaling the time-dependent effective retardation factor in hierarchical porous media with multimodal reactive mineral facies. The model extends the approach by Deng et al. (2013) in which they expanded a Lagrangian-based stochastic theory presented by Rajaram (1997) in order to describe the scaling effect of retardation factor. They used a first-order linear approximation in deriving their model to make the derivation tractable. Importantly, the linear approximation is known to be valid only to variances of 0.2. In this article we show that the model can be derived wit…
The typical temporal resolution used in modern simulations significantly exceeds characteristic time scales at which the system is driven. This is especially so when systems are simulated over time-scales that are much longer than the typical temporal scales of forcing factors. We investigate the impact of space-time upscaling on reactive transport in porous media driven by time-dependent boundary conditions whose characteristic time scale is much smaller than that at which transport is studied or observed at the macroscopic level. The focus is on transport of a reactive solute undergoing diff…
Reactive transport in saturated/unsaturated porous media is numerically upscaled to the space-time scale of a hypothetical measurement through coarse-grained space-time (CGST) averages. The reactive transport is modeled at the fine-grained Darcy scale by the actual number of molecules involved in reactions which undergo advective and diffusive movements described by global random walk (GRW) simulations. The CGST averages verify identities similar to a local balance equation which allow us to derive expressions for the flow velocity and the intrinsic diffusion coefficient in terms of averaged m…
Upscaling the Navier-Stokes-Cahn-Hilliard model for incompressible multiphase flow in inhomogeneous porous media
North University of China（中北大学）；Taiyuan University of Technology（太原理工大学）；Shandong University（山东大学）；Southern University of Science and Technology（南方科技大学）；Huazhong University of Science and Technology（华中科技大学）
We develop and validate a new model to study simultaneous erosion and deposition in three-dimensional porous media. We study the changes of the porous structure induced by the deposition and erosion of matter on the solid surface and find that when both processes are active, channelization in the porous structure always occurs. The channels can be stable or only temporary depending mainly on the driving mechanism. Whereas a fluid driven by a constant pressure drop in general does not form steady channels, imposing a constant flux always produces stable channels within the porous structure. Fur…
The macroscopic spreading and mixing of solute plumes in saturated porous media is ultimately controlled by processes operating at the pore scale. Whilst the conventional picture of pore-scale mechanical dispersion and molecular diffusion leading to persistent hydrodynamic dispersion is well accepted, this paradigm is inherently two-dimensional (2D) in nature and neglects important three-dimensional (3D) phenomena. We discuss how the kinematics of steady 3D flow at the porescale generate chaotic advection, involving exponential stretching and folding of fluid elements,the mechanisms by which i…
Biofilm growth in porous media: experiments, computational modeling at the porescale, and upscaling
Oregon State University（俄勒冈州立大学）；University of Warsaw（华沙大学）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Helmholtz Centre for Environmental Research（赫尔霍兹环境研究所）
In disordered porous media, two-phase flow of immiscible fluids (biphasic flow) is organized in patterns that sometimes exhibit fractal geometries over a range of length scales, depending on the capillary, gravitational and viscous forces at play. These forces, as well as the boundary conditions, also determine whether the flow leads to the appearance of fingering pathways, i.e., unstable flow, or not. We present here a short review of these aspects, focusing on drainage and summarizing when these flows are expected to be stable or not, what fractal dimensions can be expected, and in which ran…
Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible due to the strong coupling between scales that characterise such systems. In this work, we show how the upscaling can be carried out by applying and extending the methods presented in literature. The approach relies on the decomposition of the microscale concentration into a reactive component, given by the eigenfunction of the advection-diffusion operator, the associated eigenvalue whic…
Colloidal particles hold promise for mobilizing and removing trapped immiscible fluids from porous media, with implications for key energy and water applications. Most studies focus on accomplishing this goal using particles that can localize at the immiscible fluid interface. Therefore, researchers typically seek to optimize the surface activity of particles, as well as their ability to freely move through a pore space with minimal deposition onto the surrounding solid matrix. Here, we demonstrate that deposition can, surprisingly, promote mobilization of a trapped fluid from a porous medium …
We investigate the upscaling of diffusive transport parameters as function of pore scale material structure using a stochastic framework. We focus on sub-REV (representative elementary volume) scale where the complexity of pore space geometry leads to a significant scatter of transport observations. We study a large data set of sub-REV measurements on porosity and transport ability being a dimensionless parameter representing the ratio of diffusive flow through the porous volume and through an empty volume. We characterize transport ability as probability distribution functions (PDFs) of poros…
Diverse processes -- e.g., environmental pollution, groundwater remediation, oil recovery, filtration, and drug delivery -- involve the transport of colloidal particles in porous media. Using confocal microscopy, we directly visualize this process in situ and thereby identify the fundamental mechanisms by which particles are distributed throughout a medium. At high injection pressures, hydrodynamic stresses cause particles to be continually deposited on and eroded from the solid matrix -- notably, forcing them to be distributed throughout the entire medium. By contrast, at low injection pressu…
Transport and particulate processes are ubiquitous in environmental, industrial and biological applications, often involving complex geometries and porous media. In this work we present a general population balance model for particle transport at the pore-scale, including aggregation, breakage and surface deposition. The various terms in the equations are analysed with a dimensional analysis, including a novel collision-induced breakage mechanism, and split into one- and two-particles processes. While the first are linear processes, they might both depend on local flow properties (e.g. shear).…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field). Recently, closer to the spirit of PDF models for turbulent flows, some approaches have used this statistical viewpoint also in pore-scale transport processes (fully resolved porous media models). When a concentration field is transported, by advection and diffusion, in a heterogeneous media, in fact, spatial PDFs can be defined to characterise local fluctuation…
In particle-laden flows through porous media, porosity and permeability are significantly affected by the deposition and erosion of particles. Experiments show that the permeability evolution of a porous medium with respect to a particle suspension is not smooth, but rather exhibits significant jumps followed by longer periods of continuous permeability decrease. Their origin seems to be related to internal flow path reorganization by avalanches of deposited material due to erosion inside the porous medium. We apply neutron tomography to resolve the spatio-temporal evolution of the pore space …
Erosion and deposition during flow through porous media can lead to large erosive bursts that manifest as jumps in permeability and pressure loss. Here we reveal that the cause of these bursts is the re-opening of clogged pores when the pressure difference between two opposite sites of the pore surpasses a certain threshold. We perform numerical simulations of flow through porous media and compare our predictions to experimental results, recovering with excellent agreement shape and power-law distribution of pressure loss jumps, and the behavior of the permeability jumps as function of particl…
Acoustic waves in a slightly compressible fluid saturating porous periodic structure are studied using two complementary approaches: 1) the periodic homogenization (PH) method provides effective model equations for a general dynamic problem imposed in a bounded medium, 2) harmonic acoustic waves are studied in an infinite medium using the Floquet-Bloch (FB) wave decomposition. In contrast with usual simplifications, the advection phenomenon of the Navier-Stokes equations is accounted for. For this, an acoustic approximation is applied to linearize the advection term. The homogenization results…
In this paper, the pore network model to investigate the reaction-diffusion process in the hierarchically structured porous catalyst particle is extended to consider the phenomenon of deactivation by coking. In this framework, the interaction of internal particle pore structure and mass transfer under the condition of coke deposition are examined. A primitive experimental investigation has been performed as an introduction to the development of the model. Then, the effect of structural features namely macroporosity and pore size ratio, the deactivation properties, the maximum loading of coke a…
Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centered cubic porous unit cell on the transport, clustering, and deposition of fine particles at different Stokes numbers ($St = 0.01, 0.1, 0.5, 1, 2$) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and collision of particles with pore walls is modeled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geo…
Dynamics of fluid-fluid displacements in a model rough fracture beyond the quasistatic limit: A spectral approach
Institute of Environmental Assessment and Water Research (IDAEA), Spanish National Research Council (CSIC)（环境评估与水资源研究所，西班牙国家研究委员会）；Universitat de Barcelona（巴塞罗那大学）；University of Barcelona Institute of Complex Systems (UBICS)（巴塞罗那大学复杂系统研究所）
Porosity and Material Disorder Drive Distinct Channelization Transition
Centro de Física Teórica e Computacional, Faculdade de Ciências, Universidade de Lisboa（里斯本大学理学院理论物理与计算中心）；Debye Institute for Nanomaterials Science, Utrecht University（乌得勒支大学德拜纳米材料科学研究所）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Departamento de Física, Universidade Federal do Ceará（塞阿拉联邦大学物理系）
