Peng-Robinson Research Articles

Symbolic-Regression Aided Development of a New Cubic Equation of State for Improved Liquid Phase Density Calculation at Pressures Up to 100 MPa

For over a century, cubic equations of state (EoS) have been used to calculate density and phase equilibria of pure fluids and mixtures. Despite a century’s development with hundreds of resulting cubic EoS, their accuracy in liquid phase density calculations is still unsatisfactory. In this work, a new cubic EoS was developed to improve the accuracy of liquid phase density calculation while keeping similar accuracy of other properties. The new cubic EoS, named YFR (Yang-Frotscher-Richter) EoS, was developed based on the functional form of the Patel–Teja (PT) EoS [p = RT/(v − b) − a/(v(v + b) + c(v − b)]. In the PT EoS, parameters b and c are linked to an empirical critical compressibility factor ξc, and all these three parameters are constants for a pure fluid. By contrast, in the YFR EoS, ξc, b, and c are functions of temperature, and the equations describing this dependency were developed with symbolic regression. This is the key to improving liquid phase density calculation, although it leads to thermodynamic inconsistencies at high pressures. The application range of the new cubic EoS is thus limited to pressures up to 100 MPa. The YFR EoS was developed using nearly all pure fluids available in NIST’s REFPROP 10.0 database, with reference values computed with REFPROP. The average of the absolute value of relative deviations (AARD) of liquid phase densities calculated with the YFR EoS from reference values is approximately 2 %, compared to 3 % when using the Patel–Teja–Valderrama (PTV) EoS and 6 % when using the Peng-Robinson (PR) EoS. The YFR EoS has been implemented in our self-developed OilMixProp 1.0 software package.

Assessing the influence of thermodynamic equation of state and simulation software on modelling the CO2 solubility in physical solvents

The most useful physical solvents in the industry are Propylene Carbonate (Fluor SolventSM), Methanol (Rectisol), Dimethyl Ether of Polyethylene Glycol (DEPG - Selexol) and Sulfolane. To address the challenge of choosing the right software and property package, two commercial software packages, HYSYS 14.0 and ProMax 6.0, are used to model the CO2 solubility experimental data in the above physical solvents at operating pressures and temperatures as this two software are the most applicable software in gas treating simulations. The property packages of Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) and their regressed versions for CO2 capture purposes by Fluor Corporation and Bryan Research and Engineering LLC are utilized. The results show that the HYSYS Fluor property package demonstrates the strongest agreement with experimental CO2 solubility data in propylene carbonate. In the case of CO2 solubility in methanol, despite HYSYS showing a warning and guiding user to choose Acid Gas property package, HYSYS PR offers a more accurate match below 273.15 K compared with HYSYS Acid Gas and HYSYS Fluor property package and ProMax Polar property packages. ProMax PR and SRK demonstrate a stronger performance in modelling CO2 solubility in sulfolane at all temperatures compared to HYSYS. Both the HYSYS PR and SRK property packages show a high accuracy in modelling CO2 solubility data in DEPG.

The influence of pure compounds’ parameters on the phase behaviour of carbon dioxide + 1-hexanol binary system

New vapour–liquid–liquid and vapour–liquid equilibrium data to complement the existing ones are measured at six temperatures (308.15 K to 383.15 K) and at pressures up to 182.9 K using an analytic-static method with phases sampling via special valves (“AnTVisVarCap”, as defined by Prof. Ralf Dohrn and co-workers) for the carbon dioxide (1) + 1-hexanol (2) binary system. Four out of the six isotherm reported here are measured for the first time. The main component of the high-pressure setup is a 60 cm3 visual cell.The new isotherms are compared with the available literature which is also reviewed and analysed. It should be noted that among the data already published, only one other research group reported the compositions of both phases at equilibrium, as we did previously by using another experimental method. The new and literature data were modelled with Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) equations of state based on a semi-predictive procedure to reproduce as well as possible the minimum and the maximum of the critical curve(s) using one set of binary interaction parameters. The influence of critical data and acentric factors of pure components on the phase behaviour of their binary system is discussed. Although the values of the critical pressures and acentric factors of pure substances are not very different in the database we used, the models predict type III or IV phase behaviour with the same set of binary interaction parameters. This sensitivity, which was not observed for other systems we studied, could be explained by the alcohol structure and high asymmetry of the system. Therefore, we analysed in more depth the influence of the critical temperatures and pressures, as well as the acentric factors of carbon dioxide and 1-hexanol and exemplified for one temperature located above the system UCEP's temperature.

Assessment of dissociation enthalpies of methane hydrates in the absence and presence of ionic liquids using the Clausius-Clapeyron approach

The Clausius-Clapeyron (CC) equation is generally preferred to obtain dissociation enthalpies (ΔH) of hydrate-forming systems due to its ease of use. The application of other direct and indirect methods becomes more problematic if complex additives such as ionic liquids (ILs) are also present in the system. In this work, around 400 equilibrium data points for methane hydrates in the presence of over 80 ILs were collected from the literature in the temperature and pressure ranges of (272.10 – 306.07) K and (2.48 – 100.34) MPa, respectively. The ΔH of methane hydrates in the absence and presence of ionic liquids (ILs) have been calculated using the CC equation. The compressibility factor (z), required to calculate ΔH at each phase equilibrium condition has been obtained from three different approaches viz., Peng-Robinson (PR) equation of state, Soave-Redlich-Kwong (SRK) equation of state and Pitzer (Pz) correlation. The results were compared to the experimentally reported dissociation enthalpy (54.5 ± 1.5 kJ.mol−1) of methane hydrates. The role of the compressibility factor along with the slope of the equilibrium data set and the temperature/pressure range in determining the outcome of the CC equation has been discussed. The effect of molar mass, molar volume, and hydrate suppression temperature of the ILs on the ΔH of methane hydrates has been explored. The tested ILs do not show a systematic and significant influence on enthalpies, rather they show a large scattering in the ΔH values, which might mask any existing subtle effect of the ILs on the dissociation enthalpies. Therefore, this approach should be dealt with care to obtain molecular-level insights.

A quantum-corrected Peng‒Robinson equation of state for helium-4 from 3 K to 50 K considering quantum swelling effects through the Feynman‒Hibbs correction of the EXP-6 potential

Accurate and efficient prediction of the properties of helium-4 (He-4) via an equation of state (EOS) is a prerequisite for evaluating liquid helium-4 (LHe-4) storage technology. However, the performance of the Peng–Robinson (PR) EOS in predicting the density of LHe-4 and vapour helium-4 (VHe-4) deteriorates within the thermodynamic ranges of the LHe-4 tank: 3–50 K and 60–600 kPa. To modify the PR EOS, we establish first-order and second-order Feynman–Hibbs (FH)-corrected EXP-6 potentials and propose a reduced effective particle diameter (REPD) correlation with four parameters to consider the quantum swelling effects of LHe-4. On the basis of the rational function form of the REPD correlation, we introduce a quantum-corrected covolume term to develop a regression model for the FH-corrected Peng–Robinson (FH-PR) EOS. Moreover, to improve the effectiveness of regression near the saturation curve, we propose a hypothetical boundary consisting of the saturation curve from 3 K to the critical temperature and a virtual saturation curve from the critical pressure to 600 kPa. The results indicate that the FH − PR EOS shows satisfactory engineering application performance in predicting the density of He-4 within the studied range. Under verification conditions, the average absolute relative deviation (AARD) of the density determined via the FH − PR EOS ranges from 0.72 % to 1.77 %, and the maximum relative deviation (MRD) ranges from 2.17 % to 5.62 %. Under test conditions, the AARD of the density ranged from 1.06 % to 1.71 %, and the MRD ranged from 3.77 % to 7.38 %.

Comprehensive study of medications solubility in supercritical CO2 with and without co-solvent; Laboratory, theoretical, and intelligent approaches

Determining the dissolution characteristics of medicines in supercritical CO2 is vital for formulating innovative drug delivery systems through an efficient supercritical process. This study investigates the solubility of three poorly bioavailable drugs −Topiramate, Meclizine, and Dimenhydrinate- in supercritical CO2, both with and without ethanol co-solvent, over a temperature range of 308 K to 348 K and pressures from 17 MPa to 41 MPa. The solubility of these medicines in supercritical CO2 (binary system) is notably low, ranging from 2.5 × 10-6 − 4.54 × 10-6, 0.26 × 10-5 − 2.3 × 10-5, and 0.20 × 10-5 − 1.91 × 10-5 in mole fraction, respectively. However, in the presence of ethanol (ternary system), their supercritical solubility significantly increases by factors of 2.75–5.84, 1.40–3.20, and 2.04–4.85, respectively.The supercritical solubility of the mentioned compounds are theoretically evaluated using several approaches, including empirical models, a machine learning methodology employing a multilayer perceptron neural network, thermodynamic models based on two cubic equations of state (Peng-Robinson (PR) and Soave–Redlich–Kwong (SRK)), and a non-cubic equation of state (perturbed chain-statistical associating fluid theory (PC-SAFT)), as well as two expanded liquid models (UNIQUAC and Wilson).The findings revealed that all the specified models demonstrate acceptable accuracy in correlating the experimental data of the specified drugs in both binary and ternary systems. Among these, the PR and SRK thermodynamic models, along with some empirical models, show the best results. Furthermore, the machine learning model exhibited outstanding accuracy in forecasting the supercritical solubility of the desired drugs, with over 99.9% alignment between their predicted and experimental data.

Thermal recycling analysis in regenerative cooling channels based on liquid rocket engine cycles

For rocket cycles involving electric pumps, gas generators, expanders, and staged combustion, a thermal recycling method is proposed to provide a more realistic simulation of regenerative cooling systems in liquid rocket engines. This method simulates a real situation where the outlet of the cooling channel is thermally recycled through the turbine or preburner to the inlet of the combustion chamber. Supercritical fluid properties are determined using the extended Redlich–Kwong (RK)–Peng–Robinson (PR) real-fluid equation of state. The axisymmetric reacting flows of a thrust chamber with regenerative cooling channels are simulated using the flamelet-based lookup table. To account for the multi-injector effect in the two-dimensional axisymmetric simulation, a non-uniform velocity distribution is implemented, utilizing exponential distributions of each injector’s mass flow rate. For the hot gas temperature, coolant temperature, and cooling mass flowrate, the thermal recycling method is comparatively analyzed with the thermal decoupling method. The regeneration effect of the heated fuel is explored by evaluating the inflow energy, reaction energy, wall heat transfer, and the exit kinetic energy conversion. The thermal recycling method is developed for regeneratively cooled rocket engines with the expander, gas generator, staged combustion, and electric-pump cycles. Through this numerical procedure, the thermal recycling method is successfully applied to a liquid oxygen/methane engine and NASA’s Crew Exploration Vehicle nozzle with two types of cooling. Based on the results of the four types of rocket cycles, it is confirmed that the specific impulse increases by 1.5–2% due to the regenerative heat effect.

Estimation of the interaction parameters between carbon dioxide and an organic solvent by the Peng–Robinson equation of state via an artificial neural network

The equation of state (EoS) is a tool for estimating the thermodynamic and physical properties of compounds, including mixtures, across a range of temperatures and pressures. When dealing with mixtures, a mixing rule is required to calculate the mixture parameters. Mixing rules may involve interaction parameters, such as kij and lij, that correct for differences between components. However, obtaining this data requires specialized equipment and techniques and significant measurement time, resulting in limited reported EoS parameters. In this study, we introduce an artificial neural network (ANN) to predict interaction parameters in the van der Waals one-fluid mixing rule. These parameters are used to calculate the physical properties of mixtures using the Peng–Robinson (PR) EoS. The interaction parameters are used in two cases, namely the one-parameter and two-parameter mixing rules (OP and TP, respectively), in which only kij and both kij and lij are employed, respectively. The vapor–liquid equilibrium (VLE) data of CO2/organic solvent binary systems are collected and correlated by the PR EoS to construct a database of 1286 and 1292 parameters for the OP and TP, respectively. The molecular weight, critical temperature and pressure, acentric factor of the organic solvent, and temperature are used as input parameters for the ANN. In addition, we optimize the structure of the ANN by changing the activation function, number of neurons, and number of hidden layers. The optimized ANN uses a tanh activation function. Hidden layers are used for both the OP and TP, along with 40 and 50 neurons, respectively. The results confirm that the model can determine the interaction parameters of the PR EoS, which can be used to estimate the VLE. These results are useful for incorporation into process simulators for chemical process design.

Effects of different alkyl chain lengths on excess properties of CO2-1-Butyl-1-methyl-pyrrolidinebis(trifluoromethanesulfonyl)imide, CO2-1-hexyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide, CO2-1-octyl-1-methylpyrrolidinium bis(trifluoromethanesulfonyl)imide systems

The study investigates the solubility of carbon dioxide (CO2) in three ionic liquids [BMP][Tf2N] (1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide), [HMP][Tf2N] (1-hexyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide) and [OMP][Tf2N] (1-octyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide). The research is conducted over a temperature range of 303.15 to 363.15 K. The phase equilibria of the binary systems are predicted using the Peng-Robinson (PR) equation of state, the Wilson (WS) mixing rule and the UNIFAC activity coefficient model. The interaction parameter kij is regressed from the vapor-liquid equilibrium (VLE) experimental data. The study also calculates the excess Gibbs free energy (GE), excess enthalpy (HE), and excess entropy (SE) for these systems. The research results indicate that the length of the alkyl chain in the cation has a significant effect on the excess properties of the CO2-ionic liquid systems. As the alkyl chain length increases, the excess Gibbs free energy and excess enthalpy decrease, while the excess entropy increases. The CO2-[OMP][Tf2N] system exhibits stronger interactions between CO2 and the ionic liquid, indicating a higher capacity for CO2 absorption. The study results are helpful for optimization of CO2 capture processes and the broader comprehension of fluid phase equilibria in complex systems.

Impact of nanopore confinement on phase behavior and enriched gas minimum miscibility pressure in asphaltenic tight oil reservoirs

Miscible gas injection in tight/shale oil reservoirs presents a complex problem due to various factors, including the presence of a large number of nanopores in the rock structure and asphaltene and heavy components in crude oil. This method performs best when the gas injection pressure exceeds the minimum miscibility pressure (MMP). Accordingly, accurate calculation of the MMP is of special importance. A critical issue that needs to be considered is that the phase behavior of the fluid in confined nanopores is substantially different from that of conventional reservoirs. The confinement effect may significantly affect fluid properties, flow, and transport phenomena characteristics in pore space, e.g., considerably changing the critical properties and enhancing fluid adsorption on the pore wall. In this study, we have investigated the MMP between an asphaltenic crude oil and enriched natural gas using Peng-Robinson (PR) and cubic-plus-association (CPA) equations of state (EoSs) by considering the effect of confinement, adsorption, the shift of critical properties, and the presence of asphaltene. According to the best of our knowledge, this is the first time a model has been developed considering all these factors for use in porous media. We used the vanishing interfacial tension (VIT) method and slim tube test data to calculate the MMP and examined the effects of pore radius, type/composition of injected gas, and asphaltene type on the computed MMP. The results showed that the MMP increased with an increasing radius of up to 100 nm and then remained almost constant. This is while the gas enrichment reduced the MMP. Asphaltene presence changed the trend of IFT reduction and delayed the miscibility achievement so that it was about 61% different from the model without the asphaltene precipitation effect. However, the type of asphaltene had little impact on the MMP, and the controlling factor was the amount of asphaltene in the oil. Moreover, although cubic EoSs are particularly popular for their simplicity and accuracy in predicting the behavior of hydrocarbon fluids, the CPA EoS is more accurate for asphaltenic oils, especially when the operating pressure is within the asphaltene precipitation range.

Numerical study on collapsing cavitation bubble dynamics in cryogenic fluids

The paper addresses the implementation of a dual distribution function multiphase lattice Boltzmann method (DDF-MLBM) for studying the collapse of cavitation bubbles in cryogenic liquids. The present scheme incorporates the energy equation and imposes interparticle interactions and fluid–solid adhesive forces through the exact difference method (EDM). To accurately model phase changes and the molecular complexities of cryogenic fluids like liquid hydrogen (LH2) and liquid nitrogen (LN2), the Peng-Robinson (PR) equation of state is employed along with an acentric factor. The accuracy of the present numerical technique is evaluated using the Laplace law and the Maxwell equal area construction theorem for a two-phase liquid–vapor system in equilibrium. For transient solutions, the study compares results of heterogeneous cavitation with the analytical solution derived from the thermal Rayleigh-Plesset equation. The research investigates the impact of the distance between a cavitation bubble with an adjacent solid wall on velocity, pressure, temperature, and collapse time. Furthermore, it is assessed how surface wettability influences cavitation bubble collapse intensity. Additionally, the paper examines the collapse of a cavitation bubble cluster and evaluates the effects of different physical parameters on the collapse properties of the bubble cluster. The results underscore the significant influence of the distance between cavitation bubbles in the cluster, the distance between bubbles and the adjacent solid surface on the micro-jet velocity. Moreover, it is found that increasing the contact angle of the solid surface enhances the collapse intensity and micro-jet velocity of the collapsing bubble cluster.

Experimental measurement and thermodynamic/intelligent modeling of yellow 2 G solubility in supercritical carbon dioxide with/without co-solvent

In this study, the solubility of an azo dye, Yellow 2 G, was investigated in supercritical CO2, both with and without co-solvents (methanol and dimethyl sulfoxide (DMSO)), spanning temperatures from 308 to 338 K and pressures from 10 to 34 MPa. The supercritical solubility of Yellow 2 G ranged from 0.052×10−6 to 0.559×10−6 mole fractions, while in the presence of methanol and DMSO, it varied from 0.5×10−6 to 5.92×10−6 and 0.46×10−6 to 4.6×10−6, respectively. Co-solvents significantly increased supercritical solubility, with over a 9-fold increase with methanol and more than a 7-fold increase with DMSO. Semi-empirical models, Peng-Robinson (PR), Soave Redlich Kwong (SRK), Perturbed-Chain Statistical Associating Fluid (PCP-SAFT), and quadrupolar cubic plus association theory (qCPA) equations of state, and a multilayer perceptron (MLP) neural network were used to assess the solubility data. Among the semi-empirical models, the Khansary model for the binary system and the Jouyban and Soltani-Mazloumi models for the ternary system demonstrated the highest conformity. Among models based on equations of state, the PCP-SAFT model demonstrates the highest accuracy in correlating solubility data for both binary and ternary systems. Notably, the accuracy of the SRK model in correlating solubility data for the binary system matches that of PCP-SAFT. The proposed MLP neural network provided highly accurate estimations of Yellow 2 G solubility in both binary and ternary systems, achieving an accuracy of over 99 %.

Experimental (ρ,P,T) data of H2 + CH4 mixtures at temperatures from 278 to 398 K and pressures up to 56 MPa

The blending of hydrogen and natural gas (H2-NG) has emerged as a crucial and cost-effective means for processing hydrogen fluids through natural gas networks thereby aiding transition to net-zero energy. Nonetheless, the effective adaptation of H2-NG mixtures, especially up to 20% hydrogen concentrations, to existing natural gas distribution and storage facilities relies heavily on a comprehensive understanding of their thermophysical properties. We measured densities of three binary mixtures of hydrogen and methane (xH2 = 0.0532, 0.0858, and 0.2031) at temperatures between 278 and 398 K, and pressures up to 56 MPa using a vibrating tube densimeter (VTD). The VTD was calibrated using H2 and H2O. The measured densities were in reasonable agreements with the predictions of two thermodynamic equations of states (EoSs), Multi-Fluid Helmholtz Energy Approximation (MFHEA) and Peng-Robinson (PR). The average absolute relative deviation (AARD) for the measured density against the predictions of the PR EoS are 1.07%, 1.09%, and 0.89% for xH2 = 0.0532, 0.0858, and 0.2031 mol fractions respectively. While the AARD for the measured density against the predictions of MFHEA EoS are 0.16%, 0.16%, and 0.32% for xH2 = 0.0532, 0.0858, and 0.2031 mol fractions respective. The MFHEA EoS, which has the structure of GERG-2008, has better agreements with our density data than the PR EoS. The relative high deviations with PR EoS results from the PR's simple structure making it deficient in calculating thermal properties of natural gas in saturated-liquid and homogeneous states. In addition, the uncertainty of the measured density was determined, and the experimental data were compared with available literature data. Finally, the compressibility factor (Z), speed of sound (w), specific heat capacity at constant volume (CV), and specific heat capacity at constant pressure (Cp) were obtained from the experimental results and were compared with the predictions of MFHEA EoS. This work provides accurate density and other thermophysical data useful for engineering/process designs and modelling of H2 and natural gas systems thereby enhancing energy transition strategy.

Measurement and modelling of vapor–liquid phase equilibrium of 1,1-difluoroethane (R152a) + 1,1,2,3,3,3-hexafluoro-1-propene (R1216) at temperatures ranging from 283.15 K to 313.15 K

Compared to pure refrigerants, mixed refrigerants can effectively fulfill the demands of high efficiency, safety, and environmental preservation. An efficient mixture can be created by combining environmentally safe and non-combustible refrigerants with low global warming potential (GWP) and high latent heat hydrofluorocarbons (HFCs) in precise ratios. For this investigation, an experimental apparatus was built to obtain vapor–liquid equilibrium (VLE) data for the R152a + R1216 mixture within temperatures of 283.15 to 313.15 K. To depict the VLE characteristics of the binary systems, the Peng-Robinson (PR) equation of state (EoS) was utilized with the van der Waals (vdW) mixing rule. And to compare, the Huron and Vidal first-order (HV) and the Wong-Sandler (WS) mixing rules were utilized alongside the PR EoS and the non-random two-liquid (NRTL) activity coefficient model to correlate the acquired data. The findings indicated that the models showed strong concurrence with the empirical data. The binary mixture displays a near-azeotropic phenomenon when the mole fraction of R152a is below 0.65. The azeotropic point is fall within the experimental temperature range when the R152a liquid-phase has a mole fraction between 0.3069 and 0.4104.

Compositional Simulation for Carbon Storage in Porous Media Using an Electrolyte Association Equation of State

Summary We present a new algorithm based on automatic differentiation that enables precise computation of the derivatives of the Z-factor, facilitating the utilization of Newton’s method or coupling with a robust flow solver. Leveraging a free open-source code [MATLAB Reservoir Simulation Toolbox (MRST)], we develop an electrolyte cubic plus association (e-CPA) equation of state (EoS) model to accurately represent the injection of carbon dioxide (CO2) in brine. By integrating flow and thermodynamics, we construct an advanced compositional simulator using MRST’s object-oriented, automatic differentiation framework and the newly developed e-CPA EoS model. This simulator offers flexibility through both overall-composition and natural-variable formulations, achieved by selecting different primary variables. The Péneloux volume translation technique is employed to modify the EoS model’s volume, ensuring accurate density calculation for the mixture. Additionally, we introduce a viscosity model, e-CPA-FV, which accurately predicts the viscosity of carbon capture and storage (CCS) fluids, surpassing the accuracy of the traditional Lohrenz-Bray-Clark (LBC) model. Our simulator demonstrates superior performance in predicting CO2-brine systems compared with the standard formulation based on the Peng-Robinson (PR) EoS and can handle brine with various salts. The self-contained source code necessary to reproduce all examples is available on the open-access Zenodo digital repository (doi: 10.5281/zenodo.10691505).

Automated Equations of State Tuning Workflow Using Global Optimization and Physical Constraints

A computational model that can accurately describe the thermodynamics of a hydrocarbon system and its properties under various conditions is a prerequisite for running reservoir and pipeline simulations. Cubic Equations of State (EoS) are mathematical tools used to model the phase and volumetric behavior of reservoir fluids when compositional effects need to be considered. To anticipate uncertainty and enhance the quality of their predictions, EoS models must be adjusted to adequately match the available lab-measured PVT values. This task is challenging given that there are many potential tuning parameters, thus leading to various tuning results of questionable validity. In this paper, we present an automated EoS tuning workflow that employs a Generalized Pattern Search (GPS) optimizer for efficient tuning of a cubic EoS model. Specifically, we focus on the Peng–Robinson (PR) model, which is the oil and gas industry standard, to accurately capture the behavior of diverse multicomponent, complex hydrocarbon mixtures encountered in subsurface reservoirs. This approach surpasses the limitations of conventional gradient-based (GB) methods, which are susceptible to getting trapped in local optima. The proposed technique also allows physical constraints to be imposed on the optimization procedure. A gas condensate and an H2S-rich oil were used to demonstrate the effectiveness of the GPS algorithm in finding an optimized solution for high-dimensional search spaces, and its superiority over conventional gradient-based optimization was confirmed by automatically tracking globally optimal and physically sound solutions.

Calculating the acoustic and internal gravity wave dispersion relations in Venus's supercritical lower atmosphere

There is a growing interest in quantifying Venusian seismic events through their infrasonic signatures detected by balloon-borne sensors at ∼ 55 km altitude. The extreme pressure and temperature at Venus’s surface correspond to supercritical conditions in the planet’s deep atmosphere. Therefore, an appropriate real-gas equation of state (EoS) must be used to study the acoustic properties and thermodynamics in the Venusian lower atmosphere. In previous work, the Peng-Robinson (P-R) EoS was used to obtain the acoustic sound speed and attenuation coefficient in the lower atmosphere of Venus. Here, the P-R EoS is coupled with the fluid dynamics equations in order to derive the acoustic and internal gravity wave (IGW) dispersion equations. Results show that in Venus’s deep atmosphere, the acoustic cut-off frequency corresponds to a period of ∼480 s (0.0020 Hz), and the buoyancy frequency corresponds to a period of ∼600 s (0.0016 Hz). By comparison, the values in Earth’s lower atmosphere are ∼310 and ∼340 s, respectively. These differences in acoustic and IGW propagation characteristics will be useful in later efforts to discriminate between the various waves detected by high-altitude sensors.

Thermodynamic modeling and solubility assessment of oxycodone hydrochloride in supercritical CO2: Semi-empirical, EoSs models and machine learning algorithms

In this study, the solubility of oxycodone hydrochloride (OXH) in supercritical carbon dioxide (SC–CO2) was investigated at various conditions, temperature (308–338 K) and pressure (120–270 bar), for the first time. The solubility ranged from 0.007 to 0.109 g/L, corresponding to mole fractions ranging from 0.051 × 10−5 to 0.699 × 10−5. Three different model groups were used to analyze the experimental data. The first group comprised seven semi-empirical models, with 3–6 adjustable parameters. These models include Sparks, Sodeifian 1 and 2, Bian, Jouyban, Gordillo and Jafari-Nejad. The second group employed two state equations, namely the Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) with van der Waals mixing rule. The average absolute relative deviation percentage (AARD%) was 9.73 and 10.63 for PR and SRK, respectively. The third group utilized four machine learning algorithms including DNN, RF, MLP and DTs with the respective R2 values 0.992, 0.980, 0.964 and 0.961, respectively. All of the models exhibited satisfactory agreement with the experimental data. Finally, the enthalpies of vaporization (79.71 kJ/mol) and solvation (−19.25 kJ/mol) were calculated for the first time.

Absorption of the acid gases CO2 and H2S from a natural gas stream using the Aspen Plus® simulator

Natural gas consists mainly of methane (CH4) and other lighter hydrocarbons, but it has traces of contaminants such as carbon dioxide (CO2) and hydrogen sulfide (H2S). These gases should be eliminated or reduced to the minimum concentration percentage because they are toxic, corrosive and harmful in high concentrations, as well as to avoid obstruction of pipelines of a pipeline and to meet market specifications. The most commonly used procedure to remove CO2 and H2S from natural gas is the chemical absorption process (sweetening and/or desulphurization), using alkanolamines as solvents, and the amine most commonly used in Brazil is diethanolamine (DEA). In this study, the sweetening process was conducted at the ASPEN PLUS® Chemical Process Simulator. The simulations took place on a permanent basis, using the method of stages in equilibrium and the DEA as solvent. Parameters such as amine current inlet temperature, DEA concentration, number of stages in the absorber, and DEA current pressure were evaluated. In addition, sensitivity analyzes were conducted using the Amines, ELECTNRTL and Peng-Robinson (PR) Thermodynamic Models. As results, it was observed that the Amines model was the one that best represented the stage of sweetening natural gas (separately and in recycled form), obtaining a purer gas, with smaller fractions of CO2 and H2S.

Modeling hydrogen solubility in water: Comparison of adaptive boosting support vector regression, gene expression programming, and cubic equations of state

Predicting the solubility of hydrogen (H2) in aqueous solutions is crucial for studying reactions of hydrogen in the formation, which also affects the security and optimal design of hydrogen storage. In this research, five robust machine learning (ML) algorithms, namely adaptive boosting decision tree (AdaBoost-DT), adaptive boosting support vector regression (AdaBoost-SVR), gradient boosting decision tree (GB-DT), gradient boosting support vector regression (GB-SVR), and k-nearest neighbors (KNN) and three powerful white-box techniques, namely gene expression programming (GEP), genetic programming (GP), and group method of data handling (GMDH) were developed to accurately predict H2 solubility in pure and saline water systems. To this aim, a widespread databank containing 427 experimental data points was collected, and temperature, pressure, and salt concentration (mSalt) were considered as input variables. The validity and precision of the developed models were assessed utilizing several statistical and graphical tests. Results demonstrate that the AdaBoost-SVR smart model could obtain a superior performance and provides precise predictions with root mean square error (RMSE) of 0.000115 and determination coefficient (R2) of 0.9973. Among the white-box models, the GEP provided the best results with an RMSE of 0.000362 and an R2 of 0.9542. Although the accuracy of GEP is slightly lower than that of AdaBoost-SVR, it offers explicit and simple mathematical formula for calculating H2 solubility, which is the main advantage of white box models. The results also demonstrated that AdaBoost-SVR outperforms cubic equations of state (EOSs) such as Peng-Robinson (PR), Redlich-Kwong (RK), Soave-Redlich-Kwong (SRK), and Zudkevitch-Joffe (ZJ). Besides, trend analysis showed that AdaBoost-SVR model could match actual trends of H2 solubility change versus temperature and pressure. Finally, outlier detection analysis using the Leverage technique indicated that the majority of data points used for modeling (nearly 94 %) are reliable and placed in the valid zone.