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Journal articles on the topic 'Gibbs free energy minimization'

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Published: 4 June 2021

Last updated: 31 January 2023

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1

Koukkari, Pertti, and Risto Pajarre. "A Gibbs energy minimization method for constrained and partial equilibria." Pure and Applied Chemistry 83, no. 6 (May 4, 2011): 1243–54. http://dx.doi.org/10.1351/pac-con-10-09-36.

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The conventional Gibbs energy minimization methods apply elemental amounts of system components as conservation constraints in the form of a stoichiometric conservation matrix. The linear constraints designate the limitations set on the components described by the system constituents. The equilibrium chemical potentials of the constituents are obtained as a linear combination of the component-specific contributions, which are solved with the Lagrange method of undetermined multipliers. When the Gibbs energy of a multiphase system is also affected by conditions due to immaterial properties, the constraints must be adjusted by the respective entities. The constrained free energy (CFE) minimization method includes such conditions and incorporates every immaterial constraint accompanied with its conjugate potential. The respective work or affinity-related condition is introduced to the Gibbs energy calculation as an additional Lagrange multiplier. Thus, the minimization procedure can include systemic or external potential variables with their conjugate coefficients as well as non-equilibrium affinities. Their implementation extends the scope of Gibbs energy calculations to a number of new fields, including surface and interface systems, multi-phase fiber suspensions with Donnan partitioning, kinetically controlled partial equilibria, and pathway analysis of reaction networks.

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2

Koukkari, Pertti, Risto Pajarre, and Peter Blomberg. "Reaction rates as virtual constraints in Gibbs energy minimization." Pure and Applied Chemistry 83, no. 5 (April 4, 2011): 1063–74. http://dx.doi.org/10.1351/pac-con-10-09-09.

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The constrained Gibbs energy method has been developed for the use of immaterial entities in the formula conservation matrix of the Gibbs energy minimization problem. The new method enables the association of the conservation matrix with structural, physical, chemical, and energetic properties, and thus the scope of free energy calculations can be extended beyond the conventional studies of global chemical equilibria and phase diagrams. The use of immaterial constraints enables thermochemical calculations in partial equilibrium systems as well as in systems controlled by work factors. In addition, they allow the introduction of mechanistic reaction kinetics to the Gibbsian multiphase analysis. The constrained advancements of reactions are incorporated into the Gibbs energy calculation by using additional virtual phases in the conservation matrix. The virtual components are then utilized to meet the incremental consumption of reactants or the formation of products in the kinetically slow reactions. The respective thermodynamic properties for the intermediate states can be used in reaction rate formulations, e.g., by applying the reaction quotients.

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3

Hemmati, Sh, G. R. Pazuki, M. Vossoughi, Y. Saboohi, and N. Hashemi. "Supercritical Gasification of Biomass: Thermodynamics Analysis with Gibbs Free Energy Minimization." Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 34, no. 2 (November 30, 2011): 163–76. http://dx.doi.org/10.1080/15567030903581510.

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4

Rau, Advaith V., Ken Knott, and Kathy Lu. "Porous SiOC/SiC ceramics via an active-filler-catalyzed polymer-derived method." Materials Chemistry Frontiers 5, no. 17 (2021): 6530–45. http://dx.doi.org/10.1039/d1qm00705j.

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Effects of Fe and POSS on the phase formation of SiOC between 1100 °C and 1500 °C were studied. Fe induces higher SiO2 and SiC contents. Phase contents are calculated based on a modified Gibbs free energy minimization method.

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5

Venkatraman, Ashwin, Larry W. Lake, and Russell T. Johns. "Gibbs Free Energy Minimization for Prediction of Solubility of Acid Gases in Water." Industrial & Engineering Chemistry Research 53, no. 14 (March 25, 2014): 6157–68. http://dx.doi.org/10.1021/ie402265t.

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6

Sarkar, Rahul, Pramod Gupta, Somnath Basu, and Nidambur Bharath Ballal. "Dynamic Modeling of LD Converter Steelmaking: Reaction Modeling Using Gibbs’ Free Energy Minimization." Metallurgical and Materials Transactions B 46, no. 2 (January 7, 2015): 961–76. http://dx.doi.org/10.1007/s11663-014-0245-2.

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7

Chaikunchuensakun, Satok, Leonard I. Stiel, and Ernest L. Baker. "A Combined Algorithm for Stability and Phase Equilibrium by Gibbs Free Energy Minimization." Industrial & Engineering Chemistry Research 41, no. 16 (August 2002): 4132–40. http://dx.doi.org/10.1021/ie011030t.

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8

Néron, A., G. Lantagne, and B. Marcos. "Computation of complex and constrained equilibria by minimization of the Gibbs free energy." Chemical Engineering Science 82 (September 2012): 260–71. http://dx.doi.org/10.1016/j.ces.2012.07.041.

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9

Tang, Huiqing, and Kuniyuki Kitagawa. "Supercritical water gasification of biomass: thermodynamic analysis with direct Gibbs free energy minimization." Chemical Engineering Journal 106, no. 3 (February 2005): 261–67. http://dx.doi.org/10.1016/j.cej.2004.12.021.

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10

Nie, J. L., L. Ao, F. A. Zhao, M. Jiang, and X. T. Zu. "A first-principles study of bulk aluminum at high pressure." Canadian Journal of Physics 93, no. 8 (August 2015): 825–29. http://dx.doi.org/10.1139/cjp-2014-0616.

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Using ab initio total energy calculations based on density functional theory and a procedure based on minimization of the Gibbs free energy, we calculate the Gibbs free energy for face-centered cubic and hexagonal close-packed aluminum in the temperature range from 0 to 900 K. It is shown that at zero temperature an fcc → hcp phase transition occurs at 181 GPa, and when the temperature is increased to 900 K the phase transition pressure increases slightly. As the pressure increases, the Grüneisen parameter first decreases significantly, then increase sharply at the phase transition pressure, and finally decrease again with further increasing volume compressibility. It turns out that the temperature and pressure have considerable effects on the Grüneisen parameter in certain ranges.

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11

Pan, Huanquan, and Abbas Firoozabadi. "Complex Multiphase Equilibrium Calculations by Direct Minimization of Gibbs Free Energy by Use of Simulated Annealing." SPE Reservoir Evaluation & Engineering 1, no. 01 (February 1, 1998): 36–42. http://dx.doi.org/10.2118/37689-pa.

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Summary The computational problems in reservoir fluid systems are mainly in the critical region and in liquid-liquid (LL), vapor-liquid-liquid (VLL), and higher-phase equilibria. The conventional methods to perform phase-equilibrium calculations with the equality of chemical potentials cannot guarantee a correct solution. In this study, we propose a simple method to calculate the equilibrium state by direct minimization of the Gibbs free energy of the system at constant temperature and pressure. We use the simulated annealing (SA) algorithm to perform the global minimization. Estimates of key parameters of the SA algorithm are also made for phase-behavior calculations. Several examples, including (1) VL equilibria in the critical region, (2) VLL equilibria for reservoir fluid systems, (3) VLL equilibria for an H2S-containing mixture, and (4) VL-multisolid equilibria for reservoir fluids, show the reliability of the method. Introduction Consider the multicomponent-multiphase flash at constant temperature and pressure sketched in Fig. 1. The equilibrium state (the right side of Fig. 1) consists of np phases; each Phase j consists of n1j,n2j,n3j,. . . nncj, moles. From the second law of thermodynamics, the equilibrium state is a state in which the Gibbs free energy of the system is a minimum. The minimum of Gibbs free energy is a sufficient and necessary condition for the equilibrium state. At constant temperature and pressure (note that all calculations will be performed at this condition), the Gibbs free energy of the system in Fig. 1 can be written asEquation 1 where Gj is the Gibbs free energy of Phase j, and G is the total Gibbs free energy of the system. When G is minimized with respect to nij (i=1, 2, . . ., nc; j=1, 2, . . ., np) subject to the following constraints:material balance of Component i,Equation 2the non-negative mole number of Component i in Phase j,Equation 3 The optimized values, ni(i=1, 2, . . ., nc; j=1, 2, . . ., np) are the mole numbers of the equilibrium state. The global minimization with the constraints is difficult to implement; as a consequence, direct minimization of the Gibbs free energy has not been widely applied. Conventional Approach for Phase-Equilibrium Calculations The equality of chemical potentials of each species in all phases is often used to perform the phase-equilibrium calculations:Equation 4 The number of equations in Eq. 4 is nc×(np-1), plus nc material-balance equations given by Eq. 2; a total of nc×np equations are provided. The mole numbers nij (i=1, 2, . . ., nc; j=1, 2, . . ., np) of the equilibrium state are determined by solving these nc×np nonlinear equations. The widely used solution methods are the successive substitution method through phase-equilibrium constants Ki (i=1, 2, . . ., nc) and direct application of the Newton method. Both approaches require an initial guess and work quite well for VL equilibria except in the near-critical region. In the critical region, the successive substitution becomes intolerably slow and the Newton method may fail when the initial guess is not close to the true solution. In LL and VLL equilibria, both methods may compute false solutions. The falseness is because Eq. 4 is only a necessary condition for an equilibrium state.1 The tangent-plane-distance (TPD) approach has been introduced to recognize the false solution.1,2 The concept of stability analysis is used to derive the TPD. Tangent-Plane-Distance Approach Suppose w is a given overall composition. The mathematical expression of the TPD function isEquation 5a where D(u) is the distance function between the Gibbs free energy surface and its tangent plane at composition w. When D(u) is minimized with respect to ui(i=1, 2, . . ., nc) subject toEquations 5b and 5c the optimized value, D*, provides the stability analysis of the mixture at composition w. If D* 0, the system is absolutely stable; if D*<0, the system is unstable. The optimized composition u* is a good approximation of the incipient phase composition. The application of TPD criterion improves the reliability of conventional-phase equilibrium by providing a guideline to judge that the mixture is absolutely stable. When unstable, a good initial composition u* strengthens the convergence of the Newton or the successive substitution methods. Unfortunately, the solution to Eq. 5 is also an optimization problem with constraints. Michelson2 has solved the problem by locating the stationary points of the TPD function. This approach needs to solve (nc-1) nonlinear equations. A good initial guess is required to avoid the trivial solution. Because not all stationary points can be found with this method, phase stability cannot always be guaranteed.3 Later, we will give an example of a CO2-crude system for which the approach of locating the stationary points misses the true solution in spite of its novelty and strengths. Several methods have been proposed to improve the calculation of the TPD function. These include homotopy-continuation,4 branch and bound3 and differential geometry, and the theory of differential equations.5

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12

Silva, W. L., J. C. T. Ribeiro, E. F. da Costa Jr, and A. O. S. da Costa. "Reduction efficiency prediction of CENIBRA's recovery boiler by direct minimization of gibbs free energy." Brazilian Journal of Chemical Engineering 25, no. 3 (September 2008): 603–11. http://dx.doi.org/10.1590/s0104-66322008000300017.

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13

Khudolozhkin, V. O., and O. I. Sharova. "Oxygen regime of granulite metamorphism: Modeling by the method of Gibbs free energy minimization." Petrology 19, no. 1 (January 2011): 102–8. http://dx.doi.org/10.1134/s0869591110061013.

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14

DU, P. C., and G. A. MANSOORI. "PHASE EQUILIBRIUM OF MULTICOMPONENT MIXTURES: CONTINUOUS MIXTURE GIBBS FREE ENERGY MINIMIZATION AND PHASE RULE." Chemical Engineering Communications 54, no. 1-6 (May 1987): 139–48. http://dx.doi.org/10.1080/00986448708911903.

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15

Saxena, S. K. "Earth mineralogical model: Gibbs free energy minimization computation in the system MgOFeOSiO2." Geochimica et Cosmochimica Acta 60, no. 13 (July 1996): 2379–95. http://dx.doi.org/10.1016/0016-7037(96)00096-8.

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16

van den Berg, Adinda, Luc Dupre, Ben Van de Wiele, and Guillaume Crevecoeur. "A Mesoscopic Hysteresis Model Based on the Unconstrained Minimization of the Gibbs Free Energy." IEEE Transactions on Magnetics 46, no. 2 (February 2010): 220–23. http://dx.doi.org/10.1109/tmag.2009.2031978.

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17

JEREZ, I. J., F. MUÑOZ, and J. M. GOMEZ. "APPROACH TO A RELIABLE SOLUTION STRATEGY FOR PERFORMING PHASE EQUILIBRIUM CALCULATIONS USING MINLP OPTIMIZATION." Latin American Applied Research - An international journal 44, no. 1 (January 31, 2014): 63–70. http://dx.doi.org/10.52292/j.laar.2014.420.

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The objective of this contribution is to propose a reliable strategy to solver the problem of phase equilibrium calculations for non-ideal systems, using the Gibbs free energy minimization. This type of problem, using the Gibbs free energy minimization, is usually formulated as a Mixed Integer NonLinear Programming (MINLP) Optimization. This optimization problem allows the compositions to be associated with continuous variables, and the presence of phases in the equilibrium to be associated with the integer variables. The solution strategy proposes a bi-level approach. The first level combines a stochastic (Simulated Annealing – SA) and a local deterministic algorithm (Sequential Quadratic Programming – SQP), and solves a Non Linear Programming Problem (NLP). The continuous variables are considered at this level. The second level considers the integer variables. The advantage of this bilevel strategy lies in its easy implementation and in its proven efficiency to locate global optima with acceptable computational load. This article includes the study of the Water-Ethanol-Cyclohexane and Water-Ethanol-Glycerin systems. A comparative analysis was conducted using experimental data reported in published works and theoretical calculations by means of the Gamma-Phi classic method.

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18

Nichita, Dan Vladimir, Susana Gomez, and Eduardo Luna. "Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method." Computers & Chemical Engineering 26, no. 12 (December 2002): 1703–24. http://dx.doi.org/10.1016/s0098-1354(02)00144-8.

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19

Rossi, C. C. R. S., L. Cardozo-Filho, and R. Guirardello. "Gibbs free energy minimization for the calculation of chemical and phase equilibrium using linear programming." Fluid Phase Equilibria 278, no. 1-2 (April 2009): 117–28. http://dx.doi.org/10.1016/j.fluid.2009.01.007.

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20

Protasov, O. N., N. A. Mamonov, M. N. Mikhailov, and L. M. Kustov. "Optimization of equilibrium carbon dioxide methane reforming parameters by the Gibbs free energy minimization method." Russian Journal of Physical Chemistry A 86, no. 5 (April 4, 2012): 741–46. http://dx.doi.org/10.1134/s0036024412050305.

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21

Rodriguez Gamboa, Alexander Alberto, Joao Andrade Carvalho Junior, and Ana Maura Araujo Rocha. "Calculation of Tyre Pyrolytic Oil Combustion Products Using the Method of Gibbs Free Energy Minimization." IEEE Latin America Transactions 15, no. 6 (June 2017): 1077–83. http://dx.doi.org/10.1109/tla.2017.7932695.

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22

Teh, Y. S., and G. P. Rangaiah. "A Study of Equation-Solving and Gibbs Free Energy Minimization Methods for Phase Equilibrium Calculations." Chemical Engineering Research and Design 80, no. 7 (October 2002): 745–59. http://dx.doi.org/10.1205/026387602320776821.

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23

Gómez-García, Miguel-Ángel, Izabela Dobrosz-Gómez, and Jacek Rynkowski. "Learning on chemical equilibrium shift assessment for membrane reactors using Gibbs free energy minimization method." Education for Chemical Engineers 22 (January 2018): 20–26. http://dx.doi.org/10.1016/j.ece.2017.10.003.

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24

Sun, Amy C., and Warren D. Seider. "Homotopy-continuation method for stability analysis in the global minimization of the Gibbs free energy." Fluid Phase Equilibria 103, no. 2 (February 1995): 213–49. http://dx.doi.org/10.1016/0378-3812(94)02579-p.

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25

Martínez, Jeremías, María Antonieta Zúñiga-Hinojosa, and Richard Steve Ruiz-Martínez. "A Thermodynamic Analysis of Naphtha Catalytic Reforming Reactions to Produce High-Octane Gasoline." Processes 10, no. 2 (February 6, 2022): 313. http://dx.doi.org/10.3390/pr10020313.

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The catalytic naphtha reforming process is key to producing high-octane gasoline. Dozens of components are involved in this process in hundreds of individual catalytic reactions. Calculations of concentrations at equilibrium, using equilibrium constants, are commonly performed for a small number of simultaneous reactions. However, the Gibbs free energy minimization method is recommended for the solution of complex reaction systems. This work aims to analyze, from the point of view of thermodynamic equilibrium, the effect of temperature, pressure, and the H2/HC ratio on the reactions of the catalytic reformation process and evaluate their impact on the production of high-octane gasoline. Gibbs’s free energy minimization method was used to evaluate the molar concentrations at equilibrium. The results were compared with those obtained in the simulation of a catalytic reforming process to evaluate the optimal conditions under which the process should operate.

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26

Souza, A. T., L. Cardozo-Filho, F. Wolff, and R. Guirardello. "Application of interval analysis for gibbs and helmholtz free energy global minimization in phase stability analysis." Brazilian Journal of Chemical Engineering 23, no. 1 (March 2006): 117–24. http://dx.doi.org/10.1590/s0104-66322006000100013.

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27

Khonde, Ruta, Shubham Hedaoo, and Samir Deshmukh. "Prediction of product gas composition from biomass gasification by the method of Gibbs free energy minimization." Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 43, no. 3 (May 31, 2019): 371–80. http://dx.doi.org/10.1080/15567036.2019.1624890.

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28

Zhou, Zhenyu, and Cong Luo. "Dynamic Study on Vanadium Extraction Process in Basic Oxygen Furnance: Modeling Based on Gibbs’ Free Energy Minimization." Metals 12, no. 4 (April 2, 2022): 612. http://dx.doi.org/10.3390/met12040612.

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Vanadium extraction process demands low residual vanadium and carbon loss, and variations of dissolved elements in hot metal must be determined to achieve it. A three parts dynamic model that applies the concept of Gibbs’ free energy minimization at the slag–metal interface is proposed. Modeling simulation results shows good uniformity with plant experimental data, and the presented model can describe the vanadium extraction process in BOF qualitatively well. The effects of coolant addition and oxygen flow rate have been studied by modeling. The lack of coolant will reduce (FeO) content and elevate the molten bath temperature, which are harmful to deep vanadium removal with less carbon loss in semi-steel. The excessive oxygen flow rate has little effect on residual [V], and there is more carbon loss because of higher (FeO) content and molten bath temperature.

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29

GWIZDAŁŁA, TOMASZ M. "THE ISING MODEL STUDIED USING EVOLUTIONARY APPROACH." Modern Physics Letters B 19, no. 04 (February 28, 2005): 169–79. http://dx.doi.org/10.1142/s0217984905008153.

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Evolutionary algorithms are very powerful techniques for the search of global minima. In this work we want to present the evolutionary approach to the one of the most fundamental problems of solid state magnetism: the Ising model. For the samples built in the most simple way, i.e. only from the ±1 spins, various temperature characteristics coming from the minimization of Gibbs free energy with entropy calculated from the pair approximation are shown. The calculations have been performed for samples of different magnitude which allowed the consideration of finite size effects.

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30

Eremin, Oleg, Olga Rusal, Maria Solodukhina, Ekaterina Epova, and Georgy Yurgenson. "Thermodynamic equilibria of tailings dump pond water of Sherlovaya Gora tin-polymetallic deposit (Transbaikalia)." E3S Web of Conferences 98 (2019): 01014. http://dx.doi.org/10.1051/e3sconf/20199801014.

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The potential toxic elements (Be, U, As, Cd, Pb, Sb, Bi) were detected for mine landscape of Sherlovaya Gora tin-polymetallic deposit. Thermodynamic calculation of equilibrium for tailings dump pond water was carried out by means of “Selektor” program complex based on Gibbs free energy minimization algorithm at 25°C and 1 bar total pressure. It turned out that the mine water is supersaturated with respect to many sulphates of Ca, Mg, Sr, Zn, K, Cu, Ni, Cd, Be, Al, Ce and Y, fluorides of (Ln and Y, Sc), and Y phosphate.

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31

Sun, Lan Yi, Yong Duo Liu, Hui Zhou, and Qing Song Li. "Conceptual Design of a Coke Dry Quenching Gasification Technology." Advanced Materials Research 219-220 (March 2011): 416–19. http://dx.doi.org/10.4028/www.scientific.net/amr.219-220.416.

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In this paper, a coke dry quenching gasification (CDQG) technology using coke oven gas (COG) and steam to quench the incandescent coke is proposed. The distinct advantages of this technology include energy conservation, pollution reduction, and improvement of coke quality and full use of resources. Based on Gibbs free energy minimization principle, the flow rate and composition of the syngas could be calculated. At the same time, the impact of the flow rate of the COG on the flow rate and composition of the syngas and the exergy efficiency are analyzed. Finally, the flow rate of the COG is prudently chosen to make thermodynamic analysis of the process.

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32

Yan, Qiu Hui, Dong Zhang, Yan Ren, Xie Liu, and Xiao Hong Nan. "Simulate and Analyze of Biomass Gasification in Supercritical Water." Advanced Materials Research 803 (September 2013): 90–93. http://dx.doi.org/10.4028/www.scientific.net/amr.803.90.

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On the basis of ASPEN PLUS-based Gibbs free energy minimization, a biomass gasification model was modified by the restricted equilibrium of the RGIBBS reactor and developed and used to simulate glucose. It is showed that the simulation result and experiment result fit well. In the process of pomace gasification in supercritical water, a sensitivity analysis with temperature and pressure is performed and the research of the gas heating value has been done. From the analysis result, without using catalyst, the temperature has influenced on the gas product most and the pressure has little effect on gas product.

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33

YOON, HYOUNGJU. "THE PREDICTION OF pH BY GIBBS FREE ENERGY MINIMIZATION IN THE SUMP SOLUTION UNDER LOCA CONDITION OF PWR." Nuclear Engineering and Technology 45, no. 1 (February 2013): 107–14. http://dx.doi.org/10.5516/net.03.2011.051.

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34

Ujjwal, Utkarsh, Rahul Sikka, Balaji Gulgule, Tanmay Taraphdar, and M. K. E. Prasad. "Application of Gibbs Free Energy Minimization method using Spreadsheets to Predict Equilibrium Conversions in a Claus Reaction Furnace." i-manager's Journal on Future Engineering and Technology 7, no. 3 (April 15, 2012): 48–57. http://dx.doi.org/10.26634/jfet.7.3.1801.

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35

Fateen, Seif-Eddeen K., and Adrián Bonilla-Petriciolet. "Unconstrained Gibbs Free Energy Minimization for Phase Equilibrium Calculations in Nonreactive Systems, Using an Improved Cuckoo Search Algorithm." Industrial & Engineering Chemistry Research 53, no. 26 (June 23, 2014): 10826–34. http://dx.doi.org/10.1021/ie5016574.

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36

Huang, Y. W., M. Q. Chen, and J. J. Song. "Effect of torrefaction on the high temperature steam gasification of cellulose based upon the Gibbs free energy minimization." Energy Procedia 142 (December 2017): 603–8. http://dx.doi.org/10.1016/j.egypro.2017.12.100.

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37

Sharma, Vikrant, and Vijay Kumar Agarwal. "Equilibrium Modeling and Optimization for Gasification of High-Ash Indian Coals by the Gibbs Free Energy Minimization Method." Process Integration and Optimization for Sustainability 3, no. 4 (June 8, 2019): 487–504. http://dx.doi.org/10.1007/s41660-019-00094-7.

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38

Demidov, D. V., I. V. Mishin, and M. N. Mikhailov. "Gibbs free energy minimization as a way to optimize the combined steam and carbon dioxide reforming of methane." International Journal of Hydrogen Energy 36, no. 10 (May 2011): 5941–50. http://dx.doi.org/10.1016/j.ijhydene.2011.02.053.

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39

Sreejith, C. C., P. Arun, and C. Muraleedharan. "Thermochemical Analysis of Biomass Gasification by Gibbs Free Energy Minimization Model—Part: I (Optimization of Pressure and Temperature)." International Journal of Green Energy 10, no. 3 (March 16, 2013): 231–56. http://dx.doi.org/10.1080/15435075.2011.653846.

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40

Andre, P., M. Abbaoui, R. Bessege, and A. Lefort. "Comparison between Gibbs free energy minimization and mass action law for a multitemperature plasma with application to nitrogen." Plasma Chemistry and Plasma Processing 17, no. 2 (June 1997): 207–17. http://dx.doi.org/10.1007/bf02766816.

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41

Venkatraman, Ashwin, Birol Dindoruk, Hani Elshahawi, Larry W. Lake, and Russell T. Johns. "Modeling Effect of Geochemical Reactions on Real-Reservoir-Fluid Mixture During Carbon Dioxide Enhanced Oil Recovery." SPE Journal 22, no. 05 (April 10, 2017): 1519–29. http://dx.doi.org/10.2118/175030-pa.

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Summary Carbon dioxide (CO2) injection in oil reservoirs has the dual benefit of enhancing oil recovery from declining reservoirs and sequestering a greenhouse gas to combat climate change. CO2 injected in carbonate reservoirs, such as those found in the Middle East, can react with ions present in the brine and the solid calcite in the carbonate rocks. These geochemical reactions affect the overall mole numbers and, in some extreme cases, even the number of phases at equilibrium, affecting oil-recovery predictions obtained from compositional simulations. Hence, it is important to model the effect of geochemical reactions on a real-reservoir-fluid mixture during CO2 injection. In this study, the Gibbs free-energy function is used to integrate phase-behavior computations and geochemical reactions to find equilibrium composition. The Gibbs free-energy minimization method by use of elemental-balance constraint is used to obtain equilibrium composition arising out of phase and chemical equilibrium. The solid phase is assumed to be calcite, the hydrocarbon phases are characterized by use of the Peng-Robinson (PR) equation of state (EOS) (Robinson et al. 1985), and the aqueous-phase components are described by use of the Pitzer activity-coefficient model (Pitzer 1973). The binary-interaction parameters for the EOS and the activity-coefficient model are obtained by use of experimental data. The effect of the changes in phase behavior of a real-reservoir fluid with 22 components is presented in this paper. We observe that the changes in phase behavior of the resulting reservoir-fluid mixture in the presence of geochemical reactions depend on two factors: the volume ratio (and hence molar ratio) of the aqueous phase to the hydrocarbon phase and the salinity of the brine. These changes represent a maximum effect of geochemical reactions because all reactions are assumed to be at equilibrium. This approach can be adapted to any reservoir brine and hydrocarbon as long as the initial formation-water composition and their Gibbs free energy at standard states are known. The resultant model can be integrated in any reservoir simulator because any algorithm can be used for minimizing the Gibbs free-energy function of the entire system.

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42

Moon, K., and Ganesh R. Kale. "Energy Analysis in Combined Reforming of Propane." Journal of Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/301265.

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Combined (steam and CO2) reforming is one of the methods to produce syngas for different applications. An energy requirement analysis of steam reforming to dry reforming with intermediate steps of steam reduction and equivalent CO2addition to the feed fuel for syngas generation has been done to identify condition for optimum process operation. Thermodynamic equilibrium data for combined reforming was generated for temperature range of 400–1000°C at 1 bar pressure and combined oxidant (CO2+ H2O) stream to propane (fuel) ratio of 3, 6, and 9 by employing the Gibbs free energy minimization algorithm of HSC Chemistry software 5.1. Total energy requirement including preheating and reaction enthalpy calculations were done using the equilibrium product composition. Carbon and methane formation was significantly reduced in combined reforming than pure dry reforming, while the energy requirements were lower than pure steam reforming. Temperatures of minimum energy requirement were found in the data analysis of combined reforming which were optimum for the process.

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Luo, T., and A. Yu Chirkov. "Thermodynamic Property Calculation in Vapor-Liquid Equilibrium for Multicomponent Mixtures using Highly Accurate Helmholtz Free Energy Equation of State." Herald of the Bauman Moscow State Technical University. Series Mechanical Engineering, no. 3 (138) (September 2021): 108–21. http://dx.doi.org/10.18698/0236-3941-2021-3-108-121.

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Thermodynamic properties of multicomponent mixtures in phase equilibrium were studied. The tangent plane criterion was used for stability analysis, and the Gibbs energy minimization was employed for phase equilibrium calculation when the successive substitution didn't converge. Thermodynamic properties of a 12-component natural gas mixture in vapor-liquid equilibrium were calculated with highly accurate Helmholtz free energy equation of state GERG--2008, simplified GERG--2008 and common cubic Peng --- Robinson (PR) equation of state. Results show that in vapor-liquid equilibrium, GERG--2008 has high accuracy and works better than simplified GERG--2008 and PR-equation of state. Simplified GERG--2008 and PR-equation of state both work unsatisfactorily in vapor-liquid equilibrium calculation, especially near the saturation zone. The deviation function in GERG--2008 can significantly affect the accuracy of GERG--2008 when calculating thermodynamic properties of mixtures in vapor-liquid equilibrium

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Zheng, Yu Xin, Zhi Hua Wang, Xue Hong Wu, and Yan Li Lv. "Numerical Simulation of the Methanol Synthesis Process by Using HT-L Pulverized Coal Gasification." Advanced Materials Research 1090 (February 2015): 163–66. http://dx.doi.org/10.4028/www.scientific.net/amr.1090.163.

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The numerical simulation of the methanol synthesis process by using HT-L pulverized coal gasification is studied in the work. Pulverized coal gasification are simulated by Aspen Plus industrial systems flower software, and the optimum condition can be gained by calculation. The pulverized coal entrained-flow gasifier adopts the minimization method of Gibbs free energy. Under the given conditions of 1500°C and carbon conversion of 99%, when coal flow volume is 3265.87 kg/h and the ratio of air and coal is 4:1, the content of effective gas is maximal, and also the content of effective gas increased with increasing of the pressure.

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Vujovic, Velibor. "Determining the composition of high temperature combustion products of fossil fuel based on variational principles and geometric programming." Thermal Science 15, no. 1 (2011): 125–34. http://dx.doi.org/10.2298/tsci100928007v.

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This paper presents the algorithm and results of a computer program for calculation of complex equilibrium composition for the high temperature fossil fuel combustion products. The method of determining the composition of high temperatures combustion products at the temperatures appearing in the open cycle MHD power generation is given. The determination of combustion product composition is based on minimization of the Gibbs free energy. The number of equations to be solved is reduced by using variational principles and a method of geometric programming and is equal to the sum of the numbers of elements and phases. A short description of the computer program for the calculation of the composition and an example of the results are also given.

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Lima da Silva, Aline, and Iduvirges Lourdes Müller. "Operation of solid oxide fuel cells on glycerol fuel: A thermodynamic analysis using the Gibbs free energy minimization approach." Journal of Power Sources 195, no. 17 (September 2010): 5637–44. http://dx.doi.org/10.1016/j.jpowsour.2010.03.066.

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Bonilla-Petriciolet, Adrián, Gade Pandu Rangaiah, and Juan Gabriel Segovia-Hernández. "Constrained and unconstrained Gibbs free energy minimization in reactive systems using genetic algorithm and differential evolution with tabu list." Fluid Phase Equilibria 300, no. 1-2 (January 2011): 120–34. http://dx.doi.org/10.1016/j.fluid.2010.10.024.

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Costa, Andréa O. S., Evaristo C. Biscaia, and Enrique L. Lima. "Chemical Composition Determination at the Bottom Region of a Recovery Boiler Furnace by Direct Minimization of Gibbs Free Energy." Canadian Journal of Chemical Engineering 83, no. 3 (May 19, 2008): 477–84. http://dx.doi.org/10.1002/cjce.5450830310.

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de Oliveira, João F., Marcos L. Corazza, and Fernando A. P. Voll. "Thermodynamic Analysis of Municipal Solid Waste Gasification Under Isothermal and Adiabatic Conditions by a Gibbs Free Energy Minimization Model." Waste and Biomass Valorization 10, no. 5 (January 11, 2018): 1383–93. http://dx.doi.org/10.1007/s12649-017-0190-9.

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Wardach-Świȩcicka, Izabela, and Dariusz Kardaś. "Prediction of Pyrolysis Gas Composition Based on the Gibbs Equation and TGA Analysis." Energies 16, no. 3 (January 20, 2023): 1147. http://dx.doi.org/10.3390/en16031147.

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Conventional methods used to determine pyrolysis gas composition are based on chemical kinetics. The mechanism of those reactions is often unknown, which makes the calculations more difficult. Solving complex chemical reactions’ kinetics involving a nonlinear set of equations is CPU time demanding. An alternative approach is based on the Gibbs free energy minimization method. It requires only the initial composition and operation parameters as the input data, for example, temperature and pressure. In this paper, the method for calculating the pyrolytic gas composition from biogenic fuels has been presented, and the thermogravimetric experimental results have been adopted to determine the total gas yield. The studied problem has been reduced to the optimization method with the use of the Lagrange multipliers. This solution procedure is advantageous since it does not require knowledge of the reaction mechanism. The obtained results are in good agreement with experimental data, demonstrating the usefulness of the proposed method.

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