Finite Solution Theory for Coalitional Games

1982 ◽  
Vol 3 (4) ◽  
pp. 551-565 ◽  
Author(s):  
William F. Lucas ◽  
Kai Michaelis
Keyword(s):  
Coalitional Games ◽  
Solution Theory ◽  
Finite Solution

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

scholarly journals Adsorption for efficient low carbon hydrogen production: part 2—Cyclic experiments and model predictions

Adsorption ◽  
2021 ◽  
Author(s):  
Anne Streb ◽  
Marco Mazzotti
Keyword(s):  
Hydrogen Production ◽  
Carbon Capture And Storage ◽  
Clean Energy ◽  
Separation Performance ◽  
Low Carbon ◽  
Solution Theory ◽  
Feed Composition ◽  
Ideal Adsorbed Solution Theory ◽  
Adsorbed Solution ◽  
Adsorbed Solution Theory

Abstract Hydrogen as clean energy carrier is expected to play a key role in future low-carbon energy systems. In this paper, we demonstrate a new technology for coupling fossil-fuel based hydrogen production with carbon capture and storage (CCS): the integration of CO2 capture and H2 purification in a single vacuum pressure swing adsorption (VPSA) cycle. An eight step VPSA cycle is tested in a two-column lab-pilot for a ternary CO2–H2–CH4 stream representative of shifted steam methane reformer (SMR) syngas, while using commercial zeolite 13X as adsorbent. The cycle can co-purify CO2 and H2, thus reaching H2 purities up to 99.96%, CO2 purities up to 98.9%, CO2 recoveries up to 94.3% and H2 recoveries up to 81%. The key decision variables for adjusting the separation performance to reach the required targets are the heavy purge (HP) duration, the feed duration, the evacuation pressure and the flow rate of the light purge (LP). In contrast to that, the separation performance is rather insensitive towards small changes in feed composition and in HP inlet composition. Comparing the experimental results with simulation results shows that the model for describing multi-component adsorption is critical in determining the predictive capabilities of the column model. Here, the real adsorbed solution theory (RAST) is necessary to describe all experiments well, whereas neither extended isotherms nor the ideal adsorbed solution theory (IAST) can reproduce all effects observed experimentally.

scholarly journals Effective Separation of Prime Olefins from Gas Stream Using Anion Pillared Metal Organic Frameworks: Ideal Adsorbed Solution Theory Studies, Cyclic Application and Stability

Catalysts ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 510
Author(s):  
Majeda Khraisheh ◽  
Fares. Almomani ◽  
Gavin Walker
Keyword(s):  
Breakthrough Curves ◽  
Isotherm Models ◽  
Regeneration Ability ◽  
Solution Theory ◽  
Experimental Conditions ◽  
Ideal Adsorbed Solution Theory ◽  
Adsorbed Solution ◽  
The Stability ◽  
Adsorption Desorption ◽  
Adsorbed Solution Theory

The separation of C3H4/C3H6 is one of the most energy intensive and challenging operations, requiring up to 100 theoretical stages, in traditional cryogenic distillation. In this investigation, the potential application of two MOFs (SIFSIX-3-Ni and NbOFFIVE-1-Ni) was tested by studying the adsorption–desorption behaviors at a range of operational temperatures (300–360 K) and pressures (1–100 kPa). Dynamic adsorption breakthrough tests were conducted and the stability and regeneration ability of the MOFs were established after eight consecutive cycles. In order to establish the engineering key parameters, the experimental data were fitted to four isotherm models (Langmuir, Freundlich, Sips and Toth) in addition to the estimation of the thermodynamic properties such as the isosteric heats of adsorption. The selectivity of the separation was tested by applying ideal adsorbed solution theory (IAST). The results revealed that SIFSIX-3-Ni is an effective adsorbent for the separation of 10/90 v/v C3H4/C3H6 under the range of experimental conditions used in this study. The maximum adsorption reported for the same combination was 3.2 mmolg−1. Breakthrough curves confirmed the suitability of this material for the separation with a 10-min gab before the lighter C3H4 is eluted from the column. The separated C3H6 was obtained with a 99.98% purity.

Thermodynamic properties of multicomponent electrolyte solutions in mixed solvents. 5• HCl + NaCl + urea + water at 278.5–318.15 K

1988 ◽  
Vol 66 (4) ◽  
pp. 637-644 ◽  
Author(s):  
Dian-Yuan Men ◽  
Jia-Zhen Yang ◽  
Chun-Yu Liang ◽  
Li-Tian Zhang ◽  
Huan Gao ◽  
...  
Keyword(s):  
Mixed Solvents ◽  
Electrolyte Solutions ◽  
Absolute Temperature ◽  
Molar Enthalpy ◽  
Free Energies ◽  
Force Measurements ◽  
Solution Theory ◽  
Electrolytic Solution ◽  
Harned's Rule ◽  
Electromotive Force Measurements

This paper reports electromotive force measurements of the cells[Formula: see text]and[Formula: see text]in mixed solvents of urea, mole fraction x = 0.05, at five temperatures from 278.15 to 318.15 K. The standard potentials of Ag–AgCl electrode in mixed solvents were obtained from the emf of cell (A) for HCl of molality mA from 0.02 to 0.11 mol kg−1, both by extrapolation on the basis of an extended Debye–Hückel equation and by a polynomial approach proposed in this paper on the basis of Pitzer's electrolytic solution theory. The standard free energies of transfer for HCl are discussed. The activity coefficients of HClγA in HCl + NaCl + urea + water have also been obtained from the emf of cell (B) at constant total ionic strength I = 0.5, 1.0, 1.5, and 2.0 mol kg−1. The experimental results show that HCl obeys Harned's rule and log γA is a linear function of absolute temperature T. They also indicate that the relative partial molar enthalpy of HCl obeys a similar Harned's rule.

On the use of the adsorbed solution theory for designing adsorption separation units

1993 ◽  
Vol 3 (4) ◽  
pp. 230-237 ◽  
Author(s):  
Renato Rota ◽  
Giuseppe Gamba ◽  
Massimo Morbidelli
Keyword(s):  
Solution Theory ◽  
Adsorbed Solution ◽  
Adsorbed Solution Theory

Densities and Excess Volumes of Fused Halides

1975 ◽  
Vol 30 (1) ◽  
pp. 64-68 ◽  
Author(s):  
H. C. Brookes ◽  
R. L. Paul
Keyword(s):  
Mole Fraction ◽  
Linear Dependence ◽  
Alkali Halide ◽  
Experimental Error ◽  
Van Der Waals ◽  
Excess Volumes ◽  
Van Der Waals Interactions ◽  
Solution Theory ◽  
Conformal Solution Theory ◽  
Volumes Of Mixing

Abstract Densities of molten AgBr-AX (A = Li, Na, K, Rb, Cs; X = Br or Cl), AgBr-AgCl, KBr-NaBr, KBr-CsBr, KCl-KBr, and KCl-CsBr mixtures have been measured at 0.5 mole fraction using the method of Archimedean displacement. The excess volumes of mixing are all positive, except for the AgBr-LiBr system. Attempts to relate the excess volumes of the binary AgBr-ABr systems to the second order conformal solution theory of Reiss, Katz, and Kleppa are unsuccessful, since V E is large even when the diameter difference parameter, δ12, is close to zero. However, the excess volumes of the reciprocal AgBr-ACl systems at 0.5 mole fraction are found, within experimental error, to have a linear dependence on δ12. The positive deviations from conformal solution theory which occur for the alkali halide mixtures have been interpreted in terms of non-Coulombic polarisation and van der Waals interactions.

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