Total Average Absolute Deviation Research Articles

Research of a Thermodynamic Function (∂p∂x)T, x→0: Temperature Dependence and Relation to Properties at Infinite Dilution

In this work, we propose the idea of considering (∂p∂x)T, x→0 as an infinite dilution thermodynamic function. Our research shows that (∂p∂x)T,x→0 as a thermodynamic function is closely related to temperature, with the relation being simply expressed as: ln(∂p∂x)T, x→0=AT+B. Then, we use this equation to correlate the isothermal vapor−liquid equilibrium (VLE) data for 40 systems. The result shows that the total average relative deviation is 0.15%, and the total average absolute deviation is 3.12%. It indicates that the model correlates well with the experimental data. Moreover, we start from the total pressure expression, and use the Gibbs−Duhem equation to re-derive the relationship between (∂p∂x)T,x→0 and the infinite dilution activity coefficient (γ∞) at low pressure. Based on the definition of partial molar volume, an equation for (∂p∂x)T,x→0 and gas solubility at high pressure is proposed in our work. Then, we use this equation to correlate the literature data on the solubility of nitrogen, hydrogen, methane, and carbon dioxide in water. These systems are reported at temperatures ranging from 273.15 K to 398.15 K and pressures up to 101.325 MPa. The total average relative deviation of the predicted values with respect to the experimental data is 0.08%, and the total average absolute deviation is 2.68%. Compared with the Krichevsky−Kasarnovsky equation, the developed model provides more reliable results.

A temperature-independent prediction model predicts the vapor-liquid equilibrium of CO2-based binary mixtures

CO2-based binary mixtures are considered good alternative working fluids in the refrigeration and power cycle due to their excellent performance and environmental friendliness. The vapor-liquid phase equilibrium of CO2-based binary mixtures is the basis for calculating mixing enthalpy and heat capacity, which is essential for thermodynamic analysis. In this work, based on the vdW mixing rules, we proposed a kij model (kij=θjki-θikj). In the proposed model, ki and kj are defined as pure interaction factors of the pure components, θj is the influence factor of component j to component i, and θi is the influence factor of component i to component j. After continuous fitting and trial calculation, we developed a semi-empirical formula, which is called a temperature-independent prediction model. The model does not have any adjustable parameters, which are only related to the physical properties (critical pressure (kPa), critical temperature (K), and acentric factor) and molecular structure (carbon-carbon double bonds, carbon-fluorine, chlorine, iodine, and oxygen atoms) of the components. The temperature-independent prediction model can predict the bubble-point pressures, vapor phase molar fractions, and relative volatilities very well, which is better than the prediction model based on the vdW mixing rules by others and the group contribution model based on the excess free energy (GE) mixing rules (PR+MHV1+UNIFAC). The total average absolute relative deviation of pressures, the total average absolute deviation of vapor phase molar fractions, and the total average absolute relative deviation of relative volatilities by the temperature-independent prediction model are 2.23%, 0.0095, and 5.21%, respectively.

Correlation and prediction of solubility of hydrogen in alkenes and its dissolution properties

In this work, solubility of hydrogen in some alkenes was investigated at different temperatures and pressures. Solubility values were calculated using the Peng–Robinson equation of state. Binary interaction parameters were calculated using fitting the equation of state on experimental data, Group contribution method and Moysan correlations and total average absolute deviation for these methods was 3.90, 17.60 and 13.62, respectively. Because hydrogen solubility in Alkenes is low, Henry’s law for these solutions were investigated, too. Results of calculation showed with increasing temperature, Henry’s constant was decreased. The temperature dependency of Henry’s constants of hydrogen in ethylene and propylene was higher than to other alkenes. In addition, using Van’t Hoff equation, the thermodynamic parameters for dissolution of hydrogen in various alkenes were calculated. Results indicated that the dissolution of hydrogen was spontaneous and endothermic. The total average of dissolution enthalpy ({Delta H}^{^circ }) and Gibbs free energy ({Delta G}^{^circ }) for these systems was 3.867 kJ/mol and 6.361 kJ/mol, respectively. But dissolution of hydrogen in almost of alkenes was not an entropy-driven process.

Prediction of DES’ Vapor Pressure Using a New Corresponding State Model

Application of deep eutectic solvents in industrial chemical processes are improved over time in last decades. In this work, vapor pressures of 13 classes of DESs (DES 1-13) based on 5 salts and 7 hydrogen bond donors with various combinations of molar ratio were used between 343-393 K. The vapor pressure of the pure and aqueous solutions of DESs was calculated by different equations of state, which are based on “φ-φ” and γ-φ approachs. Additionally, Voutsas and Wagner models as corresponding-state models were modified to predict the vapor pressure of the pure and aqueous solutions of DESs. The total average absolute relative deviations of the Modified-Voutsas and Modified-Wagner models for the vapor pressure calculation of the pure and aqueous solutions of DESs were 7.03, 9.08 % and 5.47, 7.15 %, respectively. Moreover, the validity of vapor pressure calculation using the two modified models was checked with the aid of a linear equation for the average specific heat capacity of different DESs (23 classes of DESs) between 278.15-353.15 K. Results showed that the total average absolute relative deviations of the specific heat capacity of DESs using the Modified-Voutsas and Modified-Wagner models from the experimental data were 4.128 and 4.056 %, respectively.

Numerical and Galerkin’s methods for thermal performance analysis of circular porous fins with various profiles when the surface temperature is higher/lower than the air temperature

ABSTRACT The main objective of this research is to analyze the optimization and the thermal performance of circular porous fins with three different profiles: rectangular, convex, and triangular under dry surface conditions. In this research, when the surface temperature of fin is higher or lower than the air temperature was studied. Also, modeling is assumed one-dimensional and the temperature changes only in the direction of the radius of the fin. Moreover, the thermal conductivity and heat transfer coefficient are a function of porosity and temperature, respectively. The governing equations are solved using the finite difference method and the Galerkin’s method. In this study, the effect of different parameters including porous parameter (SH) and porosity, fin efficiency, and fin effectiveness on temperature distribution were investigated. In both cases, the results showed that the fin temperature distribution should be decreased by increasing the porous parameter (SH) and porosity. In addition, in both cases, the results demonstrated that the efficiency and effectiveness for the rectangular profile are higher than other profiles. In this study, the total average absolute deviation percentage was calculated and its magnitude was 1 to 2.35%.

Calculation of the second virial coefficient and molecular radius of polar and non-polar substances using a new potential function

Equations of state are vital tools for the calculation of gases and liquids properties. One of the most important EoSs is Virial EoS. One unique property of Viral EoS is that its coefficients, which are calculated from potential functions, are related to intermolecular forces. In this paper, Kihara potential function is improved based on molecular structure, and all coefficients are determined by optimization based on second Virial coefficient calculated from PVT data. A new parameter is introduced in this model which is representing the effective molecular diameter of molecules which is comparable with the calculated dimensions of molecules. The second Virial coefficient of 53 polar and non-polar molecules are calculated with the proposed potential function and classified into 5 groups based on the molecular structure. 1067 experimental data points of hydrocarbons including n-alkanes, alkenes, alcohols, chlorofluorocarbons (CFCs), hydrofluorocarbons (HFCs), Hydrochlorofluorocarbons (HCFCs), Trichloromethane, Dichloromethane, Chloromethane, 1,1,1-Trichloroethane, 1-Chlorobutane, branched alkanes, benzene, toluene, water and carbon dioxide were exploited. 610 experimental data points of the aforementioned substances were used to obtain the new model's coefficients, and the remaining data points were implemented to validate the proposed model. Additionally, the accuracy of the proposed model is compared with the other models such as Kihara, Exp-6, square-well, L-J and Stockmayer that the results reveal an enhanced accuracy. The total average absolute deviations for non-polar substances based on the proposed model, Kihara, Exp-6, square-well and L-J are 2.57, 3.14, 3.57, 2.90 and 7.85%, respectively. For polar substances, the total average absolute relative deviations based on the proposed model and Stockmayer are 3.95 and 6.69%, respectively. Also, Z compressibility factor, molar heat capacity and density of some polar and non-polar substances including water, methane, ethane, carbon dioxide, 1-butanol and 1,1,1,2-tetrafluoroethane are calculated to validate the proposed model, and the results showed that this model has good accuracy for calculation of the aforementioned properties in different temperature and pressure ranges.

Experimental Determination and Modeling of the Phase Behavior of the CO2 + Propionic Anhydride Binary System at High Pressure

The phase equilibrium of the binary system (CO2 + propionic anhydride) was determined experimentally at temperatures of 308, 313, and 323 K and pressures up to 10 MPa. Measurements were carried out in a high-pressure visual cell with variable volume. The experimental data were modeled using the Peng–Robinson equation of state and the Mathias–Klotz–Prausnitz mixing rule. A good correlation was achieved with this model, with a total average absolute deviation of 0.21%.

Prediction of surface tension of pure hydrocarbons using Esmaeilzadeh-Roshanfekr equation of state and group contribution method

In this paper, a new model with the help of Esmaeilzadeh-Roshanfekr equation of state (ER EoS) and group contribution method was proposed to obtain the surface tension of various hydrocarbons in different temperatures and ambient pressure. To this end, 7 groups (CH3, >CH2, >CH, >C<, CH, CH2, andC<) were defined that appear in the structure of hydrocarbons. 350 experimental data points of 40 hydrocarbons were also employed that 281 data points of 32 hydrocarbons were used to obtain the values of group increments and the remaining data points (69 experimental data points of 8 hydrocarbons) were used to validate the group contribution method used in the proposed model. Additionally, the accuracy of the proposed model was compared with the other equations of state such as Soave-Redlich-Kwong (SRK EoS), Peng-Robinson (PR EoS), and Van der Waals (VW EoS) that the results of the proposed model showed fewer error and better accuracy. The total average absolute relative deviations (TAARDs) of the proposed model and the other models with the help of SRK EoS, PR EoS, and VW EoS are found to be 6.54%, 12.15%, 12.57%, and 15.30%, respectively.

Modeling the volumetric properties of metals from heat of vaporization

We have applied the Song and Mason equation of state [Y. Song, E.A. Mason, Phys. Rev. A 42 (1990) 4743–4748] with a simple modification for alkali metals, alkaline earth metals, aluminum, bismuth, lead, copper and mercury. The present equation of state consists of four temperature dependent parameters. These parameters have been calculated as function of reduced temperature with the use of the law of corresponding states based on latent heat of vaporization and the liquid density at the normal boiling point. The predicted densities were compared with those obtained from the experiment. From 396 data points examined for the aforementioned metals, the total average absolute deviation was found to be 0.72%. Moreover, we indicate that the Zeno line regularity can well be predicted by the proposed model for metals.

Application of SAFT‐VR Equation of State for Prediction of Thermophysical Properties of Sugar Solutions

AbstractThe thermodynamic properties of sugar solutions, which are important solutions in food industries, have been calculated. Because of the large molecules and hydrogen bonding in the water/sugar solutions, the statistical association fluid theory of variable ranged (SAFT‐VR) equation of state was used to calculate the thermodynamic properties such as water activity, solubility, vapor pressure and boiling temperature of the aqueous sugar solutions, including glucose, sucrose and fructose. The SAFT‐VR parameters were calculated using vapor pressure and density data for water and water activity data for sugars. The total average absolute deviation percentage (AAD%) for all the calculated properties was 1.93%. The results showed that the model can accurately predict the properties of the sugar solution.Practical ApplicationsSugar solutions have important roles and uses in different industries such as food production, food preservation industries, chemical feed stock, pharmaceutical industries, metabolic reactions, industrial operations and chemical processes, such as crystallization, evaporation and selective separation. For example, water activity in a solution can be used to stop deteriorative reactions. The density of the solution is important in separation processes and mixing equipment. Solubility of sugar in water is another important property in food preservation and processes such as gasification and separation. The boiling temperature of the solution is an important thermodynamic property in different industrial processes such as purification and separation processes.

High pressure vapor–liquid equilibrium for the ternary system ethanol/(±)-menthol/carbon dioxide

In this work the phase behavior of the ternary system ethanol/(±)-menthol/CO2 was studied at the temperatures of 313 and 323K, in the pressure range 8–10MPa. Experiments were performed using a high pressure phase equilibrium apparatus with a visual cell. CO2 is more selective toward ethanol, separation factors ranging from 1.6 to 7.6 at the conditions tested. The pTxy data obtained were correlated with the Peng–Robinson equation of state combined with the Mathias–Klotz–Prausnitz mixing rule. The model gave a good fitting to the data, with a total average absolute deviation of 3.7%, and was able to predict the occurrence of a three-phase region observed experimentally at 313K and 9MPa.

Modeling and analysis of the thermal conductivities of air saturated sandstone, quartz and limestone using computational intelligence

Accurate experimental determination of the effective thermal conductivity (ETC) of porous reservoir rocks (especially under high temperature and pressure conditions) is a difficult problem and often a time-consuming and costly process. This study firstly examines the ability of the theoretical and empirical correlations for estimating the air saturated sandstone, quartz and limestone ETCs based on the models available in the literature. Optimal values of constant parameters of these correlations are found using the genetic algorithm (GA) technique. Empirical correlations have acceptable accuracy; however, they are not applicable in wide ranges of temperature and/or pressure. Also, each equation is dependent on the composition of the porous rock. In other words, they are not generalized correlations. The ability of artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS) as two generalized models are also investigated utilizing 872 experimental data points for a wide range of pressure and temperature. Temperature, pressure, porosity and bulk density are considered as the inputs of the mentioned models. An optimal topology of multi-layer perceptron neural network model (MLPNN) is determined via 10-fold cross-validation method. The total average absolute relative deviation (AARD (%)) of the developed ANN and ANFIS models for estimation of ETC are obtained 2.91% and 3.80%, respectively. The results show that the optimal ANN model is able to estimate ETC with the higher accuracy than the other correlations.

Evaluation of various types' equations of state for prediction of rate of double gas hydrate formation based on Kashchiev model in flow loop apparatus

This paper compares the effects of using various types of equations of state such as Peng Robinson (PR), Soave Redlich Kwong (SRK), Esmaeilzadeh – Roshanfeker (ER), Patel Teja (PT) and Valderrama–Patel–Teja (VPT) on the rate of hydrate formation based on the Kashchiev model for gaseous mixtures with experimental data points obtained in a mini flow loop apparatus in presence of the kinetic inhibitors (such as modified starch and l-tyrosine) at various pressures (1–4 MPa) and specified temperature (277.15 K). For this purpose, a laboratory mini flow loop apparatus was set up to measure the rate of gas hydrate formation when a hydrate forming mixture is contacted with water in the presence or absence of dissolved inhibitor under suitable temperature and pressure conditions. In each experiment, a water blend saturated with pure gas is circulated up to a required pressure. Pressure is maintained at a constant value during experimental runs by means of the required gas make-up. The total average absolute deviation was found to be 18.7%, 19.8%, 19.2%, 20.2% and 20.7% of the PR, ER, SRK, VPT and PT equations of state for calculating of gas consumption for gaseous mixtures during gas hydrate formation (in the presence and absence of kinetic gas hydrate inhibitor), respectively. Comparison results between the calculated and experimental data points of gas consumption were obtained in a flow loop indicate that the PR and ER equations of state have lower errors than the SRK, VPT and PT equations of state for this model.

Thermal Conductivity of Ionic Liquids at Atmospheric Pressure: Database, Analysis, and Prediction Using a Topological Index Method

Thermal conductivity is an important thermophysical property of ionic liquids (ILs). In this paper, a database for the thermal conductivity of ILs was established by collecting experimental data from literature covering the period from 2007 to 2013, including 359 data points, 45 ILs. The influences of temperature and the alkyl chain length of the cation on thermal conductivity were also discussed. A topological index method was proposed to estimate the thermal conductivity of ILs based on collected data which were divided into training (299 data points, 38 ILs) and testing (60 data points, 7 ILs) sets. The total average absolute deviation between the calculated and literature data was found to be 2.3%, with 2.1% for the training set and 2.9% for the testing set. The topological index method guarantees satisfactory precision with a simple form and can be easily expanded to new kinds of ILs.

A new CPA equation of state for water and primary alcohols

A new version of CPA (cubic-plus-association) equation of state (EOS) for associating fluids is proposed. This equation takes the Nasrifar–Moshfeghian (NM) cubic EOS as a frame for representing the physical interactions of fluid molecules and also an associating term from the bonding term of statistical associating fluid theory (SAFT). The resulting EOS contains five adjustable parameters, three in physical term and two in association-based term. The parameters are determined using vapour pressures and saturated liquid densities of pure associating fluids. The excellent saturated liquid density is obtained for four pure associating fluids including primary alcohols (methanol, ethanol and 1-butanol) as well as water. The total average absolute deviations of the calculated values of densities from the experimental data are within 1.71%. The present model is compared with the original CPA EOS. Results show that our model agrees well with the original one.

The Prediction of the Permeability Ratio Using Neural Networks

In this research, two novel models were presented for prediction of permeability ratio and its reduction due to the formation of calcium and strontium sulfate scales during waterflooding using multilayer perceptron, radial basis function network, and coreflooding test data. To achieve the maximum efficiency, number of neurons, training function, and activation function were optimized for a multilayer perceptron model and spread parameter was optimized for a radial basis function model. The radial basis function model only could predict trend of permeability ratio reduction in the performance stage, but the multilayer perceptron model predicted permeability ratio after waterflooding with a total average absolute deviation of 0.56%.

Evaluation of various types equations of state on prediction of rate of hydrate formation for binary gas mixtures in the presence or absence of kinetic hydrate inhibitors in a flow mini-loop apparatus

This paper compares the effects of using various types of equations of state (PR,11Peng Rabinson. PSRK,22Soave Ridlich Kowng. ER,33Esmaeilzadeh–Roshanfeker. NB44Nasrifar–Boland. and VPT55Valderrama-Patel–Teja.) for gas consumption during gas hydrate formation based on the Kashchiev and Firoozabadi model for binary gaseous mixtures such as 70% C1/30%C3, 30% C1/70% C3, 70% C1/30% i-C4, 30% C1/70% i-C4 with experimental data points obtained in a flow mini-loop apparatus in presence or absence of kinetic hydrate inhibitors at various pressures and specified temperature. A laboratory flow mini-loop apparatus is designed and built up to measure the gas consumption rate during gas hydrate formation.For the prediction of the gas consumption rate for double gas hydrate formation in a flow mini-loop apparatus, the rate equation based on the Kashchiev and Firoozabadi model for simple gas hydrate formation in batch system was developed. The total average absolute deviation was found to be 17.6%, 18.1%, 18.8%, 19.1% and 19.6% for the PR, NB, ER, PSRK and VPT equations of state for calculating gas consumption for binary gaseous mixtures during gas hydrate formation in the presence and absence of kinetic hydrate inhibitors, respectively. Comparison results between the calculated and experimental data points of gas consumption were obtained in flow loop indicate that the PR and NB equations of state have lower errors than the PSRK, ER and VPT equations of state for this model.

Volumetric properties of ionic liquids from cubic equation of state: Application to pure and mixture

In this work, we developed a cubic equation of state (CEOS) for modeling the volumetric properties of various ionic liquids (ILs). Two temperature-dependent parameters presented in the CEOS, have been determined from two sets of corresponding states correlations which are based on the critical point data or the surface tension of ILs. The predicted densities of pure ILs were compared with the experimental data over a broad pressure range from 1 to 100MPa. The total average absolute deviations (AADs) of the calculated densities of 948 data points from the experimental data are 1.82% using the critical property and 0.96% using the surface tension and liquid density as scaling parameters. Furthermore, the proposed CEOS was successfully extended to mixtures including IL+IL and IL+solvent systems. 1282 literature data points for mixtures were taken to check the reliability of the mixture version of the proposed CEOS. The AAD of the calculated densities of the mixtures using the surface tension and liquid density as scaling parameter is 0.37%. Furthermore, the excess molar volumes (VE) of the studied binary mixtures have been successfully computed by the use of the proposed CEOS.

Phase behavior and compressibility factor of two China gas condensate samples at pressures up to 95 MPa

Constant composition expansion measurements were performed using a high pressure fluid PVT system for two gas condensate samples collected from two reservoir fields in China to determine the dew point pressures and compressibility factors at different temperatures, where the experimental pressures were up to 95MPa. For the samples studied, the experimental results showed that the dew point pressures decrease with the increase of temperature and the gas compressibility factors increase with the increase of pressure in single phase zone at four temperatures. Thermodynamic models that combining equations of state with different kinds of plus-fraction splitting and critical properties of pseudo-components characterization methods were compared and optimized to describe the phase behavior and volumetric properties of gas condensate samples under high-pressure and high-temperature conditions. The preferred model has a better description for dew point pressures and gas compressibility factors with the total average absolute deviation for two samples of 0.64% and 1.56%, respectively.

Volumetric properties of mixtures involving ionic liquids from improved equation of state

The present work aims to propose alternative corresponding states correlations for temperature-dependent parameters appeared in perturbed hard-sphere equation of state (PHS EOS). The microscopic scaling constants σ, the effective hard-sphere diameter, and ɛ, the non-bonded interaction energy between two spheres are employed to construct the correlations. The modified PHS EOS is applied to model the volumetric properties of pure and mixtures containing ionic liquids (ILs). For 3127 experimental density data points examined for the studied pure ILs, the total average absolute deviation (AAD) of the predicted densities from the literature data is found to be 0.52%. Also, 978 data points for binary mixtures is examined, the AAD of the calculated densities of mixtures from those reported in the literature is found to be 0.79%. Several thermodynamic coefficients have also been successfully determined by the use of the present PHS EOS. The effect of the solvent on the excess functions of the studied binary mixtures has also been investigated using the proposed model.