Group Contribution Method for Predicting the Phase Behavior of Binary Mixtures Containing Carbon Dioxide
Volume 9, Issue 1, Winter 2012, Pages 12-22
N. Abed, K. Nasrifar
Abstract This work deals with estimation of temperature dependent binary interaction parameters (k ij) for binary systems containing CO 2 using the Soave-Redlich-Kwong equation of state with a group contribution method. In this paper six groups, namely CH 3, CH 2, CH, CH 4 (methane), C2H 6 (ethane), and CO 2 (carbon dioxide) are defined and their relevant values of group interaction parameters are optimized. Using this method, it is possible to estimate the k ij of any mixture containing carbon dioxide and hydrocarbons at any temperature along the coexistence curve. The results obtained in
this study are, in most cases, accurate.
Kinetic Modeling of Sunflower Oil Methanolysis Considering Effects of Interfacial Area of Reaction System
Volume 9, Issue 1, Winter 2012, Pages 50-59
S. Farajzadeh Bibalan, S. M. Sadrameli
Abstract In this study, a kinetic model is proposed for Sunflower oil methanolysis in which the effect of the interfacial area on the reaction system has been investigated. The model is based on the combination of mass transfer and kinetics. Rate constant of the reaction is obtained by fitting of the experimental data with the model. Based on this model, activation energy is equal to E/R=3390 K. This model was applied to the transesterification of soybean oil with some modifications on Misek’s equation and interfacial tension correlation. Methyl ester production at two different mixing intensities was evaluated. By using this model, theoretical conversion is calculated and is compared with the experimental data taken from literature. An acceptable agreement has been obtained between two sets of data. Based on the experimental data shown in the paper, agitator speed has no significant effect on the conversion. Therefore, it can be concluded that at a temperature of 55 °C or higher, the model parameter approaches to the rate constant of reaction and the agitation speed does not affect the kinetics.
Prediction of Mean Drop Size in Pulsed Packed Extraction Columns
Volume 8, Issue 4, Autumn 2011, Pages 3-10
Meisam Torab-Mostaedi, Jaber Safdari, Farzad Torabi-Hokmabadi
Abstract Sauter mean drop sizes have been measured in a pulsed packed extraction column for two liquid systems with and without mass transfer conditions. The effects of pulsation intensity, phase flow rates, and interfacial tension on drop size have been investigated under a variety of operating conditions. The drop size is influenced mainly by pulsation intensity and interfacial tension. Significant, but weaker, are the effects of continuous and dispersed phase flow rates. A precise correlation is proposed for predicting mean drop size in terms of operating variables, physical properties of the liquid systems and mass transfer direction. Good agreement between prediction and experiments is found for all operating conditions that were investigated.
Molecular Simulation of Asphaltene Aggregation in Crude Oil by Monte Carlo Method
Volume 8, Issue 3, Summer 2011, Pages 3-15
M . Faraji, A . R. Solaimany Nazar
Abstract Monte Carlo simulation is adopted to study the aggregation of asphaltene phenomenon in crude oil. Simulation is accomplished by applying two different potential functions to allow for asphaltene-asphaltene, asphaltene- resin and resin-resin interactions to take place. Asphaltene molecule is considered as a flat molecule, consisting of seven spheres. Resin molecule is considered to be a single sphere and the other hydrocarbons molecules contained in crude oil are modeled as a continuum media. The effect of media on intermolecular interactions is described by definition of a parameter that is composed of two dielectric and Hamaker constants. The effects of asphaltene concentration, temperature and solvent type on the aggregation of asphaltene molecules are investigated by applying both of the potential functions. The predicted results are compared.
An AHP-Delphi Multi-Criteria Decision Making Model with Application to Environmental Decision-Making
Volume 8, Issue 2, Spring 2011, Pages 3-17
M. Pirdashti, M. Omidi, H. Pirdashti, M. H. Hassim
Abstract Today, the advantage of biotechnology, especially from an environmental aspect, is undeniable compared to other technologies. Kimia Gharb Gostar Industries Company (KGGICO) - the largest producer of citric acid in the Middle East, is one of the companies that applies biotechnology. Citrogypsum is a by–product of citric acid production and is considered a valid residuum of this company. In this paper, acid citric production and condition of citrogypsum production in the company were introduced besides the definition of citrogypsum production and its applications around the world. Based on this information and the evaluation of present conditions regarding Iran’s demands for citrogypsum, the best priority was introduced, and strategy selection and proper programming emphasized for self-sufficiency. The Delphi technique was used to elicit expert opinions about the criteria for evaluating the usages. The criteria identified by the experts were profitability, capacity of production, the degree of investment, marketable, production ease, and time of production. The
Analytical Hierarchy Process (AHP) and Expert Choice software were used to compare the alternatives based on the criteria derived from the Delphi process.
Prediction of Gas Hydrate Forming Pressures by Using PR Equation of State and Different Mixing Rules
Volume 8, Issue 1, Winter 2011, Pages 46-55
M. Karamoddin, F. Varaminian
Abstract In this work, the ability of different mixing rules for the prediction of hydrate formation pressure are compared. For this purpose, by using Van der Waals–Plauteeuw model for solid hydrate phase and PR equation of state for calculation of fugasity of components in gas and liquid phases, the pressure of hydrate formation in different mixtures has been calculated by four different mixing rules: Van der Waals, Danesh, GNQ and Wong-Sandler, then by comparison of the calculated results with experimental data, the accuracy of the mixing rules were determined. Studied systems contain binary mixtures CH4, C2H 6, C3H 8, i-C4H 10, CO 2, and H 2S with water in hydrate forming conditions. The interaction parameters in each mixture have been optimized by using two phase equilibrium data W(V L ) and then the optimized parameters have been used for three phase equilibrium W(V L H ) calculations. Comparison of the calculated
pressure of hydrate forming with experimental pressure shows that for most mixtures in the studied temperature and pressure ranges, the GNQ mixing rule with an average percent of error 6% has more accuracy than the three other mixing rules: Van der Waals, Danesh and WS. According to the obtained results for methane equilibrium concentrations in liquid phase, it seems that Danesh mixing rule is more efficient for the prediction the mole concentrations of components. Since Danesh rule considers the polarity of the water molecule, it has greater precision in predicting the equilibrium fractions.
Drilling Stuck Pipe Prediction in Iranian Oil Fields: An Artificial Neural Network Approach
Volume 7, Issue 4, Autumn 2010, Pages 29-41
S. R. Shadizadeh, F. Karimi, M. Zoveidavianpoor
Abstract Stuck pipe is one of the most serious drilling problems, estimated to cost the petroleum industry hundreds of millions of dollars annually. One way to avoid stuck pipe risks is to predict the stuck pipe with the available drilling parameters which can be employed to modify drilling variables. In this work, Artificial Neural Network (ANN) was used for stuck pipe prediction according to the fact that this method is applicable when relationships of parameters are too complicated. Based on the drilling fluid condition from one of the Iranian oil fields, stuck pipe instances were divided into static and dynamic types. The results of this study show more than 90% accuracy for stuck pipe prediction in the investigated oilfield. The methodology presented in this paper enables the Iranian drilling industry to estimate the risk of stuck pipe occurrenc during the well planning procedure.
Measurement and Correlation of Ibuprofen in Supercritical Carbon Dioxide Using Stryjek and Vera EOS
Volume 7, Issue 4, Autumn 2010, Pages 42-49
M. Mirzajanzadeh, F. Zabihi, M. Ardjmand
Abstract Ibuprofen solubility in supercritical carbon dioxide was measured using a dynamic apparatus at a pressure between 80 and 140 bars at three different temperatures, 308.15, 313.15 and 318.15 K. The mole fraction of Ibuprofen in fluid phase was in the range of 0.015 × 10 -3 - 3.261 × 10 -3 at the mentioned operational condition. Modified Mendez-Santiago and Teja equation were used to check the consistency of the experimental data. Results were correlated using the Stryjek and Vera equation of state with the van der Waals 1-parameter (vdW1) and 2-parameters (vdW2) mixing and combining rules. Interaction parameters along with the percentage of the average absolute relative deviation (%AARD) were displayed. Also, the Lydersen group contribution methods were used for predicting the physicochemical and critical properties of the Ibuprofen.
Product Yields Prediction of Tehran Refinery Hydrocracking Unit Using Artificial Neural Networks
Volume 7, Issue 4, Autumn 2010, Pages 50-63
M. Bahmani, Kh. Sharifi, M. Shirvani
Abstract In this contribution Artificial Neural Network (ANN) modeling of the hydrocracking process is presented. The input–output data for the training and simulation phases of the network were obtained from the Tehran refinery ISOMAX unit. Different network designs were developed and their abilities were compared. Backpropagation, Elman and RBF networks were used for modeling and simulation of the hydrocracking unit. The residual error (root mean squared difference), correlation coefficient and run time were used as the criteria for judging the best network. The Backpropagation model proved to be the best amongst the models considered. The trained networks predicted the yields of products of the ISOMAX unit (diesel, kerosene, light naphtha and heavy naphtha) with good accuracy. The residual error (root mean squared difference) between the model predictions and plant data indicated that the validated model could be reliably used to simulate the ISOMAX unit. A four-lumped kinetic model was also developed and the kinetic parameters were optimized utilizing the plant data. The result of the best ANN model was compared to the result of the kinetic model. The root mean square values for the kinetic model were slightly better than the ANN model but the ANN models are more versatile and more practical tools in such applications as fault diagnosis and pattern recognition.
Simulation and Experimental Investigation of the Permeability Reduction due to Asphaltene Deposition in Porous Media
Volume 7, Issue 3, Summer 2010, Pages 3-16
S. Ashoori, A. Khaksar Manshad, N. Alizadeh, M. Masoomi, S. H. Tabatabaei
Abstract A static to dynamic approach to modeling Asphaltenes has been developed and validated. A new algorithm for static asphaltene modeling uses a multi-solid thermodynamics approach where the equality of fugacity for each component and phase is applied at equilibrium conditions. This is required for minimizing the Gibbs free energy. The fractal distribution function used for the splitting and characterization of heavy components provides accurate results. The precipitation and re-dissolution of asphaltenes are investigated for a relatively heavy crude oil from an Iranian field. A
series of experiments are designed and carried out quantitatively to obtain the permeability reduction in a slim tube. Using a dynamic reservoir simulator, a 3-dimensional asphaltene model is developed to simulate the precipitation, flocculation, deposition and its impact on permeability in a slim tube. With this approach, the asphaltene is defined as a set of component(s) that can precipitate depending on their molar percentage weight in the solution. The simulated permeability reduction due to asphaltene deposition shows good agreement with our experimental data.
Investigation of Temperature and Flow Fields in an Alternative Design of Industrial Cracking Furnaces Using CFD
Volume 7, Issue 3, Summer 2010, Pages 61-73
J. Aminian, Sh. Shahhosseini, M. Bayat
Abstract Enhanced design strategies in the industrial cracking furnaces are of practical interest for petrochemical industries. For such engineering purposes the exact simulation of temperature and flow fields in the furnace is mandatory. In this paper, a study was conducted to simulate 3D flue gas flow pattern and temperature field in the radiation section of an industrial cracking furnace in order to improve the design of the steam cracking furnaces, employing the computational fluid dynamics (CFD) technique. The steady-state Reynolds averaged Navier–Stokes (RANS) equations were solved, in a finite volume scheme for a turbulent premixed flow applying the renormalization group (RNG) version of the k
ε− model, together with global combustion kinetics for methane-hydrogen-air. Calculation of the Damkhöler number and optical-thickness was conducted to identify the appropriate methods for the numerical modeling of radiation and turbulence-chemistry interaction phenomena. The predicted results match the literature data quite well. The validated numerical procedure was then employed to investigate alternative design attributed to different burner locations. The alternative design resulted in a more uniform temperature profile on the reactor tubes as well as lower peak flame temperature.
Simple Kinetic Modeling of Selective Reduction of Nitric Oxide in Diesel Exhaust Over Cu-Zn/ZSM-5 Monolithic Catalyst
Volume 7, Issue 3, Summer 2010, Pages 74-80
A. Zuhairi Abdullah, H. Abdullah, S. Bhatia, B. Salamatinia, H. Mootabadi
Abstract An integral reactor-based kinetic model for the selective reduction of nitric oxide over Cu-Zn/ZSM-5 washcoated monolithic catalysts is reported. The active component was washcoated onto a 400 cpsi ceramic monolithic substrate at a loading of 23.6 wt. % usage 2,000 ppm iso-butane was used as the reductant. High activity without significant pressure drop was achieved at a GHSV of 16,000 h-1 . Third order polynomial satisfactorily fitted the activity versus space time data and a low activation energy of +30.3 kJ/mol was obtained. The applicability of the model was demonstrated within
300-400 ºC and space time of 0.12-0.94 s.
Continuous Lumping Model of an Industrial Refinery Isomax Reactor
Volume 7, Issue 2, Spring 2010, Pages 39-50
M. T. Sadeghi, Sh. Shahhosseini, F. Behroozshad
Abstract Hydrocracking is an important secondary process in the petroleum industry, generally used to process heavy oil cuts. The process is tailored to various needs of refineries in order to maximize middle distillates, gasoline, LPG and similar products. Therefore, kinetic modeling of hydrocracking reactors applied to upgrade vacuum heavy oil (Isomax) is important and needs to be investigated. In this work, following a brief comparison of continuous lumping model in contrast to discrete lumping model, the former was chosen to model an operational Isomax reactor in Tabriz refinery, located in the North West of Iran. In order to categorise various unknown components True Boiling Point (TBP) of the mixtures were employed as the key parameter. Hence, the hydrocracking rate constant was assumed to be an even function of true boiling point. This would facilitate reformulation of mass-balance equations in terms of rate constant as a continuous variable. In order to determine the fraction yield distribution of the species, a specific distribution function was formulated. The resulting model equations were solved numerically and the yield of various fractions as a function of reactor residence time were estimated. A comparison between model predictions and experimental data shows it can predict the weight percent of light and heavy fractions well with an acceptable accuracy.
Dynamic Simulation of an Industrial Rotary Dryer
Volume 7, Issue 2, Spring 2010, Pages 68-77
Sh. Shahhosseini, M.T. Sadeghi, H. R. Golsefatan
Abstract Solid transport phenomena drastically affect rotary drying process. A change in any solid movement variable such as particle hold up or input flow rate results in a significant variation of heat and mass transfer rates. Therefore, in this research dynamic study of these phenomena was conducted both experimentally and theoretically. Several experiments was performed employing an industrial granule dryer. The dryer length and diameter were 5 and 1 m, respectively. In each experiment one of the solid movement variables was changed and the resulting dynamic change on the process was measured. The data was used to estimate the parameters of a dynamic distributed parameter model of the system using dynamic optimization method. The data were also employed to evaluate the model. The model predictions for solid hold up and outlet flow rate were compared with those of the experimental data. The average model error for solid hold up and outlet flow rate were 5.6% and 5.4 %, respectively.
Modeling of Catalyst Effect on the Reduction Rate Enhancement of Barium Sulfate by Methane and Developing Two Environmentally Friendly Processes
Volume 7, Issue 1, Winter 2010, Pages 13-27
R. Alizadeh, E. Jamshidi, H. Ale Ebrahim, A. Afshar Ebrahimi
Abstract This article describes kinetic modeling of the reduction of barium sulfate by methane based on experimental data obtained by thermogravimetric technique. The conversion- time data have been interpreted by using the grain model for gas-solid reactions and the effect of catalyst on the kinetic parameters has been elucidated. It was found that
zinc oxide acted as a fairly strong catalyst for the reaction, especially at higher temperatures. For example, at about 950°C the reaction rate constant was increased more than 8 times by using only 2 percent of zinc oxide. Orthogonal collocation method was used for solving coupled partial differential equations of gas-solid reaction. There is a good agreement between the experimental data and results obtained from simulation. This research offers a clean method for barium carbonate production with methane as a reducing agent, decreasing CO2 emission significantly. Also, a new process for converting sulfur dioxide to elemental sulfur by a cyclic process involving barium sulfide and barium sulfate has been proposed.
A Simple One-Dimensional Model for Investigation of Heat and Mass Transfer Effects on Removal Efficiency of Particulate Matters in a Venturi Scrubber
Volume 6, Issue 4, Autumn 2009, Pages 3-14
A. Rahimi, A. Bakhshi
Abstract In the present study a mathematical model is developed in order to examine the effects of heat and mass transfers on removal efficiency of particulate matters in venturi type scrubbers. The governing equations including the variations of the particulate concentration, gas temperature, droplet temperature, diameter, and velocity are obtained based on the conservation laws and are solved numerically. In order to validate the model, necessary data was measured and collected in a commercial cement plant that uses these types of scrubbers in air pollution control applications. A good agreement between plant data and the model predictions is noticed in general. The results obtained from the model reveal that the existance of temperature difference between the gas and the liquid droplets decreases the overall removal efficiency of particulate matters. This is due to sudden reduction ofrelative velocity between the gas and droplets which is resulted from the existence ofheat and mass transfers between the two fluids, especially in the throat section. In addition, the effects ofvarious operating parameters on the extent ofreduction in the removal efficiency are examined. This study confirms that in most industrial applications ofventuri scrubbers it is necessary to use a direct or an indirect cooling tower in order to decrease the gas temperature before entering the venturi.
CFD Simulation of Catalytic Combustion of Benzene
Volume 6, Issue 4, Autumn 2009, Pages 34-44
A. Niaei, D. Salari, S. A. Hosseini
Abstract This paper reports the result of CFD simulation of catalytic oxidation of benzene on monolithic catalyst. The geometries ofthe catalyst and reactor were designed in Gambit software and simulation of catalytic oxidation was carried out in fluent 6.2. Results of simulation showed excellent agreement with the experimental data. This study confirmed the accuracy of the used model in this simulation (Mars van Krevelen). Furthermore, CFD made it possible to obtain a more accurate view ofheat transfer and fluid flow. This study confirmed CFD is the best tool for study offluid regime and heat transfer and especially, concentration of species, and surface deposition along the reactor in the chemical process.
Calculation of Physical Properties of the Methanol-Water Mixture Using Molecular Dynamics Simulation
Volume 6, Issue 4, Autumn 2009, Pages 62-72
N. Farhadian, M. Shariaty-Niassar
Abstract In this study some properties ofthe methanol-water mixture such as diffusivity, density, viscosity, and hydrogen bonding were calculated at different temperatures and atmospheric pressure using molecular dynamics simulations (MDS). The results were compared with the available experimental data as well as some theoretical models; overall indicating a good agreement. This shows the useful and effective application of MDS for determination ofphysical properties.
Experimental and CFD Studies on the Effect of the Jet Position on Mixing Performance
Volume 6, Issue 3, Summer 2009, Pages 3-12
A. Parvareh, M. Rahimi, A. Abdulaziz Alsairafi
Abstract
An Experimental and Theoretical Investigation on Thermal Performance of a Gas-Liquid Thermosyphon Heat Pipe Heat Exchanger in a Semi-Industrial Plant
Volume 6, Issue 3, Summer 2009, Pages 13-25
H. Zare Aliabadi, H. Ateshi, S. H. Noei, M. Khoram
Abstract "> Waste heat recovery is very important, because it not only reduces the expenditure of heat generation, but also it is of high priority in environmental consideration, such as reduction in greenhouse gases. One of the devices used in waste heat recovery is heat pipe heat exchanger. An experimental and theoretical research is carried out to investigate heat performance of an air to water thermosyphon heat pipe heat exchanger according to ε-NTU method. The experiments were done according to the following procedure: cold water with 0.1kg/s flows through the condensation section and hot air in a closed cycle is blown into the evaporation section. A blower with varying frequency of current turns in the mass flow rate between 0.14-0.6 kg/s and a temperature range of 125-225°C. The results of the experiments show that as the ratio of C Ch c rises, the rate of heat transfer goes up. The efficiency of the heat pipe heat exchanger remains constant as the temperature of the hot stream goes up, but the amount of heat transferred increases.
Mathematical Modeling of Fluorination Reaction of Uranium Dioxide and Evaluation of Existing Gas-Solid Reaction Models
Volume 6, Issue 2, Spring 2009, Pages 63-74
A. Niksiar, A. Rahimi
Abstract In this study a mathematical model is developed in order to simulate fluorination reaction of uranium dioxide which leads to the production of uranium hexafluoride. The model considers homogeneous reaction for intermediate solid and a heterogeneous one for unreacted shrinking core. Also, this study tries to clearly show the shortcoming of some of the well-known models that take heterogeneous reactions for both solids. In fact, one may not trust the accuracy of those models due to the importance of diffusion phenomena into the intermediate solid and the reaction taking place within it. On the other hand, neglecting the undeniable effects of some operating conditions such as temperature and particle sizes on gas concentration distribution and reaction rates may introduce large deviations. In this study, the governing equations are developed on the basis of the mass conservation law and solved numerically. Besides, for the first time,
some dimensionless equations and groups are introduced to predict reaction rates and amounts of the main and intermediate products for use in numerical procedures. Comparing the model results with corresponding experimental ones represents the desirable preciseness of the model. After validation of the model, the effect of some operating variables such as temperature and initial size of the particle are investigated on the reaction rates and conversions.
Unsteady-State Modeling of the Fluidized Bed Polyethylene Reactor
Volume 6, Issue 1, Winter 2009, Pages 23-39
A. Hassimi, N. Mostoufi, R. Sotudeh-Gharebagh
Abstract A mathematical model is developed for describing the dynamic behavior of the gas phase ethylene polymerization reactor. The model is based on the dynamic two-phase concept of fluidization in which the bubbles may contain solid particles and the emulsion is capable of containing more gas than that of minimum fluidization. The fluidized bed reactor is divided into several serial sections consisting of bubble and emulsion phases. Flow of the gas is considered as plug flow through the bubbles and perfectly mixed through the emulsion phase. Polymerization reactions occur in both emulsion and bubble phases. Variation of the process variables as well as the polymer properties were studied as a function of operating time. The bed height was controlled by the product withdrawal rate with a PID controller. The results of the model were compared with the experimental data and a good agreement was observed between the model prediction and actual data. The simulation results indicate that a significant amount of polymer production (roughly 12%) takes place in the bubbles.
Effect of Hydrocarbon Fluid Characterization on Wax Precipitation Modeling
Volume 6, Issue 1, Winter 2009, Pages 50-65
S. A. Tabatabaei-Nejad, E. Khodapanah
Abstract The hydrocarbon plus fractions that comprise a significant portion of naturally occurring hydrocarbon fluids create major problems when determining the thermodynamic properties and the volumetric behavior of these fluids by equations of
state. These problems arise due to the difficulty of properly characterizing the plus fractions (heavy ends). Proper characterization of the heavier components is important when cubic equations of state and/or solid formation thermodynamic models are used to describe complex phase behavior of reservoir fluids. The effect of heavy fractions
characterization on thermodynamic modeling of wax precipitation has been investigated using different models including Won, Pan and Proposed Models. In order to characterize the plus fraction (heavier part) as a series of pseudocomponents, a probability model that expresses the mole fraction as a continuous function of the
molecular weight has been used. The study has been conducted using several mixtures. Two different SCNs (Single Carbon Number), C 7+ and C10+, were chosen. The chosen SCNs were distributed to multicomponents of five, six, and/or ten using continuous method. The results showed that the fractioning is required to be able to predict wax precipitation. Distribution of C 10+ using a proper distribution function has shown improvement in predictions of WAT and the amount of wax deposited in comparison with the characterization of C7+ using semi-continuous approach. In predicting WAT and the amount of wax build up the developed model showed superiority over the others.
A Study on Liquid-liquid Mixing in a Stirred Tank with a 6-Blade Rushton Turbine
Volume 5, Issue 4, Autumn 2008, Pages 12-22
R. Zadghaffari, J.S. Moghaddas, J. Revstedt
Abstract The turbulent flow field generated in a baffled stirred tank was computed by large eddy simulation (LED) and the flow field was developed using the Sliding Mesh (SM) approach. In this CFD study, mixing times and power number have been determined for a vessel agitated by a 6-blade Rushton turbine. The predicted results were compared with the published experimental data. The satisfactory results of comparisons indicate the potential usefulness of this approach as a computational tool for designing stirred reactors.
Determination of the Equilibrium Parameters of Gaseous Detonations Using a Genetic Algorithm
Volume 5, Issue 3, Summer 2008, Pages 3-13
A. Heidari, K. Mazaheri
Abstract The present work is concerned with the development of a new algorithm for determination of the equilibrium composition of gaseous detonations. The elements balance equations, and the second law of thermodynamics (i.e., the minimization of the Gibbs free energy of products), are used to determine the equilibrium composition of the detonation products. To minimize the Gibbs free energy with traditional deterministic methods one needs to solve a set of highly nonlinear equations. The numerical methods in the existing equilibrium codes suffer from several drawbacks such as the divergence possibility in some equivalent ratios, and the possibility of converging to a local relative minimum in the minimization process. To overcome these drawbacks, a genetic algorithm is presented in the present study. Converging to the global minimum of Gibbs function in all equivalent ratios, and having a reasonable CPU time are the notable aspects of the proposed algorithm.