Some aspects of attenuation and dispersion of electromagnetic waves in fluid‐saturated porous rocks and applications to dielectric constant well logging

Geophysics ◽  
1982 ◽  
Vol 47 (3) ◽  
pp. 388-394 ◽  
Author(s):  
H. Pascal ◽  
F. Pascal ◽  
D. Rankin
Keyword(s):  
Mathematical Model ◽  
Dielectric Constant ◽  
Electromagnetic Waves ◽  
Well Logging ◽  
Phase System ◽  
Porous Rocks ◽  
Two Phase ◽  
Numerical Examples ◽  
Coupled Equations ◽  
Attenuation And Dispersion

The properties of attenuation and dispersion of electromagnetic (EM) waves in fluid‐filled porous rocks are analyzed. A mathematical model of a two‐phase system for such rocks is developed. From this model the coupled equations which describe the propagation are formulated and an equation of dispersion is obtained in terms of frequency and the electrical properties of the medium constituents. Several numerical examples of both coupled and noncoupled models of propagation are used to illustrate the importance of these models for the interpretation of dielectric constant well logging.

Further discussion on attenuation and dispersion of electromagnetic wave propagation in fluid‐saturated porous rocks and applications to dielectric‐constant well logging

Geophysics ◽  
1983 ◽  
Vol 48 (10) ◽  
pp. 1373-1380 ◽  
Author(s):  
H. Pascal
Keyword(s):  
Dielectric Constant ◽  
Wave Propagation ◽  
Electromagnetic Wave ◽  
Electromagnetic Wave Propagation ◽  
Phase Model ◽  
Phase System ◽  
Porous Rocks ◽  
Two Phase ◽  
Advantages And Disadvantages ◽  
Attenuation And Dispersion

This paper presents a more detailed analysis of some basic problems of electromagnetic wave propagation through a porous medium saturated with fluid, associated directly with quantitative interpretation of dielectric constant logging. The advantages and disadvantages of a new approach, in which fluid‐saturated porous rock is considered as a two‐phase system, are discussed and compared with those obtained from the single‐phase model. It is shown that the two‐phase model may provide a better interpretation of dielectric constant logging.

A Ternary, Two-Phase, Mathematical Model of Oil Recovery With Surfactant Systems

1984 ◽  
Vol 24 (06) ◽  
pp. 606-616 ◽  
Author(s):  
Charles P. Thomas ◽  
Paul D. Fleming ◽  
William K. Winter
Keyword(s):  
Mathematical Model ◽  
Oil Recovery ◽  
Arbitrary Number ◽  
The Other ◽  
Phase System ◽  
Chemical Flooding ◽  
Two Phase ◽  
Oil Displacement ◽  
Surfactant Systems ◽  
And Diffusion

Abstract A mathematical model describing one-dimensional (1D), isothermal flow of a ternary, two-phase surfactant system in isotropic porous media is presented along with numerical solutions of special cases. These solutions exhibit oil recovery profiles similar to those observed in laboratory tests of oil displacement by surfactant systems in cores. The model includes the effects of surfactant transfer between aqueous and hydrocarbon phases and both reversible and irreversible surfactant adsorption by the porous medium. The effects of capillary pressure and diffusion are ignored, however. The model is based on relative permeability concepts and employs a family of relative permeability curves that incorporate the effects of surfactant concentration on interfacial tension (IFT), the viscosity of the phases, and the volumetric flow rate. A numerical procedure was developed that results in two finite difference equations that are accurate to second order in the timestep size and first order in the spacestep size and allows explicit calculation of phase saturations and surfactant concentrations as a function of space and time variables. Numerical dispersion (truncation error) present in the two equations tends to mimic the neglected present in the two equations tends to mimic the neglected effects of capillary pressure and diffusion. The effective diffusion constants associated with this effect are proportional to the spacestep size. proportional to the spacestep size. Introduction In a previous paper we presented a system of differential equations that can be used to model oil recovery by chemical flooding. The general system allows for an arbitrary number of components as well as an arbitrary number of phases in an isothermal system. For a binary, two-phase system, the equations reduced to those of the Buckley-Leverett theory under the usual assumptions of incompressibility and each phase containing only a single component, as well as in the more general case where both phases have significant concentrations of both components, but the phases are incompressible and the concentration in one phase is a very weak function of the pressure of the other phase at a given temperature. pressure of the other phase at a given temperature. For a ternary, two-phase system a set of three differential equations was obtained. These equations are applicable to chemical flooding with surfactant, polymer, etc. In this paper, we present a numerical solution to these equations paper, we present a numerical solution to these equations for I D flow in the absence of gravity. Our purpose is to develop a model that includes the physical phenomena influencing oil displacement by surfactant systems and bridges the gap between laboratory displacement tests and reservoir simulation. It also should be of value in defining experiments to elucidate the mechanisms involved in oil displacement by surfactant systems and ultimately reduce the number of experiments necessary to optimize a given surfactant system.

scholarly journals Modeling and Analysis of Magnetic Nanoparticles Injection in Water-Oil Two-Phase Flow in Porous Media under Magnetic Field Effect

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed F. El-Amin ◽  
Ahmed M. Saad ◽  
Amgad Salama ◽  
Shuyu Sun
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Porous Media ◽  
Magnetic Nanoparticles ◽  
Additional Term ◽  
Flow In Porous Media ◽  
Phase System ◽  
Two Phase ◽  
The Mathematical Model ◽  
Nanoparticles Suspension

In this paper, the magnetic nanoparticles are injected into a water-oil, two-phase system under the influence of an external permanent magnetic field. We lay down the mathematical model and provide a set of numerical exercises of hypothetical cases to show how an external magnetic field can influence the transport of nanoparticles in the proposed two-phase system in porous media. We treat the water-nanoparticles suspension as a miscible mixture, whereas it is immiscible with the oil phase. The magnetization properties, the density, and the viscosity of the ferrofluids are obtained based on mixture theory relationships. In the mathematical model, the phase pressure contains additional term to account for the extra pressures due to fluid magnetization effect and the magnetostrictive effect. As a proof of concept, the proposed model is applied on a countercurrent imbibition flow system in which both the displacing and the displaced fluids move in opposite directions. Physical variables, including water-nanoparticles suspension saturation, nanoparticles concentration, and pore wall/throat concentrations of deposited nanoparticles, are investigated under the influence of the magnetic field. Two different locations of the magnet are studied numerically, and variations in permeability and porosity are considered.

Preparation and Microwave Dielectric Properties of xBaZn2Ti4O11-(1-x)BaNd2Ti4O12 Ceramics

2017 ◽  
Vol 726 ◽  
pp. 210-214
Author(s):  
Xu Wang ◽  
Ren Li Fu ◽  
Yue Xu ◽  
Yang Yang ◽  
Jun De Cai ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Dielectric Properties ◽  
Microwave Dielectric Properties ◽  
Solid State Reaction Method ◽  
Phase System ◽  
Microwave Ceramics ◽  
Two Phase ◽  
Microwave Dielectric ◽  
X Band ◽  
High Dielectric

xBaZn2Ti4O11–(1-x)BaNd2Ti4O12 (x = 0.18–0.30) ceramics were prepared by solid-state reaction method and their microwave dielectric properties were investigated with the purpose of finding a microwave ceramics with high dielectric constant (εr), high quality factor (Q×f ) and zero temperature coefficient of resonant frequency (τf).The two phase system BaZn2Ti4O11–BaNd2Ti4O12 affected the unit cell volume and the microstructure, the microwave dielectric properties (εr, Q×f, τf). As increasing x from 0.18 to 0.30, the main phase composition was BaNd2Ti4O12. Therefore, the εr decreased from 64.9 to 60.3 and the Q×f values raised from 11,350GHz to 13,210GHz, and the τf values decreased from 7ppm/° to -5ppm/°.The 0.22BaZn2Ti4O11–0.78BaNd2Ti4O12 ceramics sintered at 1250°C for 4 h displayed the best dielectric constant εr,Q×f and τf, as 63.9, 12380 GHz and-0.1 ppm/° respectively.

Attenuation and dispersion of compressional waves in fluid‐filled porous rocks with partial gas saturation (White model)—Part I: Biot theory

Geophysics ◽  
1979 ◽  
Vol 44 (11) ◽  
pp. 1777-1788 ◽  
Author(s):  
N. C. Dutta ◽  
H. Odé
Keyword(s):  
Seismic Waves ◽  
Equations Of Motion ◽  
Fluid Pressure ◽  
Present Theory ◽  
Biot Theory ◽  
Type I ◽  
Porous Rocks ◽  
Water Contact ◽  
Coupled Equations ◽  
Attenuation And Dispersion

An exact theory of attenuation and dispersion of seismic waves in porous rocks containing spherical gas pockets (White model) is presented using the coupled equations of motion given by Biot. Assumptions made are (1) the acoustic wavelength is long with respect to the distance between gas pockets and their size, and (2) the gas pockets do not interact. Thus, the present theory essentially is quite similar to that proposed by White (1975), but the problem of the radially oscillating gas pocket is solved in a more rigorous manner by means of Biot’s theory (1962). The solid‐fluid coupling is automatically included, and the model is solved as a boundary value problem requiring all radial stresses and displacements to be continuous at the gas‐brine interface. Thus, we do not require any assumed fluid‐pressure discontinuity at the gas‐water contact, such as the one employed by White (1975). We have also presented an analysis of all of the field variables in terms of Biot’s type I (the classical compressional) wave and, type II (the diffusion) wave. Our quantitative results are presented in Dutta and Odé (1979, this issue).

Development of a Capacitor Probe to Detect Subsurface Deterioration in Concrete

1997 ◽  
Vol 503 ◽  
Author(s):  
B. K. Diefenderfer ◽  
I. L. Al-Qadi ◽  
J. J. Yoho ◽  
S. M. Riad ◽  
A. Loulizi
Keyword(s):  
Dielectric Constant ◽  
Portland Cement ◽  
Electromagnetic Waves ◽  
Low Cost ◽  
Complex Dielectric Constant ◽  
Life Cycle Costs ◽  
Parallel Plates ◽  
Portland Cement Concrete ◽  
Cement Concrete ◽  
Set Up

ABSTRACTPortland cement concrete (PCC) structures deteriorate with age and need to be maintained or replaced. Early detection of deterioration in PCC (e.g., alkali-silica reaction, freeze/thaw damage, or chloride presence) can lead to significant reductions in maintenance costs. However, it is often too late to perform low-cost preventative maintenance by the time deterioration becomes evident. By developing techniques that would enable civil engineers to evaluate PCC structures and detect deterioration at early stages (without causing further damage), optimization of life-cycle costs of the constructed facility and minimization of disturbance to the facility users can be achieved.Nondestructive evaluation (NDE) methods are potentially one of the most useful techniques ever developed for assessing constructed facilities. They are noninvasive and can be performed rapidly. Portland cement concrete can be nondestructively evaluated by electrically characterizing its complex dielectric constant. The real part of the dielectric constant depicts the velocity of electromagnetic waves in PCC. The imaginary part, termed the “loss factor,” describes the conductivity of PCC and the attenuation of electromagnetic waves.Dielectric properties of PCC have been investigated in a laboratory setting using a parallel plate capacitor operating in the frequency range of 0.1 to 40.1MIHz. This capacitor set-up consists of two horizontal-parallel plates with an adjustable separation for insertion of a dielectric specimen (PCC). While useful in research, this approach is not practical for field implementation. A new capacitor probe has been developed which consists of two plates, located within the same horizontal plane, for placement upon the specimen to be tested. Preliminary results show that this technique is feasible and results are promising; further testing and evaluation is currently underway.

Sign in / Sign up

Export Citation Format

Share Document