Equilibrium Constant Method Research Articles

Effect of Equivalence Ratio on Composition and performance of Biogas and Gasoline Exhaust from Spark Ignition Engine by Mathematical Modeling

This paper presents the numerical computationnal of pressure, temperature and exhaust characteristics of spark ignition engine with biogas as fuel. The solution of non-linear combustion equation systems have been computed, that based on a quasi-one-dimensional engine model, high order iteration method with the equilibrium constants method. Computer program was used to calculate the mole fractions of 10 combustion products when biogas and gasoline fuel are burnt along with variable equivalence ratios. In cylinder chamber model is based on the classical two-zone approach, wherein parameters like heat transfer from the cylinder, blow by energy loss and heat release rate are also considered and calculated. Biogas is defined as fuel produced from using anaerobic digestion of biodegradable or waste materials and the constituents are C 5 H 7 O 2 N, CH 4 , CO 2 N 2 H 2 O of biogas and C 7 H1 7 of gosoline. Which general fuel model is specified by way of its C a H b O c N d values. The curve-fitted coefficients of energy were then employed to simulate air and fuels data along with frozen composition and practical chemical equilibrium routines from Gill data. The calculated data were used to plot the various pressure and temperature with the crank angle of each step of four stroke engine cycle and combustion products versus equivalence ratio. All results were compared with gasoline as reference fuel in the spark ignition engine according to the same numerical method.

Evaluation method of iodine re-evolution from an in-containment water pool after a loss of coolant accident, Part I: pH estimation of a solution with various chemicals

Radioactive iodine, which is released into the atmosphere of the containment building, is absorbed into the containment spray water and dissolved to be ionized. This iodine-rich water is then transported to the in-containment refueling water storage tank (IRWST) in APR1400 nuclear power plants. When the pH of the water is below 7, the dissolved iodine converts to molecular iodine and re-evolves from the water and returns to the atmosphere. A series of studies have been conducted in order to evaluate the iodine re-evolution from the IRWST. This study consists of two parts: the pH evaluation method and the evaluation of the iodine re-evolution. This paper presents the first part, i.e. the pH evaluation method. The equilibrium concentrations of various chemicals in a solution are determined at the minimum Gibbs’ free energy. This method is useful for complex reactant problems rather than equilibrium constants method because the latter method requires numerous equilibrium constants and there might be missing equilibrium constants associated with the solution. The calculated pH values of solutions are compared with the experimental measurements in order to validate this method and the thermodynamic data of the chemicals incorporated into the program. The estimated values for solutions are in good agreement with the experimental measurements within a difference of less than 3.3%.

Haber process and steam‐coal gasification: Two standard thermodynamic problems elucidated using two distinct approaches

ABSTRACTThe present study shows how the direct Gibbs free energy minimization technique is sometimes superior to the reaction coordinates—equilibrium constants method when the thermodynamic analysis of complex systems is performed. In this respect, the above two methods are applied for two different processes to determine their equilibrium compositions: (1) the Haber process: a simple problem consisting of a single gas‐phase reaction where both methods are expected to give the same result and (2) steam‐coal gasification process which is more complex since it involves numerous reactions and solid‐phase chemical species (i.e., coal or carbon). Thus, in the second case the reaction coordinates—equilibrium constants method fails to provide correct predictions of the equilibrium composition. In addition, the authors give the optimum conditions for the two processes: high pressure for Haber process and high temperature for steam‐coal gasification in agreement with LeChatelier principle. In order to deal with deviation from the ideal‐case assumption, the Peng–Robinson Equation of State (PR EOS) is implemented for both techniques and both case studies. All computations and figures are generated using a single computer algebra, Mathematica©. © 2015 Wiley Periodicals, Inc. Comput. Appl. Eng. Educ. 24:58–70, 2016; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21672

Numerical investigation of exhaust gas emissions for a dual fuel engine configuration using diesel and pongamia oil

The investigation presented in this paper focuses on determination of gaseous exhaust emissions by computational simulation during combustion in compression ignition engine with pongamia oil substitution. Combustion is modeled using Equilibrium Constants Method (ECM) with MATLAB program to calculate the mole fraction of 10 combustion products when pongamia oil is burnt along with diesel at variable equivalence ratio and blend ratio. It had been observed that pongamia oil substitution causes decrease in the CO emission and increase in the NOx emission as the blend ratio as well as equivalence ratio increases.

Carburisation layer evolution of Fe–Cr–Ni alloy in furnace after long term service: experimental study and numerical prediction

Owing to high temperature comprehensive properties, Fe–Cr–Ni alloys are designed to operate in corrosive gaseous environments of ethylene pyrolysis furnace. However, most premature failed tubes were caused by carburisation. In the present study, based on the Fick’s second law and equilibrium constant method, study on the carburised layer evolution of HP40Nb and KHR45A alloys by pack carburising experimental investigation and numerical simulation by MATLAB software were carried out. The results show that the experimental and simulated data agree with each other acceptably. The carburising layer rate of KHR45A alloy is much smaller than that of HP40Nb alloy due to higher contents of Cr and Ni element in the former. With increasing operating temperature ranging from 1000 to 1100°C, the maximum service lives of the two alloys sharply decrease.

A quasi-dimensional three-zone combustion model of the Diesel engine to calculate performances and emission using the Diesel-ethanol dual fuel

In the present study, develop the multi zone thermodynamic model for the simulation of a small diesel engine operating on the mixture of diesel and ethanol and comparing results with an experiment. This paper discussed analytically and provides data of nitrogen oxide and performance parameters such as power, speci20 Paramust Juntarakod and Thanakom Soontornchainacksaeng fic fuel consumption and thermal efficiency, indicated mean effective pressure. For this purpose, quasi-dimensional phenomenological three zone combustion process (unburned, adiabatic core region and boundary layer gas) has been modeled based on equilibrium constants method with MATLAB program to calculate the mole fractions of 11 combustion products when the new equilibrium constants function developed by Gill which are lowly-highly temperature dependent. To compute diesel engine cycles, zero-dimensional compression and expansion model have given by Ferguson and developed with new assumptions. These results involve various combination sequence effects of compression ratio (23-25), equivalence ratio (0.8-0.9), burn duration angle (60-70 CA) and engine speed (1000-1500 rpm) which volume fraction of fuel compositions (10-30% ethanol) (Diesel-Ethanol blend). The results of the study as the power was calculated by this method are the error range within around 5% or 0.5 kW from the maximum experiment results. The specific fuel consumption was less than 5% or 15-20 g (Fuel)/kW-hr from experiment results. The resulted show that nitrogen oxide has changed very little, corresponding results of various sequence effects. The performance parameters were changed with varying engine computing conditions. Maximum performance parameters be raised by increases the engine speed and equivalence ratio, its can increase the thermal efficiency are approximately value 15-20%.

Properties of thermodynamic equilibrium-based methane autothermal reforming to generate hydrogen

The characteristics of methane autothermal reforming to generate hydrogen were studied with thermodynamic equilibrium constant method. Results show that the methane steam reforming reaction is prone to backward at low temperature, and there is an inflection point temperature that the reaction turns forward. When steam–methane molar ratio is 2, the inflection point temperature increases with raising air–methane molar ratio. When air–methane molar ratio is 1, the inflection point temperature maintains between 700 and 800 K. Hydrogen yield increases firstly and then decreases with elevated temperature. The increase of air–methane molar ratio leads to a lower hydrogen production when temperature exceeds 1000 K. Increasing steam–methane molar ratio promotes the hydrogen production. Methane autothermal reforming occurs much more easily when temperature keeps at 1000 K and the molar ratio of air–methane and steam–methane is 1 and 2 respectively. Changing the steam–methane molar ratio can regulate H2/CO molar ratio.

Analysis of the Current Signature in a Constant-Volume Combustion Chamber

Identifying charged species and their relative concentrations as a function of initial mixture composition, temperature, and pressure can play an important role in the diagnostics and control of combustion devices. This article aims to identify important charged species and their temporal variation in a spark-ignited methane/air mixture using the equilibrium constant method. The equilibrium composition of 20 neutral and seven charged species [(e−), CHO+, H3O+, NO+, OH−, , O−] was obtained using a novel adaptation of the Newton–Raphson method for highly stiff nonlinear system of equations. A two-zone combustion model was used to study the effect of air–fuel ratio (AFR) on the temporal variation of charged species concentration. Temporal variation of the current computed from the equilibrium concentration of charged species was found to compare well with experimental data for several AFRs.

Equilibrium modeling and regression analysis of biomass gasification

In the perspective of fossil fuel depletion, global warming, climatic changes, and atmospheric pollution, the importance of renewable fuels is remarkable. Bio-hydrogen produced from locally available biomass is an efficient source of energy. For achieving hydrogen richness in gas mixture produced by thermo-chemical gasification of biomass, gasification agent used and its feed rate, and gasifier working conditions are prominent among many other factors. In the present work, formulation and simulation of a thermodynamic equilibrium model for biomass steam gasification, incorporating the yields of unconverted char and tar (in addition to gaseous products) based on equilibrium constant method is presented. The model is based on Redlich-Kwong real gas equation of state considering the equilibrium constants of two component reactions, namely methane formation and water gas shift. A generic method for the determination of equilibrium constants from the corresponding Gibbs free energy changes, incorporating real gas residual properties is adopted. Computations including solution of simultaneous non-linear equations are performed using Gauss–Newton algorithm. Producer gas composition, heating value of gas mixture (LHV), dry gas yield, and relative yields of gasification products are studied using apricot stones as the illustrative biomass material. Parametric variations with steam to biomass ratio (SBR) and temperature are analyzed and validated with reported experimental results on steam gasification. The richest hydrogen gas mixture (58.7% at SBR of 2.2) is predicted at 1000 K. SBR is found to be favorable to hydrogen concentration and combustible gas yield. But heating value (MJ/Nm3) can be enhanced with hike in temperature of gasification only. More than 45% (77% excluding steam) is dry gas in the products of gasification above 700 K. Regression analysis is performed using the data for thirty five biomass materials simulated by the real gas model. Based on the statistically tested regression model for accuracy, parametric correlations are formulated for LHV and product gas composition for steam gasification.

Dry reforming of methane - Review of feasibility studies

Starting from carbon dioxide and methane, the dry reforming of methane produces synthesis gas which is a mixture of hydrogen and carbon monoxide. Although this concept has many environmental and economic incentives, unfortunately, there are no commercial processes for dry reforming of methane. In this paper a review of feasibility studies is presented. Firstly, a comparison between the steam reforming and the dry reforming of methane is performed as well as a study of the production of methanol and sulfur-free diesel from the dry reforming of methane. Furthermore, a thermodynamic analysis is carried out by the method of equilibrium constants, for defining the thermodynamic limit and the optimum conditions.

Modeling of Carburization and Thermal Stress Analysis for Ethylene Cracking Furnace Tube

The ethylene cracking furnace tube is one of the most important components of an ethylene cracking furnace. Carburization of furnace tube is one of the most important causes which lead the tube to fail. In this paper, the model that describes diffusion of carbon and the precipitation of carbides was established based on Fick’ law and equilibrium constant method. The finite difference method was adopted to simulate the distribution of carbon concentration. By applying the model, the distribution of carbon concentration along thickness in HP-Nb tubes was predicted for the different service times. According to the temperature distribution of furnace tube, obtained by the analysis of heat transfer, the thermal stresses of the furnace tube with various carburization extents were analyzed by using the finite element code ABAQUS for the actual heating process of an ethylene cracking furnace. The analysis results show that the maximum circumferential thermal stress exists near the inner wall of the carburized tube, which usually causes cracking of the carburized tube along the longitudinal direction.

Computation of air chemical equilibrium composition until 30000K - Part I

An algorithm was developed to obtain the air chemical equilibrium composition. The air was considered to be composed of 79% N 2 and 21% O 2 , and the models are 5 chemical species, N 2 , O 2 , NO , N , O , NO+ , e-, respectively. The air chemical equilibrium composition is obtained through the equilibrium constants method and it was used the Absolute Newton method for convergence. The algorithm can be coupled as a subroutine into a Computational Fluid Dynamics code, given the flow field over an atmosphere reentry vehicle where, due to high velocities, dissociative chemical reactions and air ionization can occur. This work presents results of air chemical equilibrium composition for pressures of 1, 5, 10, 50 and 100 atm in a temperature range from 300 to 30000K.

Mathematical modeling on the effect of equivalence ratio in emission characteristics of compression ignition engine with hydrogen substitution

The investigation presented in this paper concerns on the computational simulation of emissions characteristics in compression ignition engine with hydrogen substitution. Combustion process has been modeled based on Equilibrium Constants Method (ECM) with MATLAB program to calculate the mole fractions of 18 combustion products when hydrogen is burnt along with diesel fuel at variable equivalence ratios. It can be observed that hydrogen substitution causes significant increase in NH 3, H 2, atom H emissions during rich combustion and OH, NO 2, HNO 3 emissions during lean combustion. As the equivalence ratio increases during rich combustion, mole fractions of HCN, CH 4, CO and atom C decreases with increment of hydrogen substitution. N 2, atom N and CO 2 emissions decrease whereas no significant changes in O 2, NO, O 3 and atom O emissions throughout all equivalence ratios as hydrogen is added to the combustion.

Thermodynamic analysis of combustion processes and pollutants emission using nonlinear optimization approach

AbstractMathematical formulation and modeling of combustion processes is an important tool in the understanding of this phenomenon. Determination of equilibrium temperature and composition is often the first stage in calculation of combustion characteristics. There are number of different techniques for simulation of combustion process. In this study a basic model has been developed based on the minimization of Gibb's free energy to simulate the combustion processes. A nonlinear mathematical optimization has been developed based on Lagrange multipliers and solved using Quasi‐Newton method written in MathCAD environment. The effect of various parameters such as initial temperature, pressure, and equivalence ratio on the equilibrium temperature and composition has been investigated. In contrast with the equilibrium constant method, obtained results out of this work show that the maximum flame temperature for normal paraffins occurs around the equivalence ratio of 1.05. In addition, from environmental point of view, effects of different conditions on the emission of pollutants in a combustion process have been studied. The simulation results showed that the NO and NO2 emission rates pass through a maximum point and there is an optimum point where the NOCO emission could be minimized. Copyright © 2010 Curtin University of Technology and John Wiley & Sons, Ltd.

Solving Chemical Equilibrium Problems Online

Analysis of chemical equilibria is a topic covered in both undergraduate and graduate courses such as physical chemistry, chemical thermodynamics, and engineering thermodynamics. Manual calculation of problems that require a student to solve for species concentrations, partial pressures, or mole fractions usually involves the method of equilibrium constants. Exercises in homework assignments or in-class examinations are frequently limited to reactions that involve no more than four gas-phase species as the resulting arithmetic required to solve for the unknown quantity becomes too cumbersome and prone to error. Students who invest the requisite time in manually solving complex equilibrium problems in homework assignments need a tool to verify their answers. A Java Web application (“applet”) has been developed to assist chemistry students who encounter general multiphase equilibrium problems involving many species. In addition to students, chemistry educators and professional researchers will benefit from a user-friendly and free-to-use software package that can numerically compute equilibrium distributions for arbitrary reactions. The applet we present can be used to analyze complex reactions involving twenty or more species, and one such reaction, the combustion of isooctane and air, is presented as an example.

Temperature Dependence of 1H and 17O NMR Shifts of Water: Entropy Effect

Density functional theory together with statistical thermodynamics based on the equilibrium constants method and concept of orientational entropy were applied to reproduce the temperature dependences of 1H and 17O nuclear magnetic resonance (NMR) chemical shifts in liquid water. Despite a rather simple theoretical model, a satisfactory agreement between calculated NMR quantities and corresponding experimental data was found. By using only a single adjustable parameter of arbitrary directionality, we succeeded to imitate the first-order temperature effect for both (1H and 17O) NMR signals in the neat water. 1H and 17O magnetic shielding tensors of water molecules in various water clusters have been calculated using the density functional theory. The full geometry optimization was performed using Becke's three-parameter hybrid method and the Lee–Yang–Parr correlation functional (B3LYP) combined with 6-311++G** basis set. Magnetic shielding tensors have been calculated using the modified hybrid functional of Perdew, Burke and Ernzerhof, and the gauge-including atomic orbital approach was applied to ensure gauge invariance of the results. Solvent effects were taken into account by the polarized continuum model.

Computation of Equilibrium-State in Gas/Solid Materials Systems

The determination of equilibrium-state in gas-solid materials systems is of practical interest; this consists of finding the values of intensive variables such as mole-fractions, partial pressures, activities or chemical potentials of constituents that occur in the gaseous and solid phases for stipulated temperature, pressure and initial reactant-gas composition. The mass-action iterative equilibrium constant method, shown to be a direct derivative of the minimization of Gibbs free energy, was used to compute the equilibrium-state in the carburizing and decarburizing iron-carbon heat treatment systems. By suitably combining the equilibrium partial pressure data with the extent of reaction formalism, the optimum feed-gas mixtures that ensured neutral atmospheres were determined.

Modeling chemical speciation of copper in River Yamuna at Delhi, India

Chemical modeling of copper in the river Yamuna was attempted by an equilibrium constant method, using a computer program COCSOC developed for the purpose. Concentrations of metals (Cu, Ca and Mg), ligands (organics, carbonates and bicarbonates) and stability constants of the probable complexes were the inputs for the modified Newton-Raphson iteration. The model adequately predicted concentrations of various copper species, even without taking into consideration solid phases, other competing metals and ligands. The free cupric ion concentrations estimated were in the range of 10-17 to 10-16M, undetectable by ion selective electrodes in the water from the river. The non-convergence of equilibrium computations for certain data sets at some sampling sites indicates the prevailing non-equilibrium conditions in the river due to large-scale release of ligands and metal ions through several drains.

Modeling of Silicon Vapor Phase Epitaxy Using Stefan-Maxwell Formalism

The vapor-phase homoepitaxy of monocrystalline silicon by reduction of chlorosilanes is modeled using a novel approach. With digital computer calculation, the growth rate of silicon is predicted under ambient pressure (1.0 atm or 101.325 kPa) in the high-temperature regime 1200—1600 K, where silicon growth is expected to be mass-transport limited. This study considers four different initial stoichiometries, namely, 0.1% SiH4 + 0.4% HCl + H2, 0.1% SiCl4 + H2, 0.5% SiCl4 + H2, and 0.2% SiHCl3 + H2 in the Si-Cl-H system in order to make comparisons between the predicted and the experimentally determined growth rates. By combining the iterative equilibrium constant method with the Stefan-Maxwell relations for diffusion in a multi-component gas-phase, the respective molar fluxes of nine gaseous species that include SiCl4, SiHCl3, SiH2Cl2, SiH3Cl, SiH4, SiCl2, SiCl, SiCl3, and Si(g) were computed for steady-state condition; and the data on fluxes enabled the determination of the net silicon flux to the surface of the substrate. The computed rates were compared to the measured deposition rates of silicon.

計算状態図と材料設計への展開 新規熱力学平衡計算ソフトウェア（ＣａＴＣａｌｃ）の開発

Thermodynamic equilibrium calculation is sometimes difficult in a system when minor but important species are present, when only stoichiometric condensed phases are stable and the gas phase is absent, and when multiple minima are present in the Gibbs free energy of some non-ideal solution phases. New program is being developed to overcome these problems. The free-energy minimization method is implemented to determine thermodynamic equilibrium similarly to other conventional programs. However, the gas phase in equilibrium is assumed to be present even when the gas phase is unstable under the specified condition, similar to the equilibrium constant method. Chemical potentials of the system components are always determined uniquely by this additional condition, and the vapor pressure and composition can be calculated. Furthermore, an automatic routine that introduces multiple phases with different compositions and checks their stability is incorporated to detect possible phase-splitting in non-ideal solution phases.