Object-oriented approach for the pore-scale simulation of DC electrical conductivity of two-phase saturated porous media

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. E67-E79 ◽  
Author(s):  
Emmanuel Toumelin ◽  
Carlos Torres-Verdín
Keyword(s):  
Thin Films ◽  
Electrical Conductivity ◽  
Porous Media ◽  
Random Walk ◽  
Water Saturation ◽  
Pore Space ◽  
Pore Network ◽  
Pore Scale ◽  
Exchange Cations ◽  
Wet Rocks

Archie’s empirical power laws are strictly valid only for homogeneous, water-wet (WW) rocks deprived of microporosity or substantial clay-exchange cations. When these conditions are not met, non-Archie electrical behavior arises whereby relationships among rock resistivity, porosity, and water saturation no longer exhibit power-law dependence. Currently, such an unreliable behavior of empirical laws can be quantified only through pore-scale modeling of electrical conductivity under specific sets of geometric assumptions and with substantial computation memory requirements. We introduce a new geometric concept to simulate direct-current electrical-conductivity phenomena in arbitrary rock models on the basis of 3D grain and pore objects that include explicit distributions of intragranular porosity, clay-exchange cations, nonwetting fluid blobs, thin films, and pendular rings. These objects are distributed in the pore space following simple heuristic principles of drainage/imbibition that honorcapillary-pressure curves. They provide a simple way to parameterize the 3D pore space and to calculate the electrical conductivity of porous media saturated with two immiscible fluid phases by way of diffusive random walks within the brine-filled pore space. Not only is the random-walk method memory efficient but it also allows the inclusion of clay/brine cation exchange surfaces otherwise not possible with conventional pore-network models. By comparing results stemming from random-walk, pore-network, and percolation simulations, we show the importance of grain surface roughness and thin film thickness, even in water-wet rocks where those factors usually are neglected. For the case of strongly oil-wet rocks, we show that thin films, snap-offs, and pore microgeometry have a primary impact on hysteresis-dominated rock resistivity during imbibition (increasing water saturation). Our simulation method agrees well overall with percolation simulation results and is advantageously unaffected by assumptions concerning site-percolation imbibition.

Numerical Modeling of Multi-Frequency Complex Dielectric Permittivity Dispersion of Sedimentary Rocks

Geophysics ◽  
2021 ◽  
pp. 1-69
Author(s):  
Artur Posenato Garcia ◽  
Zoya Heidari
Keyword(s):  
Numerical Simulation ◽  
Dielectric Permittivity ◽  
Numerical Simulations ◽  
Dielectric Response ◽  
Water Saturation ◽  
Pore Scale ◽  
Simulation Results ◽  
Wet Rocks ◽  
Permittivity Measurements ◽  
The Impact

The dielectric response of rocks results from electric double layer (EDL), Maxwell-Wagner (MW), and dipolar polarizations. The EDL polarization is a function of solid-fluid interfaces, pore water, and pore geometry. MW and dipolar polarizations are functions of charge accumulation at the interface between materials with contrasting impedances and the volumetric concentration of its constituents, respectively. However, conventional interpretation of dielectric measurements only accounts for volumetric concentrations of rock components and their permittivities, not interfacial properties such as wettability. Numerical simulations of dielectric response of rocks provides an ideal framework to quantify the impact of wettability and water saturation ( Sw) on electric polarization mechanisms. Therefore, in this paper we introduce a numerical simulation method to compute pore-scale dielectric dispersion effects in the interval from 100 Hz to 1 GHz including impacts of pore structure, Sw, and wettability on permittivity measurements. We solve the quasi-electrostatic Maxwell's equations in three-dimensional (3D) pore-scale rock images in the frequency domain using the finite volume method. Then, we verify simulation results for a spherical material by comparing with the corresponding analytical solution. Additionally, we introduce a technique to incorporate α-polarization to the simulation and we verify it by comparing pore-scale simulation results to experimental measurements on a Berea sandstone sample. Finally, we quantify the impact of Sw and wettability on broadband dielectric permittivity measurements through pore-scale numerical simulations. The numerical simulation results show that mixed-wet rocks are more sensitive than water-wet rocks to changes in Sw at sub-MHz frequencies. Furthermore, permittivity and conductivity of mixed-wet rocks have weaker and stronger dispersive behaviors, respectively, when compared to water-wet rocks. Finally, numerical simulations indicate that conductivity of mixed-wet rocks can vary by three orders of magnitude from 100 Hz to 1 GHz. Therefore, Archie’s equation calibrated at the wrong frequency could lead to water saturation errors of 73%.

Chemotaxis under flow disorder shapes microbial dispersion in porous media 

2021 ◽  
Author(s):  
Pietro de Anna ◽  
Amir A. Pahlavan ◽  
Yutaka Yawata ◽  
Roman Stocker ◽  
Ruben Juanes
Keyword(s):  
Porous Media ◽  
Dispersion Coefficient ◽  
Pore Space ◽  
Low Flow ◽  
Pore Scale ◽  
Porous Rocks ◽  
Chemical Gradients ◽  
Deep Earth ◽  
Bacterium Bacillus Subtilis ◽  
Bacterium Bacillus

<div> <div> <div> <p>Natural soils are host to a high density and diversity of microorganisms, and even deep-earth porous rocks provide a habitat for active microbial communities. In these environ- ments, microbial transport by disordered flows is relevant for a broad range of natural and engineered processes, from biochemical cycling to remineralization and bioremediation. Yet, how bacteria are transported and distributed in the sub- surface as a result of the disordered flow and the associ- ated chemical gradients characteristic of porous media has remained poorly understood, in part because studies have so far focused on steady, macroscale chemical gradients. Here, we use a microfluidic model system that captures flow disorder and chemical gradients at the pore scale to quantify the transport and dispersion of the soil-dwelling bacterium Bacillus subtilis in porous media. We observe that chemotaxis strongly modulates the persistence of bacteria in low-flow regions of the pore space, resulting in a 100% increase in their dispersion coefficient. This effect stems directly from the strong pore-scale gradients created by flow disorder and demonstrates that the microscale interplay between bacterial behaviour and pore-scale disorder can impact the macroscale dynamics of biota in the subsurface.</p> </div> </div> </div>

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>

Capillary-Dominated Fluid Displacement in Porous Media

2019 ◽  
Vol 51 (1) ◽  
pp. 429-449 ◽  
Author(s):  
Kamaljit Singh ◽  
Michael Jung ◽  
Martin Brinkmann ◽  
Ralf Seemann
Keyword(s):  
Porous Media ◽  
Pore Space ◽  
Contact Angles ◽  
Pore Scale ◽  
Fluid Displacement ◽  
Invasion Pattern ◽  
Theoretical Considerations ◽  
Displacement Processes ◽  
Synchrotron Microtomography ◽  
Relevant Material

Liquid invasion into a porous medium is a phenomenon of great importance in both nature and technology. Despite its enormous importance, there is a surprisingly sparse understanding of the processes occurring on the scale of individual pores and of how these processes determine the global invasion pattern. In particular, the exact influence of the wettability remains unclear besides the limiting cases of very small or very large contact angles of the invading fluid. Most quantitative pore-scale experiments and theoretical considerations have been conducted in effectively two-dimensional (2D) micromodels and Hele–Shaw geometries. Although these pioneering works helped to unravel some of the physical aspects of the displacement processes, the relevance of 2D models has not always been appreciated for natural porous media. With the availability of X-ray microtomography, 3D imaging has become a standard for exploring pore-scale processes in porous media. Applying advanced postprocessing routines and synchrotron microtomography, researchers can image even slow flow processes in real time and extract relevant material parameters like the contact angle from the interfaces in the pore space. These advances are expected to boost both theoretical and experimental understanding of pore-scale processes in natural porous media.

A physically based model for the electrical conductivity of partially saturated porous media

2020 ◽  
Vol 223 (2) ◽  
pp. 993-1006
Author(s):  
Luong Duy Thanh ◽  
Damien Jougnot ◽  
Phan Van Do ◽  
Nguyen Van Nghia A ◽  
Vu Phi Tuyen ◽  
...  
Keyword(s):  
Electrical Conductivity ◽  
Porous Media ◽  
Fractal Dimension ◽  
Water Saturation ◽  
Theoretical Models ◽  
Fluid Composition ◽  
Physically Based Model ◽  
Partially Saturated ◽  
Proposed Model ◽  
Physically Based

SUMMARY In reservoir and environmental studies, the geological material characterization is often done by measuring its electrical conductivity. Its main interest is due to its sensitivity to physical properties of porous media (i.e. structure, water content, or fluid composition). Its quantitative use therefore depends on the efficiency of the theoretical models to link them. In this study, we develop a new physically based model that takes into account the surface conductivity for estimating electrical conductivity of porous media under partially saturated conditions. The proposed model is expressed in terms of electrical conductivity of the pore fluid, water saturation, critical water saturation and microstructural parameters such as the minimum and maximum pore/capillary radii, the pore fractal dimension, the tortuosity fractal dimension and the porosity. Factors influencing the electrical conductivity in porous media are also analysed. From the proposed model, we obtain an expression for the relative electrical conductivity that is consistent with other models in literature. The model predictions are successfully compared with published experimental data for different types of porous media. The new physically based model for electrical conductivity opens up new possibilities to characterize porous media under partially saturated conditions with geoelectrical and electromagnetic techniques.

scholarly journals Pore network extraction from pore space images of various porous media systems

2017 ◽  
Vol 53 (4) ◽  
pp. 3424-3445 ◽  
Author(s):  
Zhixing Yi ◽  
Mian Lin ◽  
Wenbin Jiang ◽  
Zhaobin Zhang ◽  
Haishan Li ◽  
...  
Keyword(s):  
Porous Media ◽  
Pore Space ◽  
Pore Network ◽  
Space Images ◽  
Media Systems

Scaling of Transport Properties of Reservoir Material at Low Saturations of a Wetting Phase

1994 ◽  
Vol 367 ◽  
Author(s):  
Y. Carolina Araujo ◽  
Pedro G. Toledo ◽  
Hada Y. Gonzalez
Keyword(s):  
Electrical Conductivity ◽  
Porous Media ◽  
Transport Properties ◽  
Capillary Pressure ◽  
Power Law ◽  
Scaling Laws ◽  
Pore Space ◽  
Conductivity Data ◽  
Phase Saturation ◽  
Electrical Conductivity Data

AbstractTransport properties of natural porous media have been observed to obey scaling laws in the wetting phase saturation. Previous work relates power-law behavior at low wetting phase saturations, i.e., at high capillary pressures, to the thin-film physics of the wetting phase and the fractal character of the pore space of porous media. Here, we present recent combined porousplate capillary pressure and electrical conductivity data of Berea sandstone at low saturations that lend support to the scaling laws. Power law is interpreted in terms of the exponent m in the relation of surface forces and film thickness and the fractal dimension D of the interface between pore space and solid matrix. Simple determination of D from capillary pressure and m from electrical conductivity data can be used to rapidly determine wetting phase relative permeability and capillary dispersion coefficient at low wetting phase saturations.

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 Validation of pore network model for hygric property calculation

2019 ◽  
Vol 282 ◽  
pp. 02024
Author(s):  
Muhammad Islahuddin ◽  
Chi Feng ◽  
Steven Claes ◽  
Hans Janssen
Keyword(s):  
Moisture Content ◽  
Pore Structure ◽  
Network Model ◽  
Building Materials ◽  
Pore Space ◽  
Pore Network ◽  
Pore Network Model ◽  
Pore Scale ◽  
Structure Information ◽  
Hygric Properties

Hygric properties can be estimated directly from pore structure information, represented by a network of regularly shaped pores, extracted from a pore structure image to conserve the real topology. On this network, pore-scale models of moisture behaviour determine the hygric properties of moisture storage and transport. The reliability of this approach is validated with a sintered-glass filter. Despite its more limited heterogeneity and pore size range relative to typical porous building materials, it provides a good basis for validating crucial pore-scale moisture processes. Measured storage data compare well to the estimated ad- and desorption moisture retention curves as well as to the saturated and capillary moisture content. Furthermore, the simulated whole-range moisture permeability curve agrees acceptably with measured data. The variation in modelling the pore space as a pore network model is also analysed by considering two distinct pore network extraction methods. The measured and simulated moisture contents agree well for the whole capillary range. Moreover, the resulting transport properties are generally accurate for the whole moisture content range. On the other hand, the estimated vapour permeabilities show notable variations between the two pore network models.

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