scholarly journals Reduced Model for Properties of Multiscale Porous Media with Changing Geometry

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 28 ◽  
Author(s):  
Malgorzata Peszynska ◽  
Joseph Umhoefer ◽  
Choah Shin
Keyword(s):  
Porous Media ◽  
Reactive Transport ◽  
Multiple Scales ◽  
Pore Space ◽  
Type Model ◽  
Crystal Formation ◽  
Pore Filling ◽  
Reduced Models ◽  
Flow And Transport ◽  
The Impact

In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities.

scholarly journals A homogenised model for flow, transport and sorption in a heterogeneous porous medium

2021 ◽  
Vol 932 ◽  
Author(s):  
L.C. Auton ◽  
S. Pramanik ◽  
M.P. Dalwadi ◽  
C.W. MacMinn ◽  
I.M. Griffiths
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Multiple Scales ◽  
Effective Diffusivity ◽  
Rectangular Lattice ◽  
Mathematical Framework ◽  
Anisotropic Flow ◽  
Flow And Transport ◽  
Soft Porous Media ◽  
The Impact

A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for this purpose. Here, we consider a two-dimensional microstructure comprising an array of obstacles of smooth but arbitrary shape, the size and spacing of which can vary along the length of the porous medium. We use homogenisation via the method of multiple scales to systematically upscale a novel problem involving cells of varying area to obtain effective continuum equations for macroscale flow and transport. The equations are characterised by the local porosity, a local anisotropic flow permeability, an effective local anisotropic solute diffusivity and an effective local adsorption rate. These macroscale properties depend non-trivially on the two degrees of microstructural geometric freedom in our problem: obstacle size and obstacle spacing. We exploit this dependence to construct and compare scenarios where the same porosity profile results from different combinations of obstacle size and spacing. We focus on a simple example geometry comprising circular obstacles on a rectangular lattice, for which we numerically determine the macroscale permeability and effective diffusivity. We investigate scenarios where the porosity is spatially uniform but the permeability and diffusivity are not. Our results may be useful in the design of filters or for studying the impact of deformation on transport in soft porous media.

Pore-scale study of effects of surface roughness on the transport of interfacial reactive tracers during primary drainage process

2021 ◽  
Author(s):  
Huhao Gao ◽  
Alexandru Tatomir ◽  
Nikolaos Karadimitriou ◽  
Holger Steeb ◽  
Martin Sauter
Keyword(s):  
Surface Roughness ◽  
Porous Media ◽  
Reactive Transport ◽  
Capillary Condensation ◽  
Field Method ◽  
Phase Field Method ◽  
Pore Scale ◽  
Water Films ◽  
Mobile Mass ◽  
The Impact

<p>Porous media surface roughness strongly influences the transport of solutes during drainage, due to the formation of thick water films (capillary condensation) on the porous media surface. In the case of interfacial-reacted, water-based solutes, these water films increase both the production of the solute, due to the increased number of fluid-fluid interfaces, and the loss of the solute by the retention in the stagnant water films. The retention of the solute in flowing water is described by a mobile mass retention term. This study applies the pore-scale direct simulation with the phase-field method based continuous solute transport (PFM-CST) model on the kinetic interfacial sensitive (KIS) tracer reactive transport during primary drainage in a 2D slit with a wall with variable fractal geometries. The capillary-associated moving interface is found to be larger for rough surfaces than smoother ones. The results confirm that the impact of roughness regarding the film-associated interfacial area can be partly, or totally masked, in a drained slit. It is found that the mobile mass retention term is increased with larger volumes of capillary condensed water films. To conclude, it is also found that the surface roughness factor has a non-monotonic relationship with the overall production rate of solute mass in moving water.</p>

Reactive transport in porous media with local mixing limitation: A Lagrangian modeling approach

2020 ◽  
Author(s):  
Guillem Sole-Mari ◽  
Daniel Fernàndez-Garcia ◽  
Xavier Sanchez-Vila ◽  
Diogo Bolster
Keyword(s):  
Porous Media ◽  
Reactive Transport ◽  
Mathematical Formulation ◽  
Random Motion ◽  
Concentration Fluctuations ◽  
Local Concentration ◽  
Flow And Transport ◽  
Transport In Porous Media ◽  
Lagrangian Modeling ◽  
Rate Interaction

<p>Hydrological models are unable to fully resolve subsurface flow and transport down to the microscale. Instead, modelers usually work with upscaled flow and transport properties that represent the behavior of the system at a given coarse scale. While this approach is justified from a practical standpoint, it disregards the local heterogeneity of porous media flows, which tend to produce mixing-limited reactive transport behaviors that cannot be captured by classical modeling approaches. While some innovative methods have been suggested in the past in order to address this problem, none of them has proposed a mathematical formulation which can potentially reproduce the generation, transport and decay of local concentration fluctuations and their impact on chemical reactions, for general initial and boundary conditions. Here, we propose a Lagrangian approach based on the random motion of fluid particles that locally mix following a Multi-Rate Interaction by Exchange with the Mean (MRIEM) formulation. Concentration fluctuations in the proposed model display the typical behavior associated to transport in porous media with mixing-limited conditions. Experimental results of reactive transport are successfully reproduced by the model.</p>

Multiphase-Flow and Reactive-Transport Validation Studies at the Pore Scale by Use of Lattice Boltzmann Computer Simulations

SPE Journal ◽  
2017 ◽  
Vol 22 (03) ◽  
pp. 940-949 ◽  
Author(s):  
Edo S. Boek ◽  
Ioannis Zacharoudiou ◽  
Farrel Gray ◽  
Saurabh M. Shah ◽  
John P. Crawshaw ◽  
...  
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Capillary Pressure ◽  
Computer Simulations ◽  
Relative Permeability ◽  
Lattice Boltzmann ◽  
Reactive Transport ◽  
Pore Space ◽  
Processing Unit ◽  
Space Images

Summary We describe the recent development of lattice Boltzmann (LB) and particle-tracing computer simulations to study flow and reactive transport in porous media. First, we measure both flow and solute transport directly on pore-space images obtained from micro-computed-tomography (CT) scanning. We consider rocks with increasing degree of heterogeneity: a bead pack, Bentheimer sandstone, and Portland carbonate. We predict probability distributions for molecular displacements and find excellent agreement with pulsed-field-gradient (PFG) -nuclear-magnetic-resonance (NMR) experiments. Second, we validate our LB model for multiphase flow by calculating capillary filling and capillary pressure in model porous media. Then, we extend our models to realistic 3D pore-space images and observe the calculated capillary pressure curve in Bentheimer sandstone to be in agreement with the experiment. A process-based algorithm is introduced to determine the distribution of wetting and nonwetting phases in the pore space, as a starting point for relative permeability calculations. The Bentheimer relative permeability curves for both drainage and imbibition are found to be in good agreement with experimental data. Third, we show the speedup of a graphics-processing-unit (GPU) algorithm for large-scale LB calculations, offering greatly enhanced computing performance in comparison with central-processing-unit (CPU) calculations. Finally, we propose a hybrid method to calculate reactive transport on pore-space images by use of the GPU code. We calculate the dissolution of a porous medium and observe agreement with the experiment. The LB method is a powerful tool for calculating flow and reactive transport directly on pore-space images of rock.

scholarly journals Wettability control on multiphase flow in patterned microfluidics

2016 ◽  
Vol 113 (37) ◽  
pp. 10251-10256 ◽  
Author(s):  
Benzhong Zhao ◽  
Christopher W. MacMinn ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Contact Angles ◽  
Flow In Porous Media ◽  
Wetting Transition ◽  
Pore Scale ◽  
Displacement Efficiency ◽  
Pore Filling ◽  
Wide Range ◽  
The Impact

Multiphase flow in porous media is important in many natural and industrial processes, including geologic CO2 sequestration, enhanced oil recovery, and water infiltration into soil. Although it is well known that the wetting properties of porous media can vary drastically depending on the type of media and pore fluids, the effect of wettability on multiphase flow continues to challenge our microscopic and macroscopic descriptions. Here, we study the impact of wettability on viscously unfavorable fluid–fluid displacement in disordered media by means of high-resolution imaging in microfluidic flow cells patterned with vertical posts. By systematically varying the wettability of the flow cell over a wide range of contact angles, we find that increasing the substrate’s affinity to the invading fluid results in more efficient displacement of the defending fluid up to a critical wetting transition, beyond which the trend is reversed. We identify the pore-scale mechanisms—cooperative pore filling (increasing displacement efficiency) and corner flow (decreasing displacement efficiency)—responsible for this macroscale behavior, and show that they rely on the inherent 3D nature of interfacial flows, even in quasi-2D media. Our results demonstrate the powerful control of wettability on multiphase flow in porous media, and show that the markedly different invasion protocols that emerge—from pore filling to postbridging—are determined by physical mechanisms that are missing from current pore-scale and continuum-scale descriptions.

scholarly journals NUMERICAL SIMULATING THE CHEMICAL INTERACTION OF FLUID WITH ROCK AT THE PORE SCALE

2021 ◽  
Vol 2 (3) ◽  
pp. 46-54
Author(s):  
Tatyana S. Khachkova ◽  
Vadim V. Lisitsa
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Reactive Transport ◽  
Chemical Interaction ◽  
Pore Space ◽  
Heterogeneous Reactions ◽  
Pore Scale ◽  
Active Components ◽  
Flow And Transport ◽  
The Finite Difference Method

The article presents a numerical algorithm for modeling the chemically reactive transport in a porous medium at a pore scale. The aim of the study is to research the change in the geometry of the pore space during the chemical interaction of the fluid with the rock. First, fluid flow and transport of chemically active components are simulated in the pore space. Heterogeneous reactions are then used to calculate their interactions with the rock. After that, the change in the interface between the liquid and the solid is determined using the level-set method, which allows to handle changes in the topology of the pore space. The algorithm is based on the finite-difference method and is implemented on the GP-GPU.

Impact of chaotic mixing on reactive transport: experiment in porous media at high Pe and Da

2021 ◽  
Author(s):  
Hugo Sanquer ◽  
Joris Heyman ◽  
Tanguy Le Borgne ◽  
Khalil Hanna
Keyword(s):  
Porous Media ◽  
Reactive Transport ◽  
3D Imaging ◽  
Fluid Phase ◽  
Reaction Rates ◽  
Transport Processes ◽  
Chaotic Mixing ◽  
Pore Scale ◽  
Chemical Gradients ◽  
The Impact

<p>Solute transport in porous media plays a key role in a range of chemical and biological processes, including contaminant degradation, precipitation, dissolution and microbiological dynamics. Increasing evidences have shown that the conventional complete mixing assumption at the pore scale can lead to a strong overestimation of reaction rates. Recent 3D imaging experiments of mixing in porous media suggest that these pore scale chemical gradients may be sustained by chaotic mixing dynamics. However, the consequences of such chaotic mixing on reactive processes are unknown.</p><p>In this work, we use reactive transport experiments coupled to 3D imaging to investigate the impact of micro-scale chaotic flows on mixing-limited reactions in the fluid phase.  We use optical index matching and laser-induced fluorescence to characterize the pore scale distribution of reactive product concentration for a range of Peclet and Damkhöler numbers. We use these measurements to develop a reactive lamellar theory that quantifies the impact of pore scale chemical gradients induced by chaotic mixing on effective reaction rates. These results provide new perspectives for upscaling reactive transport processes in porous media.</p>

Modeling wormhole formation in digital rock samples: the role of segmentation and permeability-porosity relationships

2020 ◽  
Author(s):  
Rishabh Prakash Sharma ◽  
Max P. Cooper ◽  
Anthony J.C. Ladd ◽  
Piotr Szymczak
Keyword(s):  
Acid Concentration ◽  
Flow Rate ◽  
Reactive Transport ◽  
Pore Space ◽  
Small Variation ◽  
Power Laws ◽  
Linear Interpolation ◽  
Constitutive Relationship ◽  
Dissolution Experiment ◽  
The Impact

<p>In this work we have investigated numerically the formation of channelised dissolution patterns, termed “wormholes”, using initial pore geometries generated from tomographic images of limestone cores. We have employed an OpenFOAM-based Darcy-scale numerical solver,  <em>porousFoam</em>, which combines a Darcy/Darcy-Brinkman flow solver and a reactive transport solver in an evolving pore space. Simulated geometries, of both final and intermediate steps, are compared to dissolution experiments on samples the initial pore geometry is generated from, with the same acid concentration and flow rate applied. </p><p>The initial condition of porosity distribution is set from X-Ray Computed Microtomography (XCMT) images via three phase segmentation into macroporosity, microporosity, and grain regions. Porosity values for microporous regions are set using linear interpolation between pore and grain grayscale values [1]. The inlet boundary conditions of flow rate and acid concentration are set as in the dissolution experiment. To test the effect of the permeability-porosity constitutive relationship we have investigated several options including power laws of varying exponent, and the Carman-Kozeny relation. We have also analyzed the impact of using Darcy versus Darcy-Brinkman flow solvers. Despite a qualitatively similar appearance to experimental results, the simulated wormholes are usually significantly thicker than their experimental counterparts, a fact noted by other researchers as well [2]. We comment on possible reasons for this discrepancy and on the limitations of Darcy-scale solvers in general. Additionally, we find that higher exponents in the power law makes the numerical dissolution very sensitive to grayscale threshold values as a small variation in this value changes the path of the wormhole.</p><p> </p><p>[1] Luquot, L., Rodriguez, O., and Gouze, P.: Experimental characterization of porosity structure and transport property changes in limestone undergoing different dissolution regimes, Transport Porous Med., 101, 507–532, 2014.</p><p>[2] Yue Hao, Megan Smith, Yelena Sholokhova, Susan Carroll, CO2-induced dissolution of low permeability carbonates. Part II: Numerical modeling of experiments, Advances in Water Resources, 62, 388-408, 2013 </p>

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