scholarly journals A Generalized Technique for Eliminating Species in Complex Chemical Equilibrium Calculations

1969 ◽  
Vol 17 (5) ◽  
pp. 960-971 ◽  
Author(s):  
N. Z. Shapiro
Keyword(s):  
Chemical Equilibrium ◽  
Complex Chemical ◽  
Equilibrium Calculations

scholarly journals An overview of computational methods for chemical equilibrium and kinetic calculations for geochemical and reactive transport modeling

2017 ◽  
Vol 89 (5) ◽  
pp. 597-643 ◽  
Author(s):  
Allan M. M. Leal ◽  
Dmitrii A. Kulik ◽  
William R. Smith ◽  
Martin O. Saar
Keyword(s):  
Numerical Methods ◽  
Chemical Equilibrium ◽  
Reactive Transport ◽  
Mass Action ◽  
Transport Modeling ◽  
Partial Equilibrium ◽  
Integration Scheme ◽  
Reactive Transport Modeling ◽  
Kinetic Calculations ◽  
Equilibrium Calculations

AbstractWe present an overview of novel numerical methods for chemical equilibrium and kinetic calculations for complex non-ideal multiphase systems. The methods we present for equilibrium calculations are based either on Gibbs energy minimization (GEM) calculations or on solving the system of extended law of mass-action (xLMA) equations. In both methods, no a posteriori phase stability tests, and thus no tentative addition or removal of phases during or at the end of the calculations, are necessary. All potentially stable phases are considered from the beginning of the calculation, and stability indices are immediately available at the end of the computation to determine which phases are actually stable at equilibrium. Both GEM and xLMA equilibrium methods are tailored for computationally demanding applications that require many rapid local equilibrium calculations, such as reactive transport modeling. The numerical method for chemical kinetic calculations we present supports both closed and open systems, and it considers a partial equilibrium simplification for fast reactions. The method employs an implicit integration scheme that improves stability and speed when solving the often stiff differential equations in kinetic calculations. As such, it requires compositional derivatives of the reaction rates to assemble the Jacobian matrix of the resultant implicit algebraic equations that are solved at every time step. We present a detailed procedure to calculate these derivatives, and we show how the partial equilibrium assumption affects their computation. These numerical methods have been implemented in Reaktoro (reaktoro.org), an open-source software for modeling chemically reactive systems. We finish with a discussion on the comparison of these methods with others in the literature.

scholarly journals Optimization of Ethanol Autothermal Reforming Process with Chemical Equilibrium Calculations

2009 ◽  
Vol 3 (3) ◽  
pp. 79-85
Author(s):  
D. Markova ◽  
K. Valters ◽  
G. Bažbauers
Keyword(s):  
Chemical Equilibrium ◽  
Autothermal Reforming ◽  
Process Efficiency ◽  
Maximum Efficiency ◽  
Hydrogen Energy ◽  
Hydrogen Yield ◽  
Process Factors ◽  
Reforming Gas ◽  
Critical Process ◽  
Equilibrium Calculations

Optimization of Ethanol Autothermal Reforming Process with Chemical Equilibrium Calculations The dependence of carbon formation, hydrogen yield and efficiency of the ethanol autothermal reforming process on critical process factors is studied in the work by using chemical equilibrium calculations with a process simulation model made in the ChemCAD environment. The studied process factors are carbon-to-steam ratio S/C, air-to-fuel ratio λ and temperature in the reactor TATR. Since the goal of the reforming process is to achieve possibly higher values of H2 concentration in the reforming gas, by operating reformer at the maximum efficiency at the same time, the optimization of the reforming process was done by using objective functions which include hydrogen yield and the amount of heat supplied to the process. As a result it was found that the maximum process efficiency, which is defined as the ratio of obtained hydrogen energy to the energy supplied to the process in the studied range of process factors is 0,61, and this value can be achieved at λ value of 0,1, S/C values of 2,5-3 and temperatures in the reactor TATR 680 - 695°C. Hydrogen yield under these conditions is 4,41-4,55 mol/molC2H5OH.

scholarly journals Chemical equilibrium in AGB atmospheres: successes, failures, and prospects for small molecules, clusters, and condensates

2020 ◽  
Vol 637 ◽  
pp. A59 ◽  
Author(s):  
M. Agúndez ◽  
J. I. Martínez ◽  
P. L. de Andres ◽  
J. Cernicharo ◽  
J. A. Martín-Gago
Keyword(s):  
Gas Phase ◽  
Chemical Equilibrium ◽  
Equilibrium Composition ◽  
Building Blocks ◽  
Carbon Clusters ◽  
Agb Stars ◽  
Circumstellar Envelopes ◽  
General Chemical ◽  
First Time ◽  
Equilibrium Calculations

Chemical equilibrium has proven extremely useful for predicting the chemical composition of AGB atmospheres. Here we use a recently developed code and an updated thermochemical database that includes gaseous and condensed species involving 34 elements to compute the chemical equilibrium composition of AGB atmospheres of M-, S-, and C-type stars. We include for the first time TixCy clusters, with x = 1–4 and y = 1–4, and selected larger clusters ranging up to Ti13C22, for which thermochemical data are obtained from quantum-chemical calculations. Our main aims are to systematically survey the main reservoirs of each element in AGB atmospheres, review the successes and failures of chemical equilibrium by comparing it with the latest observational data, identify potentially detectable molecules that have not yet been observed, and diagnose the most likely gas-phase precursors of dust and determine which clusters might act as building blocks of dust grains. We find that in general, chemical equilibrium reproduces the observed abundances of parent molecules in circumstellar envelopes of AGB stars well. There are, however, severe discrepancies of several orders of magnitude for some parent molecules that are observed to be anomalously overabundant with respect to the predictions of chemical equilibrium. These are HCN, CS, NH3, and SO2 in M-type stars, H2O and NH3 in S-type stars, and the hydrides H2O, NH3, SiH4, and PH3 in C-type stars. Several molecules have not yet been observed in AGB atmospheres but are predicted with non-negligible abundances and are good candidates for detection with observatories such as ALMA. The most interesting ones are SiC5, SiNH, SiCl, PS, HBO, and the metal-containing molecules MgS, CaS, CaOH, CaCl, CaF, ScO, ZrO, VO, FeS, CoH, and NiS. In agreement with previous studies, the first condensates predicted to appear in C-rich atmospheres are found to be carbon, TiC, and SiC, while Al2O3 is the first major condensate expected in O-rich outflows. According to our chemical equilibrium calculations, the gas-phase precursors of carbon dust are probably acetylene, atomic carbon, and/or C3, while for silicon carbide dust, the most likely precursors are the molecules SiC2 and Si2C. In the case of titanium carbide dust, atomic Ti is the major reservoir of this element in the inner regions of AGB atmospheres, and therefore it is probably the main supplier of titanium during the formation of TiC dust. However, chemical equilibrium predicts that large titanium-carbon clusters such as Ti8C12 and Ti13C22 become the major reservoirs of titanium at the expense of atomic Ti in the region where condensation of TiC is expected to occur. This suggests that the assembly of large TixCy clusters might be related to the formation of the first condensation nuclei of TiC. In the case of Al2O3 dust, chemical equilibrium indicates that atomic Al and the carriers of Al-O bonds AlOH, AlO, and Al2O are the most likely gas-phase precursors.

Chemical Equilibrium

2021 ◽  
pp. 254-275
Author(s):  
Christopher O. Oriakhi
Keyword(s):  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Chemical Equilibrium ◽  
Equilibrium Position ◽  
Dynamic Equilibrium ◽  
Reaction Conditions ◽  
The Relationship ◽  
Equilibrium Calculations

Chemical Equilibrium reviews the principles of equilibrium in systems of gases and liquids, starting with the concepts of reversible and irreversible reactions and dynamic equilibrium. The equilibrium constant (K) and reaction quotient (Q) are described, and comparison of K and Q is used to determine the direction in which a reaction must proceed to reach equilibrium. Calculations involving K in terms of concentration and pressure are presented. The relationship between the magnitude of K, the equilibrium position and the concentrations of reactants and products is discussed for both homogeneous and heterogeneous equilibria. The chapter ends with a qualitative treatment of equilibrium based on Le Chatelier’s principle, as well as how changes in reaction conditions can disturb a chemical equilibrium and how the chemical reaction responds to those changes.

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