Resistivity‐porosity‐particle shape relationships for marine sands

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1250-1268 ◽  
Author(s):  
P. D. Jackson ◽  
D. Taylor Smith ◽  
P. N. Stanford

A laboratory investigation has been made of formation factor‐porosity relationships (formation factor being the ratio of the resistivity of a porous medium to the resistivity of the pore‐fluid), using natural and artificial sand samples whose grains varied widely in both size and shape. All samples obeyed Archie’s law, [Formula: see text] (where FF is the formation factor and n is the porosity) including mixtures of two differently shaped particle types. The exponent m was dependent on the shape of the particles, increasing as they became less spherical, while variations in size and spread of sizes appeared to have little effect. The results have been combined to produce an FF/n relationship, with an error “envelope”, which may be applicable to marine sediments in general, being in agreement with published data for marine clays. It is also suggested that the exponent m may be a better measure of the “tortuosity” of porous media than the formulas quoted in the literature.

2019 ◽  
Vol 219 (2) ◽  
pp. 866-876 ◽  
Author(s):  
Luong Duy Thanh ◽  
Damien Jougnot ◽  
Phan Van Do ◽  
Nguyen Van Nghia A

SUMMARY Electrical conductivity is one of the most commonly used geophysical method for reservoir and environmental studies. Its main interest lies in its sensitivity to key properties of storage and transport in porous media. Its quantitative use therefore depends on the efficiency of the petrophysical relationship to link them. In this work, we develop a new physically based model for estimating electrical conductivity of saturated porous media. The model is derived assuming that the porous media is represented by a bundle of tortuous capillary tubes with a fractal pore-size distribution. The model is expressed in terms of the porosity, electrical conductivity of the pore liquid and the microstructural parameters of porous media. It takes into account the interface properties between minerals and pore water by introducing a surface conductivity. Expressions for the formation factor and hydraulic tortuosity are also obtained from the model derivation. The model is then successfully compared with published data and performs better than previous models. The proposed approach also permits to relate the electrical conductivity to other transport properties such as the hydraulic conductivity.


1967 ◽  
Vol 7 (03) ◽  
pp. 266-272 ◽  
Author(s):  
W. Douglas Von Gonten ◽  
R.L. Whiting

Abstract Regression analysis was used to correlate the physical properties of 478 sandstone and 90 carbonate core samples. Porosity, permeability, electrical formation resistivity factor, capillary pressure and the sonic velocity of the shear and compressional waves were measured. Prediction equations for porosity, permeability and electrical formation resistivity factor were found which should be useful in understanding the relationships between the physical properties of porous media in formation evaluation. Introduction The physical properties of porous media are important to the petroleum engineer and geologist. To evaluate fully the potential and behavior of a subsurface formation such as a petroleum reservoir, certain physical properties of the porous medium must be known. The problem of accurately determining physical properties of subsurface formations has not been solved because many determinations must be made by indirect measurements and because of the difficulties caused by complex pore structure and presence of clays in most naturally occurring porous media. Due to the difficulty in measuring some of the physical properties of porous media, it would be advantageous to be able to predict a certain physical property of a rock from other physical properties of the rock which could be measured more easily and more accurately. Since most potential reservoir rocks are heterogeneous, relationships between the physical properties are very complex and thus far no satisfactory correlations based on theory or laboratory models have been developed. It appears that empirical relationships obtained by measuring the physical properties of a large number of samples of naturally occurring porous media and applying regression analysis to develop for one physical property in terms of other rock properties is the best approach. REVIEW LITERATURE The three physical properties used as dependent variables for correlating purposes were porosity, permeability and formation factor. Since formation factor is more difficult to determine, a brief review of the literature is provided on this property. The first work on determining formation factors was published by Archie in 1942. He defined this property of a porous medium as Ro ...............................(1) F =RW where Ro is the resistivity of the porous medium when completely saturated with a brine of resistivity Rw. Archie found the best correlation between formation factor and porosity was the following equation, F = - m..................................... (2) where is the porosity fraction and m is the constant characteristic of the rock. The value of m was 1.3 for unconsolidated sand packs, and ranged from 1.8 to 2.0 for consolidated sandstones. In 1950 Patnode and Wyllie and De Witte observed that the formation factor as determined by Eq. 1 was valid only when the porous medium contained no conductive solids such as clay or shale. When conductive solids are -present the formation factor is also dependent on the resistivity of the saturating fluid. Therefore, in samples containing conductive solids the formation factor decreased as resistivity of the saturating fluid increased. Because of this, the measured formation factor was called the apparent formation factor and was designated Fa. Patnode and Wyllie proposed the following equation. SPEJ P. 266ˆ


2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal

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.


Author(s):  
Swayamdipta Bhaduri ◽  
Pankaj Sahu ◽  
Siddhartha Das ◽  
Aloke Kumar ◽  
Sushanta K. Mitra

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.


Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa

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).


2015 ◽  
Vol 1101 ◽  
pp. 471-479
Author(s):  
Georges Freiha ◽  
Hiba Othman ◽  
Michel Owayjan

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.


1972 ◽  
Vol 12 (02) ◽  
pp. 89-95 ◽  
Author(s):  
Ahmad H.M. Totonji ◽  
S.M. Farouq Ali

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


2021 ◽  
Author(s):  
Alexandru Tatomir ◽  
Huhao Gao ◽  
Hiwa Abdullah ◽  
Martin Sauter

<p>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.</p><p>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.</p><p>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.</p><p>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.</p><p> </p><p> </p><p>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 14:200–208. https://doi.org/10.1016/j.ijggc.2013.01.020</p><p>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</p>


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