scholarly journals Analysis of Membrane Transport Equations for Reverse Electrodialysis (RED) Using Irreversible Thermodynamics

2020 ◽  
Vol 21 (17) ◽  
pp. 6325
Author(s):  
Wojciech Kujawski ◽  
Andriy Yaroshchuk ◽  
Emiliy Zholkovskiy ◽  
Izabela Koter ◽  
Stanislaw Koter
Keyword(s):  
Transport Equation ◽  
Membrane Transport ◽  
Power Density ◽  
Irreversible Thermodynamics ◽  
Transport Equations ◽  
Membrane Thickness ◽  
Membrane Conductivity ◽  
Reverse Electrodialysis ◽  
Linear Transport Equation ◽  
Simplifying Assumptions

Reverse electrodialysis (RED) is an electro-membrane process for the conversion of mixing energy into electricity. One important problem researchers’ face when modeling the RED process is the choice of the proper membrane transport equations. In this study, using experimental data that describe the membrane Nafion 120 in contact with NaCl aqueous solutions, the linear transport equation of irreversible thermodynamics was applied to calculate the power density of the RED system. Various simplifying assumptions about transport equation (i.e., four-, three-, and two-coefficients approaches) are proposed and discussed. We found that the two-coefficients approach, using the membrane conductivity and the apparent transport number of ions, describes the power density with good accuracy. In addition, the influence of the membrane thickness and the concentration polarization on the power density is also demonstrated.

scholarly journals The Influence of Concentration and Temperature on the Membrane Resistance of Ion Exchange Membranes and the Levelised Cost of Hydrogen from Reverse Electrodialysis with Ammonium Bicarbonate

Membranes ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 135
Author(s):  
Yash Dharmendra Raka ◽  
Robert Bock ◽  
Håvard Karoliussen ◽  
Øivind Wilhelmsen ◽  
Odne Stokke Burheim
Keyword(s):  
Ion Exchange ◽  
Waste Heat ◽  
Ammonium Bicarbonate ◽  
Operating Efficiency ◽  
Membrane Thickness ◽  
Ion Exchange Membranes ◽  
Reverse Electrodialysis ◽  
Ohmic Resistance ◽  
Production Of Hydrogen ◽  
The Impact

The ohmic resistances of the anion and cation ion-exchange membranes (IEMs) that constitute a reverse electrodialysis system (RED) are of crucial importance for its performance. In this work, we study the influence of concentration (0.1 M, 0.5 M, 1 M and 2 M) of ammonium bicarbonate solutions on the ohmic resistances of ten commercial IEMs. We also studied the ohmic resistance at elevated temperature 313 K. Measurements have been performed with a direct two-electrode electrochemical impedance spectroscopy (EIS) method. As the ohmic resistance of the IEMs depends linearly on the membrane thickness, we measured the impedance for three different layered thicknesses, and the results were normalised. To gauge the role of the membrane resistances in the use of RED for production of hydrogen by use of waste heat, we used a thermodynamic and an economic model to study the impact of the ohmic resistance of the IEMs on hydrogen production rate, waste heat required, thermochemical conversion efficiency and the levelised cost of hydrogen. The highest performance was achieved with a stack made of FAS30 and CSO Type IEMs, producing hydrogen at 8.48× 10−7 kg mmem−2s−1 with a waste heat requirement of 344 kWh kg−1 hydrogen. This yielded an operating efficiency of 9.7% and a levelised cost of 7.80 € kgH2−1.

Asymptotic theory of the linear transport equation in anisotropic media

2008 ◽  
Vol 49 (8) ◽  
pp. 083504 ◽  
Author(s):  
Richard Sanchez ◽  
Jean Ragusa ◽  
Emiliano Masiello
Keyword(s):  
Transport Equation ◽  
Asymptotic Theory ◽  
Anisotropic Media ◽  
Linear Transport ◽  
Linear Transport Equation

A linear transport equation for wave phenomena

1987 ◽  
Vol 16 (8) ◽  
pp. 1041-1094 ◽  
Author(s):  
Marijan Ribarič ◽  
Luka Sušteršič
Keyword(s):  
Transport Equation ◽  
Linear Transport ◽  
Linear Transport Equation ◽  
Wave Phenomena

scholarly journals A Stabilized DG Cut Cell Method for Discretizing the Linear Transport Equation

2020 ◽  
Vol 42 (6) ◽  
pp. A3677-A3703
Author(s):  
Christian Engwer ◽  
Sandra May ◽  
Andreas Nüßing ◽  
Florian Streitbürger
Keyword(s):  
Transport Equation ◽  
Cell Method ◽  
Linear Transport ◽  
Cut Cell ◽  
Linear Transport Equation

Interactions of cell volume, membrane potential, and membrane transport parameters

1980 ◽  
Vol 238 (5) ◽  
pp. C196-C206 ◽  
Author(s):  
E. Jakobsson
Keyword(s):  
Membrane Potential ◽  
Cell Volume ◽  
Membrane Transport ◽  
Numerical Solutions ◽  
Transport Equations ◽  
Time Varying ◽  
Transport Parameters ◽  
Animal Cells ◽  
Analytic Expressions ◽  
Solute Species

Equations have been written and solved that describe for animal cells the relationships among membrane transport, cell volume, membrane potential, and distribution of permeant solute. The essential system consists of n + 2 equations, where n is the number of permeant solute species. The n of the equations are the n transport equations for the permeant species, one for each species. The other two equations are statements of 1) the condition for bulk electroneutrality inside the cell and 2) the condition for isotonicity between the interior and exterior of the cell. Numerical solutions have been obtained in both the steady-state and time-varying cases for transport equations that are physically and phenomenologically reasonable. In addition to numerical solutions analytic expressions are presented that show the ranges of membrane parameters essential for volume regulation; for values of membrane parameters beyond explicitly defined bounds, the equations do not have real, positive solutions for cell volume.

22.—The Linear Transport Equation. The Degenerate Case c = 1. I. Full-range Theory

1976 ◽  
Vol 75 (4) ◽  
pp. 259-282 ◽  
Author(s):  
C. G. Lekkerkerker
Keyword(s):  
Transport Equation ◽  
Full Range ◽  
Stellar Atmosphere ◽  
Spectral Theorem ◽  
Milne Problem ◽  
Linear Transport ◽  
Propagation Of Light ◽  
Linear Transport Equation ◽  
Range Theory ◽  
New Treatment

SynopsisThe aim of this paper is to give a functional analytic treatment of the homogeneous and inhomogeneous linear transport equation in the case that the parameter c occurring in that equation equals 1. The larger part of the paper is devoted to the study of a certain operator T−1 A in the space L2(– 1, 1). A peculiarity not arising in the case c < 1 (treated amongst others by Hangelbroek) is that, for c = 1, the operator T−1A has a double eigenvalue 0 and that it is no longer hermitian. The Spectral Theorem is used to diagonalise the operator as far as possible, and full-range and half-range formulae are derived. The results are applied inter alia to give a new treatment of the Milne problem concerning the propagation of light in a stellar atmosphere.

scholarly journals Theoretical power density from salinity gradients using reverse electrodialysis

2012 ◽  
Vol 20 ◽  
pp. 170-184 ◽  
Author(s):  
David A. Vermaas ◽  
Enver Guler ◽  
Michel Saakes ◽  
Kitty Nijmeijer
Keyword(s):  
Power Density ◽  
Reverse Electrodialysis ◽  
Salinity Gradients
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