Fugacity Coefficients Research Articles

Scale translation yields insights into gas adsorption under nanoconfinement

This work describes a scale-translating simulation framework to investigate gas adsorption behavior in nanoconfined pores. The framework combines molecular simulations (MSs), equation of state (EoS), and lattice Boltzmann (LB) simulations. MSs reveal the physics of methane adsorption in nano-sized pores, where input values of fugacity coefficients are optimized based on EoS predictions. Then, an LB free-energy model, which incorporates a viral EoS, upscales intermolecular forces and estimates adsorption behavior via a proposed fluid–wall interaction model. Armed with the values of the LB interaction parameter as a function of pressure, the LB model is used to predict fluid behavior in irregular nanopores, and the results are validated against reference MS data. The LB model is then used to study adsorption behavior at a continuum scale in representative organic shale nanopores based on finely characterized Vaca Muerta shale samples. The results show that methane adsorption could significantly increase contained fluids by 10%–25% in pores smaller than 20 nm. However, in larger pores (40 nm to 90 nm), adsorption's impact diminishes to 2%–3%, suggesting sorption's negligible role beyond a 40 nm pore size.

Equilibrium Study of Carbon Dioxide Reforming of Methane to Syngas

Fugacity coefficients for the components in the gas mixture are determined using the Soave–Redlich–Kwong (SRK) equation of state. The Gibbs free energy minimization method is employed to determine the equilibrium composition of the components for CO2 reforming of CH4 to syngas. To utilize CO2 efficiently and avoid carbon deposition, CO2 composition in the initial feed should not be greater than 1 (nCH4,0 = 1), and the reaction is preferably operated at atmospheric pressure. Setting nCH4,0:nCO2,0 to 1:1, and increasing nO2,0 in the feed from 0 to 1.0 to adjust the initial composition, results in a decrease in the syngas equilibrium yield, and a increase in both nCO2,e and nH2O,e. The temperature required for complete carbon deposition removal decreased. Considering the effective utilization of CO2 at nCH4,0:nCO2,0 1:1, it is recommended to set nO2,0 in the feed to less than 0.5.

Atmospheric Chemistry of Secondary and Hybrid Atmospheres of Super Earths and Sub-Neptunes

The atmospheres of small exoplanets likely derive from a combination of geochemical outgassing and primordial gases left over from formation. Secondary atmospheres, such as those of Earth, Mars, and Venus, are sourced by outgassing. Persistent outgassing into long-lived, primordial, hydrogen–helium envelopes produces hybrid atmospheres of which there are no examples in the solar system. We construct a unified theoretical framework for calculating the outgassing chemistry of both secondary and hybrid atmospheres, where the input parameters are the surface pressure, oxidation, and sulfidation states of the mantle, as well as the primordial atmospheric hydrogen, helium, and nitrogen content. Nonideal gases (quantified by the fugacity coefficient) and nonideal mixing of gaseous components (quantified by the activity coefficient) are considered. Both secondary and hybrid atmospheres exhibit a rich diversity of chemistries, including hydrogen-dominated atmospheres. The abundance ratio of carbon dioxide to carbon monoxide serves as a powerful diagnostic for the oxygen fugacity of the mantle, which may conceivably be constrained by James Webb Space Telescope spectra in the near future. Methane-dominated atmospheres are difficult to produce and require specific conditions: atmospheric surface pressures exceeding ∼10 bar, a reduced (poorly oxidized) mantle, and diminished magma temperatures (compared to modern Earth). Future work should include photochemistry in these calculations and clarify the general role of atmospheric escape. Exoplanet science should quantify the relationship between the mass and oxygen fugacity for a sample of super Earths and sub-Neptunes; such an empirical relationship already exists for solar system bodies.

Thermodynamic Modeling of Solubility of Some Antibiotics in Supercritical Carbon Dioxide Using Simplified Equation of State Approach

Antibiotics are playing crucial role in the treatment of humans since the last few centuries. Their usage has several benefits along with side effects. The efficacy of antibiotics for the treatment of ailments may be retained by controlling the drug dosage. This may be achieved with supercritical fluid technology (SFT). The antibiotic drug solubility in supercritical carbon dioxide (scCO2) is available only at specific temperature and pressure conditions, for effective utilization of SFT, solubility at various conditions are required. Equation of state (EoS) method is used for solubility data modeling and it requires critical properties of the solute, molar volume of the solute and sublimation pressure of the solute along with fugacity coefficient, pressure and temperature. These properties are estimated using group contribution methods. For antibiotics solute critical properties, molar volume and sublimation pressure are unavailable and existing group contribution methods are also not applicable due to the lack of functional group contributions in their techniques. Thus, there is a need to address EoS methodology without using solute properties. Hence, a new EoS methodology for solubility modeling is, proposed without using critical properties of the solute, molar volume of the solute and vapour pressure of the solute. Thus, this study focuses on the development of new solubility model that correlates antibiotics using equation of state (EoS). Importantly, the proposed solubility model does not use the critical properties of the antibiotics. Correlating ability of the proposed model is indicated in terms of regression coefficient and arithmetic average relative deviation percentage (AARD %).

Use of Thermodynamically Consistent Phase Equilibrium Data to Obtain a Generalized Padé-Type Model for the Henry’s Constants of Gases in Ionic Liquids

A generalized Padé-type expression is proposed for Henry’s constant of gases in ionic liquids. The constants are determined using an equation of state, and generalized expressions for the Henry’s constants of the gases in the ionic liquids are proposed. The solute gases included in the study were oxygen, hydrogen, and carbon monoxide in three solvent ionic liquids ([MDEA][Cl], [Bmim][PF6], and [Hmim][TF2N]). The Valderrama–Patel–Teja equation of state with the mixing rules of Kwak and Mansoori are employed to correlate the solubility data, to examine the thermodynamic consistency of the experimental data, and to determine the fugacity (fi) for each concentration (xi) of the solute gas in the liquid phase. From these data, the fugacity coefficients (fiL/xi) are determined to obtain Henry´s constant as Hi = lim(fiL/xi) when xi→0. The calculated Henry’s constants are correlated in terms of the temperature and acentric factor of the gases to finally obtain a generalized expression for Henry´s constant, Hi.

DNS of a non-premixed CH4/O2 flame in a supercritical CO2 environment

3D Direct Numerical Simulation (DNS) is performed to investigate turbulent non-premixed methane oxy-combustion in a CO2-rich environment at supercritical conditions (300 bar). The study focuses on a shear-layer configuration typical of slot burners, where the central slot carries the fuel and the oxidant mixture O2/CO2 flows on both sides of the central jet. The simulation solves the compressible Navier–Stokes equations coupled with the translated volume formulation of the Peng–Robinson cubic equation of state (VTPR-EoS), utilizing a reduced 23-species kinetic scheme derived from the ARAMCO 2.0 complete mechanism. The extremely high pressure results in turbulent scales smaller than those observed at lower pressures. Both premixed and diffusion flame zones are identified, with heat primarily released in non-premixed rich regions, leading to a CO mass fraction of up to 0.55. The flow exhibits uphill (counter-gradient) diffusion for both CO2 and H2O, primarily influenced by the interaction of binary diffusion coefficients and individual species chemical potential gradients. Values in the range of 2.52−2.62 are obtained for the fractal dimension of temperature iso-surfaces. Mixture fraction probability density functions (PDFs) are compared with the standard presumed β−PDF, revealing an underestimation of mixing. Differently from flames at atmospheric pressures, the Dufour effect in the energy diffusion flux, is not negligible. Furthermore, fugacity coefficients must be considered in the calculation of chemical species kinetic rates.

Machine learning-based prediction of CO2 fugacity coefficients: Application to estimation of CO2 solubility in aqueous brines as a function of pressure, temperature, and salinity

Fugacity is a fundamental thermodynamical property of gas and gas mixtures to determine their behavior and dynamics in complex systems. Fugacity can be deduced experimentally from the measurements of volume as a function of pressure at constant temperature or calculated iteratively using analytical equations of states (EOS). Experimental measurement is time-consuming, and analytical models based on EOS are computationally demanding, especially when an approximate but quick estimation is desired. In this work, machine learning (ML) is employed as a viable alternative to analytical EOSs for quick and accurate approximation of CO2 fugacity coefficients. Five different ML algorithms are used to estimate the fugacity coefficients of pure CO2 as a function of pressure (≤ 2000 bar) and temperature (≤ 1000 °C). A combination of experimental and pseudo-experimental (obtained from an analytical EOS) data of CO2 fugacity coefficients is used to train, validate, and test the models. The best results were found using the Extreme Gradient Boosting algorithm, which showed a mean square error of only 0.0002 in the validation data and an average deviation of only 1.3% in the test data (pure prediction). To quantify the effectiveness of the machine learning techniques, results from the best-performing model are compared with two state-of-the-art analytical models. The ML model with significantly less computational complexity showed similar accuracy to the analytical models. The estimated fugacity data are then used to compute the CO2 solubility in aqueous NaCl solution of different concentrations, and a maximum deviation of only 3.2% from the experimental data is observed.

Bridging adsorption behavior of confined CH[formula omitted]-CO[formula omitted] binary mixtures across scales

An accurate understanding of the competitive adsorption of CH4-CO2 binary mixtures in nano-confined systems is critical for engineering CO2 storage in shale gas reservoirs. Due to difficulties in making reliable experimental observations in nano-scale, atomistic simulations (ASs), such as the Grand Canonical Monte Carlo (GCMC) method, provide a viable approach to studying the adsorption behavior of confined fluids. ASs are, however, limited in the size of the compositional domain due to the high computational cost. This work proposes a framework that combines AS and the lattice Boltzmann (LB) method to bridge the physics of confined fluids across scales. The Peng–Robinson equation of state (PR-EoS) produces fugacity coefficients, which serve as input for conducting multi-component GCMC simulations. These GCMC simulations explore the competitive adsorption behavior of CH4-CO2 in nano-slits at various composition, pressure, and channel-width conditions. Both components generate adsorption layers with high densities near the walls with CO2 preferentially adsorbing compared to CH4 on the organic walls of carbon sheets. At the mesoscale, a pseudopotential model represents the intermolecular forces in multi-component, multiple-relaxation-time LB simulations. The LB simulations are in good agreement with the GCMC results, allowing us to obtain values for tunable LB parameters. We then extend the use of LB to simulate adsorption behavior in complex networks with nano-sized channels. The phase behavior and fluid properties in the complex geometries of nano-channels differ from nano-slits and bulk systems. The bridging of physics from GCMC (microscale) to LB (mesoscale) via the macroscale PR-EoS connects the adsorption behavior of binary systems across scales.

A mega study of antibiotics contamination in Eastern aquatic ecosystems of China: occurrence, interphase transfer processes, ecotoxicological risks, and source modeling

Understanding the occurrence, sources, transfer mechanisms, fugacity, and ecotoxicological risks of antibiotics play a pivotal role in improving the sustainability and ecological health of freshwater ecosystems. Therefore, in order to determine the levels of antibiotics, water and sediment samples were collected from multiple Eastern freshwater ecosystems (EFEs) of China, including Luoma Lake (LML), Yuqiao Reservoir (YQR), Songhua Lake (SHL), Dahuofang Reservoir (DHR), and Xiaoxingkai Lake (XKL), and were analyzed using Ultra Performance Liquid Chromatography/Tandem Mass Spectrometry (UPLC-MS/MS). EFEs regions are particularly interesting due to higher urban density, industrialization, and diverse land use in China. The findings revealed that a collective total of 15 antibiotics categorized into four families, which included sulfonamides (SAs), fluoroquinolones (FQs), tetracyclines (TCs), and macrolides (MLs), exhibited high detection frequencies, indicating widespread antibiotic contamination. The pollution levels in the water phase were in the order of LML > DHR > XKL > SHL > YQR. The sum concentration of individual antibiotics for each water body ranged from not detected (ND) to 57.48 ng/L (LML), ND to 12.25 ng/L (YQR), ND to 57.7 ng/L (SHL), ND to 40.50 ng/L (DHR), and ND to 26.30 ng/L (XKL) in the water phase. Similarly, in the sediment phase, the sum concentration of individual antibiotics ranged from ND to 15.35 ng/g, ND to 198.75 ng/g, ND to 1233.34 ng/g, ND to 388.44 ng/g, and ND to 862.19 ng/g, for LML, YQR, SHL, DHR, and XKL, respectively. Interphase fugacity (ffsw) and partition coefficient (Kd) indicated dominant resuspension of antibiotics from sediment to water, causing secondary pollution in EFEs. Two groups of antibiotics, namely MLs (erythromycin, azithromycin, and roxithromycin) and FQs (ofloxacin and enrofloxacin), showed a medium-high level of adsorption tendency on sediment. Source modeling (PMF5.0) identified wastewater treatment plants, sewage, hospitals, aquaculture, and agriculture as the major antibiotic pollution sources in EFEs, contributing between 6% and 80% to different aquatic bodies. Finally, the ecological risk posed by antibiotics ranged from medium to high in EFEs. This study offers valuable insights into the levels, transfer mechanisms, and risks associated with antibiotics in EFEs, enabling the formulation of large-scale policies for pollution control.

Optimizing Sour Gas Qualification Testing—Modeling the Effects of Temperature and Total Pressure on H2S Fugacity, Activity, and Solubility Coefficients up to 138 MPa and 204°C

Traditionally, the sour severities of high-pressure high-temperature (HPHT) oil and gas production wells were assessed by H2S partial pressure (PH2S): The mole fraction of H2S in the gas (yH2S) multiplied by the total pressure (PT). However, PH2S usually over-predicts the actual sour severity of HPHT systems, leading to suboptimal material selection choices. To reflect recent advances in thermodynamic modeling and to avoid over-conservatism, after careful deliberation, ANSI/NACE MR0175-2021/ISO 15156-2:2022 recently expanded the number of sour severity metrics to four: PH2S, fugacity (fH2S), chemical activity (aH2S), and dissolved concentration (CH2S) of the aqueous phase. The new metrics are often computationally derived and account for thermodynamic nonidealities, which are significant at HPHT conditions. Regardless of the preferred metric, quantifying the sensitivity of each metric to a wide range of temperatures and total pressures is critical when conducting H2S service assessments. In this article, the effect of increasing temperature and total pressure on the thermodynamically derived apparent H2S solubility (KH2S = CH2S/PH2S) was investigated. KH2S is a critical parameter for quantifying changes in H2S phase behavior/sour severity of HPHT systems. Apparent KH2S values were calculated by two different thermodynamic models and benchmarked to two publicly available H2S/H2O datasets up to 120°C and 10.3 MPa equilibrated in a brine containing 165,000 mg/L Cl−. The model that provided the best match to the experimental data was later used in a much broader thermodynamic sensitivity study of the H2S/CH4/H2O/NaCl “oilfield” system. For this sensitivity analysis, changes in fH2S, aH2S, CH2S, and KH2S were individually modeled between 4°C and 204°C, at total pressures up to 138 MPa, and in brines containing up to 25 wt% NaCl (180,000 mg/L Cl−). Lastly, a comparison of the predicted sour severity by pseudo-PH2S, fH2S, and CH2S metrics, over the same temperature and total pressure parameter space, is presented.

Accurate Analytical Evaluation of Fugacity Coefficient of Gases

Accurate Analytical Evaluation of Fugacity Coefficient of Gases

The unexpected weirdness of rate-based simulation of some high-pressure column operations

Diffusion is the process by which molecules move. One way to model multicomponent diffusion is with a version of Fick’s law: (J) = - [D] d(c)/dz where [D] is a matrix of multicomponent diffusion coefficients. [D] is the product of two other matrices, one of which involves partial derivatives of the fugacity or activity coefficients. It is usually the case that all of the elements on the main diagonal of [D] have a positive value. Wambui Mutoru and Firoozabadi (2011, 2012) showed that CO2-rich and N2-rich hydrocarbon systems could have main diagonal elements of [D] that are negative. Using rate-based column simulations, we have found that these negative main diffusion coefficients readily occur in some high-pressure distillation operations. We investigate these processes in more detail and explore the consequences for the design and operation of columns in which this phenomenon is predicted to occur.

Solubility of ibrutinib in supercritical carbon dioxide (Sc-CO2): Data correlation and thermodynamic analysis

Ibrutinib (PCI-32765), marketed under the trade name IMBRUVICA, is a first-in-class irreversible inhibitor drug of Bruton tyrosine kinase (BTK). In the current research, its solubility was measured at operational conditions 120–270 bar and 308–338 K, for the first time. The drug solubility has been reported between 3.90×10-6 to 1.30×10-5 based on mole fraction. Analysis of the curves confirms strong dependency of ibrutinib solubility to operational conditions due to their direct effect on solvating power of solvent. Also, pressure effect was more pronounced at the higher temperatures and the cross-over point was located around 170 bar. Besides, theoretical investigation and computational approach were carried out to correlate and extrapolate the experimental solubility of this medicine using thermodynamic models based on different approaches; semi-empirical models, activity coefficient (modified model of Margules), fugacity coefficient (mPR and mRK cEoSs) and dilute solution theory by the model of Wang-Tavlarides. Best correlation results were obtained by the modified model of Margules (AARD = 6.68%) and the empirical model of Jouybanet al., (9.62%). Additionally, different enthalpies of ibrutinib-Sc-CO2 system were estimated.

Vapor-liquid equilibrium of carbon dioxide solubility in a deep eutectic solvent (choline chloride: MDEA) and a mixture of DES with piperazine-experimental study and modeling

In recent decays, many investigators have carried out the CO2 absorption in ionic liquids, but these green solvents are expensive and hard to prepare. In recent years, researchers have introduced deep eutectic (DES) solvents composed of a hydrogen bond donor and a hydrogen bond acceptor. DES melting point is usually lower than the ideal solution of its constituents' components and is in the liquid phase at room temperature. In this work, we have measured CO2 solubility in a deep eutectic solvent composed of choline chloride and methyldiethanolamine (MDEA) in a molar ratio of 1–6. We carried out experiments at 323.15, 333.15, and 343.15 K within the 1–50 bar pressure range. Besides, we added piperazine (Pz) as a physical solvent at 5, 10, and 15 wt% to the DES. Based on the obtained results, we observed enhancing pressure and reducing temperature led to increasing CO2 absorption. Also, increasing piperazine caused to intensify the CO2 absorption in the mixture of the DES + Pz system. Finally, we used a thermodynamic approach for the computation of the vapor–liquid equilibria of the present systems. We applied the Peng-Robinson (PR) equation of state to calculate the gas fugacity coefficient in the vapor phase. The non-random two-liquid (NRTL) activity coefficient model was used to compute the non-ideality of the liquid mixture. The modeling results were in very good agreement with the experimental data.

DL-KF modeling for acceleration of flash calculations in phase equilibrium using deep learning methods

Improving the robustness and efficiency of flash calculations in phase equilibrium is crucial for reservoir simulation. DL-KF (Deep Learning for K-values and Fugacity Calculation) modeling is proposed to accelerate phase equilibrium calculation using deep learning methods, in which the three-steps neural networks are included: ANN-STAB (Artificial Neural Network for Stability Test) model, ANN-KV (Artificial Neural Network for K-values Calculation) model and ANN-FUG (Artificial Neural Network for Fugacity Calculation) model respectively. The ANN-STAB model is generated to test phase stability. When temperature, pressure and feed composition are given, the phase classification is obtained directly with very low computation cost. In the ANN-KV model, initial K-values are determined by trained networks instead of employing Wilson equation employed in traditional flash calculation. Its initial estimations of K-values significantly reduce the number of iterations and avoid converging to incorrect or unphysical solutions. The ANN-FUG model is built to replace the fugacity coefficient calculation in traditional flash calculation algorithms, and simplifies the nonlinear calculation of internal iterative calculation. These three artificial neural network models are embedded into the traditional algorithms to accelerate flash calculations. The framework considers the complete physical process of the algorithms of flash calculations in phase equilibrium calculations using deep learning methods, and it can also guarantee the conservation of component mass, which is crucial for phase equilibrium calculations and reservoir simulation. The proposed DL-KF modeling is validated and compared with the original equation of state modeling and three other deep learning methods using two typical hydrocarbon fluid cases. A sample of C3H8-CO2-heavy oil systems from Huabei oilfield and a PVT experiment in Tahe oilfield are used to examine the DL-KF modeling. The physical properties of oil sample of Bakken reservoir with CO2 injection are also investigated. These results reveal that the DL-KF methoding is accurate and efficient for accelerating phase equilibrium calculations of reservoir fluids.

Impact of thermodynamic hypotheses on the calculation of the quantity of CO2 stored in a saline aquifer

The aim of this paper is to study the impact of thermodynamics models on the CO2 storage capacity of an aquifer, by using modelling and simulation of transport phenomena in porous media. The aquifer is represented here by a simplified three phase isothermal non-reacting medium composed by an inert solid phase and two binary (CO2 and H2O) fluid phases. The mathematical description is classically developed by the volume averaging method. For each phase, the conservation equations of mass, momentum and energy alongside thermodynamic laws and boundary conditions are first written. They are then integrated over a representative elementary volume in order to establish the description at the local scale. In a thermodynamic point of view, two kinds of models have been implemented and compared. The first one assumes that the gas and liquid phases are ideal. On the contrary, in the second approach, non-ideal thermodynamics is taken into account by calculating an activity coefficient (γ-φ approach) for the liquid phase and a fugacity coefficient (PengRobinson approach) for the gas phase. Results show, among other things, that the amount of CO2 dissolved in the liquid phase is significantly reduced with the non-ideal approach compared to the ideal case. These results highlight the interest of considering non-ideal phases in more complex models.

Distribution, source finding, ecological hazard assessment, and water-sediment exchange rate of polychlorinated biphenyl (PCB) congeners in South Pars Industrial Zone, Iran.

South Pars Industrial Zone is located near an Assaluyeh city on the coast of the Persian Gulf and is known as the energy capital of Iran. In this study, environmental and health effects due to PCB congeners had an assessment. In this study, 10 air stations, 10 seawater, and sediments stations were systematically selected and sampled in two seasons. Air, seawater, and sediment pollution made by polychlorinated biphenyls (PCBs) were evaluated. Seawater-sediment exchange conditions using the fugacity coefficient reviewed. PCB levels in marine sediments, seawater, and air based on the analysis of the obtained data were 107.33-172.92ng/g, ND-135.68ng/L, and ND-4.4ng/m3, respectively. The highest concentration was observed in the vicinity of refineries, petrochemicals, and petroleum export facilities. These values had increased significantly compared to values of studies, conducted in similar areas. The sources were electrical wastes, storage sites, power generation units, and wastewater treatment. The ecological risk of seawater was assessed to be low to high, while sediment risks were reported with a low to moderate risk range. In 70% of the stations, the predominant transfer was from sediments to seawater; sediments were in fact the secondary source of seawater pollution. It is suggested for the area to be continuously monitored, while engineering and management measures should be adopted to improve the situation and also prevent the spread of pollution.

Accurate Effective Diffusivities in Multicomponent Systems

Mass transfer is an omnipresent phenomenon in the chemical and related industries for which effective diffusivities (Di,eff) constitute a useful and simple mathematical tool, especially when dealing with multicomponent mixtures. Although several models have been published for Di,eff they generally involve simplifying assumptions that severely restrict their use. The current work presents the derivation of accurate analytical equations for Di,eff, which take into account the nonideal behavior of multicomponent mixtures. Additionally, it is demonstrated that for an ideal mixture the new model reduces to the well-known equations of Bird et al., which are the exact analytical solution for ideal systems. The procedure for Di,eff estimation is described in detail and exemplified with two chemical reactions: the liquid phase ethyl acetate synthesis and the high pressure gas phase methanol synthesis. Relative to the Bird et al. ideal equations the effective diffusivities calculated with the new model show differences up to 38% for ethyl acetate synthesis when using UNIFAC model to evaluate activity coefficients. For methanol synthesis, deviations from −23% to 22% are found using PC-SAFT equation of state (EoS) and from −49% to 24% when applying the Peng–Robinson EoS to estimate fugacity coefficients. Comparisons are also performed with the models by Wilke, Burghardt and Krupiczka, Kubota et al., and Kato et al. The worst results are achieved by the Wilke and Kubota et al. equations for the liquid phase and gas phase reactions, respectively. Furthermore, it is shown that substantial errors in effective diffusivity calculations may occur when deviations from the ideal behavior are unaccounted for. This can be avoided by adopting the new rigorous approach here presented.

Comparison of pure component thermodynamic properties from CHEMCAD with direct calculation using the Soave–Redlich–Kwong equation of state

Gas-phase thermodynamic properties are routinely calculated with equations of state in process design software such as CHEMCAD [1], and users should be able to verify the calculations. In a previous study, we reproduced the enthalpy, entropy, compressibility factors, and fugacity coefficients obtained from CHEMCAD using the Lee–Kesler method [2, 3], and later extended this study to include the Peng–Robinson equation of state [4, 5]. An interesting feature of the earlier work is that compressibility and fugacity coefficients in CHEMCAD did not match up precisely with our independent calculations. We therefore extended the study to include the Soave–Redlich–Kwong (SRK) equation of state [6, 7]. Our results show consistency for most of the 48 molecules studied, with percent error in enthalpy decreasing significantly for the SRK method to generally less than 0.002% compared to about 0.3-1% for the Lee–Kesler and Peng–Robinson methods. Unlike the previous two studies, we now see nearly perfect agreement in the compressibility and fugacity coefficient. Furthermore, we show that compressibility and fugacity coefficient remain constant in CHEMCAD even when the equation of state is changed. For enthalpy, while the results are much closer than in the previous studies, we see deviations for methane, air, carbon monoxide, carbon dioxide, nitrogen, and oxygen. Discrepancies in entropy were also observed for bromine, carbon dioxide, chlorine, hydrogen sulfide, and nitrous oxide.

Laboratory determination and thermodynamic analysis of alendronate solubility in supercritical carbon dioxide

Alendronic acid, with the commercial name of Alendronate, is a bisphosphonate medicine which is generally used orally to treat the osteoporosis and Paget's disease of bones. However, its absorption is poor, and its oral bioavailability is <1%. So, development of novel delivery systems to enhance its bioavailability and reduce its side effects is essential.The design a modern drug delivery systems, through supercritical carbon dioxide (scCO2) as a green solvent, which is known as an efficient solution to increase the drug bioavailability, reduce toxicity and side effects. Solubility of pharmaceutical substances in scCO2 is an essential parameter that must be determined for this purpose.Here, solubility of Alendronate was experimentally studied in the span of 0.01 × 10−4 to 1.5 × 10−4 (equilibrium mole fraction), at 308–338 K and 120–300 bar. Also, obtained experimental values were correlated by two fugacity coefficient models (PR-EoS and SRK-EoS), and two activity coefficient models (modified Wilson and UNIQUAC). All these models could successfully correlate the Alderonate solubility values. Meanwhile, the solubility data obtained from the SRK-EoS (AARD% = 10.11) and modified Wilson’s model (AARD% = 11.52) are more accurately fitted to the experimental data.