Induced polarization and pore radius — A discussion

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D519-D526 ◽  
Author(s):  
Andreas Weller ◽  
Zeyu Zhang ◽  
Lee Slater ◽  
Sabine Kruschwitz ◽  
Matthias Halisch
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Diffusion Coefficients ◽  
Pore Radius ◽  
Mercury Porosimetry ◽  
Induced Polarization ◽  
Reliable Estimate ◽  
Characteristic Relaxation Time ◽  
A Value ◽  
Apparent Diffusion

Permeability estimation from induced polarization (IP) measurements is based on a fundamental premise that the characteristic relaxation time [Formula: see text] is related to the effective hydraulic radius [Formula: see text] controlling fluid flow. The approach requires a reliable estimate of the diffusion coefficient of the ions in the electrical double layer. Others have assumed a value for the diffusion coefficient, or postulated different values for clay versus clay-free rocks. We have examined the link between a widely used single estimate of [Formula: see text] and [Formula: see text] for an extensive database of sandstone samples, in which mercury porosimetry data confirm that [Formula: see text] is reliably determined from a modification of the Hagen-Poiseuille equation assuming that the electrical tortuosity is equal to the hydraulic tortuosity. Our database does not support the existence of one or two distinct representative diffusion coefficients but instead demonstrates strong evidence for six orders of magnitude of variation in an apparent diffusion coefficient that is well-correlated with [Formula: see text] and the specific surface area per unit pore volume [Formula: see text]. Two scenarios can explain our findings: (1) the length scale defined by [Formula: see text] is not equal to [Formula: see text] and is likely much longer due to the control of pore-surface roughness or (2) the range of diffusion coefficients is large and likely determined by the relative proportions of the different minerals (e.g., silica and clays) making up the rock. In either case, the estimation of [Formula: see text] (and hence permeability) is inherently uncertain from a single characteristic IP relaxation time as considered in this study.

Changes in the apparent diffusion coefficient of water and T2 relaxation time in gerbil hippocampus after mild ischemia

Neuroreport ◽  
2000 ◽  
Vol 11 (15) ◽  
pp. 3333-3336 ◽  
Author(s):  
Lidong Zhu ◽  
Nobuhito Saito ◽  
Osamu Abe ◽  
Toshiyuki Okubo ◽  
Haruyasu Yamada ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Apparent Diffusion Coefficient ◽  
T2 Relaxation Time ◽  
T2 Relaxation ◽  
Apparent Diffusion

A Power-Law Mixing Rule for Predicting Apparent Diffusion Coefficients of Binary Gas Mixtures in Heavy Oil

2017 ◽  
Vol 140 (5) ◽  
Author(s):  
Hyun Woong Jang ◽  
Daoyong Yang ◽  
Huazhou Li
Keyword(s):  
Diffusion Coefficient ◽  
Apparent Diffusion Coefficient ◽  
Heavy Oil ◽  
Diffusion Coefficients ◽  
Gas Mixtures ◽  
Gas Diffusion ◽  
Gas Mixture ◽  
Mixing Rule ◽  
Heavy Oils ◽  
Apparent Diffusion

A power-law mixing rule has been developed to determine apparent diffusion coefficient of a binary gas mixture on the basis of molecular diffusion coefficients for pure gases in heavy oil. Diffusion coefficient of a pure gas under different pressures and different temperatures is predicted on the basis of the Hayduk and Cheng's equation incorporating the principle of corresponding states for one-dimensional gas diffusion in heavy oil such as the diffusion in a pressure–volume–temperature (PVT) cell. Meanwhile, a specific surface area term is added to the generated equation for three-dimensional gas diffusion in heavy oil such as the diffusion in a pendant drop. In this study, the newly developed correlations are used to reproduce the measured diffusion coefficients for pure gases diffusing in three different heavy oils, i.e., two Lloydminster heavy oils and a Cactus Lake heavy oil. Then, such predicted pure gas diffusion coefficients are adjusted based on reduced pressure, reduced temperature, and equilibrium ratio to determine apparent diffusion coefficient for a gas mixture in heavy oil, where the equilibrium ratios for hydrocarbon gases and CO2 are determined by using the equilibrium ratio charts and Standing's equations, respectively. It has been found for various gas mixtures in two different Lloydminster heavy oils that the newly developed empirical mixing rule is able to reproduce the apparent diffusion coefficient for binary gas mixtures in heavy oil with a good accuracy. For the pure gas diffusion in heavy oil, the absolute average relative deviations (AARDs) for diffusion systems with two different Lloydminster heavy oils and a Cactus Lake heavy oil are calculated to be 2.54%, 14.79%, and 6.36%, respectively. Meanwhile, for the binary gas mixture diffusion in heavy oil, the AARDs for diffusion systems with two different Lloydminster heavy oils are found to be 3.56% and 6.86%, respectively.

scholarly journals Diffusional Properties of Methanogenic Granular Sludge: 1H NMR Characterization

2003 ◽  
Vol 69 (11) ◽  
pp. 6644-6649 ◽  
Author(s):  
Piet N. L. Lens ◽  
Rakel Gastesi ◽  
Frank Vergeldt ◽  
Adriaan C. van Aelst ◽  
Antonio G. Pisabarro ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Nmr Spectroscopy ◽  
Diffusion Coefficients ◽  
Metal Sulfide ◽  
Free Water ◽  
Granular Sludge ◽  
Self Diffusion ◽  
Nmr Characterization ◽  
Self Diffusion Coefficient

ABSTRACT The diffusive properties of anaerobic methanogenic and sulfidogenic aggregates present in wastewater treatment bioreactors were studied using diffusion analysis by relaxation time-separated pulsed-field gradient nuclear magnetic resonance (NMR) spectroscopy and NMR imaging. NMR spectroscopy measurements were performed at 22°C with 10 ml of granular sludge at a magnetic field strength of 0.5 T (20 MHz resonance frequency for protons). Self-diffusion coefficients of H2O in the investigated series of mesophilic aggregates were found to be 51 to 78% lower than the self-diffusion coefficient of free water. Interestingly, self-diffusion coefficients of H2O were independent of the aggregate size for the size fractions investigated. Diffusional transport occurred faster in aggregates growing under nutrient-rich conditions (e.g., the bottom of a reactor) or at high (55°C) temperatures than in aggregates cultivated in nutrient-poor conditions or at low (10°C) temperatures. Exposure of aggregates to 2.5% glutaraldehyde or heat (70 or 90°C for 30 min) modified the diffusional transport up to 20%. In contrast, deactivation of aggregates by HgCl2 did not affect the H2O self-diffusion coefficient in aggregates. Analysis of NMR images of a single aggregate shows that methanogenic aggregates possess a spin-spin relaxation time and self-diffusion coefficient distribution, which are due to both physical (porosity) and chemical (metal sulfide precipitates) factors.

scholarly journals The mobility of sodium on tungsten

1935 ◽  
Vol 150 (869) ◽  
pp. 58-76 ◽  
Keyword(s):  
Activation Energy ◽  
Diffusion Coefficient ◽  
Work Function ◽  
Direct Measurement ◽  
Diffusion Coefficients ◽  
Condensation Coefficient ◽  
Alkali Earth ◽  
Adsorbed Films ◽  
A Value ◽  
Two Phases

Although the existence as well as some of the properties of adsorbed films of alkali and alkali earth metals on metals of higher work function have long been known, it is only recently that these films have been shown to be capable of migrating over the surface of the adsorbent, and that attempts have been made to measure diffusion coefficients and the activation energy associated with the diffusion. Langmuir and Taylor, investigating the properties of cæsium films, found it necessary to postulate that the cæsium was mobile in order to account for the high value (α ≅ 1.0) for the condensation coefficient on quite concentrated films. Later they were able to make a direct measurement of the diffusion coefficient. They obtained a value of D at 812° K of 3.4 x 10 -5 cm 2 secs -1 , and an activation energy of 0.61 volt. Langmuir has also shown that cæsium films exist in two phases and has measured the diffusion coefficient by following the movement of the boundary between these two phases.

scholarly journals Quantifying T 2 relaxation time changes within lesions defined by apparent diffusion coefficient in grey and white matter in acute stroke patients

2019 ◽  
Vol 64 (9) ◽  
pp. 095016 ◽  
Author(s):  
Robin A Damion ◽  
Michael J Knight ◽  
Bryony L McGarry ◽  
Rose Bosnell ◽  
Peter Jezzard ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
White Matter ◽  
Apparent Diffusion Coefficient ◽  
Acute Stroke ◽  
Stroke Patients ◽  
Apparent Diffusion ◽  
Time Changes

scholarly journals Secondary Reduction in the Apparent Diffusion Coefficient of Water, Increase in Cerebral Blood Volume, and Delayed Neuronal Death after Middle Cerebral Artery Occlusion and Early Reperfusion in the Rat

1999 ◽  
Vol 19 (12) ◽  
pp. 1354-1364 ◽  
Author(s):  
Menno van Lookeren Campagne ◽  
G. Roger Thomas ◽  
Harold Thibodeaux ◽  
James T. Palmer ◽  
Simon P. Williams ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Cerebral Blood Volume ◽  
Vascular Occlusion ◽  
T2 Relaxation Time ◽  
T2 Relaxation ◽  
Early Reperfusion ◽  
Occlusion Time ◽  
Contrast Enhanced ◽  
Apparent Diffusion

It has been reported recently that very delayed damage can occur as a result of focal cerebral ischemia induced by vascular occlusion of short duration. With use of diffusion-, T2-, and contrast-enhanced dynamic magnetic resonance imaging (MRI) techniques, the occlusion time dependence together with the temporal profile for this delayed response in a rat model of transient focal cortical ischemia have been established. The distal branch of the middle cerebral artery was occluded for 20, 30, 45, or 90 minutes. Twenty minutes of vascular occlusion with reperfusion exhibited no significant mean change in either the apparent diffusion coefficient of water (ADC) or the T2 relaxation time at 6, 24, 48, or 72 hours after reperfusion ( P = 0.97 and 0.70, respectively). Ninety minutes of ischemia caused dramatic tissue injury at 6 hours, as indicated by an increase in T2 relaxation times to 135% of the contralateral values ( P < 0.01). However, at intermediate periods of ischemia (30 to 45 minutes), complete reversal of the ADC was seen at 6 hours after reperfusion but was followed by a secondary decline over time, such that a 25% reduction in tissue ADC was seen at 24 as compared with 6 hours ( P < 0.02). This secondary response was accompanied by an increase in cerebral blood volume (CBV), as shown by contrast-enhanced dynamic MRI (120% of contralateral values; P < 0.001), an increase in T2 relaxation time (132%; P < 0.01), together with clear morphological signs of cell death. By day 18, the mean volume of missing cortical tissue measured with high-resolution MRI in animals occluded for 30 and 45 minutes was 50% smaller than that in 90-minute occluded animals ( P < 0.005). These data show that ultimate infarct size is reduced after early reperfusion and is occlusion time dependent. The early tissue recovery that is seen with intermediate occlusion times can be followed by cell death, which has a delayed onset and is accompanied by an increase in CBV.

Apparent Diffusion Coefficient, Fractional Anisotropy and T2 Relaxation Time Measurement

2007 ◽  
Vol 17 (4) ◽  
pp. 230-238 ◽  
Author(s):  
Xiao-Qi Ding ◽  
Jürgen Finsterbusch ◽  
Oliver Wittkugel ◽  
Christian Saager ◽  
Einar Goebell ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Apparent Diffusion Coefficient ◽  
Fractional Anisotropy ◽  
Time Measurement ◽  
T2 Relaxation Time ◽  
T2 Relaxation ◽  
Relaxation Time Measurement ◽  
Apparent Diffusion

scholarly journals A spatiotemporal theory for MRI T2 relaxation time and apparent diffusion coefficient in the brain during acute ischaemia: Application and validation in a rat acute stroke model

2015 ◽  
Vol 36 (7) ◽  
pp. 1232-1243 ◽  
Author(s):  
Michael J Knight ◽  
Bryony L McGarry ◽  
Harriet J Rogers ◽  
Kimmo T Jokivarsi ◽  
Olli HJ Gröhn ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Apparent Diffusion Coefficient ◽  
Cerebral Ischaemia ◽  
Future Application ◽  
Acute Ischaemia ◽  
Cellular Environment ◽  
Apparent Diffusion ◽  
Cytotoxic Oedema

The objective of this study is to present a mathematical model which can describe the spatiotemporal progression of cerebral ischaemia and predict magnetic resonance observables including the apparent diffusion coefficient (ADC) of water and transverse relaxation time T2. This is motivated by the sensitivity of the ADC to the location of cerebral ischaemia and T2 to its time-course, and that it has thus far proven challenging to relate observations of changes in these MR parameters to stroke timing, which is of considerable importance in making treatment choices in clinics. Our mathematical model, called the cytotoxic oedema/dissociation (CED) model, is based on the transit of water from the extra- to the intra-cellular environment (cytotoxic oedema) and concomitant degradation of supramacromolecular and macromolecular structures (such as microtubules and the cytoskeleton). It explains experimental observations of ADC and T2, as well as identifying the rate of spread of effects of ischaemia through a tissue as a dominant system parameter. The model brings the direct extraction of the timing of ischaemic stroke from quantitative MRI closer to reality, as well as providing insight on ischaemia pathology by imaging in general. We anticipate that this may improve patient access to thrombolytic treatment as a future application.

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