Measuring diffusion using the differential form of Fick's law and magnetic resonance imaging

Muir, Colleen E.; Lowry, Brian; Balcom, Bruce J.

doi:10.1088/1367-2630/13/1/015005

Cited by 17 publications

(9 citation statements)

References 12 publications

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“…Therefore, an experimental setup with cylindrical geometry and known boundary conditions have been used to determine the oxygen transport coefficients in water and swollen hydrogels with an NMR spectroscopic method. Alternatively, NMR imaging techniques could be used to determine the spatial and temporal variations of the signal associated to the observed nucleus in a volume of interest . Thus, the concentration of oxygen could be determined in space and time within a sample and D could be calculated directly from Fick's differential equation, Equation , independently of geometrical considerations.…”

Section: Resultsmentioning

confidence: 99%

“…Alternatively, NMR imaging techniques could be used to determine the spatial and temporal variations of the signal associated to the observed nucleus in a volume of interest. [ 78,79 ] Thus, the concentration of oxygen could be determined in space and time within a sample and D could be calculated directly from Fick's differential equation, Equation 8 , independently of geometrical considerations.…”

Section: Oxygen Permeation Coeffi Cientsmentioning

confidence: 99%

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Determination of Oxygen Permeability in Acrylic‐Based Hydrogels by Proton NMR Spectroscopy and Imaging

Compañ

Mollá

Vallejos

et al. 2014

Macro Chemistry & Physics

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Polymer network membranes with a high capacity for water absorption are obtained by radical polymerization of N‐[2‐(2‐hydroxyethoxy)ethyl]methacrylamide (HEEMAM). The permeability, solubility, and diffusion coefficients of oxygen in hydrogels are determined using nuclear magnetic resonance (NMR) methods based on the paramagnetic effect of dissolved oxygen gas on the proton spin‐lattice relaxation times of water, and the results are compared with those obtained with electrochemical procedures. The results of NMR measurements of oxygen transport coefficients in distilled water show excellent agreement with corresponding literature values. The results of the potentiostatic and NMR oxygen transport measurements in hydrogels are in reasonable agreement and support the viability of the NMR method.

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Section: Resultsmentioning

confidence: 99%

Section: Oxygen Permeation Coeffi Cientsmentioning

confidence: 99%

Determination of Oxygen Permeability in Acrylic‐Based Hydrogels by Proton NMR Spectroscopy and Imaging

Compañ

Mollá

Vallejos

et al. 2014

Macro Chemistry & Physics

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“…Although there may be concern regarding the swelling of a polymer during sorption leading to a nonlinear steady‐state, concentration profile, Crank has shown that it is not the nonlinear isotherm that is of consequence, but rather concentration‐dependent diffusion coefficients which give rise to non‐linear concentration profiles. There have been numerous investigations examining the transient mass transfer process and the development of the concentration profile within the sample 18–20 revealing that our assumption of a linear concentration profile is valid when the diffusion coefficient is approximately constant. In addition, the concentration profiles of permeating solvents in polymer membranes have been measured by in situ confocal Raman spectroscopy with “depth scans” through the membrane to validate the multicomponent transport in the membrane 21,22 …”

Section: Theorymentioning

confidence: 99%

Payne cell gravimetric measurements in polymer‐solvent systems for diffusion coefficients and isotherm data

Zielinski

Altınkaya

Garcia³

2020

J of Applied Polymer Sci

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The discussion focuses on the application of a Payne cell to the measurement of diffusion and solubility coefficients in polymer/solvent systems. Payne cells have, thus far, been used exclusively to measure steady-state permeation rates of solvents. An analytical model has been developed to describe transient gravimetric sorption and desorption measurements performed with a Payne cell. The model has been validated by a complementary numerical simulation and has been applied to evaluate diffusion and solubility coefficients in two different toluene-silicone rubber systems. The data measured using the Payne cell are found to compare very well with diffusion coefficient and isotherm data measured by traditional gravimetric sorption experiments.

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“…Given the various influence factors such as temperature, pressure, oil saturation, permeability, wettability, etc., the measurements of concentration and volume-related properties are often difficult to perform and interpret. The available techniques for measuring diffusivity can be divided into two main categories: direct and indirect techniques. − X-ray computer-assisted tomography (CAT), − nuclear magnetic resonance (NMR), , and sampling analysis , are three representative direct test methods. They usually generate the diffusion concentration profile directly, and then, the diffusion coefficients are estimated through Fick’s law.…”

Section: Introductionmentioning

confidence: 99%

Determination of the Diffusion Coefficient of Supercritical CO₂ in Low-Permeability Formation Cores

Guo

Jia

et al. 2020

Energy Fuels

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CO2 diffusion in the oil phase in the presence of porous media is of great importance to forecast the performance of enhanced oil recovery and carbon dioxide capture and storage. When CO2 is brought into contact with an oil phase, diffusion occurs. The indirect pressure-decay methodology has been applied successfully to determine the mutual diffusion coefficients of supercritical CO2 and crude oil at temperature of 65 °C. Theoretically, a one-dimensional double-way mass transfer model incorporating the capillary and adsorption effects of porous media has been constructed to quantify the mutual dynamic diffusion coefficients. The crude oil has been characterized into five pseudo-components for the accurate description of the phase behavior of CO2 gas and oil phases. An optimization method along with the PR equation of state is employed to determine each component’s diffusion coefficients in the gas and oil phases for the purpose of minimization of the difference between the experimental data and calculated results. Satisfactory agreements are obtained with a merely 0.97% pressure difference when a variable diffusion coefficient is implemented. The short-time experimental test and a long-time-duration calculation are recommended for further diffusion investigation. The capillary analysis gave a regressed fractal dimension of 2.7049 with the average absolute deviation of 0.602%. The adsorption phenomenon can be greatly influenced by the existence of heavy components. The heavier the components, the greater their impact on adsorption. Furthermore, a faster and enhanced diffusion process is observed at high pressure and temperature. The combination of several complex mechanisms leads to the initial gradual increase of the diffusion coefficient with time, and then, it arrives at a plateau, which is slightly different from the previous diffusion coefficient changing tendency mentioned in the literature. In the presence of a low-permeability formation core, the determined diffusion coefficients of CO2 in the gas and liquid phases are increased from 4.38 × 10–9 to 6.21 × 10–9 and 6.16 × 10–10 to 9.21 × 10–10 m2/s when the system pressure is decreased from 18.2 to 12.11 MPa, respectively. In addition, the capillary effect can lead to a reduction of the diffusion coefficient in the oil phase but has little effect on the diffusion coefficient in the gas phase.

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Measuring diffusion using the differential form of Fick's law and magnetic resonance imaging

Cited by 17 publications

References 12 publications

Determination of Oxygen Permeability in Acrylic‐Based Hydrogels by Proton NMR Spectroscopy and Imaging

Determination of Oxygen Permeability in Acrylic‐Based Hydrogels by Proton NMR Spectroscopy and Imaging

Payne cell gravimetric measurements in polymer‐solvent systems for diffusion coefficients and isotherm data

Determination of the Diffusion Coefficient of Supercritical CO₂ in Low-Permeability Formation Cores

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Measuring diffusion using the differential form of Fick's law and magnetic resonance imaging

Cited by 17 publications

References 12 publications

Determination of Oxygen Permeability in Acrylic‐Based Hydrogels by Proton NMR Spectroscopy and Imaging

Determination of Oxygen Permeability in Acrylic‐Based Hydrogels by Proton NMR Spectroscopy and Imaging

Payne cell gravimetric measurements in polymer‐solvent systems for diffusion coefficients and isotherm data

Determination of the Diffusion Coefficient of Supercritical CO2 in Low-Permeability Formation Cores

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Determination of the Diffusion Coefficient of Supercritical CO₂ in Low-Permeability Formation Cores