SRK Equation Research Articles

Optimization of crossover SRK equation of state for thermodynamic properties calculation of CO2

In recent years, the CO2 super/transcritical power cycle has gained significant attention as the most widely studied power cycle. The accurate thermodynamic properties data is very important for cycle design and performance analysis. In this study, the Kiselev's crossover method based on the renormalization group theory is used to improve the classic SRK equation of state in non-critical region and reproduce the critical fluctuation phenomenon in critical region. The nonlinear equations method and interior-point method are used in the parameter fitting of crossover SRK (CSRK) to get the optimal parameters. The replaced method avoids the problem that Newton iteration method is prone to divergence and falling into local optima. The thermodynamic properties of CO2 including the VLE properties, heat capacity and speed of sound are calculated by CSRK, respectively. The results show the calculation of the non-critical region is improved, and the critical fluctuation phenomenon in the near-critical region is described accurately, especially the second-order thermodynamic properties calculation results is improved from 3.65 % to 2.80 % compared with our previous work.

Experimental and thermodynamic investigation of gemifloxacin solubility in supercritical CO2 for the production of nanoparticles

The effective use of the supercritical technology in the production of new pharmaceutical formulations with greater bioavailability requires the determination of the solubility of pharmaceutical substances in supercritical CO2 (scCO2) at different conditions. In the current work, the solubility of an antibacterial compound, Gemifloxacin, was measured at various temperatures (308 to 338 K), and pressures (120 to 300 bar). This compound has a poor solubility in scCO2 (0.02 × 10−4 to 0.67 × 10−4 mole fraction or 0.0156 to 0.5891 g.kg−1). Furthermore, some popular empirical models and three thermodynamic approaches (SRK and PR equations of state, and the regular solution model) were applied to correlate and predict the solubility of Gemifloxacin in scCO2. The regular solution model with temperature-dependent solubility parameter (mean AARD% = 2.32–4.34) and the SRK-based model (mean AARD% = 7.47), exhibited the highest accuracy in fitting the experimental data.

Propán-propilén elegy elválasztásának vizsgálata VRC rendszerrel

In this study a propane-propylene separation is investigated with traditional distillation column and with vapor recompression column (VRC). It is a very energy-intensive process, mainly because the boiling points of the components differ only slightly. The systems with the same parameters of the feed are investigated with Unisim Design® process simulation software with SRK equation of state. The results show that in case of the traditional and VRC system the quality and quantity of the products are the similar, but the energy stream of the VRC system is much lower than the traditional column’s. During the study not only the energy consumption but also the costs of the utility streams are calculated. The traditional distillation column includes a reboiler and a condenser, while the VRC system has energy streams from a compressor and a condenser. The calculation results show that the cost of the utility streams used in the VRC system is 15.5% of the costs of the utility streams in the conventional system.

The Joule–Thomson effect of (CO2 + H2) binary system relevant to gas switching reforming with carbon capture and storage (CCS)

The Joule–Thomson effect is one of the important thermodynamic properties in the system relevant to gas switching reforming with CCS. In this work, a set of apparatus was set up to determine the Joule–Thomson effect of binary mixtures (CO2 + H2). The accuracy of the apparatus was verified by comparing with the experimental data of carbon dioxide. The Joule–Thomson coefficients (μJT) for (CO2 + H2) binary mixtures with mole fractions of carbon dioxide (xCO2= 0.1, 0.26, 0.5, 0.86, 0.94) along six isotherms at various pressures were measured. Five equations of state EOSs (PR, SRK, PR, BWR and GERG-2008 equation) were used to calculate the μJT for both pure systems and binary systems, among which the GERG-2008 predicted best with a wide range of pressure and temperature. Moreover, the Joule–Thomson inversion curves (JTIC) were calculated with five equations of state. A comparison was made between experimental data and predicted data for the inversion curve of CO2. The investigated EOSs show a similar prediction of the low-temperature branch of the JTIC for both pure and binary systems, except for the BWRS equation of state. Among all the equations, SRK has the most similar result to GERG-2008 for predicting JTIC.

A study on the Joule-Thomson effect of during filling hydrogen in high pressure tank

With the development of the hydrogen fuel cell automobile industry, higher requirements are put forward for the construction of hydrogen energy infrastructure, the matching of parameters and the control strategy of hydrogen filling rate in the hydrogenation process of hydrogenation station. Fuel for hydrogen fuel cell vehicles comes from hydrogen refueling stations. At present, the technological difficulty of hydrogenation is mainly reflected in the balanced treatment of reducing the temperature rise of hydrogen and shortening the filling time during the fast filling process. The Joule-Thomson (JT) effect occurs when high-pressure hydrogen gas passes through the valve assembly, which may lead to an increase in hydrogen temperature. The JT effect is generally reflected by the JT coefficient. According to the high pressure hydrogen in the pressure reducing valve, the corresponding JT coefficients were calculated by using the VDW equation, RK equation, SRK equation and PR equation, and the expression of JT effect temperature rise was deduced, which revealed the hydrogen temperature variation law in the process of reducing pressure. Make clear the relationship between charging parameters and temperature rise in the process of decompression; the flow and thermal characteristics of hydrogen in the process of decompression are revealed. This study provides basic support for experts to achieve throttling optimization of related pressure control system in hydrogen industry.

A prediction model to predict the thermodynamic conditions of gas hydrates

Gas Hydrate modelling has gained huge attention in the past decade due to its increase in usage for various energy as well as environmental applications at an industrial scale. As the experimental approach is highly expensive and time-consuming, modelling is the best way to predict the conditions before the actual applications at industrial scales. The commercial software currently existing uses the equation of states (EOS) to predict the thermodynamic conditions of gas hydrates. But, in certain cases, the prediction by using EOS fails to predict the hydrate conditions accurately. Therefore, there arose a need for an accurate prediction model to estimate the hydrate formation conditions. So, in this work, an accurate prediction model has been proposed to predict the thermodynamic equilibrium conditions of the gas hydrate formation. The performance of prediction accuracy for the proposed model is compared with those of the SRK equation of state and Peng Robinson (PR) Equation of state. It was observed that in most of the cases the proposed model has predicted the thermodynamic conditions more accurately than the PR and SRK equation of state. This work helps in understanding the limitations of EOS for the prediction hydrate conditions. Also, the current work helps in strengthening the conventional statistical modelling technique to predict the hydrate conditions for a broader range.

Experimental measurement and thermodynamic modeling of Chlorothiazide solubility in supercritical carbon dioxide

Chlorothiazide, with the brand name Diuril, is used as a diuretic as well as an antihypertensive drug. This medicine with very slight solubility in water and low permeability is categorized in the class IV of Biopharmaceutical Classification System (BCS) and possess low bioavailability. Therefore, enhancement of the drug solubility would be of great importance to reduce its dosage and consequently side effects. Decrement of Chlorothiazide particles size to micro/nano scale using a supercritical carbon dioxide (scCO2)-based method can be an efficient approach to enhance its bioavailability and therapeutic efficiency. To select and design a proper supercritical micronization/nanonization method, solubility of Chlorothiazide in scCO2 should be determined which is conducted in this work by gravimetric method. In this study, solubility of Chlorothiazide in scCO2 was obtained at various operating conditions (308–338K and 130–290 bar). It was found between 0.417 × 10−5 to 1.012 × 10−5 mol mol−1 (mole fraction) for Chlorothiazide. Moreover, the obtained values were correlated through five empirical models (Chrastil, Mendez-Santiago and Teja (MST), Kumar- Johnston (K-J), Bartle, and Garlapati-Madras), as well as SRK and PR equations of state. All of the mentioned models have shown satisfactory correlation accuracy for the drug solubility. Meanwhile, the K-J model with the minimum AARD% value of 3.15 and the PR-EoS with the mean AARD% value of 6.51 have the highest precision to fit the experimental data. Also, the extrapolative ability of the mentioned empirical models to predict the Chlorothiazide solubility outside the considered range of operating conditions was investigated.

Compressed liquid densities for cyclopentane/n-heptane mixtures from 293.15 K to 363.15 K at pressures up to 70 MPa

The compressed liquid densities of pure cyclopentane, n-heptane and its binary mixtures were measured with the vibrating-tube densimeter. The temperature ranges were from 293.15 K to 363.15 K and the pressures up to 70 MPa. The density data were correlated with the Tammann-Tait equation. The excess molar volumes, isothermal compressibility and isobaric thermal expansivity were calculated and discussed. In addition, the SRK and PR equation of state and the corresponding volume-translation equations were used to predict the densities of the mixtures, and the predictive accuracy was analyzed.

Vapor-liquid equilibrium experiment and prediction of excess property of new working pair CO2-[BMP][Tf2N] in absorption refrigeration system: Expérience d'équilibre vapeur-liquide et prédiction de la propriété excédentaire de la nouvelle paire de travail CO2-[BMP][Tf2N] dans un système de réfrigération à absorption

Solubility of CO2 in ionic liquids (ILs) is of great importance in absorption refrigeration system as new working pairs. Vapor-liquid equilibrium (VLE) of CO2 in [BMP][Tf2N] (1-butyl-1-methyl-pyrrolidine bis(trifluoromethylsulfonyl)imide) is carried out experimentally using the experiment system at temperature range 303.15 K-363.15 K. The experimental results show that the solubility of CO2 in [BMP][Tf2N] can reach up to 0.1235–0.5324 (molar fraction) within temperature range 283.15∼363.15 K and pressure range of 0.2∼5 MPa. The solubility of CO2 in [BMP][Tf2N] increases with increase of temperature and pressure. The VLE data of CO2-[BMP][Tf2N] binary system is correlated with two models (SRK equation of state +WS mixing rule +UNIFAC activity coefficient model and PR equation of state +WS mixing rule +UNIFAC activity coefficient model). The excess Gibbs free energy (GE), excess enthalpy (HE) and excess entropy (SE) of the system are obtained and the interaction parameters kij is regressed based on the VLE of CO2-[BMP][Tf2N] binary system. The variation trend of GE, HE and SE are obtained with temperature, pressure and molar fraction of CO2. The calculation results show that the accuracy of SRK equation of state is slightly higher than that of PR equation of state in CO2-[BMP][Tf2N] binary system. The accuracy of SRK equation of state and PR equation of state decreases with increase of temperature and pressure.

Method for prediction of liquid-vapor critical points in binary mixtures: geometrical-EOS model

A new method for predicting the Liquid- Vapor critical point of binary mixture, is presented, which is based in geometrical distances. Actually, the method is based on the minimization of the distance between the experimental and calculated values of the critical temperatures and critical pressures. The SRK and PR equations of state along with classical mixing rules of van der Waals were used as thermodynamic models to calculate the critical point of a given mixture. The proposed method requires that the mixture parameters a, b, and the covolume ε = b/v of each equation of state be determined at each iteration by solving the resulting cubic equation. For nine binary mixtures containing: hydrocarbon derivatives, carbon dioxide and alcohols are studied. The AARE of the calculated values is about 0.86% for critical temperature and 2.07% for critical pressure. Good agreements are found between the calculated results and experimental data. The technique is a general purpose one and can be applied in connection with other thermodynamic models.

Prediction of Carbon Dioxide Solubility in Monoethylene Glycol /Water Mixtures Employing SRK and PR-EOS with Two Different Mixing Rules

A thermodynamic models of binary system carbon dioxide (1) - mixture (monoethylene glycol (MEG)/water) (2) at pressure up to 5 bar and temperatures (288-348 K) are established using SRK and PR equation of state (EOS). Modified van der Waal’s and quadratic mixing rules are coupled with the two Equation of state. Prediction of carbon dioxide in pure water and MEG were studied as well using same equations. Average absolute deviation in liquid-phase compositions percentage AADx % used for adjustable parameter optimization. The predicted results are showed very good agreement with the experimental data in all the systems examined. Quadratic mixing rule in all systems gives AADx % lower than Modified van der Waal’s and the values differences can be ignored.

Analysis of real gas equation of state for CFD modelling of twin screw expanders with R245fa, R290, R1336mzz(Z) and R1233zd(E)

Abstract Positive displacement expanders are widely investigated and theirs models commonly use the REFPROP database to evaluate fluid properties. However, estimating procedures in CFD models using REFPROP result in heavy use of CPU time. Therefore, a study has been carried out to determine if simpler methods for fluid property estimation are suitable. The ANSYS CFX solver used includes a number of cubic equations of state, namely, the Redlich Kwong, Soave Redlich Kwong, Aungier Redlich Kwong and Peng Robinson. To determine their suitability, performance simulations were carried out with each of them, on a twin screw expander with a 4/5 rotor configuration and an “N” rotor profile, operating with R245fa, R290, R1336mzz(Z) and R1233zd(E). For each considered equation, the expander's performance results deviation from those obtained using REFPROP is evaluated. These results show that the ideal gas equation of state gives predictions of flow and power that deviate significantly from those determined with REFPROP. The alternatively available cubic equations give far better agreement. Of these, the RK equation has the highest deviation, although it differs by only 2.2% maximum from the REFPROP values. The PR equation yields the closest agreement with a deviation of the order of only 0.8%, while the deviation with both SRK and ARK equations is less than 1.1% maximum, practically negligible. Apart from the good agreement obtained, the use of the real gas equations, in place of REFPROP, resulted in a saving of approximately 43% in CPU operating time to obtain same level of convergence of the solver.

Numerical simulation of water hammer in liquid methane feedline based on two compressible fluid models

In order to improve the capability of distributed parameter modeling for water hammer of liquid methane propellant in a staged combustion cycle engine simulation library, pipeline flow models are established based on two different compressible fluid assumptions. One is the slightly compressible fluid assumption and the other is the completely compressible fluid. For the completely compressible fluid model, the SRK equation of state is utilized to calculate the pressure rather than the internal energy fitting formula. And for slightly compressible fluid model, the pressure equation is deduced from continuity equation by introducing sound velocity equation. One-dimensional finite volume method is used so that the two models could work well with other component models of a staged combustion cycle engine simulation library which are all programmed in Modelica language. The pressure surges of the liquid methane in a system are predicted due to valve closure. The results show a principal difference of pressure surge frequencies between two models, which is caused by the different ways of calculation of pressure. In addition, a method of numerical oscillation suppression for completely compressible fluid model is proposed and a best value of oscillation suppression coefficient is given in the present paper.

English

In recent years, many natural gas reservoirs have been discovered with varying CO2 contents, many of which are at supercritical conditions. Calculation of compressibility factors for such reservoirs is important. Therefore, this research presents an extensive review of the various methods to calculate the compressibility factor for different natural gases containing CO2 at various temperatures and pressures. It also provides a comprehensive evaluation of the accuracy of well-known and recently published mixing rules, as well as various Z-factor correlations. Finally, a set of new correlations is presented to calculate the gas compressibility factor with reasonable accuracy. The Z-factor from the proposed correlations, as well as the PR and SRK equations of state are examined against several measured Z-factors for natural gases at supercritical conditions. The proposed correlations have a correlation coefficient of 96% and can be used to calculate compressibility at high pressures and temperatures. Key words: CO2, natural gas mixtures, Z-factor, compressibility factor, correlations.

Simulation of a NGCC Power Generation Plant for the Production of Electricity from CO2 Emissions Part II: SNGCC Power Plant

The objective of the first part of the investigation was to use Aspen Plus software and the Redlich-Kwong-Soave equation of state in order to simulate an adiabatic methanation reactor for the production of synthetic natural methane (SNG) using 1 kg/hr of carbon dioxide. In this paper, we define the Synthetic Natural Gas Combined Cycle (SNGCC) as a combined cycle power plant where the fuel is synthetic natural gas (SNG) produced by a methanation reactor. The feed of the methanation reactor is the recycled stream of carbon dioxide of a CO2 capture unit treating the flue gas of the SNGCC power plant. The objective of the second part of the investigation is the utilization of Aspen plus software with SRK equation of state for the simulation of the SNGCC power plant. The metallurgical limitation of the gas turbine was fixed at 1300°C in this investigation. For effective absorption by amine solutions, the molar percentage of CO2 in the flue gas should be higher than 10%. Moreover, in order to reduce technical problems linked to oxidative degradation of amine in the CO2 capture plant, the percentage of O2 in the flue gas should also be lower than 5%. To reach this goal, the primary air for combustion has 10% excess air (compared to stoichiometric air) and 37% of the flue gas leaving the SNGCC is recirculated as the secondary air for cooling the turbine. As a result, the concentration of CO2 and O2 of the flue gas entering the CO2 capture unit were respectively equal to 10.2% and 2.01%. The simulation results of the SNGCC power plant indicate that 6.6 MJ of electricity are produced for each kg of carbon dioxide recycled from the CO2 capture unit of the power plant. In other terms, the production of the 24.88 kg/hr of synthetic natural gas (SNG) consumes 62.36 kg/hr of recycled carbon dioxide and 16.4 kg/hr of hydrogen. The SNG produced by the methanation reactor of the power plant generates 114 kW of electricity. It is assumed in this paper that the hydrogen needed for the methanation of carbon dioxide is a product of a catalytic reforming plant that produces gasoline from heavy naphta fraction of an atmospheric distillation unit of crude oil.

Thermodynamic modeling and experimental measurement of semi-clathrate hydrate phase equilibria for CH4 in the presence of cyclohexane (CH) and tetra-n-butyl ammonium bromide (TBAB) mixture

In the current study, the effect of tetra-n-butyl ammonium bromide (TBAB) and cyclohexane mixture on CH4 semi-clathrate hydrate formation was studied. Semi-clathrate dissociation conditions for CH4 + TBAB + cyclohexane + water were investigated at different concentrations of TBAB (0.05, 0.10, and 0.15) mass fraction in the presence of cyclohexane at the pressure and temperature ranges of 1–8 MPa and 275.1–295 K, respectively. In addition, a thermodynamic model was suggested to predict the phase equilibria of our system, which is divided into four phases, where the van der Waals–Platteeuw Solid Solution Theory has been used to predict the hydrate phase. For gas phase, The SRK equation of state was applied. For oil phase, the cyclohexane activity coefficient in the organic phase was calculated by the non-random two-liquid model (NRTL). Finally, to determine the activity coefficient of the electrolyte species in the aqueous phase, the semi-empirical electrolyte NRTL (eNRTL) activity model was used. The results showed that the proposed model has an acceptable agreement with the experimental semi-clathrate hydrate dissociation data with an approximately average absolute relative deviation of 5.4%.

Thermodynamic modeling of ternary systems containing imidazolium-based ionic liquids and acid gases using SRK, Peng-Robinson, CPA and PC-SAFT equations of state

In this study, the cubic and the associative equations of state are applied to model the VLE data of ternary systems containing ionic liquids. In the first section, the simultaneous solubility of CO2 and H2S in the ionic liquids [omim][Tf2N], [omim][PF6] and [bmim][PF6] is modeled and the selective absorption of CO2/H2S is investigated at the temperatures T/K = (303.15 and 343.15) and the pressures P/MPa = (0.1 and 1). According to the obtained results, the percent deviations in pressure were varying between 6.0 and 10.8 for the SRK EoS, 6.0 and 10.6 for the PR EoS, 2.6 and 9.6 for the CPA EoS and 3.4 and 6.1 for the PC-SAFT EoS. Also, percent deviations in vapor phase composition were varying between 3.1 and 4.9 for the SRK EoS, 3.3 and 4.9 for the PR EoS, 3.1 and 7.0 for the CPA EoS and 3.8 and 4.9 for the PC-SAFT EoS. In the selectivity calculations, at high ionic liquid concentrations, the cubic models predict the selectivity drop; while the associative models present increasing trend. In the second section, the CO2 solubility in ethanol and [emim][Tf2N] as well as the mixture of ethanol and [emim][Tf2N] is modeled and the experimental points were tested for thermodynamic consistency. According to the obtained results, the percent deviation in pressure of the ternary systems was 3.9 for the SRK EoS, 3.9 for the PR EoS, 3.8 and 4.0 for the CPA EoS and 3.1 and 3.2 for the PC-SAFT EoS. In the same temperature and pressure, the CO2 solubility decrease when the concentration of ethanol increases, and the proposed models can describe this phase behavior.

Uncertainty Quantification in high-density fluid radial-inflow turbines for renewable low-grade temperature cycles

The inclusion of uncertainties in the design of turbines for renewable low-grade temperature power cycles is becoming a crucial aspect in the development of robust and reliable power blocks capable of handling a better range of efficiencies over a wider range of operational conditions. Modelling high-density fluids using existing Equations of State adds complexity to improving the system efficiency and little is known on the effect that the uncertainties of Equations of State parameters may have on the turbine efficiency. The purpose of this paper is to quantify the influence of coupled uncertain variables on the total-to-static efficiency of a radial-inflow Organic Rankine Cycle turbine with a high-density fluid R143a in a low-grade temperature renewable power block. To this end, a stochastic solution is obtained by combining a multi-dimensional generalized Polynomial Chaos approach with a full three-dimensional viscous turbulent Computational Fluid Dynamics solver for high-density radial-inflow turbines. Both operational conditions (inlet total temperature, rotational speed and mass flow rate) and Equations of State parameters (critical pressure and critical temperature) are investigated, highlighting their importance for turbine efficiency based on the consideration of three Equations of State, namely, Peng-Robinson, Soave-Redlich-Kwong, and HHEOS. This study, which is performed for both nominal and off-design operational conditions, highlights the inlet temperature as the most influential operational uncertain parameters, while the critical pressure is the most sensitive parameter for the three Equations of State tested. More importantly, it demonstrates a higher level of sensitivity of the SRK Equations of State, in particular at off-design operational conditions. This is a crucial aspect to take into account for the robust designs of Organic Rankine Cycle turbines for low-grade temperature renewable power cycles working at various conditions. It is expected that the proposed stochastic approach may consequently positively support the renewable energy sector to develop more robust and viable systems.

Screening of HFCs and Fluoroethers as Alternatives to R134a Using SRK EoS

The volumetric and thermodynamic properties of fluorinated ethers such as trifluoromethyl-1-H-pentafluoroethylether, F-oxetane, 2-H-heptafluoropropane, pentafluorodimethylether, F-methyl methyl ether, perfluorodoxolane, pentafluorodimethoxymethane and HFCs such as trifluoroethane, heptafluoropropane, difluoroethane, pentafluoropropane, ethyl fluoride as alternatives to replace R134a have been predicted using SRK equation of state over the temperature range from − 25 °C to + 55 °C. Theoretical analysis is carried out using ten-point vapour compression cycle for screening of candidate refrigerants. The results of analysis have been used to ascertain standard refrigeration parameters in respect of each of the candidate refrigerants. The analysis indicates that the performances of difluoroethane, ethyl fluoride, pentafluorodimethylether and F-oxetane are better than that of R134a.

Implementation of electrolyte CPA EoS to model solubility of CO2 and CO2 + H2S mixtures in aqueous MDEA solutions

Abstract The electrolyte version of SRK plus association equation of state (eSRK-CPA EoS) was employed to correlate CO2 solubility in MDEA aqueous solutions. The applied model comprises the classic form of CPA EoS including SRK EoS plus Wertheim association term in addition to MSA theory and Born terms so that the two last terms are responsible for the long-range interactions. A reaction-containing bubble pressure computation technique comprising two nested loops was utilized to model the systems. The internal loop, calculates the liquid phase concentrations via reaction, mass and charge balance equation solving, whereas, the vapor phase concentrations will be obtained in the external one. 470 experimental data were used to correlate binary subsystems and the H2O + MDEA + CO2 ternary system. Since, there not exist any binary VLE data for MDEA + CO2 subsystem, two fitting scenarios were applied. At the first scenario, the binary interaction parameter was assumed equal to zero, while, in second approach the parameter was obtained through ternary system correlation. Both scenarios show very good accuracy in that the Absolute Average Deviation percentages (AAD) obtained were 19.12% and 18.85%, respectively. Also, to show the efficiency of the used model, a comparison between our results and those of the best-known models was made. Finally, having model parameters for H2S solubility from our previous work [A. Afsharpour, Petroleum Science and Technology 35 (3) (2017) 292-298], simultaneous solubility of CO2 + H2S mixtures in MDEA solutions was predicted using the eSRK-CPA EoS with no new optimizable parameters. As the results show, the applied model has a good performance for correlation and prediction of acid gas solubility in a wide range of pressures, temperatures, acid gas loadings, and MDEA concentrations.