scholarly journals Measurement and Simulation of the Nonlocal Dispersion Tensor in Porous Media

2021 ◽  
Author(s):  
◽  
Mark Warwick Hunter
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Parameter Space ◽  
Capillary Flow ◽  
Pulse Sequence ◽  
Blood Perfusion ◽  
Model Systems ◽  
Length Scales ◽  
Dispersion Tensor ◽  
Nonlocal Dispersion

<p>Nuclear Magnetic Resonance (NMR) techniques have been used extensively to characterise dispersion and diffusion in porous media. The completely non-invasive nature of the measurements and the ability to measure opaque samples provide the makings for an excellent tool. Detailed understanding of the microstructure of porous media leads to the ability to model and predict macroscopic effects such as ground water flow, oil extraction, blood perfusion and enable understanding of industrial catalytic reactors. The range of properties that NMR is capable of measuring is extensive but one particular quantity, the nonlocal dispersion tensor has long been identified as an ideal way to characterise dispersive effects at short time and length scales. The nonlocal dispersion tensor is a quantity that is included in theory proposed by Koch and Brady (1987) to explain non-Fickian dispersive behaviour. Demonstrated here is, for the first time, a method to measure the tensor. Details of the newly developed NMR pulse sequence and the post processing technique required to extract the nonlocal dispersion tensor are given. Successful measurements have been undertaken on model systems such as capillary flow and Couette flow. This enabled direct comparison with analytically calculated quantities and excellent agreement is found, thus verifying the methodology. A complete set of nonlocal dispersion components has been identified and measured in a model porous medium, in this case a random beadpack of monosized spheres. The new measurements provide the ability to infer and characterise the nature of fluid correlations, particularly at short length scales. In parallel, a simulation suite based on a lattice Boltzmann calculation (implemented by a co-worker Dr Andrew Jackson), has been used to independently generate the same nonlocal components as measured. The simulations have also been used to guide the design of further NMR experiments, to further investigate aspects of the new parameter space that the nonlocal dispersion tensor provides and to explore parts of the parameter space that are inaccessible by NMR. Finally, the methodology was adapted to enable nonlocal dispersion measurements on a 'real' porous medium, a Bentheimer sandstone.</p>

scholarly journals Measurement and Simulation of the Nonlocal Dispersion Tensor in Porous Media

2021 ◽  
Author(s):  
◽  
Mark Warwick Hunter
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Parameter Space ◽  
Capillary Flow ◽  
Pulse Sequence ◽  
Blood Perfusion ◽  
Model Systems ◽  
Length Scales ◽  
Dispersion Tensor ◽  
Nonlocal Dispersion

<p>Nuclear Magnetic Resonance (NMR) techniques have been used extensively to characterise dispersion and diffusion in porous media. The completely non-invasive nature of the measurements and the ability to measure opaque samples provide the makings for an excellent tool. Detailed understanding of the microstructure of porous media leads to the ability to model and predict macroscopic effects such as ground water flow, oil extraction, blood perfusion and enable understanding of industrial catalytic reactors. The range of properties that NMR is capable of measuring is extensive but one particular quantity, the nonlocal dispersion tensor has long been identified as an ideal way to characterise dispersive effects at short time and length scales. The nonlocal dispersion tensor is a quantity that is included in theory proposed by Koch and Brady (1987) to explain non-Fickian dispersive behaviour. Demonstrated here is, for the first time, a method to measure the tensor. Details of the newly developed NMR pulse sequence and the post processing technique required to extract the nonlocal dispersion tensor are given. Successful measurements have been undertaken on model systems such as capillary flow and Couette flow. This enabled direct comparison with analytically calculated quantities and excellent agreement is found, thus verifying the methodology. A complete set of nonlocal dispersion components has been identified and measured in a model porous medium, in this case a random beadpack of monosized spheres. The new measurements provide the ability to infer and characterise the nature of fluid correlations, particularly at short length scales. In parallel, a simulation suite based on a lattice Boltzmann calculation (implemented by a co-worker Dr Andrew Jackson), has been used to independently generate the same nonlocal components as measured. The simulations have also been used to guide the design of further NMR experiments, to further investigate aspects of the new parameter space that the nonlocal dispersion tensor provides and to explore parts of the parameter space that are inaccessible by NMR. Finally, the methodology was adapted to enable nonlocal dispersion measurements on a 'real' porous medium, a Bentheimer sandstone.</p>

scholarly journals Measurement and simulation of the nonlocal dispersion tensor in porous media

2007 ◽  
Vol 25 (4) ◽  
pp. 563
Author(s):  
M.W. Hunter ◽  
A.N. Jackson ◽  
P.T. Callaghan
Keyword(s):  
Porous Media ◽  
Dispersion Tensor ◽  
Nonlocal Dispersion

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

Capillary Imbibition Dynamics in Porous Media

2014 ◽  
Author(s):  
Swayamdipta Bhaduri ◽  
Pankaj Sahu ◽  
Siddhartha Das ◽  
Aloke Kumar ◽  
Sushanta K. Mitra
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Paper Strip ◽  
Capillary Imbibition ◽  
Flow Physics ◽  
Fundamental Understanding ◽  
Paper Based Microfluidics ◽  
To Come

The phenomenon of capillary imbibition through porous media is important both due to its applications in several disciplines as well as the involved fundamental flow physics in micro-nanoscales. In the present study, where a simple paper strip plays the role of a porous medium, we observe an extremely interesting and non-intuitive wicking or imbibition dynamics, through which we can separate water and dye particles by allowing the paper strip to come in contact with a dye solution. This result is extremely significant in the context of understanding paper-based microfluidics, and the manner in which the fundamental understanding of the capillary imbibition phenomenon in a porous medium can be used to devise a paper-based microfluidic separator.

scholarly journals Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Data Driven ◽  
Reduced Order ◽  
Medium Formulation ◽  
Flow Resistances

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

Mathematical Formulation of the Global Coefficients of Transmission and Reflection of Ultrasonic Waves in Bi-Phase Porous Medium

2015 ◽  
Vol 1101 ◽  
pp. 471-479
Author(s):  
Georges Freiha ◽  
Hiba Othman ◽  
Michel Owayjan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Wave Propagation ◽  
Mathematical Formulation ◽  
Ultrasonic Waves ◽  
Ultrasonic Wave Propagation ◽  
Local Coefficients ◽  
Important Field ◽  
New Formulation ◽  
Transmission And Reflection

The study of signals propagation inside porous media is an important field especially in the biomedical research related to compact bones. The purpose of this paper is to determine a mathematical formulation of the global coefficients of transmission and reflection of nondestructive ultrasonic waves in any bi-phase porous medium. Local coefficients of transmission and reflection on the interface of the porous medium will be determined based on a study of boundary conditions. The behavior of different waves inside the porous medium will be developed so that we can derive a new formulation of global coefficients that takes interior phenomena into consideration. Results are found independently of the geometrical and physical characteristics of the medium. Note that this study is based on normal incident ultrasonic wave propagation.

Solvent Flooding Displacement Efficiency in Relation to Ternary Phase Behavior

1972 ◽  
Vol 12 (02) ◽  
pp. 89-95 ◽  
Author(s):  
Ahmad H.M. Totonji ◽  
S.M. Farouq Ali
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Phase Behavior ◽  
Ternary Phase ◽  
Ternary Systems ◽  
Ternary Mixtures ◽  
Displacement Mechanism ◽  
Irreducible Water Saturation ◽  
Experimental Runs

Abstract The chief objective of the study was to exercise control on the system phase behavior through the use of mixtures of two alcohols exhibiting opposite phase behavior characteristics in the alcohol-hydrocarbon-water system involved. Such systems were employed in displacements in porous media to ascertain their effectiveness. Introduction Displacement of oil and water in a porous medium by a mutually miscible alcohol or other solvent has been the subject of numerous investigations. This process, in spite of its limited scope as an oil recovery method, has certain mechanistic features that are of value in gaining an understanding of some of the newer recovery techniques (e.g., the Maraflood* process). The works of Gatlin and Slobod, proposing piston-like displacement of oil and water by a miscible alcohol; of Taber et al., describing the displacement mechanism in terms of the ternary phase behavior involved; and of Holm and Csaszar, defining displacement mechanism in terms of phase velocity ratio, are major contributions in this area. In a later work, Taber and Meyer suggested the addition of small amounts of oil and water (as the case may be) to the alcohol used for displacement, since this helped to obtain piston-like displacements with systems that are usually characterized by the efficient displacement of either oil or water. APPARATUS, EXPERIMENTAL PROCEDURE, AND SIMULATOR PROCEDURE, AND SIMULATOR The procedure employed for determining the equilibrium phase behavior of ternary systems involved the titration of a hydrocarbon-water (or brine) mixture by the particular solvent (pure alcohol, or alcohol mixture) for the determination of the binodal curve, and the analysis by refractive index measurement of ternary mixtures having known compositions for the determination of the tie lines. Since the procedure is valid for strictly ternary systems, its use in this case where essentially quaternary systems are involved would yield the total alcohol content rather than the correct proportion of each alcohol. The ternary diagrams presented should be viewed with this limitation in mind. presented should be viewed with this limitation in mind. The apparatus used for experimental runs in porous media consisted of a positive displacement Ruska pump and a core encased in a steel pipe. Suitable sampling apparatus and auxiliary equipment were employed. Most runs consisted of injecting a slug of the particular solvent into a core initially containing a residual oil (waterflood) or irreducible water saturation, at a constant rate, and then following the slug by water or brine. The effluent samples collected were analyzed for the hydrocarbon, water and alcohol in order to plot the production histories. Complete experimental details and fluid production histories. Complete experimental details and fluid properties are given in Ref. 6. Table 1 lists the properties properties are given in Ref. 6. Table 1 lists the properties of the porous media used. Computer simulations of some of the experimental runs, as well as exploratory simulations, were carried out using the method earlier reported. The method basically consists in the representation of a porous medium by a certain number of cells containing immobile oil (or oleic) and water (or aqueous) fractions into which alcohol is injected in a stepwise manner allowing for phase changes. SPEJ P. 89

Estimation of the fluid-fluid interfacial area using kinetic interface sensitive tracers in dynamic porous media experiments

2021 ◽  
Author(s):  
Alexandru Tatomir ◽  
Huhao Gao ◽  
Hiwa Abdullah ◽  
Martin Sauter
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Two Phase Flow ◽  
Organic Liquid ◽  
Column Experiment ◽  
Interfacial Area ◽  
Breakthrough Curves ◽  
Water Soluble ◽  
Phase Flow ◽  
Two Phase

&lt;p&gt;Fluid-fluid interfacial area (IFA) in a two-phase flow in porous media is an important parameter for many geoscientific applications involving mass- and energy-transfer processes between the fluid-phases. Schaffer et al. (2013) introduced a new category of reactive tracers termed kinetically interface sensitive (KIS) tracers, able to quantify the size of the fluid-fluid IFA. In our previous experiments (Tatomir et al., 2018) we have demonstrated the application of the KIS tracers in a highly-controlled column experiment filled with a well-characterized porous medium consisting of well-sorted, spherical glass beads.&lt;/p&gt;&lt;p&gt;In this work we investigate several types of glass-bead materials and natural sands to quantitatively characterize the influence of the porous-medium grain-, pore-size and texture on the mobile interfacial area between an organic liquid and water. The fluid-fluid interfacial area is determined by interpretation of the breakthrough curves (BTCs) of the reaction product of the KIS tracer. When the tracer which is dissolved in the non-wetting phase meets the water, an irreversible hydrolysis process begins leading to the formation of two water-soluble products. For the experiments we use a peristaltic pump and a high precision injection pump to control the injection rate of the organic liquid and tracer.&lt;/p&gt;&lt;p&gt;A Darcy-scale numerical model is used to simulate the immiscible displacement process coupled with the reactive tracer transport across the fluid-fluid interface. The results show that the current reactive transport model is not always capable to reproduce the breakthrough curves of tracer experiments and that a new theoretical framework may be required.&lt;/p&gt;&lt;p&gt;Investigations of the role of solid surface area of the grains show that the grain surface roughness has an important influence on the IFA. . Furthermore, a linear relationship between the mobile capillary associated IFA and the inverse mean grain diameter can be established. The results are compared with the data collected from literature measured with high resolution microtomography and partitioning tracer methods. The capillary associated IFA values are consistently smaller because KIS tracers measure the mobile part of the interface. Through this study the applicability range of the KIS tracers is considerably expanded and the confidence in the robustness of the method is improved.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;Schaffer M, Maier F, Licha T, Sauter M (2013) A new generation of tracers for the characterization of interfacial areas during supercritical carbon dioxide injections into deep saline aquifers: Kinetic interface-sensitive tracers (KIS tracer). International Journal of Greenhouse Gas Control 14:200&amp;#8211;208. https://doi.org/10.1016/j.ijggc.2013.01.020&lt;/p&gt;&lt;p&gt;Tatomir A, Vriendt KD, Zhou D, et al (2018) Kinetic Interface Sensitive Tracers: Experimental Validation in a Two-Phase Flow Column Experiment. A Proof of Concept. Water Resources Research 54:10,223-10,241. https://doi.org/10.1029/2018WR022621&lt;/p&gt;

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