Influence of Microgeometry on Membrane Potential of Shaly Sands

1990 ◽  
Vol 195 ◽  
Author(s):  
Pabitra N. Sen
Keyword(s):  
Electrical Conductivity ◽  
Membrane Potential ◽  
Pore Space ◽  
Geometrical Parameters ◽  
Formation Factor ◽  
Water Conductivity ◽  
Shaly Sand ◽  
Local Geology ◽  
Geometrical Factors

ABSTRACTThe microgeometry of the pore space influences the membrane potential Em. and theDC electrical conductivity σ of a shaly sand in a similar manner, independent of the details of the geometry: Em and σ being related via the conductivities of cations and σanions;σ=σcation + σ onion, and Em α σ cation/(σcation + σanion). This explicit relationship is used to investigate the role of the geometrical factors which influence both Em and σ in a related manner. The dependence of σ on the water conductivity σw can be well approximated with four geometrical parameters which can be obtained from the slopes and the interceptsof σ vs. σw curve at high and low salinities. We show that these geometrical factors appear in the expression for Em a well. These geometrical parameters (one of them is the formation factor) vary from rock to rock, and any trend in these parameters depend on the local geology.

Influence of microgeometry on membrane potential of shaly sands

Geophysics ◽  
1989 ◽  
Vol 54 (12) ◽  
pp. 1543-1553 ◽  
Author(s):  
Pabitra N. Sen
Keyword(s):  
Membrane Potential ◽  
Pore Space ◽  
Geometrical Parameters ◽  
Formation Factor ◽  
Empirical Formulas ◽  
Water Conductivity ◽  
Shaly Sand ◽  
Local Geology ◽  
Geometrical Factors

The microgeometry of the pore space influences the membrane potential [Formula: see text] and the dc electrical conductivity σ of a shaly sand in a similar manner, independent of the details of the geometry. [Formula: see text] and σ are related via the conductivities of cations and anions [Formula: see text] and [Formula: see text], and [Formula: see text]. This explicit relationship is used to investigate the role of the geometrical factors that influence both [Formula: see text] and σ in a related manner. The dependence of σ on water conductivity [Formula: see text] can be well approximated with four geometrical parameters, which can be obtained from the slopes and the intercepts of curves of σ versus [Formula: see text] at high and low salinities. I show how these geometrical factors appear in the expression for [Formula: see text] as well. The geometrical parameters, one of them being the formation factor, vary from rock to rock; and any trend in the parameters depends on the local geology. For the data on a group of 140 different cores, the geometrical factors could be well approximated by functions of porosity, cementation exponent, and charge density, to give a simple conductivity formula analogous to the empirical formulas that are most widely used in formation evaluation. These empirical factors are used to obtain an approximate formula for [Formula: see text].

Correspondence between membrane potential and conductivity

Geophysics ◽  
1991 ◽  
Vol 56 (4) ◽  
pp. 461-471 ◽  
Author(s):  
P. N. Sen
Keyword(s):  
Membrane Potential ◽  
Transport Number ◽  
Activity Ratio ◽  
Ionic Concentration ◽  
Salinity Range ◽  
Liquid Junction Potential ◽  
Formation Factor ◽  
Liquid Junction ◽  
Water Conductivity ◽  
Junction Potential

Combining the membrane potential [Formula: see text] with the corresponding ideal membrane potential [Formula: see text] and the liquid junction potential [Formula: see text], for the same activity ratio, gives [Formula: see text]. [Formula: see text] and [Formula: see text] are the reciprocal of the average of the reciprocal water conductivity and reciprocal of cation and anion conductivities, and [Formula: see text]; and [Formula: see text] is the average of the ratio of the water to the rock conductivity [Formula: see text] with respect to [Formula: see text], where t is the transport number for the Na ion, [Formula: see text] is the ionic concentration, and [Formula: see text] is the activity coefficient. This relationship is independent of any model and does not even refer to the value of clay counterion concentration. Combining σ with [Formula: see text] gives the saturation dependent formation factor F, and thus the interpretation of shaly sands becomes no more difficult than for clean sands. Experimental data on 27 rocks for which both membrane potential and conductivity were measured by Smits (1968) and Waxman and Smits (1968) over a large salinity range are used to verify this relationship.

Numerical estimation of electrical conductivity in saturated porous media with a 2-D lattice gas

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 766-772 ◽  
Author(s):  
Michel Küntz ◽  
Jean Claude Mareschal ◽  
Paul Lavallée
Keyword(s):  
Electrical Conductivity ◽  
Porous Media ◽  
Power Law ◽  
Lattice Gas ◽  
Effective Conductivity ◽  
Pore Space ◽  
Solid Matrix ◽  
Conductivity Ratio ◽  
Saturated Porous Media ◽  
Formation Factor

A 2-D lattice gas is used to calculate the effective electrical conductivity of saturated porous media as a function of porosity and conductivity ratio [Formula: see text] between the pore‐filling fluid and the solid matrix for various microscopic structures of the pore space. The way the solid phase is introduced allows the porosity ϕ to take any value between 0 and 1 and the geometry of the pore structure to be as complex as desired. The results are presented in terms of the formation factor [Formula: see text], with [Formula: see text] the effective conductivity of the saturated rock and [Formula: see text] the conductivity of the fluid. It is shown that the formation factor F as a function of the porosity ϕ follows a power law [Formula: see text], equivalent to the empirical Archie’s law. The exponent m varies with the microgeometry of the pore space and could therefore reflect the microstructure at the macroscopic scale. The prefactor a of the power law, however, is close to 1 regardless of the microstructure. For a given microgeometry of the pore space, the variation of the residual electrical conductivity of the solid matrix induced by a finite conductivity ratio [Formula: see text] does not significantly influence the variation of the effective conductivity of the fluid‐solid binary mixture unless the porosity is low.

Influence of temperature on electrical conductivity on shaly sands

Geophysics ◽  
1992 ◽  
Vol 57 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Pabitra N. Sen ◽  
Peter A. Goode
Keyword(s):  
Electrical Conductivity ◽  
Temperature Dependence ◽  
Pore Space ◽  
Clay Content ◽  
Large Temperature ◽  
Measured Temperature ◽  
Water Conductivity ◽  
Influence Of Temperature ◽  
Counter Ions ◽  
Influence Of Temperature On

In boreholes, temperatures vary and to extract hydrocarbon saturation from conductivity measurements, the influence of temperature on water and rock conductivities must be accounted for. The mobility [Formula: see text] of the counter‐ions due to clays and the electrical conductivity of pore‐filling brine show large changes with variation in temperature, whereas the microgeometry of the pore space exhibits negligible change. Using this idea, the temperature dependence of [Formula: see text] is extracted using data on dc electrical conductivity of shaly sands (σ) containing varying amounts of clay. The mobility of [Formula: see text] counter‐ions is found to vary approximately linearly with temperature. This explicit relationship is tested by comparing the predicted temperature dependence against the measured temperature dependence of conductivity of a set of rocks with high and low clay content. While the rock conductivity shows a large temperature dependence, the resistivity index is less sensitive to temperature. An approximate formula, which is superior to Arps’s formula, for water conductivity as a function of temperature is obtained.

Analysis of electrical conduction in the grain consolidation model

Geophysics ◽  
1987 ◽  
Vol 52 (10) ◽  
pp. 1402-1411 ◽  
Author(s):  
Lawrence M. Schwartz ◽  
Stephen Kimminau
Keyword(s):  
Electrical Conductivity ◽  
Grain Growth ◽  
Pore Space ◽  
Formation Factor ◽  
Minimum Area ◽  
Simulation Techniques ◽  
Fluid Saturation ◽  
Diagenetic Processes ◽  
Consolidation Model ◽  
Spherical Grains

In the grain consolidation model the diagenetic processes of compaction and cementation are represented in terms of the growth of an array of originally spherical grains. Grain growth toward the nodes of the pore space leads to an electrical formation factor F(ϕ) that increases slowly as the porosity ϕ decreases. By contrast, grain growth toward the throats of the pore space leads to a rapidly increasing F(ϕ). In all the cases we have examined, the value of the percolation threshold, [Formula: see text] is less than 0.055. Network simulation techniques have been developed to calculate the electrical conductivity of the ordered versions of the grain consolidation model. We find that the minimum‐area approximation employed in our earlier work is generally quite satisfactory. The network techniques can also be used to model the effects of mixed pore‐space fluid saturation, with results that are physically reasonable although not necessarily in agreement with empirical rules regarding saturation.

ROLE OF ADDED PHOSPHOGYPSUM AND HUMIC ACIDS IN THE KINETIC RELEASE OF SALT FROM SALT AFFECTED SOIL (SALINE – SODIC)

2020 ◽  
pp. 15-27
Keyword(s):  
Electrical Conductivity ◽  
Humic Acids ◽  
Release Rate ◽  
Release Kinetics ◽  
Sodium Adsorption Ratio ◽  
Salt Affected Soil ◽  
Two Factors ◽  
Dissolved Ions ◽  
Kinetic Release

In order to study the effect of phosphogypsum and humic acids in the kinetic release of salt from salt-affected soil, a laboratory experiment was conducted in which columns made from solid polyethylene were 60.0 cm high and 7.1 cm in diameter. The columns were filled with soil so that the depth of the soil was 30 cm inside the column, the experiment included two factors, the first factor was phosphogypsum and was added at levels 0, 5, 10 and 15 tons ha-1 and the second-factor humic acids were added at levels 0, 50, 100 and 150 kg ha-1 by mixing them with the first 5 cm of column soil and one repeater per treatment. The continuous leaching method was used by using an electrolytic well water 2.72 dS m-1. Collect the leachate daily and continue the leaching process until the arrival of the electrical conductivity of the filtration of leaching up to 3-5 dS m-1. The electrical conductivity and the concentration of positive dissolved ions (Ca, Mg, Na) were estimated in leachate and the sodium adsorption ratio (SAR) was calculated. The results showed that the best equation for describing release kinetics of the salts and sodium adsorption ratio in soil over time is the diffusion equation. Increasing the level of addition of phosphogypsum and humic acids increased the constant release velocity (K) of salts and the sodium adsorption ratio. The interaction between phosphogypsum and humic acids was also affected by the constant release velocity of salts and the sodium adsorption ratio. The constant release velocity (K) of the salts and the sodium adsorption ratio at any level of addition of phosphogypsum increased with the addition of humic acids. The highest salts release rate was 216.57 in PG3HA3, while the lowest rate was 149.48 in PG0HA0. The highest release rate of sodium adsorption ratio was 206.09 in PG3HA3, while the lowest rate was 117.23 in PG0HA0.

Radio and Electrical Measurements on Glacial Streams

1987 ◽  
Vol 33 (114) ◽  
pp. 239-242
Author(s):  
M. E. R. Walford
Keyword(s):  
Electrical Conductivity ◽  
Water Channel ◽  
Water System ◽  
Low Frequency ◽  
Water Channels ◽  
Radiative Loss ◽  
Radio Waves ◽  
Electrical Measurements ◽  
Water Conductivity ◽  
Glacier Surface

AbstractWe discuss the suggestion that small underwater transmitters might be used to illuminate the interior of major englacial water channels with radio waves. Once launched, the radio waves would naturally tend to be guided along the channels until attenuated by absorption and by radiative loss. Receivers placed within the channels or at the glacier surface could be used to detect the signals. They would provide valuable information about the connectivity of the water system. The electrical conductivity of the water is of crucial importance. A surface stream on Storglaciären, in Sweden, was found, using a low-frequency technique, to have a conductivity of approximately 4 × 10−4 S m−1. Although this is several hundred times higher than the conductivity of the surrounding glacier ice, the contrast is not sufficient to permit us simply to use electrical conductivity measurements to establish the connectivity of englacial water channels. However, the water conductivity is sufficiently small that, under favourable circumstances, radio signals should be detectable after travelling as much as a few hundred metres along an englacial water channel. In a preliminary field experiment, we demonstrated semi quantitatively that radio waves do indeed propagate as expected, at least in surface streams. We conclude that under-water radio transmitters could be of real practical value in the study of the englacial water system, provided that sufficiently robust devices can be constructed. In a subglacial channel, however, we expect the radio range would be much smaller, the environment much harsher, and the technique of less practical value.

scholarly journals Intracellular Na+ Modulates Pacemaking Activity in Murine Sinoatrial Node Myocytes: An In Silico Analysis

2021 ◽  
Vol 22 (11) ◽  
pp. 5645
Author(s):  
Stefano Morotti ◽  
Haibo Ni ◽  
Colin H. Peters ◽  
Christian Rickert ◽  
Ameneh Asgari-Targhi ◽  
...  
Keyword(s):  
Heart Failure ◽  
Membrane Potential ◽  
In Silico ◽  
Sinoatrial Node ◽  
In Silico Analysis ◽  
Ankyrin B ◽  
Deficient Mice ◽  
Silico Analysis ◽  
Bursting Activity

Background: The mechanisms underlying dysfunction in the sinoatrial node (SAN), the heart’s primary pacemaker, are incompletely understood. Electrical and Ca2+-handling remodeling have been implicated in SAN dysfunction associated with heart failure, aging, and diabetes. Cardiomyocyte [Na+]i is also elevated in these diseases, where it contributes to arrhythmogenesis. Here, we sought to investigate the largely unexplored role of Na+ homeostasis in SAN pacemaking and test whether [Na+]i dysregulation may contribute to SAN dysfunction. Methods: We developed a dataset-specific computational model of the murine SAN myocyte and simulated alterations in the major processes of Na+ entry (Na+/Ca2+ exchanger, NCX) and removal (Na+/K+ ATPase, NKA). Results: We found that changes in intracellular Na+ homeostatic processes dynamically regulate SAN electrophysiology. Mild reductions in NKA and NCX function increase myocyte firing rate, whereas a stronger reduction causes bursting activity and loss of automaticity. These pathologic phenotypes mimic those observed experimentally in NCX- and ankyrin-B-deficient mice due to altered feedback between the Ca2+ and membrane potential clocks underlying SAN firing. Conclusions: Our study generates new testable predictions and insight linking Na+ homeostasis to Ca2+ handling and membrane potential dynamics in SAN myocytes that may advance our understanding of SAN (dys)function.

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