Redlich-Kwong Equation Research Articles

Theoretical Studies of Supercritical Real-Fluid Oxidations of Diverse Fuels by Using the 3rd-order Virial Equation of State with Nonlinear Effects

The 3rd-order Virial equation of state (EoS) with nonlinear effects was constructed and applied to simulate various real-fluid fuel oxidations, including hydrocarbons and oxygenated fuels under supercritical conditions. The real-fluid effects for hydrocarbon and oxygenated fuel oxidations have been discussed by using the Redlich-Kwong (RK) and the 3rd-order Virial methods. The compressibility factors calculated using the 3rd-order Virial EoS possess better agreements with experimental data for H2, N2, and H2O at different temperatures and below 300 atm than the previous 2nd-order Virial EoS and the RK EoS. The calculations of thermodynamic properties by using the 3rd-order Virial EoS also showed a better agreement with experimental data for H2O than using the RK EoS. The RK method exhibited contradictory speciation predictions against the ideal-gas 0-D and 1-D simulations in H2O and N2/CO2 diluent gases, respectively, while the 3rd-order Virial method kept its consistency. Especially, the ignition delay simulation by using the 3rd Virial EoS is extended to the operation conditions relevant to the recent SpaceX Starship Raptor engines in CH4/O2 mixture at 600 atm. It shows the decreases in the ignition delay times by 3 times by including the real-fluid impact. The simulation results were also compared with a series of existing experimental data for ammonia, larger alkanes, and gasoline blends, which show significant real-fluid effects at low temperatures. Instead of inputting critical pressure and temperature parameters of different species manually in the typical empirical methods with high inconvenience and uncertainties, the required parameters in the 3rd-order Virial method can be directly obtained from the input transport document for real-fluid computations.

Analysis of the Effect of Sampling Probe Geometry on Measurement Accuracy in Supersonic Gas Flow

The accuracy of sampling of gas components has a significant impact on the measurement of various performance parameters in the combustion chamber of an aero-engine. In order to investigate the effect of the probe geometry of a six-point gas sampling probe on sampling accuracy in supersonic gas flow, a three-dimensional probe gas flow characteristic solution model is established through numerical simulation methods of components of transport and fluid–solid coupling. Probes with three angles of 28°, 30°, and 32° and an optimized conical probe are constructed. The sampling accuracy of the probes with different geometries is compared and evaluated by the deviation of the component volume fraction before and after sampling and the resulting combustion efficiency error. This paper presents a set of calculation methods for solving the relative deviation of volume fraction by an iterative method based on the ideal gas law and the Redlich–Kwong equation (R-K equation). The method is designed to solve the exact component volume fraction problem in the simulation calculation. The study results demonstrate that the 28° and optimized conical probes improve sampling accuracy more effectively than the original 30° structure. The deviation of the volume fractions of the two structures is less than 1.7%, and the combustion efficiency error is less than 0.09%. The developed iterative calculation method can significantly reduce the theoretical calculation error to less than 0.06%. The experimental data of the test bench are in good agreement with the simulation results, thereby demonstrating the reliability and accuracy of the sampling probe following structural optimization.

A Reduced Kinetics Model for the Oxidation of Transcritical/Supercritical Gasoline Surrogate/Ethanol Mixtures Using Real Gas State Equations

ABSTRACT Efforts to combat the harmful effects of vehicle emissions on our environment and health include exhaust emissions and fuel efficiency regulations. One promising solution is direct fuel injection in supercritical conditions, where the fuel mixture is above critical temperature and pressure. This study presents a reduced kinetics mechanism (129 species and 1015 reactions) utilizing real gas equations to simulate the combustion of supercritical/transcritical gasoline surrogate/ethanol blends. It was developed by combining two reduced models – a Toluene reference fuel (TRF) with a Diisobutylene (DIB) and an ethanol model – and validated through simulations of ignition delay time (IDT). The Arrhenius parameters of key reactions for each fuel component were modified to improve accuracy. An adjusted Redlich-Kwong cubic state equation was employed to segregate each surrogate mixture tested as supercritical, transcritical, or subcritical. The new mechanism was then validated against experimental results using high-pressure conditions and the cubic Peng-Robinson and Redlich-Kwong equation of state parameters. Critical properties of each species were obtained through Joback’s Group Method and the Ambrose-Walton vapor pressure equation. The TRF/DIB/E mechanism results were consistent with shock tube experimental data at high pressure, indicating a potential for modeling combustion in ultra-high pressure direct injection engines.

Numerical study on effect of operating pressures on CRKEC-based two-stage ejector

The two-stage ejector mixing-diffuser section in this study was computed using the Redlich-Kwong equation of state. The ejector was designed based on the constant rate of kinetic energy change (CRKEC) approach. The water vapor mixing diffuser profile and flow properties were calculated using a one-dimensional gas dynamic model. For the numerical investigation, the estimated geometrical profile based on the input design and operating conditions was utilized. ANSYS-Fluent 14.0 was em-ployed for the numerical study. The analysis was conducted under both on-design and off-design scenarios using the standard k-ε turbulence model. The impact of operating factors on flow behavior and entrainment ratios was investigated at off-design conditions. The findings demonstrated that the operational total pressures of the primary, secondary, and exit flows are a function of the two-stage ejector (TSE) entrainment ratio. With a higher exit pressure and more secondary/entrained flows, the entrain-ment ratio increases. However, altering the primary flow pressure in ways other than for the design conditions reduces the entrainment ratio.

Real Gas Effects in High-Pressure Ignition of n-Dodecane/Air Mixtures.

This work studies the real gas effects on the autoignition of hydrocarbon fuels under high pressures, using normal dodecane (n-dodecane) as the representative fuel and the Redlich-Kwong equation of state (EoS) as the real gas description. It is demonstrated that the real gas description yields a shorter ignition delay time (IDT) compared with the ideal gas description, especially in low-temperature regimes which could encompass the negative temperature coefficient (NTC) phenomena and has a stronger dependence on the molecular volume than the attractive potential. The study further shows that high pressure facilitates low-temperature reaction pathways, where the compressibility factors of key reactants contribute to real gas effects. Moreover, the results suggest that accounting for real gas behavior leads to an increase in the formation of polycyclic aromatic hydrocarbons (PAHs), which, in turn, promotes soot generation.

Modeling gas–liquid equilibrium of carbon dioxide in mixtures of (1-butyl-3-methyl-imidazolium acetate + 1-(2-aminoethyl) piperazine + water) and (1-butyl-3-methyl-imidazolium acetate + bis (3-aminopropyl) amine + water) by electrolyte non-random two liquid (e-NRTL) model

Targeting the control in emissions of post-combustion carbon dioxide capture from large point sources, a simulation approach towards the estimation of important thermodynamic property parameters useful in designing of carbon capture and sequestration technologies is being proposed. In the current work, simulation is carried out for modeling the gas – liquid equilibrium of CO2 in two aqueous mixtures of ionic liquid 1-butyl-3-methyl imidazolium acetate ([bmim][Ac]) and amines viz. ([bmim][Ac] + 1-(2-aminoethyl) piperazine) (AEP) and ([bmim][Ac] + bis (3-aminopropyl) amine) (APA). The experimental CO2 solubilities were taken from our previously published work and is regressed with electrolyte–Non-Random Two Liquid (e-NRTL) model for the liquid phase while Redlich-Kwong (RK) equations of state (EOS) was used to model the gas phase. Various thermodynamic parameters of importance and concentration of species in the mixtures were regressed in the model using Aspen Plus 14.

Prediction Model of Lean Coal Adsorption of Power Plant Flue Gas.

To minimize errors in calculating coal flue gas adsorption capacity due to gas compressibility and to preclude prediction inaccuracies in abandoned mine flue gas storage capacity for power plants, it is imperative to account for the influence of compression factor calculation accuracy while selecting the optimal theoretical adsorption model. In this paper, the flue gas adsorption experiment of a power plant with coal samples gradually pressurized to close to 5 MPa at two different temperatures is carried out, and the temperature and pressure data obtained from the experiment are substituted into five different compression factor calculation methods to calculate different absolute adsorption amounts. The calculated adsorption capacities were fitted into six theoretical adsorption models to establish a predictive model suitable for estimating the coal adsorption capacity in power plant flue gas. Results reveal significant disparities in the absolute adsorption capacity determined by different compression factors, with an error range of 0.001278-7.8262 (cm3/kg). The Redlich-Kwong equation of state emerged as the most suitable for the flue gas of the selected experimental coal sample and the chosen composition ratio among the five compression factors. Among the six theoretical adsorption models, the Brunauer-Emmett-Teller model with three parameters demonstrated the highest suitability for predicting the adsorption capacity of coal samples in power plant smoke, achieving a fitting accuracy as high as 0.9922 at 49.7 °C.

WITHDRAWN: Comparative Analysis of Asphaltene Deposition Methods : Stability indices, Stability plots, and Equation of state

Asphaltene deposition is one of the major problems that hinder hydrocarbon production. It can occur anywhere between the reservoir and the surface. Therefore, it is imperative that there be a procedure for minimizing the deposition of asphaltene in the production flow lines. There are several screening criteria that can be considered to determine the asphaltene deposition. This research will conduct a comprehensive study on different methodologies to determine the stability of asphaltene: the first category is the stability criteria using indices such as: the colloidal instability index (CII), the colloidal stability index (CSI), the stability index (SI), and the asphaltene stability predicting model (ANJIS). These four methods are used to predict the stability of asphaltene using SARA analysis. The fifth one is called modified CII which uses the compositions analysis of reservoir fluids, instead of SARA analysis, to determine the stability of asphaltene. The second method uses SARA Analysis to predict the stability via plots such as: Stankiewics plot (SP), De Boer plot, Sepulveda stability criterion (SCP). The third method is using compositional analysis of reservoir fluids and the equation of state model to predict the asphaltene onset pressure (AOP). In the last method Soave Redlich Kwong (SRK) equation of state model was used to predict asphaltene precipitations.In this work, a dataset of 166 was created which includes reservoir information, depth, compositional analysis, and SARA analysis. These data are used to study the potential of asphaltene deposition at the reservoir level. It was found that the stability criteria using indices and plots shows discrepancy in the results. The only two methods that show all the datasets are stable are the modified CII and the EOS model. As far as predicting asphaltene stability is concerned, the EOS method, based on compositional analysis and the thermodynamic model, appears to be the most reliable and trustworthy method. The other methods presented are observational rather than thermodynamic. Using these criteria is intended as a quick and fast estimate of the stability potential of asphaltene, not for planning or management of asphaltene deposition issues.

Numerical model development for critical region flow and thermodynamic transitions of CO2 fluids in microchannel

Dramatic changes of thermophysical properties in the vicinity of critical point brings significant accelerating effect on the thermodynamic transitions of fluid. This study performs a confined geometric design with CO2 fluids passing through the critical zone in microchannel. Such a problem formulation combines the compressible Navier-Stokes equations with different property formulations to obtain critical anomaly effects at complex critical transport coefficients. Three equations of state (van der Waals (vdW), Redlich-Kwong (R-K) and Peng-Robinson (P-R) state equations) and their corresponding thermodynamic relations are derived in solving the governing equations of flow and heat transfer equations. Basic results are found to be consistent with theoretical asymptotic analysis, with linearly curves of pressure and a sudden shift of density (425 kg/m3–502 kg/m3) and velocity (0.82 m/s to 0.97 m/s) profiles when the microchannel flow across the critical region. The cascade effect between weakened radial thermal conductivity (λ ∼ (ρ – 1)-1/2, cp ∼ (ρ - 1)−2) and enhanced fluid expansion (βp ∼ (ρ - 1)−2) in the critical region is also shown to cause a sharp negative transition in temperature. In addition, the simulations demonstrate a qualitative comparison for three state equations, and the distinctions in quantitative terms (negative temperature value are −0.1 (vdW), −0.17 (R-K), and − 0.23(P-R)) are found to originate from stronger divergence characteristics (the specific heat cp and thermal expansion coefficients βp) in P-R gases than vdW and R-K gases.

Effects of real gas equations on the fast-filling process of compressed hydrogen storage tank

Hydrogen-fueled, fuel-cell-powered cars offer environmentally friendly alternative for near future. One of the critical part of this technology is to store hydrogen efficiently and securely. Many different methods have been developed to store hydrogen. The most popular storage method for hydrogen storage in vehicles is compressible hydrogen storage tanks due to their lightweight and efficiency. One of the most important factors during filling is the filling time. During rapid filling, the tank temperature rises significantly, which can cause damage to the tank and create a dangerous situation. In this research, CFD simulation has been made for fast filling condition for compressible hydrogen storage tanks. It was decided to use the k-ε turbulence model and different real gas equations for numerical simulation. The effects of four different real gas equations and also ideal gas equation on the temperature, the pressure, and filling times are investigated numerically. As a result of the simulation, it was concluded that the use of different real gas equations does not have a significant effect on the temperature and the pressure of the storage tank. However, the filling duration of storage tank is slightly affected by usage of different real gas equations. Filling durations of hydrogen according to Redlich-Kwong equation of state increased for Soave-Redlich-Kwong equation 1.3 %, for Aungier Redlich-Kwong equation 1.5 %, for Peng-Robinson's equation of state 5.85 %, for ideal gas equation of state 24.2 %.

Thermodynamic Modeling and Process Simulation of Kumkol Crude Oil Refining

The Crude Distillation Unit (CDU) mechanism is commonly regarded as the first stage in petroleum refining. In this study, Aspen Plus® is used to simulate the basic process of a CDU, which consists of an Atmospheric Distillation Column (ATC) and a Vacuum Distillation Column (VC). These columns are fed with two types of crude oil: KUMKOL from Kazakhstan and Soviet Export Blend, in the proportions of 0.75:0.25, 0.50:0.50, and 0.25:0.75, respectively. The goal was to do a parametric analysis and analyze the resultant streams of naphtha, kerosene, Atmospheric Gas Oil (AGO), Light Vacuum Gas Oil (LVGO), and Heavy Vacuum Gas Oil (HVGO). The simulation used the CHAO-SEA thermodynamic model, which included the Chao-Seader correlation, the Scatchard-Hildebrand model, the Redlich-Kwong equation of state, the Lee-Kesler equation of state, and the API gravity technique. Temperature, pressure, mass flow, enthalpy, vapor percentage, and average molecular weights of the streams at various phases within the CDU system were estimated. For both the ATC and VC columns, curves indicating Temperature- Pressure vs the number of stages, as well as ASTM D86 (temperature) versus stream volume % distillation, were developed. The results show that when compared to feed streams containing 0.25 and 0.50 StdVol of Kumkol Kazakhstan Oil, the feed stream with 0.75 StdVol produces more Heavy, Medium, and Light Vacuum Gas Oil (H-VGO, M-VGO, and L-VGO), as well as more Vacuum Gas (VG). These findings indicate that Kumkol Kazakhstan Oil is of high quality and has fewer contaminants, such as sulfur when compared to other accessible mixes throughout the world.

Geometric similitude concept and Redlich–Kwong equation of state to predict thermal conductivity of choline chloride class of deep eutectic solvent

Geometric similitude concept and Redlich–Kwong equation of state to predict thermal conductivity of choline chloride class of deep eutectic solvent

Interpretation of covolume in an extension of the Redlich–Kwong equation of state for real gases

Interpretation of covolume in an extension of the Redlich–Kwong equation of state for real gases

Performance of a high capacity polyamine: Measurement and modeling of the solubility of carbon dioxide in aqueous solutions of 1, 4-bis (3-amino-propyl) piperazine and its heat of absorption

This study focused on measuring the carbon dioxide (CO2) uptake capacity of an amine, 1, 4-Bis (3-aminopropyl) piperazine. The solubility of CO2 was measured at 313.15 K and 333.15 K for three amine concentrations (10, 20, and 30 wt%) of importance in industry and different CO2 partial pressures up to 2.4 MPa. CO2 loadings (mol of CO2/mol amine) were measured using the pressure decay method. At all concentrations, 1,4-Bis(3-aminopropyl) piperazine showed a higher CO2 loading compared to two benchmark amines namely, ethanolamine (MEA) and Piperazine (PZ). The proposed amine had also a higher capacity for CO2 than all other polyamines found in the literature, except, 3, 3 ’-Iminobis (N, N-dimethyl-propylamine) which has two tertiary and one secondary amino group. The experimental measurements were modeled comprehensively with the electrolyte–Non-Random Two Liquid (NRTL) model and the Redlich-Kwong (RK) equation of state (EOS) for the gas phase. The binary NRTL and molecule–ion pair parameters were regressed and reported. The overall percentage of the average absolute deviation (%AAD) between the experimental and estimated values for the temperature, pressure, and mole fractions were 0.12%, 0.07%, and 0.32%, respectively. Finally, the heats of absorption of CO2 in 1, 4-Bis (3-aminopropyl) piperazine were calculated using the Gibbs-Helmholtz equation based on the obtained experimental solubility data. The modeling results for MEA, DEA, and MDEA between the elec-NRTL and the soft-SAFT models were compared. The estimation of the heat of absorptions for the amines was almost the same.

Investigation of the Solubility of Methane and Ethane in Hybrid Sweetening Solutions of 2-Aminoethanol and 1-Methylpyrrolidin-2-one/Water

Hydrocarbons of natural gas are captured by the solvent in the gas-sweetening absorption process and added to losses in production. Therefore, knowledge of hydrocarbon solubilities in solvents is required to assess and overcome these losses. In this study, the solubility of the main components of natural gas, methane and ethane, in n-methyl-2-pyrrolidone and monoethanolamine-based solvents was determined at the temperature of 313.15 K and pressures up to 2.366 MPa. Mass fractions of 0.10, 0.20, and 0.30 amine in the solutions were used in measurements that were performed using a static-synthetic method. The experimental data were modeled using the Soave–Redlich–Kwong Equation of State. Experimental results showed that the replacement of the aqueous part of conventional monoethanolamine solvents with n-methyl-2-pyrrolidone increased the solubility of desirable components of natural gas which is a negative side effect. The addition of monoethanolamine to n-methyl-2-pyrrolidone outperformed the Purisol solvent in terms of carbon dioxide absorption and decreased hydrocarbon solubility.

Effects of effluent pressure on the thermal cracking of crude oil: insights from thermal simulation experiments and phase analysis

This study discusses the anhydrous glass tube isothermal pyrolysis simulation for a crude oil, in order to explore the effects of effluent pressure on crude oil cracking. The results of gas chromatograph indicate that effluent pressure promotes the cracking of crude oil, increasing yields of C1–C5 saturates but inhibiting the generation of olefins. According to the calibration result of Soave–Redlich–Kwong equation of state, fluid phase transitions occur at very high effluent pressures, resulting in constant effluent pressure with no further increase in cracking efficiency and with invariant yields of pyrolysates. This study suggests that fluid phase transitions should be considered in petroleum exploration, which can help us to precisely determine the type of petroleum resources.

Diffusion Coefficient and Absorption of Carbonyl Sulfide in 1-Hexyl-3-methylimidazolium Bis (Trifluoromethyl) Sulfonylimide ([hmim][Tf2N

The solubility of carbonyl sulfide (COS) and also the diffusion coefficients of COS, carbon dioxide, and hydrogen sulfide were experimentally investigated in 1-hexyl-3-methylimidazolium bis(trifluoromethyl) sulfonylimide ([hmim][Tf2N]). The solubility was measured using a static apparatus, and the acid gas diffusivity was obtained by monitoring pressure drop with low initial pressure via the so-called semi-infinite volume method. All experimental absorption trials were carried out in the range of low and medium pressures and temperatures from (313.15 to 353.15) K. Furthermore, all diffusion coefficient experiments were determined at a temperature from (313.15 to 333.15) K and low pressure to some extent to be acceptable in the semi-infinite volume approach. The experimental results were correlated using the Shiflett and Yokozeki versions of the Redlich–Kwong equation of state. In addition, Henry’s law constants and the thermodynamic properties of dissolution at infinite dilution were calculated and discussed.

Isobaric Vapor–Liquid Equilibrium of the Binary Mixtures Toluene + Styrene and Styrene + α-Methylstyrene

Isobaric vapor–liquid equilibria of the binary mixtures toluene + styrene at 30 and 40 kPa and styrene + α-methylstyrene at 20 and 25 kPa were measured applying a recirculation still. The measured vapor–liquid equilibrium data were modeled adopting the non-random two-liquid (NRTL) excess Gibbs energy model with the RK (Redlich–Kwong) equation of state. The NRTL binary interaction parameter optimization was carried out employing own measured data and literature data for the toluene + styrene system. The applied model correlates well with the experimental data at the pressure range of 101–30 kPa. Moreover, the NRTL binary parameter regression was performed applying own measured data and literature data separately for the styrene + α-methylstyrene system. The model fitted with the parameters obtained from own measured data described the multiphase behavior of the system better than the parameters obtained from literature data. Additionally, the binary systems showed ideal behavior over the whole range of investigation as the calculated activity coefficients approached unity and no azeotropes were observed.

Equationsof state in multiphase lattice Boltzmann method revisited.

The single-component multiphase fluids can be described by a single equationof state (EOS), and various EOSs have been employed in the multiphase lattice Boltzmann (LB) method. In this work, we revisit five commonly used EOSs, including the van der Waals EOS, the Redlich-Kwong EOS, the Redlich-Kwong-Soave EOS, the Peng-Robinson EOS, and the Carnahan-Starling EOS. The recent multiphase LB model with self-tuning EOS is employed because of its thermodynamic consistency in a strict sense and clear physical picture at the microscopic level. First, the way to incorporate these multiphase EOSs is proposed. Two scaling factors are introduced to independently adjust the surface tension and interface thickness, and the lattice sound speed is EOS-dependent to ensure the numerical stability. Then, numerical tests are conducted to validate the incorporations of these EOSs and compare their numerical performances. The surface tension and interface thickness are set to the same values for different EOSs in the comparisons. The liquid and gas densities, surface tension, and interface thickness by the LB simulation agree well with the thermodynamic results. The maximum density ratios achieved with different EOSs are at the same level and could be very close to each other when the interface thickness is relatively small. The effects of multiphase EOS, density ratio, and dimensionless relaxation time on the spurious current are discussed in detail. It is interesting to find the van der Waals EOS shows the best numerical performance in reducing the spurious current.

Validation of Soave–Redlich–Kwong equation of state coupled with a classical mixing rule for sound speed of non-ideal gas mixture of oxygen-hydrogen as liquid rocket propellants

Numerical simulations of inlet jets flow of propellants in the main combustion chamber equipped in a liquid rocket engine have been conducted by compressible CFD technics employing a van der Waals-type equation of state (EOS) and chemical reaction models. Various simulations have been already conducted both for combustion and non-combustion state in the chamber; however, the accuracy of EOS for the mixture of propellant employing a classical mixing rule (CMR), particularly for the sound speed, has not been understood well. Therefore, we have validated the applicability of Soave–Redlich–Kwong (SRK) EOS as one of the van der Waals-type EOSs coupled with the CMR for the sound speed using molecular dynamics (MD) simulations against an imaginary model of oxygen-hydrogen mixture system. We found that SRK EOS coupled with a well-employed CMR can reproduce the sound speed in the MD simulations within a relative error of several percent and that the CMR hardly increases the deviation of the SRK EOS in the single component. The present results suggest that the SRK EOS with the CMR cannot be the main factor to cause critical errors in the CFD based on RANS, which will give reliability to current CFD simulations for internal flows in a combustion chamber of a liquid rocket engine.