scholarly journals Chaotic mixing in three-dimensional porous media

2016 ◽  
Vol 803 ◽  
pp. 144-174 ◽  
Author(s):  
Daniel R. Lester ◽  
Marco Dentz ◽  
Tanguy Le Borgne
Keyword(s):  
Porous Media ◽  
Molecular Diffusion ◽  
Three Dimensional ◽  
Building Blocks ◽  
Chaotic Advection ◽  
Pore Scale ◽  
Scalar Mixing ◽  
Power Law Distribution ◽  
Porous Network ◽  
Macroscopic Models

Under steady flow conditions, the topological complexity inherent to all random three-dimensional (3D) porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a 3D fluid mechanical analogue of the baker’s map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence, pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW), which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We find that the chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with the longitudinal advection, whereas the topological constraints associated with two-dimensional porous media limit the mixing to scale algebraically. These results decipher the role of wide transit time distributions and complex topologies on porous media mixing dynamics, and provide the building blocks for macroscopic models of dilution and mixing which resolve these mechanisms.

Pore-scale Mixing and the Evolution from Anomalous to Normal Hydrodynamic Dispersion

2021 ◽  
Author(s):  
Marco Dentz ◽  
Alexandre Puyguiraud ◽  
Philippe Gouze
Keyword(s):  
Porous Media ◽  
Large Scale ◽  
Molecular Diffusion ◽  
Pore Space ◽  
Breakthrough Curves ◽  
Heterogeneous Porous Media ◽  
Hydrodynamic Dispersion ◽  
Pore Scale ◽  
Sandstone Sample ◽  
Flow Variability

<p>Transport of dissolved substances through porous media is determined by the complexity of the pore space and diffusive mass transfer within and between pores. The interplay of diffusive pore-scale mixing and spatial flow variability are key for the understanding of transport and reaction phenomena in porous media. We study the interplay of pore-scale mixing and network-scale advection through heterogeneous porous media, and its role for the evolution and asymptotic behavior of hydrodynamic dispersion. In a Lagrangian framework, we identify three fundamental mechanisms of pore-scale mixing that determine large scale particle motion: (i) The smoothing of intra-pore velocity contrasts, (ii) the increase of the tortuosity of particle paths, and (iii) the setting of a maximum time for particle transitions. Based on these mechanisms, we derive an upscaled approach that predicts anomalous and normal hydrodynamic dispersion based on the characteristic pore length, Eulerian velocity distribution and Péclet number. The theoretical developments are supported and validated by direct numerical flow and transport simulations in a three-dimensional digitized Berea sandstone sample obtained using X-Ray microtomography. Solute breakthrough curves, are characterized by an intermediate power-law behavior and exponential cut-off, which reflect pore-scale velocity variability and intra-pore solute mixing. Similarly, dispersion evolves from molecular diffusion at early times to asymptotic hydrodynamics dispersion via an intermediate superdiffusive regime. The theory captures the full evolution form anomalous to normal transport behavior at different Péclet numbers as well as the Péclet-dependence of asymptotic dispersion. It sheds light on hydrodynamic dispersion behaviors as a consequence of the interaction between pore-scale mixing and Eulerian flow variability. </p>

Immiscible Displacement at Pore Level for Correlated Porous Media

1998 ◽  
Vol 09 (06) ◽  
pp. 837-849 ◽  
Author(s):  
A. M. Vidales ◽  
J. L. Riccardo ◽  
G. Zgrablich
Keyword(s):  
Porous Media ◽  
Pore Space ◽  
Three Dimensional ◽  
Immiscible Displacement ◽  
Porous Network ◽  
Buoyancy Forces ◽  
Correlation Strength ◽  
Pore Level

Immiscible displacement at pore level on a three-dimensional correlated porous network is simulated allowing flow of the wetting phase along crevices of the pore walls (possibility of snap-off in throats) and advance through the centers of the pore space with different pore and throat filling conditions, leading to a cooperative filling. When these two mechanisms compete, different patterns arise. We study the effect of the correlation strength on the onset of each pattern. We do not take buoyancy forces into account.

scholarly journals Pore-scale investigation of the displacement fluid mechanics during two-phase flows in natural porous media under the dominance of capillary forces

Georesursy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 4-12
Author(s):  
Timur R. Zakirov ◽  
Maxim G. Khramchenkov
Keyword(s):  
Porous Media ◽  
Pore Space ◽  
Three Dimensional ◽  
Capillary Forces ◽  
High Temporal Resolution ◽  
Pore Scale ◽  
Two Phase Flows ◽  
Two Phase ◽  
Pressure Drops ◽  
Mobile Interfaces

This paper presents the results of numerical simulations of two-phase flows in porous media under capillary forces dominance. For modeling of immiscible two-phase flow, the lattice Boltzmann equations with multi relaxation time operator were applied, and the interface phenomena was described with the color-gradient method. The objective of study is to establish direct links between quantitative characteristics of the flow and invasion events, using high temporal resolution when detecting simulation results. This is one of the few works where Haines jumps (rapid invasion event which occurs at meniscus displacing from narrow pore throat to its wide body) are considered in three-dimensional natural pore space, but the focus is also on the displacement mechanics after jumps. It was revealed the sequence of pore scale events which can be considered as a period of drainage process: rapid invasion event during Haines jump; finish of jump and continuation of uniform invasion in current pore; switching of mobile interfaces and displacement in new region. The detected interface change, along with Haines jump, is another distinctive feature of the capillary forces action. The change of the mobile interfaces is manifested in step-like behavior of the front movement. It was obtained that statistical distributions of pressure drops during Haines jumps obey lognormal law. When investigating the flow rate and surface tension effect on the pressure drop statistics it was revealed that these parameters practically don’t affect on the statistical distribution and influence only on the magnitude of pressure drops and the number of individual Haines jumps.

scholarly journals Stochastic Dynamics of Lagrangian Pore‐Scale Velocities in Three‐Dimensional Porous Media

2019 ◽  
Vol 55 (2) ◽  
pp. 1196-1217 ◽  
Author(s):  
Alexandre Puyguiraud ◽  
Philippe Gouze ◽  
Marco Dentz
Keyword(s):  
Porous Media ◽  
Stochastic Dynamics ◽  
Three Dimensional ◽  
Pore Scale

scholarly journals Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media

2014 ◽  
Vol 90 (1) ◽  
Author(s):  
Matteo Icardi ◽  
Gianluca Boccardo ◽  
Daniele L. Marchisio ◽  
Tiziana Tosco ◽  
Rajandrea Sethi
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Three Dimensional ◽  
Pore Scale ◽  
Solute Dispersion

scholarly journals Numerical Simulation on Hydromechanical Coupling in Porous Media Adopting Three-Dimensional Pore-Scale Model

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jianjun Liu ◽  
Rui Song ◽  
Mengmeng Cui
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Pore Pressure ◽  
Three Dimensional ◽  
Confining Pressure ◽  
Scale Model ◽  
Micro Ct ◽  
Pore Scale ◽  
Hydromechanical Coupling ◽  
Rock Matrix

A novel approach of simulating hydromechanical coupling in pore-scale models of porous media is presented in this paper. Parameters of the sandstone samples, such as the stress-strain curve, Poisson’s ratio, and permeability under different pore pressure and confining pressure, are tested in laboratory scale. The micro-CT scanner is employed to scan the samples for three-dimensional images, as input to construct the model. Accordingly, four physical models possessing the same pore and rock matrix characteristics as the natural sandstones are developed. Based on the micro-CT images, the three-dimensional finite element models of both rock matrix and pore space are established by MIMICS and ICEM software platform. Navier-Stokes equation and elastic constitutive equation are used as the mathematical model for simulation. A hydromechanical coupling analysis in pore-scale finite element model of porous media is simulated by ANSYS and CFX software. Hereby, permeability of sandstone samples under different pore pressure and confining pressure has been predicted. The simulation results agree well with the benchmark data. Through reproducing its stress state underground, the prediction accuracy of the porous rock permeability in pore-scale simulation is promoted. Consequently, the effects of pore pressure and confining pressure on permeability are revealed from the microscopic view.

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