Statistical Associating Fluid Theory Equation Research Articles

PρT measurements of 3-aminopropan-1-ol and N-(2-hydroxyethyl)morpholine from (293.15 to 473.15) K and up to 40 MPa and modeling with modified Tait and PC-SAFT equations

New density data has been reported for 3-aminopropan-1-ol (AP) and N-(2-hydroxyethyl)morpholine (NHEM) at temperatures ranging from (293.15–473.15) K at 19 pressures ranging from (0.1–40) MPa. The experimental measurements were carried out using an Anton Paar high-pressure vibrating tube densimeter with a combined expanded uncertainty of 1 kg m−3 at a 95 % confidence level. Contributions considered in the uncertainty analysis included the impurities in the materials used and apparatus specification. In addition, the density and speed of sound at ambient pressure (81.5 kPa) and temperatures (293.15–343.15) K were measured. The experimental density data were correlated with the modified Tait equation. Values of thermal expansion coefficient (αP ) and isothermal compressibility (κT) were calculated. The work is completed with the modeling of the experimental data using the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The parameters of the PC-SAFT equation of state, for the pure compounds, were determined by fitting the equation to the liquid PρT experimental data. Thermodynamic properties such as thermal expansion coefficient (αP), isothermal compressibility (κT), isobaric heat capacity (CP), and speed of sound (u) were calculated with the obtain parameters. Good agreement between experimental data and derived properties represented the modeling accuracy with the obtained parameters.

A study on thermophysical properties of binary mixtures of n-hexane with benzene and some alkyl-substituted benzenes within temperature range (293.15–323.15) K: Experimental and modeling approach

The current work reports densities and sound speeds, and related thermodynamic excess properties, namely excess molar volumes and excess isentropic compressibilities, measured at temperatures from (293.15 to 323.15) K and under atmospheric pressure conditions for binary mixtures of n-hexane with benzene, toluene, ethylbenzene, o-xylene, m-xylene, and p-xylene. Redlich-Kister polynomial correlated the thermodynamic excess properties to test the quality of experimental data. Excess properties contributed to understanding molecular interactions between involved molecules and the peculiarities of their packing in the mixture. The Jouyban-Acree model was used to correlate the mixtures' experimental densities, sound speeds, and their related derived properties, namely isobaric thermal expansivities and isentropic compressibilities. The average absolute percentage deviation of the correlated values from the experimental ones was better than 0.036 %, 0.058 %, 0.040 %, and 0.146 % for density, sound speed, isobaric thermal expansivity, and isentropic compressibility, respectively, attesting to the robustness of the Jouyban-Acree correlations. Additionally, the Perturbed Chain Statistical Associating Fluid Theory Equation of State modeled the densities of the current mixtures. Schaaff's Collision Factor Theory and Nomoto's relation were compared for their ability to model the sound speeds of the mixtures. The efficacy of these models was tested by computing the average absolute percentage deviations between experimental and computed values. The modeled densities are reasonably concordant with experimental data, with an overall deviation of 0.02 %. Notably, Nomoto's relation exhibited superior performance over Schaaff's theory in modeling sound speeds of current mixtures, with an overall deviation of 0.33 %. The current findings underline the efficacy and versatility of the used models for thermodynamic modeling in systems of varying complexity.

Application of volume‐translated rescaled perturbed‐chain statistical associating fluid theory equation of state to pure compounds using an expansive experimental database

AbstractThe performance of the perturbed‐chain statistical associating fluid theory‐type equations of state (PC‐SAFT‐type EOSs) is compromised in predicting properties of pure compounds in the critical region. In our previous research, we introduced an improved volume‐translated rescaled PC‐SAFT EOS (VTR‐PC‐SAFT EOS) by incorporating a dimensionless distance‐function. Such VTR‐PC‐SAFT EOS is built based on a critical point‐based PC‐SAFT EOS that can reproduce the critical temperature, critical pressure, and critical molar volume of pure compounds. VTR‐PC‐SAFT EOS is found to significantly improve the accuracy of phase behavior predictions in both critical and noncritical regions for pure compounds. In this study, we assess the performance of VTR‐PC‐SAFT EOS in reproducing the critical and noncritical properties of 251 pure compounds, encompassing 20 distinct chemical species. The testing results indicate that, compared to the other three PC‐SAFT‐type EOSs, the VTR‐PC‐SAFT EOS can consistently provide more accurate representations of critical and noncritical properties of 251 pure compounds.

Interactions at the interfaces of the H2-brine-cement systems at elevated pressures for H2 storage

There is a global demand on assessment of potential subsurface gas storage sites in view of safely injecting hydrogen or carbon dioxide. One relevant aspect that has already been subject to thorough investigation is the mutual interaction of all participating compounds in terms of the wetting behaviour that on its turn is directly related to the predominating capture mechanisms. Given the diversity of the geophysical and geochemical circumstances, transferability of results from work conducted on one geological site to another location is limited. For instance, there is a large number of publications on wettability of many different rock types in hydrogen atmosphere that are partly controversal and strictly applicable only to the respective reported system. Hence, there is a gap in finding general model approaches that serve for a holistic understanding of predominating mechanisms and building the fundamentals for predicting the behaviour of systems that have not been studied so far. The presented work addresses this gap by quantifying mutual interactions of the participating phases in a solid-liquid-gas systems and determining the respective interfacial tensions, γSV (solid-vapor), γLV, (liquid-vapor) and γSL (solid-liquid).Neumann and Good demonstrated how to determine the solid-fluid interfacial tension based on the contact angle and the liquid-gas interfacial tension by calculating a so-called molecular interaction parameter. Up to date, this method has been applied, among others, for systems containing CO2 and solids such a teflon, glass, and steel. The methodology could be confirmed by testing systems comprising steel - H2O - CH4 /H2 and comparing the results to the aforementioned literature data.As one of the critical parts in H2 underground storage, the completion system containing a common well cement, H2 and brine was subject to this work. The interfacial tension between H2 and brine as well as the contact angle between the fluid phases and the cement were investigated experimentally up to 20 MPa, temperatures from 313.15 to 353.15 K and NaCl – concentrations of up to 10% wt. As a theoretical approach, the interfacial tension of the system H2O+H2 was investigated using the density gradient theory (DGT) in combination with the perturbed chain statistical associating fluid theory equation of state (PC-SAFT). Finally, the H2-cement interfacial tension is determined through the calculation of a so-called molecular interaction parameter. The interfacial tension data of H2O+H2 experimentally and theoretically determined in this work agree among each other as well as with previous literature data. Likewise, agreement was found between the brine+H2 interfacial tension and previous studies. The contact angle appears to be influenced mostly by pressure, producing a less H2O/brine-wet system as pressure increases. The H2-cement interfacial tension decreases from approximately 150 mN/m down to 100 mN/m, as the pressure increases from 0.1 to 20 MPa. The presented data suggest H2 to be slightly adsorbed on the one hand but the capillary entry pressure to decrease on the other, causing concerns regarding the integrity of the completion system.

Viscosity measurement and correlation for dense fluid mixture of carbon dioxide and ethanol at 313–343 K and 15–30 MPa

The viscosity ηm of dense fluid mixtures of carbon dioxide and ethanol was determined from the pressure drop between the inlet and outlet of a packed bed using the Ergun equation at temperatures from 313.2 K to 343.2 K and pressures from 15 MPa to 30 MPa over the entire range of ethanol composition. The ηm values for the fluid mixtures decreased with increasing temperature and increased with increasing pressure under isocratic conditions. In addition, the values measured ηm with Ergun eq. were correlated with the equation combining the Eyring theory and the perturbed chain statistical associating fluid theory equation of state (PC-SAFT EoS) and with that based on the rough hard-sphere (RHS) model proposed by Dymond and Assael. The accuracies of the Eyring + PC-SAFT EoS and the RHS model were 8.7% and 12%, respectively, in terms of average relative deviation for 80 conditions over the entire range of ethanol composition.

Thermodynamic analysis of a dual-pressure evaporation high-temperature heat pump with low GWP zeotropic mixtures for steam generation

High-temperature heat pumps (HTHPs) have gained attention due to their economic and environmental benefits in utilizing industrial waste heat for steam generation. This study focuses on improving the HTHPs’ performance by employing two-stage separation and dual-pressure evaporation technology in the auto-cascade heat pump cycle. Additionally, binary zeotropic refrigerant mixtures with low-GWP are selected using the polar perturbed-chain statistical associated fluid theory (PC-SAFT) equation of state. The findings indicate that the R1234ze(E)&R1233zd(E) refrigerant mixture outperforms other potential alternatives, exhibiting a thermodynamic effectiveness 0.85%–1.86% higher than the benchmark mixture, R134a&R245fa. The improved cycle demonstrates significant enhancements, achieving a 45.17% increase in heat source utilization efficiency and a 24.48% improvement in COP compared to the basic auto-cascade cycle. Effective temperature matching between refrigerant mixtures and heat sources/sinks is guaranteed in the improved cycle. Moreover, a parameter analysis reveals that increasing the subcooling degree of the cascaded heat exchanger and the separation dryness fraction at separator 2 enables improvements in both COP and heat source utilization efficiency. These findings provide valuable insights into the design of steam generation heat pumps and the selection of refrigerant mixtures.

Thermophysical properties of ethyl levulinate and n-alkanol systems

Some thermophysical properties such as densities, speeds of sound, refractive indices, and heat flows of the binary systems ethyl levulinate and n-alkanols (methanol, ethanol, 1-propanol, and 1-butanol) are reported in the temperature range T = (283.15–313.15) K and at p = 100 kPa. From these experimental data, the excess properties were calculated and correlated with the composition using a modified Redlich–Kister equation. The excess molar volumes were negative for short-chain alcohols and positive for 1-propanol and 1-butanol. The excess refractive indices exhibited the opposite behaviour. The excess isentropic compressibilities were negative and the excess molar enthalpies, were positive. The perturbed chain statistical associating fluid theory equation of state (PC-SAFT EoS) was successfully applied to correlate the densities of the mixtures, and good qualitative results in the computation of the excess molar enthalpy were obtained. Furthermore, Schaaff’s collision factor theory (SCFT) and the Laplace mixing rule were coupled with PC-SAFT to predict the speed of sound and the refractive index, respectively.

CO2 solubility and absorption rate analysis of a mixed poly(oxymethylene) dimethyl ethers (PODE3–5) solution

Efficient and economical carbon capture is critical to counteract the diverse problems of global warming. In this work, the solubility of carbon dioxide (CO2) in different poly(oxymethylene) dimethyl ethers (PODE) solutions was experimentally investigated at temperatures from 278.15 to 308.15 K and pressures up to 1.2 MPa. The Henry's law constants of CO2 in the PODE system were determined and compared with other types of physical absorbents, which revealed PODE3–5 has great CO2 absorption ability in terms of molar and mass fraction. Meanwhile, the initial absorption rate of the physical absorption process of PODE3–5 was calculated and compared with commercially available absorbents using a gas absorption rate relationship. It was shown that the absorption rate of PODE3–5 in the CO2 absorption process is faster than that of other commercial absorbents. The CO2 solubility data of PODE3–5 were also correlated using the Jou-Mather model and the perturbed-chain statistical association fluid theory (PC-SAFT) equation of state model, and the recycling performance of the PODE3–5 absorbent was tested.

Application of PC‐SAFT EoS and SCFT for the modeling of thermophysical properties comprising deep eutectic solvent and alcohols

AbstractZinc (II) chloride based deep eutectic solvent (DES) were formed by mixing zinc (II) chloride with phosphoric acid. Fourier‐transform infrared spectroscopy was used to identify any possible shifts when the two compounds were assorted, and differential scanning calorimetry (SDT Q600 V20.9 Build 2D) was utilized to evaluate the formation of deep eutectic solvent. Densities, , and speed of sound, u, of [ZnCl2][phosphoric acid] 1:2.5 with methanol, ethanol, or propanol have been measured at T = (293.15, 303.15, 308.15, and 313.15) K and at atmospheric pressure. Excess molar volumes ( ), isentropic compressibilities ( ), deviation in isentropic compressibility ( ), and intermolecular free length ( ) were calculated from the densities, and speed of sound, respectively. To fit the excess molar volumes and deviation in isentropic compressibilities, the Redlich–Kister smoothing polynomial was used. Also, we have used perturbed chain statistical associating fluid theory equation of state (PC‐SAFT EoS) for modeling the densities of the binary mixtures, and Schaaff's collision factor theory (SCFT) and Nomoto's relation (NR) were used for modeling the speed of sounds for the binary mixtures.

High-pressure densities of 2-(dimethylamino) ethanol and 2-(diethylamino) ethanol: Measurement and modeling with new modified Tait and PC-SAFT equations of state

New experimental high-temperature, high-pressure (HTHP) density data of two alkanolamines, namely 2-(dimethylamino) ethanol and 2-(diethylamino) ethanol was measured in a wide range of temperatures (293.15–473.15 K) and pressures (0.1–40 MPa). The density measurements were performed using an Anton Paar high-pressure vibrating tube densimeter. The combined expanded uncertainty in the reported densities, at a 95% confidence level with taking into account the impurities of materials and apparatus specification was 1kg·m−3. The density and speed of sound at ambient pressure (81.5 kPa) and temperatures (293.15–343.15 K) were also measured. The experimental density data were correlated, as a function of pressure and temperature, using the new modified Tait equation, and derived properties including thermal expansion coefficient (αP) and isothermal compressibility (κT) were calculated. The modeling results in this work have been obtained by using the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The parameters of the PC-SAFT equation of state (EOS), for pure compounds, were firmly determined by fitting the equation to the liquid PρT experimental data. With these parameters, thermodynamic properties such as thermal expansion coefficient (αP), isothermal compressibility (κT), isobaric heat capacity (CP), and speed of sound (u) were calculated. Good agreement between the results and experimental data and derived properties represented the modeling accuracy with the obtained parameters.

The Effect of Binary Interaction Parameters and Induced Association on the Performance of the PC-SAFT Equation of State: Validation against a Benchmark Database of High-Quality Binary-System Data

The performance of the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) equation of state (EoS) using classical mixing rules, induced-association schemes for mixtures exhibiting cross-association phenomena between two components that do not self-associate, and one regressed temperature-independent binary interaction parameter (kij) per mixture is assessed using a high-quality reference database containing binary-system data for various properties. The binary mixtures that are included in the database are divided into nine categories (Binary Association Codes, BACs) according to their ability to be involved in a hydrogen bond. Grading of the EoS is done by applying an already published procedure with certain modifications that were also published recently. An important feature is the inclusion of a performance indicator, called the “Success Ratio” (SR), that quantifies the percentage of experimental data points which the model can qualitatively reproduce. The original marks of the PC-SAFT EoS when implemented with classical mixing rules, no induced-association scheme, and a kij parameter set equal to zero are recalculated with the modified grading procedure and are directly compared with the new marks obtained in this work. The effect of including induced-association effects in PC-SAFT for mixtures that belong to BAC6, BAC7, and BAC8 (mixtures in which cross-association takes place without both components being self-associating) is also investigated. The effect of regressing cross-association parameters vs regressing kij parameters for mixtures belonging to the BAC6 group (mixtures in which cross-association arises although the two components do not self-associate) is showcased. The final optimized PC-SAFT EoS utilizes classical mixing rules, induced-association effects (using regressed cross-association parameters for some binary systems belonging to BAC6 and a predictive method for BAC7 and BAC8), and one temperature-independent kij parameter per binary mixture (except for binary systems belonging to BAC6 for which cross-association parameters were adjusted). The final average mark of the optimized EoS is 9.3/20.

Toward Advanced, Predictive Mixing Rules in SAFT Equations of State

A novel mixing rule that bridges the Statistical Associating Fluid Theory (SAFT)-type equations of state and activity coefficient models is proposed. Applying this mixing rule to the PC-SAFT equation of state is the focus of this article. In comparison to the original PC-SAFT equation, and even the underlying activity coefficient model, this mixing rule provides high-accuracy predictions of equilibrium properties for a range of mixtures, being able to predict phenomena that neither PC-SAFT or the underlying activity coefficient model would be able to predict on their own. A few limitations are identified including the case of cross-associating mixtures, due to the difficulty of separating associative interactions from dispersive interactions in activity coefficient models. Nevertheless, it is also shown that the new mixing rule is able to predict bulk properties very accurately, including volumetric properties which activity coefficient models alone are not able to predict. Given that one is able to use predictive activity coefficient models within this mixing rule, such as UNIFAC and COSMO-SAC, this new mixing rule opens the doors for the development of fully predictive SAFT equations of state for mixture systems.

Group-contribution SAFT equations of state: A review

We present a review and thorough assessment of recent advances and applications of group-contribution methods (GCMs) implemented in the Statistical Associating Fluid Theory (SAFT) equations of state (EoSs). Modern SAFT EoSs are some of the most advanced and effective thermodynamic models for industrial applications, because they are predictive and have a strong molecular foundation. GCMs are simple and useful approaches that can enhance the predictive ability and applicability of EoSs, for successful evaluation of thermodynamic properties of complex systems. A major advantage of using a GCM is the transferability of functional group parameters, i.e., a single set of parameters can be used for a functional group found in more than one homologous group. Because such a GCM requires less effort in system-specific model fitting and regression, it has also been incorporated into the SAFT-framework, yielding various incarnations of GCM SAFT EoSs. These versatile EoSs have been applied by many researchers to a wide variety of fluids and mixtures, including electrolytes, ionic liquids, polymers, petroleum fluids, biofuels, solvents for CO2 capture, and computer-aided molecular design.

Vapor-liquid equilibrium for the {R-OH + R-palmitate} systems at 50.3 and 101.3 kPa

Fossil sources of energy become focus of many debates due to the pollution caused by them. In this scenario, renewable fuels, as biodiesel, are studied to improve their production efficiency and become more competitive with fossil fuels and even substitute them. Biodiesel, produced by the transesterification reaction, is constituted by a mixture of fatty acid esters and needs to be separated from its reactional solution in order to be commercialized. To improve the separation processes, the thermodynamic behavior of the mixtures involving components of the biodiesel needs to be known. Aiming this, the vapor–liquid equilibrium (VLE) of the methanol + methyl palmitate and ethanol + ethyl palmitate systems was analyzed at 50.3 and 101.3 kPa and the experimental data were submitted to a thermodynamic consistency test and thermodynamic modeling with the Peng-Robinson (PR), Group Contribution Volume Translated Peng-Robinson (GC-VT-PR) and the Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) equations of state. Experimental data were considered thermodynamically consistent, and the modeling showed good results in terms of the lowest relative deviations of temperature and vapor mole fraction obtained with the GC-VT-PR and PC-SAFT models.

Calculation of azeotropic properties for binary mixtures with the PC-SAFT equation of state

In this work, we present a novel approach to predict the location of azeotropes for binary mixtures using the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT).The proposed method requires as input the pure-component parameters of the PC-SAFT equation: the segment number (m), the hard-core segment diameter (σ), and the segment-segment interaction energy parameter (ε/k) for every pure non-associating fluid. By using these parameters, PC-SAFT estimates with accuracy the azeotropes properties of binary mixtures as well as the successful prediction of vapour-liquid equilibria for many non-associating binary systems. In order to improve the predictive ability of the PC-SAFT equation, the interaction parameters of 8 binary systems containing novel refrigeration fluid, were estimated from binary vapour–liquid equilibrium data. For comparison, the data were also modelled using the (PR-MC-WS-NRTL) thermodynamic model. Good agreements are found between the calculated results and reference data and the relative error does not exceed 3.69% and 0.97% for the molar fraction and the pressure respectively.

A Comparison between the Perturbed-Chain Statistical Associating Fluid Theory Equation of State and Machine Learning Modeling Approaches in Asphaltene Onset Pressure and Bubble Point Pressure Prediction during Gas Injection.

Predicting asphaltene onset pressure (AOP) and bubble point pressure (Pb) is essential for optimization of gas injection for enhanced oil recovery. Pressure-Volume-Temperature or PVT studies along with equations of state (EoSs) are widely used to predict AOP and Pb. However, PVT experiments are costly and time-consuming. The perturbed-chain statistical associating fluid theory or PC-SAFT is a sophisticated EoS used for prediction of the AOP and Pb. However, this method is computationally complex and has high data requirements. Hence, developing precise and reliable smart models for prediction of the AOP and Pb is inevitable. In this paper, we used machine learning (ML) methods to develop predictive tools for the estimation of the AOP and Pb using experimental data (AOP data set: 170 samples; Pb data set: 146 samples). Extra trees (ET), support vector machine (SVM), decision tree, and k-nearest neighbors ML methods were used. Reservoir temperature, reservoir pressure, SARA fraction, API gravity, gas–oil ratio, fluid molecular weight, monophasic composition, and composition of gas injection are considered as input data. The ET (R2: 0.793, RMSE: 7.5) and the SVM models (R2: 0.988, RMSE: 0.76) attained more reliable results for estimation of the AOP and Pb, respectively. Generally, the accuracy of the PC-SAFT model is higher than that of the AI/ML models. However, our results confirm that the AI/ML approach is an acceptable alternative for the PC-SAFT model when we face lack of data and/or complex mathematical equations. The developed smart models are accurate and fast and produce reliable results with lower data requirements.

Modeling vapor–liquid equilibrium and liquid–liquid extraction of deep eutectic solvents and ionic liquids using perturbed‐chain statistical associating fluid theory equation of state. Part II

AbstractThis study aims to use perturbed‐chain statistical associating fluid theory (PC‐SAFT) to describe the phase behavior of systems containing deep eutectic solvents (DESs) and ionic liquids (ILs). The DESs are based on tetrabutylammonium chloride and tetrabutylammonium bromide as hydrogen bond acceptors, and levulinic acid and diethylene glycol as hydrogen bond donors in the mole ratio of 1:2 and 1:4, respectively. Predictions of phase equilibria by PC‐SAFT were compared with the results of COnductor like Screening MOdel for Real Solvents (COSMO‐RS) and non‐random two‐liquid (NRTL). In this work, low viscosity ether‐ and pyridinium‐based ILs [EnPy][NTf2] and [CmPy][NTf2] were used for vapor–liquid equilibrium systems, while 1‐(2‐methoxyethyl)‐1‐methylpyrrolidinium bis(trifluoromethylsulfonyl)‐amide and 1‐propyl‐3‐methylimidazolium bis{trifluoromethylsulfonyl}imide with n‐heptane + thiophene and n‐hexane + ethylbenzene were used in the liquid–liquid extraction, respectively. In the last part, the phase behavior of the mixtures of perfluoroalkylalkanes with their linear alkane counterparts was studied and compared with the SAFT‐Mie pair potential.

A rigorous approach for characterising the limiting optimal efficiency of working fluids in organic Rankine cycles

Organic Rankine cycles (ORCs) are a standard and simple layout to convert thermal energy to mechanical energy and, subsequently, electrical energy. On the one hand, it is essential to select the proper working fluids. On the other hand, criteria to choose optimal operation conditions are also necessary. This contribution presents a rigorous and general approach based on the Helmholtz energy function to analyse the optimal performance of an organic Rankine cycle irrespective of the working fluid. The new approach is applied for the n-alkane series and a set of refrigerants using the perturbed-chain statistical association fluid theory (PC-SAFT) equation of state as a calculation tool. The study reveals that a dry global optimum cannot be achieved without partial condensation, and guidelines to avoid this fact are shown. Also, it is parametrically demonstrated that the optimum behaviour of an organic Rankine cycle is not directly connected to the isentropic behaviour of the fluids. However, it is proved that a slightly dry fluid is more suitable for a good performance than a very dry fluid, because the optimum range of expansion lies in a feasible range of temperature, avoiding problems with the limit of the solid phase.

Modeling Subsurface Hydrogen Storage With Transport Properties From Entropy Scaling Using the PC‐SAFT Equation of State

AbstractHydrogen is a promising alternative to carbon based energy carriers and may be stored in large quantities in subsurface storage deposits. This work assesses the impact of static (density and phase equilibria) and dynamic (viscosity and diffusion coefficients) properties on the pressure field during the injection and extraction of hydrogen in the porous subsurface. In a first step, we derive transport properties for water, hydrogen and their mixture using the Perturbed‐Chain Statistical Associating Fluid Theory equation of state in combination with an entropy scaling approach and compare model predictions to alternative models from the literature. Our model compares excellently to experimental transport coefficients and models from literature with a higher number of adjustable parameters, such as GERG2008, and shows a clear improvement over empirical correlations for transport coefficients of hydrogen. In a second step, we determine the effect of further model reduction by comparing our against a much simpler model applying empirical transport coefficients from the literature. For this purpose, hydrogen is periodically injected into and extracted out of a dome‐shaped porous aquifer under a caprock. Our results show that density and viscosity of hydrogen have the highest impact on the pressure field, and that a thermodynamic model like the new model presented here is essential for modeling the storage aquifer, while keeping the number of coefficients at a minimum. In diffusion‐dominated settings such as the diffusion of hydrogen through the caprock, our developed diffusion coefficients show a much improved dependence on temperature and pressure, leading to a more accurate approximation of the diffusive fluxes.

On the Effect of the Hard-sphere Term on the Statistical Associating Fluid Theory Equation of State

The hard-sphere system is the reference fluid for most versions of the statistical associating fluid theory (SAFT) equation of state (EoS). In the SAFT-type equations of state, the hard-sphere equation directly affects the reference term and through the radial distribution function, indirectly affects the chain and association terms. Although there are various EoSs for describing the thermodynamic behavior of the hard-sphere fluid, the Carnahan-Starling EoS has traditionally been used to express the hard-sphere contribution in SAFT-type models. In this work, we integrated eight hard-sphere EoS in the simplified SAFT EoS and parameterized the resulting EoS with pressure-density-temperature data. Then, using modified versions of the simplified SAFT (SSAFT), we calculated the thermodynamic properties including pressure, density, temperature, saturated vapor-pressure, isochoric heat capacity, isobaric heat capacity, and speed of sound, for ethane, butane, hexane, and hexatriacontane, and compared the results. In general, the results of calculations show that although the modified Carnahan-Starling, Kolafa, and Carnahan-Starling EoSs have had the best results, considering the simplicity and straightforwardness of the Carnahan-Starling EoS, this EoS is a reasonable choice for developing SAFT-type equations of state.