Soave Redlich Kwong Equation Research Articles

Prediction of thermodynamic behavior of binary mixtures by applying the crossover approach to Soave–Redlich–Kwong equation of state

Thermodynamic analysis of binary mixtures near the critical region is essential for many chemical process designs. In this research, based on isomorphism principle and incorporating general crossover approach the original Soave–Redlich–Kwong (SRK) equation of state (EOS) was developed for the binary mixtures. We have introduced an additional term in the crossover function in order to take into account the difference between the classical critical parameters and the real critical parameters. The applicability of this crossover EOS was verified against methane–ethane mixture to describe their thermodynamic properties over a wide range of thermodynamic states, because of their wide applications. It is shown that based on this approach we can received too much more accuracy for predicting thermodynamic properties in comparison with classical form of SRK EOS.

Vapor–Liquid Equilibrium Measurements for Carbon Dioxide + Cyclohexene + Squalane at High Pressures Using a Synthetic Method

Growing interest in the study of production conditions in the presalt led to the need to study complex systems at high pressures and temperatures, such as up to 70 MPa and up to 393 K. The aim of this work is to obtain vapor–liquid equilibrium data at high pressures and temperatures for hydrocarbon systems with carbon dioxide (CO2). To obtain these data, an experimental setup and procedure using a synthetic cell were designed. Experimental data of the binary system CO2 + cyclohexene (C6H10) and CO2 + squalane (C30H62) over a range of temperature between 303 and 398 K and the ternary system CO2 + C6H10 + C30H62 at various temperatures (318–393 K) and compositions are reported. It is noteworthy that the reported measurements in this work were not studied in the literature, and experimental data may contribute to industrial and scientific interests. The phase behavior of the system was also described using the Soave–Redlich–Kwong equation of state together with Mathias–Copeman alpha function. Interaction par...

Comparative study of vapour-liquid equilibrium and density modelling of mixtures related to carbon capture and storage with the SRK, PR, PC-SAFT and SAFT-VR Mie equations of state for industrial uses

Carbon capture and storage (CCS) is nowadays considered as one of the most promising methods to counterbalance the CO2 emissions from the combustion of fossil fuels, natural gas processing, cement manufacturing, etc. In dealing with the transport and the storage of CO2-rich streams, design of a safe and optimum process requires the knowledge of thermophysical properties (especially density) of CO2-rich mixtures. Consequently, the development of accurate thermodynamic models to evaluate these properties plays a key role in the context of CCS. This work is focused on comparing the capability of four Equations of State (EoSs) in modelling the Vapour-Liquid Equilibrium (VLE) and the density of binary mixtures of interest in the field of CCS. Two Cubic EoSs (CEoS), the original Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) EoSs, and two Statistical Associating Fluid Theory-based EoSs, namely the Perturbed Chain (PC-SAFT) EoS and the Variable Range SAFT-VR Mie EoS have been considered. These EoSs were compared (with both zero and regressed binary interaction parameters) with respect to VLE and density data of 108 binary mixtures of five main gaseous components (CO2, CH4, C2H6, N2, and H2S). Concerning the cubic EoS, the Peneloux volume translation was used to better correlate densities. The comparison reveals that on average the most accurate VLE and density predictions are obtained with the SAFT-based EoSs, while similar results in VLE calculations are obtained with the four EoSs when regressed binary interaction parameters are used. The SAFT-VR Mie EoS is on average more accurate for the description of VLE and density data than the other studied models.

Estimating the solubility of different solutes in supercritical CO2 covering a wide range of operating conditions by using neural network models

A new neural network-based model is proposed for solute solubility in supercritical carbon dioxide (CO2). The solubility of fifteen solutes in supercritical carbon dioxide at different temperatures and pressures are estimated. Four neural network models have been tested to investigate the generalize-ability of each network. The results from different semi-empirical models, namely Chrastil, Kumar and Johnston, Bartle, Mendez-Santiago and Teja, the Peng–Robinson and Soave–Redlich–Kwong equation of state models are compared to the one estimated by using the proposed neural network model. The average absolute deviation (AAD) of 5.42% compared to those of density-based and equation of state models, representing the reasonable accuracy of the developed model for estimating the solubility of solutes in supercritical fluid extraction process.

A combined thermo-kinetic analysis of various methane reforming technologies: Comparison with dry reforming

Dry reforming of methane is one of the few chemical reactions which can effectively convert carbon dioxide (CO2), a major green-house gas, into a valuable chemical precursor, syngas (a mixture of CO and H2), that can be converted into chemicals and fuels via different synthesis routes such as the Fischer Tropsch synthesis. The inherent limitations of dry reforming reaction, for instance, rapid catalyst deactivation by coke deposition and the very high energy requirements, has restricted its use as a commercial technology. This study was performed to evaluate the potential of overcoming the limitations of dry reforming by integrating it with other commercial methane reforming technologies such as steam reforming and partial oxidation reforming in the context of industrial operating conditions. A thermodynamic and kinetic analysis of the combined reforming has been conducted using the software suite MATLAB®. The aim of this complicated assessment is to identify optimized combination of the three reformers and also the corresponding operating conditions that would utilize significant amount of CO2 while ensuring CO2 fixation, minimum carbon formation and optimum energy requirements. The thermodynamic equilibrium product distribution calculations involved the Peng Robinson (PR), Redlich Kwong (RK) and Soave Redlich Kwong (SRK) equations of state (EOS) to identify the best EOS that accounts for the non-ideality associated with the high pressure operation. The study evaluated simultaneous effects of temperature (200°C–1200°C), pressure (1–20bar) and feed mole ratios (of methane, steam, carbon dioxide and oxygen) on the equilibrium product distribution. The addition of oxygen and steam to dry reforming helped in decreasing energy requirements while simultaneously increasing the syngas yield ratio (H2:CO ratio). The numerical evaluation revealed an optimized operating condition of ∼750°C at 1bar pressure at a feed mole ratio CH4:H2O:O2:CO2 of 1:0.4:0.3:1. For this optimization, the system boundaries were limited only to a reformer block without considering the upstream and dowstream processes. At this optimized condition, the carbon deposition was eliminated and the CO2 conversion was observed to be 47.84% with an energy requirement of 180.26kJ. The study is further extended to include kinetic analysis of combined dry and steam reforming of methane. The preliminary findings of kinetic evaluation indicated an excellent agreement between combined kinetic model with the thermodynamic equilibrium results.

CFD simulations of turbulent nonreacting and reacting flows for rocket engine applications

A consistent real gas framework based on a preconditioning scheme is implemented into the CFD code TASCOM3D to simulate nonreacting and reacting turbulent flows with transcritical injection. All thermodynamic properties and partial derivatives are rigorously evaluated from the reduced residual Helmholtz energy by use of fundamental thermodynamic relations. The Soave–Redlich–Kwong equation of state with an optional volume translation is employed in combination with high-pressure models for the calculation of fluid transport properties. Three test cases are simulated to validate the implemented real gas framework using different turbulence modeling strategies. A good match between numerical and experimental data is obtained.

Density modelling of ionic liquids using the electrolyte Soave–Redlich–Kwong equation of state

A considerable amount of literature has recently been published on the study of ionic liquids (ILs). Due to their diversity and to the possibility of being designed to fit a specific application, predictive tools are required to understand their properties and their behaviour when mixed with other substances. One of these tools is thermodynamic modelling with equations of state (EoS). In this work, the Soave–Redlich–Kwong equation of state, coupled to the Debye–Hückel electrolyte model, was applied to correlate the densities of pure ILs. It was assumed that the ILs were totally dissociated, forming a binary mixture of cations and anions. In the modelling, the required EoS parameters were assessed through group contribution methods. One scale parameter was introduced to buffer the uncertainty of the calculations, and it was tuned to fit the model to the ILs’ measured densities. Three strategies were adopted to describe the densities in a wide range of temperatures and pressures: (i) adjusting this single IL parameter in order to fit the model to the reported densities at low pressure; (ii) determining it from one measured datum and (iii) from the obtained parameters in the second approach, generating an empirical function that correlates them with their molar masses. At 0.1MPa (458 data points), the overall absolute average deviations from the experimental data were 0.9%, 1.3% and 4.0% for each of these strategies, respectively. High-pressure densities were also predicted (3270 points), with computed deviations from the measurements of 1.4%, 1.4% and 3.4%. The proposed method can be used for IL density predictions, as a function of temperature and pressure, when no or only one measured datum is available.

Water content of light n‐alkanes: New measurements and cubic‐plus‐association equation of state modeling

Light hydrocarbon gases such as methane, ethane, propane, and butane or other so called gaseous solvents have been suggested as steam additives to improve bitumen recovery and energy efficiency. The water content of these gases is one of the key requirements in the simulation and design of solvent‐aided thermal heavy oil recovery processes. In this work, we present new experimental data for the water content of these gases at high temperatures (up to 493.15 K) and moderate pressures (P < 6 MPa). The experimental data was regenerated using the cubic‐plus‐association equation of state. The Soave–Redlich–Kwong equation of state is used to treat the physical interactions. The association interactions are captured using Wertheim's first‐order thermodynamic perturbation theory. A set of binary interaction parameters is proposed to calculate the water content of methane, ethane, propane, and n‐butane at the operating conditions of the thermal heavy oil and bitumen recovery processes. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1384–1389, 2017

Helium substitution of natural gas hydrocarbons in the analysis of their hydrate

This communication successfully characterises the thermodynamic phase equilibrium conditions for a synthetic natural gas comprising of methane, ethane, propane, i-butane, n-butane, i-pentane, n-pentane and carbon dioxide. Experimental determination of the hydrate stabilization effects of the present hydrate formers was performed using a novel approach involving helium substitution of each hydrate guest species in an otherwise identical synthetic natural gas. Results in the ranges of 30–180 bar largely agreed with the van der Waals-Platteeuw (vdW-P) models in Aspen HYSYS and Calsep PVTsim with Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state. The substitution of propane and i-butane significantly shifted hydrate equilibrium conditions to lower temperatures at a given pressure and was confirmed with the Clausius-Clapeyron equation. A slope of −17372 K was calculated for the original gas mixture, a value 3000 and 2000 K steeper than an identical mixture with the substitution of propane and i-butane respectively. Dissociation enthalpies were also calculated; 100.7 (±0.4) kJ/mol for hydrates of the original gas and 87.8 (±0.4) and 94.9 (±0.8) kJ/mol for hydrates of the propane and i-butane substituted gas. Reliability and consistency of the presented results is complimented by a propagated relative uncertainty of ±1.28%.Computed data was used to calculate dissociation enthalpies and Clausius-Clapeyron slopes, both of which are consistent with experimental calculations when using PR and SRK equations. The helium substitution approach in the experimental determination of the extent of hydrate stabilization in a complex gas mixture provided by each possible hydrate former is a viable method. Results are particularly important to the general design of refinement processes, as they provide real implications on the changes in hydrate equilibrium conditions for a natural gas separation process.

Phase equilibria prediction model for semiclathrate hydrates formed from CH4, CO2, and N2 in the presence of tetra-n-butyl ammonium bromide

ABSTRACTIn this work, a prediction model was studied and carried out to predict phase equilibrium conditions for semiclathrate hydrates formed from the ternary system of liquid water, tetra-n-butyl ammonium bromide, and CO2, CH4, or N2. Based on the Soave–Redlich–Kwong equation of state along with the Chen–Guo model, the predictions of phase equilibria of semiclathrates of CO2, CH4, and N2 + pure water/tetra-n-butyl ammonium bromide aqueous solution has been made. A new correlation for activity relating to the system temperature and tetra-n-butyl ammonium bromide concentration has been proposed. The prediction results were analyzed and showed good agreement with the experimental data.

Influence of MEA and piperazine additives on the desulfurization ability of MDEA aqueous for natural gas purification

The influence of monoethanolamine (MEA) and piperazine added into methyldiethanolamine (MDEA) aqueous solution on the desulfurization of natural gas was investigated by the method of equilibrium data determination in this paper. Four kinds of equilibrated systems, i.e. H2S-NG-MEA-water, H2S-NG-MDEA-water, H2S-NG-(MEA-MDEA)-water, H2S- NG-(MEA-MDEA-PZ)-water at the temperature ranging from 298.15 to 333.15 K were measured in a glass-jacketed gas absorption cell with a double-drive impeller device. The results show that the H2S partial pressure increases with the increase of H2S loading in liquid phase along an isotherm. The addition of MEA and PZ is beneficial for improving the desulfuration ability of MDEA. The ability of H2S absorption for the four mixed alkanolamine systems is MEA > (MEA-MDEA-PZ) > (MEA-MDEA) > MDEA according to the order of size. The four equilibrium data can be well correlated with the Soave–Redlich–Kwong equation of state and electrolyte-NRTL activity coefficient model. The overall mean relative errors of total pressure and H2S partial pressure between the calculated and experimental data of the four systems are 3.30 and 3.07 %, respectively. The experimental and calculated results are very useful for desulfuration and purification process of natural gas or other industrial gases.

Vapor–Liquid Equilibrium for Methanol + Methyl Palmitate near the Critical Temperature of Methanol

The vapor–liquid equilibrium for a methanol + methyl palmitate system was measured using a flow-type method at a pressure range of 1.86–8.81 MPa and a temperature range of 493–543 K, which is near the critical temperature of methanol (512.64 K). The mole fractions of methyl palmitate in the vapor phase were nearly zero, and the errors were also close to zero at all temperatures. The measuring errors of the liquid phase were slightly higher than those of the vapor phase. The Soave–Redlich–Kwong equation of state (SRK EOS), the Peng–Robinson equation of state (PR EOS), and the Cubic-Plus-Association equation of state (CPA EOS) combined with the Adachi–Sugie (AS) mixing rule were employed to correlate the measured data. The correlated results are consistent with the measured data. Because of their accuracy and concise calculation, the SRK and PR EOSs are better choices for correlating the methanol + methyl palmitate system when considering the accuracy and conciseness of calculating.

Steady state, oscillations and chaotic behavior of a gas inside a cylinder with a mobile piston controlled by PI and nonlinear control

This paper analyzes the behavior of nitrogen inside a closed cylinder with a mobile piston actuated by a nonlinear spring, a viscous damper and a control force which compensates partially the effect of the high gas pressure. Two helical heating coils are placed inside the cylinder and with their flow rates controlled by means of a linear controller of type proportional plus integral (PI) and another nonlinear control law to provide an approximately isothermal gas behavior. Based on the analysis of the mechanical and thermal subsystems and the control laws, a justification of the parameter values is presented and corroborated through analytical solutions that are obtained by approximate methods. To investigate the thermodynamic equilibrium conditions, the Soave–Redlich–Kwong and the Redlich–Kwong state equations are analyzed and compared, showing that the Soave–Redlich–Kwong equation is superior. The Melnikov method has been used to obtain sufficient conditions for chaotic behavior, which has also been investigated by means of the sensitive dependence, Lyapunov exponents and the power spectral density. The validity of the proposed model has been analyzed by using the compressibility chart for the nitrogen, and the analytical calculations have been verified through full numerical simulations.

Solubility of CO2 in [1-n-butylthiolanium][Tf2N]+toluene mixtures: liquid-liquid phase split separation and modelling.

Carbon dioxide has been shown to be an effective antisolvent gas for separating organic compounds from ionic liquids (ILs) by inducing a liquid-vapour to liquid-liquid-vapour transition. Using carbon dioxide, toluene can be separated from imidazolium, phosphonium and pyridinum cation-based ILs with the bis(trifluoromethylsulfonyl)imide anion, which is relatively hydrophobic and has a high toluene solubility. A new IL with relatively low viscosity is tested here for the same toluene separation process: 1-n-butylthiolanium bis(trifluoromethylsulfonyl)imide. Carbon dioxide solubility in binary and ternary systems containing toluene and 1-n-butylthiolanium bis(trifluoromethylsulfonyl)imide is measured at 298.15 and 313.15 K up to 7.4 MPa. Solubility behaviour in this IL is similar to imidazolium-based ILs with the same anion. However, phase split pressures are lower when 1-n-butylthiolanium bis (trifluoromethylsulfonyl)imide is used instead of 1- n-hexyl-3-methylimidazolium bis(trifluoromethylsu- lfonyl)imide at the same conditions of temperature and initial composition of toluene in the IL. Solubility data are modelled with the conductor-like screening model for real solvents combined with the Soave-Redlich-Kwong equation of state, which provides good qualitative results.

Design optimization of partial admission axial turbine for ORC service

An analysis of the application of a single stage partial admission axial turbine in organic Rankine cycle is presented. The cycle is utilized to recover the heat rejected by an internal combustion engine. The selected fluid is R245fa, whose real gas behavior is relevant under the studied conditions, as modeled by the Redlich–Kwong–Soave equation of state. A loss model for the flow through the axial blades is proposed in this work based on the boundary layer theory, the concept of diffusion factor, wind tunnel cascade tests available in literature and the conservation equations for compressible flow. The basic geometry and dimensions needed to achieve maximum turbine efficiency are determined under several subcritical and supercritical cycle conditions by means of a restrained design optimization algorithm. The single stage turbine preliminary design is shown to be greatly influenced by media compressibility and the use of convergent-divergent profiled nozzles is promising to achieve the highest possible performance potential, especially at high evaporator pressure conditions.

Phase equilibria in process design for the production of polymers derived from carbon dioxide

The optimisation of an innovative process where carbon dioxide (CO2) is used as raw material for the production of polyurethane precursors relies strongly on the physical properties and phase equilibria of the mixtures involved. In this work, we present experimental results for high-pressure phase equilibria of systems involving CO2, propylene oxide, different polyether carbonate polyols (CO2-PET) and propylene carbonate, at pressures up to 8 MPa and temperatures between 373 K and 393 K. Low-pressure phase equilibria were determined for the system CO2-PET + propylene carbonate, at temperatures between 373 K and 414 K, at pressures below 30 hPa. Furthermore, the solubility of nitrogen in CO2-PET was determined at room temperature at pressures up to 0.5 MPa. Different apparatus were employed in this work, based on synthetic methods.The high-pressure experimental results were modelled with the Soave–Redlich–Kwong equation of state, with the Péneloux–Rauzy volume translation and Mathias–Klotz–Prausnitz mixing rules. The ability of the method to predict multicomponent phase equilibria using parameters fitted to binary data only was tested. Low-pressure results were modelled using the Non-Random Two Liquid (NRTL) model.

Evaluation of prediction models for the physical parameters in natural gas liquefaction processes

The natural gas liquefaction process is a complicated and dynamic thermal system. Operation conditions change during the process of compression, throttling and heat transfer, which inevitably leads to changes of the thermodynamic property parameters and the phase state of the natural gas and refrigerants. Performing a simulation of the liquefaction process is one of the main methods to improve the economic efficiency of the process and to reduce the production cost; such a simulation can be conducted using a process simulation software package, such as Aspen HYSYS, Aspen Plus, SIMSCI PRO-II and Honeywell UniSim Design. Accurate prediction of the thermodynamic properties of natural gas and refrigerants with the change of working conditions, such as density, specific heat capacity, enthalpy, and entropy, is of significant importance for the simulation of natural gas liquefaction processes. There are many types of property methods embedded in simulation software. Because each property method achieves good performance in a certain range of working conditions, it is crucial to choose the proper method to conduct the simulation. The Soave–Redlich–Kwong equation, the Peng–Robinson equation and the Lee–Kesler–Plocker equation are the main calculation models for physical parameters in natural gas liquefaction processes. According to a literature review, the GERG-2008 equation shows high precision in calculating the thermodynamic properties and phase equilibrium of natural gas and similar mixtures in a wide range of temperature and pressure. Based on accurate experimental data, a comprehensive comparison and analysis among these equations is conducted in this paper. The GERG-2008 equation is recommended as the basis for the calculation of the physical parameters in natural gas liquefaction processes.

Application of the functional renormalization group method to classical free energy models

A simple functional renormalization group method is presented to correct the behavior of classical free energy models near the critical point. This approach is applied to the Soave–Redlich–Kwong equation of state to illustrate its ability to better reproduce the phase behavior of simple fluids and to understand the influence of its parameters on the shape of the vapor‐liquid phase diagram. The method is then extended to account for the correlations induced by intramolecular bonds. It is then applied to a first‐order thermodynamic perturbation theory for chain fluids to examine fluids composed of linearly bonded Lennard‐Jones atoms. Unlike previous approaches for applying renormalization group corrections to chain fluids, this is able to accurately reproduce the critical point without predicting an overly flat liquid‐vapor coexistence region. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2985–2992, 2015

Comparison of SRK and CPA equations of state for phase equilibrium of binary and ternary systems containing aromatics

In this work, the binary and ternary vapor–liquid and liquid–liquid equilibrium (VLE and LLE) data of different systems including N-formylmorpholine (NFM), alkanes, aromatics are collected from previously published literature and then modeled using two different equations of state including Soave–Redlich–Kwong (SRK) and cubic-plus-association (CPA). Since the main purpose of this work is set on the evaluation of the SRK and CPA EoS's capability for modeling of polar systems and to know the importance of association part of CPA EoS, binary and ternary systems of NFM are considered as the objective function. Besides, this investigation is directed in a way that a single “engineering approach” obtains for applying CPA to NFM–aromatic mixtures. Respect to this, different approaches are used to find the functionality of modeling using CPA EoS. These approaches including 3 association schemes for pure NFM (assuming a non-associating compound or a self-associating fluid with two or four association sites) and different possibilities to model mixtures of NFM+Ethylene Glycol (EG) and aromatics (application of just one interaction parameter kij or assuming cross-association interactions leads to obtain relevant parameters either via a combining rule). At last, based on the obtained results it is concluded that CPA is a powerful model that can be used for predictions of binary and ternary mixture properties even without adjustable interaction parameters. In addition, the results revealed that the functionality of the CPA EoS is higher than the SRK EoS in most of the cases especially for predicting the vapor pressure of NFM solvent.

A generalized Kiselev crossover approach applied to Soave–Redlich–Kwong equation of state

Three different variants of the crossover Soave–Redlich–Kwong equation of state are applied to describe the equilibrium behaviour of 72 common non-associating fluids – 27 hydrocarbons (including the first 10 n-alkanes), 36 halogenated refrigerants, 5 cryogenics (fluorine, oxygen, nitrogen, argon and carbon monoxide) and 4 other industrially important inorganic fluids (carbon dioxide, sulfur dioxide, nitrous oxide and sulfur hexafluoride). The model contains six compound dependent parameters.Two of them (a0 and b of the classical part) are adjusted on the critical experimental temperature and the critical pressure. In a first model denoted as model A, the four remaining parameters are fitted to describe the saturated liquid and vapour densities and vapor pressures as well as PVT data at pressures up to P=3×Pc. In the second model (model B), the dispersion softness m is expressed as a function of the acentric factor ω and a relation between two of the crossover parameters is employed; the number of fitted parameters is thus reduced to two. Based on model B, we suggested our final Model C, in which all the parameters can be determined from the critical point, acentric factor or rectlinear diameter. This model is superior to the classical Soave–Redlich–Kwong equation of state because it improves considerably the description of the liquid densities over the whole coexistence region. Contrary to equations of state optimized to reproduce the liquid densities at low temperatures, the crossover equation does not overpredict the critical temperature and pressure. Model C is applied to describe the equilibrium behaviour of two compounds not included in the parameterization, hexafluoropropene (HFO1216) and hexafluoropropene oxide (HFPO).