scholarly journals Erratum to: Comparison of the potential coefficient models of the Standard Earth (II and III) and the GEM 5 and GEM 6

1975 ◽  
Vol 118 (1) ◽  
pp. 443-445 ◽  
Author(s):  
R. H. Rapp
Keyword(s):  
Potential Coefficient

scholarly journals Electro-Osmotic Behavior of Polymeric Cation-Exchange Membranes in Ethanol-Water Solutions

Entropy ◽  
2020 ◽  
Vol 22 (6) ◽  
pp. 692
Author(s):  
V. María Barragán ◽  
Juan P. G. Villaluenga ◽  
Víctor Morales-Villarejo ◽  
M. Amparo Izquierdo-Gil
Keyword(s):  
Cation Exchange ◽  
Streaming Potential ◽  
Membrane System ◽  
Electrolyte Solutions ◽  
Joule Effect ◽  
Potential Coefficient ◽  
Water Solutions ◽  
Onsager Reciprocity ◽  
Ethanol Content ◽  
Reciprocity Relations

The aim of this work is to apply linear non-equilibrium thermodynamics to study the electrokinetic properties of three cation-exchange membranes of different structures in ethanol-water electrolyte solutions. To this end, liquid uptake and electro-osmotic permeability were estimated with potassium chloride ethanol-water solutions with different ethanol proportions as solvent. Current–voltage curves were also measured for each membrane system to estimate the energy dissipation due to the Joule effect. Considering the Onsager reciprocity relations, the streaming potential coefficient was discussed in terms of ethanol content of the solutions and the membrane structure. The results showed that more porous heterogeneous membrane presented lower values of liquid uptake and streaming potential coefficient with increasing ethanol content. Denser homogeneous membrane showed higher values for both, solvent uptake and streaming coefficient for intermediate content of ethanol.

scholarly journals Saturation Dependence of the Streaming Potential Coefficient

2020 ◽  
pp. 73-100
Author(s):  
Laurence Jouniaux ◽  
Vincent Allègre ◽  
Renaud Toussaint ◽  
Fabio Zyserman
Keyword(s):  
Streaming Potential ◽  
Potential Coefficient

Seismo-electric Conversion in Sandstones and Shales using 2 Different Experimental Approaches, Modelling and Theory

2020 ◽  
Author(s):  
Paul Glover ◽  
Rong Peng ◽  
Piroska Lorinczi ◽  
Bangrang Di
Keyword(s):  
Zeta Potential ◽  
Numerical Modelling ◽  
Clay Minerals ◽  
Shale Gas ◽  
Streaming Potential ◽  
Oil Reservoirs ◽  
Low Permeability ◽  
Experimental Measurements ◽  
Frequency Range ◽  
Potential Coefficient

<p>The development of seismo-electric (SE) exploration techniques relies significantly upon being able to understand and quantify the strength of frequency-dependent SE conversion. However, there have been very few SE measurements or modelling carried out. In this paper we present two experimental methods for making such measurements, and examine how the strength of SE conversion depends on frequency, porosity, permeability, and why it is unusual in shales. The first is based on an electromagnetic shaker and can be used in the 1 Hz to 2 kHz frequency range. The second is a piezo-electric water-bath apparatus which can be used in the 1kHz to 500 kHz frequency range.</p><p>The first apparatus has been tested on samples of Berea sandstone. Both the in-phase and in-quadrature components of the streaming potential coefficient have been measured with an uncertainty of better than ±4%. The experimental measurements show the critical frequency at which the quadrature component is maximal, and the frequency of this component is shown to agree very well with both permeability and grain size. The experimental measurements have been modelled using several different methods.</p><p>The second apparatus was used to measure SE coupling as a function of porosity and permeability, interpreting the results using a micro-capillary model and current theory. We found a general agreement between the theoretical curves and the test data, indicating that SE conversion is enhanced by increases in porosity over a range of different frequencies. However, SE conversion has a complex relationship with rock permeability, which changes with frequency, and which is more sensitive to changes in the petrophysical properties of low-permeability samples. This observation suggests that seismic conversion may have advantages in characterizing low permeability reservoirs such as tight gas and tight oil reservoirs as well as shale gas reservoirs.</p><p>We have also carried out SE measurements on Sichuan Basin shales (permeability 1.47 – 107 nD), together with some comparative measurements on sandstones (0.2 – 60 mD). Experimental results show that SE conversion in shales is comparable to that exhibited by sandstones, and is approximately independent of frequency in the seismic frequency range (<1 kHz). Anisotropy which arises from bedding in the shales results in anisotropy in the streaming potential coefficient. Numerical modelling has been used to examine the effects of varying zeta potential, porosity, tortuosity, dimensionless number and permeability. It was found that SE conversion is highly sensitive to changes in porosity, tortuosity and zeta potential in shales. Numerical modelling suggests that the cause of the SE conversion in shales is enhanced zeta potentials caused by clay minerals, which are highly frequency dependent. This is supported by a comparison of our experimental data with numerical modelling as a function of clay mineral composition from XRD measurements. Consequently, the sensitivity of SE coupling to the clay minerals suggests that SE exploration may have potential for the characterization of clay minerals in shale gas and shale oil reservoirs.</p>

Nonautonomous solitons in terms of the double Wronskian determinant for a variable-coefficient Gross–Pitaevskii equation in the Bose–Einstein condensate

2016 ◽  
Vol 30 (09) ◽  
pp. 1650103 ◽  
Author(s):  
Chuan-Qi Su ◽  
Yi-Tian Gao ◽  
Qi-Min Wang ◽  
Jin-Wei Yang ◽  
Da-Wei Zuo
Keyword(s):  
Bound State ◽  
Einstein Condensate ◽  
Pitaevskii Equation ◽  
Bilinear Forms ◽  
Spectral Parameters ◽  
Potential Coefficient ◽  
Wronskian Determinant ◽  
Bose Einstein Condensate ◽  
Double Wronskian ◽  
Bose Einstein

Under investigation in this paper is a variable-coefficient Gross–Pitaevskii equation which describes the Bose–Einstein condensate. Lax pair, bilinear forms and bilinear Bäcklund transformation for the equation under some integrable conditions are derived. Based on the Lax pair and bilinear forms, double Wronskian solutions are constructed and verified. The [Formula: see text]th-order nonautonomous solitons in terms of the double Wronskian determinant are given. Propagation and interaction for the first- and second-order nonautonomous solitons are discussed from three cases. Amplitudes of the first- and second-order nonautonomous solitons are affected by a real parameter related to the variable coefficients, but independent of the gain-or-loss coefficient [Formula: see text] and linear external potential coefficient [Formula: see text]. For Case 1 [Formula: see text], [Formula: see text] leads to the accelerated propagation of nonautonomous solitons. Parabolic-, cubic-, exponential- and cosine-type nonautonomous solitons are exhibited due to the different choices of [Formula: see text]. For Case 2 [Formula: see text], if the real part of the spectral parameter equals 0, stationary soliton can be formed. If we take the harmonic external potential coefficient [Formula: see text] as a positive constant and let the real parts of the two spectral parameters be the same, bound-state-like structures can be formed, but there are only one attractive and two repulsive procedures. For Case 3 [[Formula: see text] and [Formula: see text] are taken as nonzero constants], head-on interaction, overtaking interaction and bound-state structure can be formed based on the signs of the two spectral parameters.

scholarly journals Frequency-Dependent Streaming Potential of Porous Media—Part 1: Experimental Approaches and Apparatus Design

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
P. W. J. Glover ◽  
J. Ruel ◽  
E. Tardif ◽  
E. Walker
Keyword(s):  
Streaming Potential ◽  
Electrical Current ◽  
Potential Coefficient ◽  
Frequency Dependent ◽  
Electrokinetic Phenomena ◽  
High Frequencies ◽  
Design Build ◽  
Experimental Approaches ◽  
Electro Magnetic ◽  
Piezoelectric Drive

Electrokinetic phenomena link fluid flow and electrical flow in porous and fractured media such that a hydraulic flow will generate an electrical current andvice versa. Such a link is likely to be extremely useful, especially in the development of the electroseismic method. However, surprisingly few experimental measurements have been carried out, particularly as a function of frequency because of their difficulty. Here we have considered six different approaches to make laboratory determinations of the frequency-dependent streaming potential coefficient. In each case, we have analyzed the mechanical, electrical, and other technical difficulties involved in each method. We conclude that the electromagnetic drive is currently the only approach that is practicable, while the piezoelectric drive may be useful for low permeability samples and at specified high frequencies. We have used the electro-magnetic drive approach to design, build, and test an apparatus for measuring the streaming potential coefficient of unconsolidated and disaggregated samples such as sands, gravels, and soils with a diameter of 25.4 mm and lengths between 50 mm and 300 mm.

A new look at absorption in high-energy electron diffraction

1989 ◽  
Vol 47 ◽  
pp. 486-487
Author(s):  
D.M. Bird ◽  
Q.A. King
Keyword(s):  
Electron Diffraction ◽  
High Energy ◽  
Complex Numbers ◽  
High Energy Electron ◽  
Standard Assumption ◽  
Potential Coefficient ◽  
Elastic Part ◽  
Total Potential ◽  
The Individual ◽  
Image Position

People seldom take absorption very seriously in electron diffraction calculations. Since the work of Hashimoto et al. it has been common practice to set the absorbative part of the potential coefficient V′g to be one tenth of the elastic part Vg. Although this may not be a bad approximation in simple metals, there is no reason why it should apply to more complicated structures. Here, Vg may be small because of interference between different atoms in the unit cell, but the same cancellation might not occur in V′g because the individual atomic contributions to Vg and V′g need not scale in the same way. In fact, the absorbative contribution increases more rapidly with atomic number than the elastic part. This effect is particularly marked in non-centrosymmetric crystals, where V′g and Vg need not have the same phase. Both V′g and Vg are now complex numbers which we write as(1)The squared modulus of the total potential coefficient now becomes(2)If g → −g, ϕ and ϕ′ change sign, so if the phase difference is non-zero the overall magnitude of the +g and −g potential coefficients are not equal. The standard assumption is that |V′g| = 0.1|Vg| and ϕg − ϕ′g = 0, which ignores corrections to the magnitude of Vg of order | V′g/Vg|.

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