scholarly journals Critical behaviour of binary mixtures: Calculation by the Heidemann-Khalil method

2020 ◽  
Vol 48 (5-6) ◽  
pp. 497-525
Author(s):  
HICHEM GRINE ◽  
HAKIM MADANI ◽  
SAIDA FEDALI

The critical temperature and critical pressure are two important parameters to characterize a particular fluid. In this paper, we have studied the critical points of 24 binary mixtures containing hydrocarbon derivatives, carbon dioxide and alcohols. Computations were performed using the Heidemann-Khalil method, combined with the following equations of state (Eos): van der Waals (vdW), Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR). The Newton-Raphson method was used to solve a set of nonlinear equations in three independent variables (molar fraction x, temperature T and volume V). Comparisons between predicted and available reference data are given to evaluate the accuracy of the thermodynamic model employed. The average absolute relative error (AARE) of the simulated data was less than 0.2% for critical temperature and 3% for critical pressure. A good agreement has been found between model prediction and reference data.

2016 ◽  
Vol 35 (10) ◽  
pp. 1037-1045 ◽  
Author(s):  
Jun Cai ◽  
Xiaolu Zhang ◽  
Kuaishe Wang ◽  
Chengpeng Miao

AbstractThe hot deformation behavior of BFe10-1-2 cupronickel alloy was investigated over wide ranges of deformation temperature and strain rate. The physics-based constitutive model was developed to predict the dynamic recovery (DRV) behavior of BFe10-1-2 cupronickel alloy at elevated temperatures. In order to verify the validity of the developed constitutive equation, the correlation coefficient (R) and average absolute relative error (AARE) were introduced to make statistics. The results indicated that the developed constitutive equation lead a good agreement between the calculated and experimental data and can accurately characterize the hot DRV behaviors for the BFe10-1-2 cupronickel alloy.


1987 ◽  
Vol 109 (1) ◽  
pp. 58-62
Author(s):  
S. C. Bhaduri ◽  
H. K. Varma

An analytical method has been proposed to calculate thermodynamic properties of refrigerant-absorbent mixtures of polar molecules. The critical pressure, critical temperature, critical volume and experimental dipole moment of pure components are required in the proposed method. The calculated properties have been compared with the available experimental data and results reported in the literature. The comparison shows very good agreement. Thus, this method is recommended for use with refrigerant-absorbent pairs having polar molecules.


Author(s):  
David Beitel ◽  
Spencer McNee ◽  
Fraser McLaughlin ◽  
Luis F. Miranda-Moreno

Bicycle flow data is crucial for transportation agencies to evaluate and improve cycling infrastructure. Average annual daily bicyclists (AADB) is commonly used in research and practice as a metric for cycling studies such as ridership analysis, infrastructure planning, and injury risk. AADB is estimated by averaging the daily cyclist totals measured throughout the year using a long-term automated bicycle counter, or by using long-term bicycle counting data to extrapolate data from a short-term counting site. Extrapolation of a short-term bicycle counting site requires an accurate and complete set of daily factors from a group of references: long-term bicycle counters. In practice, validation of reference data is done manually, an exercise that is time-consuming but crucial as significant error can be introduced into AADB extrapolation if reference data are not validated. This paper proposes an automated method to validate long-term bicycle count data and interpolate anomalous portions of data. As part of this work, the methods are validated using a relatively large dataset of automated bicycle counts. For validation of our approach, data anomalies are created artificially in a way that removes data (first trial), or reduces counts to 25% or 40% of the measured bicycle counts (second and third trials), for 6 hours, 12 hours, and full days. Of the more than 100 generated anomalies, the validation process flagged approximately 90% in the first and second trials and 80% in the third trial. The average absolute relative error of the interpolated daily values was approximately 10% for all three trials.


2020 ◽  
Vol 41 (12) ◽  
Author(s):  
Ulrich K. Deiters ◽  
Ian H. Bell

Abstract When applied to asymmetric binary mixtures (e.g., methane + pentane or heavier alkanes, hydrogen-containing mixtures), the GERG equation of state (GERG-2004 or GERG-2008) predicts critical curves with physically unreasonable temperature maxima above the critical temperature of the heavier component. These maxima are associated with physically impossible vapor–liquid equilibria. The phenomenon is probably caused by corrections for critical anomalies that were built into the empirical pure-fluid equations of state forming the foundation of the GERG model. These corrections ensure that the model represents thermodynamic data of pure fluids quite well even close to their critical points. For mixtures, however, the corrections can cause artifacts.


2016 ◽  
Vol 139 (2) ◽  
Author(s):  
K. K. Botros ◽  
J. Geerligs ◽  
B. Rothwell ◽  
T. Robinson

Shock tube tests were conducted on a number of binary CO2 mixtures with N2, O2, CH4, H2, CO, and Ar impurities, from a range of initial pressures and temperatures. This paper provides examples of results from these tests. The resulting decompression wave speeds are compared with predictions made utilizing different equations of state (EOS). It was found that, for the most part (except for binaries with H2), the GERG-2008 EOS shows much better performance than the Peng–Robinson (PR) EOS. All binaries showed a very long plateau in the decompression wave speed curves. It was also shown that tangency of the fracture propagation speed curve would normally occur on the pressure plateau, and hence, the accuracy of the calculated arrest toughness for pipelines transporting these binary mixtures is highly dependent on the accuracy of the predicted plateau pressure. Again, for the most part, GERG-2008 predictions of the plateau are in good agreement with the measurements in binary mixtures with N2, O2, and CH4. An example of the determination of pipeline material toughness required to arrest ductile fracture is presented, which shows that prediction by GERG-2008 is generally more conservative and is therefore recommended. However, both GERG-2008 and PR EOS show much worse performance for the other three binaries: CO2 + H2, CO2 + CO, and CO2 + Ar, with CO2 + H2 being the worst. This is likely due to the lack of experimental data for these three binary mixtures that were used in the development of these EOS.


2009 ◽  
Vol 23 (26) ◽  
pp. 3091-3096 ◽  
Author(s):  
JIANXIANG TIAN ◽  
HUA JIANG ◽  
YI XU

Experimentally, a maximum point in the curve of the saturated property ψ=(1-Tr)Pr versus the saturated temperature was postulated (High Temp.-High Press.26 (1994) 427). Here, Tr is the saturated temperature reduced by the critical temperature and Pr is the saturated pressure reduced by the critical pressure. Later, this behavior was applied to assure the saturated vapor pressure critical amplitudes (Appl. Phys. Lett.90 (2007) 141905). In this paper, we indicate that theory of equation of state (EOS) can predict this maximum point. The EOSs we study are the combinations of the hard sphere repulsions and some normally used attractions such as the Redlich–Kwong attraction. We find the EOSs with Redlich–Kwong attractive terms give out the results in the experimental range.


1962 ◽  
Vol 2 (03) ◽  
pp. 197-202
Author(s):  
Robert B. Grieves ◽  
George Thodos

Abstract A method has been developed for predicting the critical temperatures and critical pressures of binary mixtures of carbon dioxide, hydrogen sulfide, nitrogen, hydrogen, carbon monoxide and oxygen with the normal paraffin hydrocarbons. For carbon-dioxide and hydrogen-sulfide systems, relations are presented that take into account the peculiar behavior of mixtures with closely boiling components, such as carbon dioxide-ethane and hydrogen sulfide-propane mixtures which exhibit minimum critical temperature points. For hydrogen, nitrogen and carbon-monoxide systems, the extreme critical behavior caused by wide differences in pure component properties is established. In addition, those fixed gas-paraffin systems which resemble paraffin-paraffin systems are also accounted for. For a mixture of known composition, the pure component critical temperatures, critical pressures and normal boiling points are all that are required to determine its critical point. Graphical relations are presented relating Tc and Pc of the mixture to the pure component properties. From the treatment of 12 carbon-dioxide and hydrogen-sulfide systems reported in the literature (74 mixtures), the expected error for the critical temperature is approximately 1.5 per cent, and for the critical pressure, approximately 2 per cent. From the treatment of six hydrogen, nitrogen and carbon-monoxide systems reported in the literature (30 mixtures), the expected error for both the critical temperature and critical pressure is approximately 2.5 per cent. The relationships, which have been developed with only normal paraffins as the hydrocarbon components, may be extended to those isoparaffins and olefins which fall within the allowable volatility ranges. Introduction Many of the fixed gases - carbon dioxide, hydrogen sulfide, nitrogen, hydrogen, carbon monoxide and oxygen - occur in natural mixtures with hydrocarbons. Carbon dioxide and hydrogen sulfide are frequent components of the fluids produced from underground petroleum reservoirs. Nitrogen, carbon dioxide and hydrogen sulfide are present in varying quantities in most natural gases and gas-condensate well effluents. Hydrogen mixtures are of considerable interest in many phases of refining processes of petroleum. The determination of the critical temperatures and critical pressures of such mixtures is of value in vapor-liquid equilibrium studies, for the prediction of the characteristics of underground reservoirs, and for reduced-state correlations of PVT, transport and thermodynamic properties. The accurate estimation of the critical point for binary mixtures is an important initial step toward a complete analysis for the establishment of the critical temperatures and pressures of multicomponent mixtures. Methods for predicting the critical temperatures and critical pressures of binary hydrocarbon systems have already been presented in the literature. It is possible to apply these existing methods to fixed gas-paraffin mixtures but due to their unusual critical behavior, values calculated deviate considerably from experimental values. For systems containing trace quantities of the fixed gases, these methods are acceptable; however, for systems containing more than 5 mol per cent of the fixed gases, these utterly fail to produce reasonable critical values. Consequently, in this study a method has been developed for handling such binary mixtures over the entire composition range. CARBON-DIOXIDE AND HYDROGEN-SULFIDE SYSTEMS The critical behavior and the vapor pressure behavior of mixtures of carbon dioxide and hydrogen sulfide with paraffinic hydrocarbons may be quite similar or quite dissimilar to that of paraffin-paraffin mixtures, depending on the volatilities of the components involved. The critical temperature and normal boiling point of carbon dioxide are very close to the corresponding values for ethane, while its critical pressure is considerably higher than that of ethane. SPEJ P. 197^


2021 ◽  
Vol 18 (38) ◽  
pp. 188-213
Author(s):  
Victor L. MALYSHEV ◽  
Yana F. NURGALIEVA ◽  
Elena F. MOISEEVA

Introduction: Today, there are four main groups of methods for calculating the compressibility factor of natural gas: experimental measurements, equations of state, empirical correlations, modern methods based on genetic algorithms, neural networks, atomistic modeling (Monte Carlo method and molecular dynamics). A correctly chosen method can improve the accuracy of calculating gas reserves and predicting its production and processing. Aim: To find the optimal methods for calculating the z-factor following the characteristic thermobaric conditions. Methods: To determine the best method for calculating the compressibility factor, the effectiveness of using various empirical correlations and equations of state to predict the compressibility factor of hydrocarbon systems (reservoir gases and separation gases) of various compositions were evaluated by comparing numerical results with experimental data. Results and Discussion: Based on 824 experimental values of the compressibility factor for 235 various gas mixtures in the pressure range from 0.1 to 94 MPa and temperatures from 273 to 437 K, the optimal equation of state and empirical correlation dependence for accurate z-factor prediction was found. It is shown that for all gas mixtures the Peng-Robinson equation of state with the shift parameter and Brusilovsky equation of state allow achieving best results. For these methods, the average absolute relative error does not exceed 2%. Among the correlation dependences, the best results are shown by the Sanjari and Nemati Lay; Heidaryan, Moghadasi and Rahimi correlations with an error not exceeding 3%. Conclusions: It was found that for the proposed methods, the reduced pressure has a more significant effect on the accuracy of the calculated values than the reduced temperature. It is shown that when studying acid gas mixtures with a carbon dioxide content of more than 10%, the equations of state better describe the phase behavior of the system in comparison with empirical correlations.


Author(s):  
V.P. Bondarenko ◽  
O.O. Matviichuk

Detail investigation of equilibrium chemical reactions in WO3–H2O system using computer program FacktSage with the aim to establish influence of temperature and quantity of water on formation of compounds of H2WO4 and WO2(OH)2 as well as concomitant them compounds, evaporation products, decomposition and dissociation, that are contained in the program data base were carried out. Calculations in the temperature range from 100 to 3000 °С were carried out. The amount moles of water added to 1 mole of WO3 was varied from 0 to 27. It is found that the obtained data by the melting and evaporation temperatures of single-phase WO3 are in good agreement with the reference data and provide additionally detailed information on the composition of the gas phase. It was shown that under heating of 1 mole single-phase WO3 up to 3000 °С the predominant oxide that exist in gaseous phase is (WO3)2. Reactions of it formation from other oxides ((WO3)3 and (WO3)4) were proposed. It was established that compound H2WO4 is stable and it is decomposed on WO3 and H2O under 121 °C. Tungsten Oxide Hydrate WO2(OH)2 first appears under 400 °С and exists up to 3000 °С. Increasing quantity of Н2О in system leads to decreasing transition temperature of WO3 into both liquid and gaseous phases. It was established that adding to 1 mole WO3 26 mole H2O maximum amount (0,9044–0,9171 mole) WO2(OH)2 under temperatures 1400–1600 °С can be obtained, wherein the melting stage of WO3 is omitted. Obtained data also allowed to state that that from 121 till 400 °С WO3–Н2O the section in the О–W–H ternary system is partially quasi-binary because under these temperatures in the system only WO3 and Н2O are present. Under higher temperatures WO3–Н2O section becomes not quasi-binary since in the reaction products WO3 with Н2O except WO3 and Н2O, there are significant amounts of WO2(OH)2, (WO3)2, (WO3)3, (WO3)4 and a small amount of atoms and other compounds. Bibl. 12, Fig. 6, Tab. 5.


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