Modeling Of Phase Behavior Research Articles

A Derivative-less Approach for Generating Phase Envelopes

Petroleum engineers are often interested in the phase envelope that describes the characteristics of the pore fluids. These phase envelopes are normally generated by conducting laboratory measurements involving expensive PVT equipment and trained personnel. By using an Equation of State (EOS) based computer model that requires some hydrocarbon composition data, these envelopes can be generated almost instantly. An algorithm for generating a complete phase envelope using computer modeling was proposed by Michelsen. His procedure, based on EOS modeling, may sometimes suffer from convergence issues, especially near the critical region. In addition, his procedure requires the partial derivatives of fugacity, which are often difficult to get. In this work a phase behavior model was developed that incorporates some modifications to Michelsen’s algorithm avoiding the need for calculating these derivatives, which in turn put fewer requirements on the data and computation. These modifications allowed running the model successfully for different hydrocarbon systems without any convergence issues. Because the new model does not have to deal with the partial derivatives of fugacity, it can work with any EOS based phase behavior model. The new method has been applied to three different reservoir fluids and shows an exact match with the phase envelope generated using commercial software.

The ability of artificial neural network in prediction of the acid gases solubility in different ionic liquids

In this work, the solubility of carbon dioxide and hydrogen sulfide, in different ionic liquids (ILs) have been investigated by applying the artificial neural networks (ANNs). According to the economic benefits of CO2 as an inexpensive, non-toxic sources of carbon, many studies have done in capturing of CO2 from the main resources in ILs due to their specific properties such as negligible vapor pressure. Solubility is a key parameter in the phase equilibria calculations. According to the complexity of ILs structure, the phase behavior modeling for these systems is complicated. ANNs are the nonlinear mathematical models which can make a relation between the inputs and the outputs. In this paper 2930 and 664 solubility data of CO2 and H2S are used respectively. Network was trained, validated and tested by 70, 15 and 15 percent of total data with one hidden layer through hyperbolic tangent sigmoid transfer function. Optimum neurons are 23 and 14 for CO2 and H2S solubility respectively. AAD% and R2 are 3.58 percent and 0.9947 for CO2 and 2.07 and 0.9987 for H2S system. In addition, the Peng–Robinson EoS with and without optimized kij and an empirical correlation with different constants are used to compare their deviations with the ANN model. Results showed that the ANN model can correlate the solubility of acid gases in ILs with a high accuracy and its error is minimum among three approaches.

Hydrate and Phase Behavior Modeling in CO2-Rich Pipelines

Carbon dioxide transport will be a key part of any Carbon Capture and Storage (CCS) system. Generally for CCS, flow assurance modeling of these pipelines has been restricted to pure CO2 systems; however CO2 streams coming from capture processes are not pure and contain various components. These fluids have a certain level of moisture, so dehydration is needed before delivering CO2 rich fluid to the export pipeline, in order to prevent potential hydrate formation, two-phase flow and corrosion in the export line. In this contribution, the hydrate phase equilibria of the binary CO2 + (N2 or CH4 or O2 or Ar or CO) systems in the presence of a free water phase were determined as well as direct hydrate dissociation conditions of liquid CO2 in absence of a free phase. A rigorous and generalized model is presented to predict the phase behavior, hydrate dissociation pressures and the dehydration requirements of CO2 rich gases. A statistical thermodynamic approach, with the Cubic-Plus-Association equation of state, is employed to model the phase equilibria. The hydrate-forming conditions are modeled by the solid solution theory of van der Waals and Platteeuw. Predictions of the developed model are first validated using simple systems and then for more complicated synthetic multicomponent systems. Showing that accurate phase behavior prediction of CO2 rich stream is critical for accurate predictions of the hydrate phase behavior of these fluids.

Phase Behavior Modeling of Asphaltene Precipitation for Heavy Crude Including the Effect of Pressure and Temperature

Despite numerous experimental and modeling studies, the role of temperature changes on phase behavior modeling of asphaltene precipitation and, in consequence, developing of asphaltene phase envelope in heavy crudes, remains a topic of debate in the literature. In this work, a computer code based on the non-isothermal improved solid model has been developed and used for predicting asphaltene precipitation data for one of the Iranian heavy crudes at different levels of temperature and pressure. The parameters of the non-isothermal model were tuned using three onset pressures at three different temperatures, and the asphaltene phase envelope was developed. The results showed that at high temperatures, increasing the temperature results in a lower amount of asphaltene precipitation and also it causes the convergence of lower and upper boundaries of asphaltene phase envelope. This work illustrates successful application of non-isothermal improved solid model for developing the asphaltene phase envelope of heavy crude.

Phase Behavior and Adsorption of Pure Substances and Mixtures and Characterization in Nanopore Structures by Density Functional Theory

Summary Phase behavior in shale remains a mystery because of various complexities and effects. One complexity is from nanopores, in which phase behavior is significantly affected by the interaction between the pore surfaces and fluid molecules. The result is the heterogeneous distribution of molecules that cannot be described by bulk-phase thermodynamic approaches. Statistical thermodynamic methods can describe the phase behavior in nanopores. In this work, we apply an engineering density functional theory (DFT) combined with the Peng-Robinson equation of state (EOS) to investigate the adsorption and phase behavior of pure substances and mixtures in nanopores, and include the characterization of pore structure of porous media. The nanopores are represented by carbon-slit pores each consisting of two parallel planar-infinite structureless graphite surfaces. The porous media are activated carbons and dry coal, each modeled by an array of polydisperse carbon-slit pores. We study the influence of multiple factors on phase transitions of various pure light species and their mixtures in nanopores. We find that capillary condensation and hysteresis are more likely in heavier hydrocarbons, at lower temperatures, and in smaller pores. For pure hydrocarbons in nanopores, the phase change always occurs below the critical temperature and saturation pressure. For mixtures in nanopores, there may be a phase change above the cricondentherm. We characterize the pore structure of porous media to obtain the pore-size distribution (PSD), surface area (SA), and pore volume (PV) on the basis of the measured adsorption isotherms of pure substances. Then, we use the computed PSD to predict the adsorption of mixtures in porous media. There is agreement between the experiments and our predictions. This work is in the direction of phase-behavior modeling and understanding in shale media.

Measurement and Phase Behavior Modeling (Dew Point+Bubble Point) of Co2 Rich Gas Mixture

Measurement and Phase Behavior Modeling (Dew Point+Bubble Point) of Co2 Rich Gas Mixture

Four-Fluid-Phase, Fully Implicit Simulation of Surfactant Flooding

Summary The Microemulsion phase behavior model based on oleic/aqueous/surfactant pseudophase equilibrium, commonly used in chemical-flooding simulators, is coupled to Gas/Oil/Water phase equilibrium in our new four-fluid-phase, fully implicit in-house research reservoir simulator (IHRRS) (Moncorgé et al. 2012). The method consists of splitting the equilibrium into two stages, in which all the components other than surfactant are equilibrated first—by use of a black-oil, K-value, or equation of state (EOS) model—and the resulting Gas, Oil, and Water phases are then lumped into pseudophases to be equilibrated by use of the Microemulsion model. This subdivision in stages is conceptual, and at each converged timestep the four phases (Gas, Oil, Water, and Microemulsion, when simultaneously present) will be in equilibrium with each other. The fluid properties (such as densities, viscosities, and interfacial tensions) and rock/fluid properties (such as relative permeabilities) required in the transport equations are evaluated with models from well-known industrial or academic simulators. Surfactant flooding being usually implemented as a tertiary recovery mechanism, on fields for which complete models that we do not wish to modify already exist, particular care is devoted to ensuring continuity of the physics at the onset of surfactant injection. Our code is first validated against a reference academic chemical-flooding simulator, on a 1D, three-fluid-phase (Oil/Water/Microemulsion) coreflood. Second, as application examples where it is necessary to account for four phases in equilibrium, we consider a scenario where the chemical flood is preceded by a vaporizing Gas drive, as well as a scenario where dissolved gas is released by the Oil during the flooding process. Some aspects of our implementation, such as numerical dispersion vs. timestep length and nonlinear convergence, are also discussed; in particular, we show that numerical performance is not degraded by the four-phase equilibrium.

Supercritical fluids and gas-expanded liquids as tunable media for multiphase catalytic reactions

Solvents play a vital role in multiphase catalysis. They are selected to perform several functions during liquid phase catalytic transformations such as solubilizing reactants, facilitating product/catalyst separation, increasing reaction rates, enhancing solubilities of gaseous reactants (such as O2, CO, H2) in the liquid phase, and providing heat capacity to effectively manage the heat of reaction. This review discusses such roles of conventional solvents in multiphase catalytic processes such as hydroformylation, carbonylation, hydrogenation and oxidation. For each of these chemistries, industrially relevant examples are presented, highlighting the advantages and limitations of the conventional solvents used therein. Further, it is shown how the pressure-tunable properties of supercritical fluids (SCFs) and gas-expanded liquids (GXLs) have been exploited in such systems to develop novel multiphase catalytic technology concepts. GXLs in particular provide advantages such as rate intensification, efficient feedstock utilization, enhanced process safety, waste minimization and reduced use of volatile organic solvents, all at relatively mild pressures and temperatures. Conventional reactors and reaction engineering tools that integrate phase behavior (for reactions and separations), catalytic kinetics and multiphase reactor modeling may be applied for the rational development of multiphase reactors using GXLs. Quantitative economic and environmental impact analyses during early stages of process development provide valuable research and process engineering guidance for developing practically viable GXL processes. The Rh catalyzed hydroformylation in CO2-expanded liquids and methyltrioxorhenium-based ethylene epoxidation are highlighted as exemplars of GXL-based technology concepts. Emerging feedstocks, such as plant-based biomass, shale gas and sequestered CO2, that require new catalytic conversion technologies to produce chemical intermediates, offer excellent opportunities for using tunable solvents.

Prediction of phase equilibrium of clathrate hydrates of multicomponent natural gases containing CO2 and H2S

The sour natural gas readily forms hydrates and stays stable at higher temperatures and lower pressures and hence is responsible for plugging, corroding the pipelines and causing other flow assurance-related issues. Predictions of formation and dissociation conditions of these hydrates are necessary in applications for preventing such hazards primarily due to the blockages of pipelines. However, natural gases from the gas reservoirs can have combinations of different concentrations of each of the following constituents, CH4, C2H6, C3H8, C4H10, N2, CO2 and H2S. Presence of high concentrations of CO2 and/or H2S along with other components is often found in natural gas, thereby limiting the accurate functioning of several of the available phase behavior models. The major limitation for their inaccuracy can be attributed to the complexity involving CO2 and H2S in hydrate systems. In this work, a new thermodynamic computing approach is developed for predicting the phase equilibria for hydrates of multicomponent sour natural gases (with CO2 and H2S) from different natural gas systems. The model of Chen and Guo (1998) (Chem. Eng. J., 71, 145, 1998) is extended for the multicomponent sour natural gas hydrate system using the Kihara potential functions to model the guest–host interaction energies. In addition, a semi-empirical form is proposed to calculate the equilibrium hydrate temperature for hydrates of natural gas with and without CO2 and H2S. The developed model is fitted with 12 sets of experimental data on the phase equilibria of sour natural gas hydrate system and found to be satisfactory. The average absolute deviation pressure percentage (AADP%) for most of the cases studied is observed to be well within 10%, thus proving its efficacy. The present model can, therefore, find potential applications for developing mitigation techniques for flow assurance issues and for robust natural gas and hydrate reservoir models containing sour gases.

PC-SAFT modeling of asphaltene phase behavior in the presence of nonionic dispersants

This study introduced a new method to characterize asphaltenes in PC-SAFT equation of state (EOS) and correctly model the effect of nonionic dispersants on the thermodynamic behavior of asphaltenes. Our approach is to combine microscale parameters from Molecular Dynamics (MD) simulations with Perturbed Chain Statistical Associating Fluid Theory (PC-SAFT) to develop a comprehensive model that enables the prediction of macroscopic behavior such as the amount and onset of asphaltene precipitation at various pressures, temperatures, and fluid compositions. More specifically, association parameters were considered for asphaltene molecules and determined by equating the Gibbs energy of association calculated by PC-SAFT EOS to the one obtained from MD simulations. A correlation was derived to relate the association energy parameter (ɛAB) of asphaltenes to the molar weight of their aromatic cores. Our model showed that asphaltene association energy is affected by temperature and solvent type and is inversely proportional to the solubility parameter of the medium. The hetero-segment approach in PC-SAFT EOS was adopted to accurately characterize asphaltene molecules and their non-association parameters in PC-SAFT were determined based on the molecular weight and aromaticity factor of asphaltenes. Moreover, the average aggregation number of asphaltene nanoaggregates was calculated using the Wertheim association theory. This model was applied to predict asphaltene precipitation envelopes for three different live crude oils and showed excellent agreement with experimental data in the literature. Additionally, the model could correctly predict the amount of asphaltene precipitation upon addition of nonionic dispersants.

Determination of Saturation Pressures and Swelling Factors of Solvent(s)–Heavy Oil Systems under Reservoir Conditions

Techniques have been developed to experimentally and theoretically determine saturation pressures and swelling factors of solvent(s)–heavy oil systems under reservoir conditions. Experimentally, PVT tests are performed to measure saturation pressures and swelling factors of a C3H8–heavy oil system and a CH4–C3H8–heavy oil system under reservoir conditions, respectively. Theoretically, the volume-translated Peng–Robinson equation of state (PR-EOS) together with the modified alpha function has been used to model phase behavior of the aforementioned solvent(s)–heavy oil systems. A binary interaction parameter (BIP) correlation has been developed for CH4–heavy oil systems based on the literature data. As for the CH4–C3H8–heavy oil system with a fixed composition, both saturation pressure and swelling factor increase with temperature. The PR-EOS together with the modified alpha function and the newly developed BIP correlation is able to predict the saturation pressures and swelling factors of the CH4–C3H8–heav...

Tie-Simplex-Based Phase-Behavior Modeling in an IMPEC Reservoir Simulator

Summary Recently, tie-simplex-based phase-behavior modeling in reservoir simulators has been applied and investigated as a potential method for improving the computational speed of equation-of-state (EOS) -based reservoir simulators. We implemented compositional-space adaptive tabulation (CSAT), the most promising tie-simplex-based method, in UTCOMP, the University of Texas' in-house IMPEC compositional reservoir simulator, to investigate its computational efficiency compared with the phase-behavior algorithm in UTCOMP. The results show that applying CSAT only to skip stability analysis does improve computational time, but only when a significant portion of the gridblocks are in the single-phase region and no other technique for avoiding stability analysis is used. However, in most cases, there is little or no computational advantage to use of CSAT when the simple option in UTCOMP is used where stability analysis is skipped for blocks surrounded by single-phase regions. We explore in detail the performance of CSAT, which depends significantly on the specific gas flood modeled, and the number of tie-lines generated during adaptive tabulation. The results shed light on applicability of CSAT in the IMPEC-type compositional reservoir simulators and show that the advantages of CSAT in this type of simulator are not as great as are reported in the literature for fully implicit or adaptive implicit formulations.

Extrapolation/interpolation of infinite dilution, activity coefficient as well as liquid and solid solubility between solvents: Part 1. Alkane solvents

Infinite dilution activity coefficients play a vital role in modeling of phase and chemical equilibrium behavior. From the dependence of the limiting activity coefficient of a solute on the solvent, important properties like liquid and solid solubility in these solvents can be deduced. Although a large amount of experimental information is available in the open literature as well as from thermophysical data banks such as the Dortmund Data Bank (DDB), the behavior of high boiling solutes in low boiling solvents is often not known, partly due to difficulties in experimental determination.A method for the extrapolation of infinite dilution activity coefficients and thus the liquid and solid solubility of any solute in different solvents within one solvent family is under development. Results of a method applicable to any solute in a large variety of different saturated hydrocarbon compounds are presented in this paper.In this method, the activity coefficient is assumed to consist of a combinatorial and residual contribution. In the case of alkane solvents, only this combinatorial contribution changes when going from one solvent to another. Several well known combinatorial expressions were evaluated and were found to produce poor extrapolations in many instances. Quite surprisingly, free-volume combinatorial expressions performed best even for some of the rather low molecular weight compounds used in this test.A new empirically modified free-volume expression is proposed which allows for accurate extrapolation. Additional activity coefficient data have been determined via GLC (gas–liquid chromatography) to validate the method. In most cases extrapolations were within 10% of the experimental findings and safely within or close to the scatter of literature data.The method allows for example the safe estimation of the infinite dilution behavior as well as liquid and solid solubility of high boiling components in hydrocarbons from data for high boiling solvents usually determined easily by gas–liquid chromatography. Additionally, the newly developed combinatorial expression for infinite dilution data should be able to greatly improve other predictive mixture models, e.g. UNIFAC, mod. UNIFAC and COSMO-RS type models in the cases when large molecules in low molecular weight solvents are considered. This was verified for a larger number of experimental limiting activity coefficient data from literature.

Glyceride Lipid Formulations: Molecular Dynamics Modeling of Phase Behavior During Dispersion and Molecular Interactions Between Drugs and Excipients

Little is known about the microstructure of lipid-based formulations, or how their structure changes as they disperse in the lumen of the gastrointestinal tract. We used molecular dynamics (MD) simulation to study such formulations at the molecular level as they interact with water during dispersion. We studied a simple lipid formulation, by itself and in the presence of drugs. The formulation contained mono- and di-lauroyl glycerides at 0-75% (w)/w water. Acyclovir, danazol, hydrocortisone, ketoprofen or progesterone, were included to investigate their dynamic behavior and localization during dispersion. Micro-structuring of the formulation was evident at all water concentrations. As the water content increased, the microstructure evolved from a continuous phase containing isolated water molecules, to a reverse micellar solution and finally to a system containing lamellar lipids with large pools of free water. Drugs partitioned into the aqueous and lipid domains principally under the influence of hydrogen bonding and hydrophobic interactions. Drugs located preferentially to the interfaces between water and lipid where they are able to make both hydrophobic and hydrophilic interactions. Molecular dynamics simulations offer an unprecedented view of the structure of lipid-based formulations and has considerable potential as an in silico tool for formulators.

High pressure phase behavior modeling of asymmetric alkane + alkane binary systems with the RKPR EOS

Very asymmetric hydrocarbon mixtures present an interesting academic challenge for their modeling. In addition, they are becoming more important technologically, since the world oil reserves are becoming heavier in average.The RKPR EOS was developed in recent years in order to consider asymmetric systems and allow for a good representation of densities for different types of compounds while maintaining the relative simplicity of cubic equations of state. In this work the RKPR EOS is applied for the first time for the correlation of phase behavior in the series of binary systems methane+n-alkane and ethane+n-alkane. In addition to the use of attractive and repulsive interaction parameters with quadratic mixing rules, the role of the extra degree of freedom that the RKPR model offers for setting the pure compound parameters was also examined. A new table of RKPR pure compound parameters was defined for n-alkanes. A comparative study was made with the Peng–Robinson EOS, based on following the same optimization procedure for interaction parameters.

Three-Dimensional Scheme of Supercritical Carbon Dioxide Extraction of Heavy Hydrocarbon Mixture in (Pressure; Temperature; Recovery) Coordinates

A heavy hydrocarbon mixture represented by C17–C31 carbon groups was investigated to determine extraction recoveries by supercritical carbon dioxide in the ranges of 12–65 MPa for pressure and 50–90 °C for temperature. The purpose of the study was to obtain a three-dimensional scheme of the SC–CO2/heavy hydrocarbon mixture system in pressure–temperature–recovery coordinates, which allows the prediction and numerical modeling of phase behavior. At lower temperatures, high recoveries were attained at lower pressures. The highest recovery of 93% was obtained at 70 °C and 56 MPa. The recoveries greater than 65% were determined at the breakover points where the pressure increased by 7 MPa with a temperature increase of 10 °C. The phase envelope, 3D scheme, and the equations describing the boundaries of the system are presented.

Phase behavior of mixture of supercritical CO2 + ionic liquid: Thermodynamic consistency test of experimental data

Various models have been applied composed of the Peng‐Robinson equation of state (PR‐EoS) and the Soave‐Redlich‐Kwong equation of state (SRK‐EoS) associated with three mixing rules including the following: Wong‐Sandler (WS), van der Waals one (vdW1), and van der Waals two (vdW2) for phase behavior modeling of mixtures of supercritical CO2 + different ionic liquids in vapor–liquid equilibrium (VLE) region. It has been found that the PR EoS implying the WS mixing rule can be used as a reliable thermodynamic model to perform a thermodynamic consistency test on the experimental data of phase behaviors of the supercritical CO2 + ionic liquid systems (19 commonly‐used ionic liquids have been studied). The results show that 40% of the experimental data seem to be thermodynamically consistent, 55.5% seem to be thermodynamically inconsistent, and 4.5% seem to be not fully consistent. © 2013 American Institute of Chemical Engineers AIChE J, 59: 3892–3913, 2013

Molecular Thermodynamic Modeling of Gelation and Demixing in Solution of Cross-Associating Chains

A molecular thermodynamic model has been proposed that extends the previously known mean field theory of self-association to systems of cross-associating polymers. The extended theory has been applied to model gelation and phase behavior for mixtures of two associating polymers in a good solvent. The gelation threshold is described analytically. Relation between the new theory and SAFT (Macromolecules 2012, 45, 6686−6696 has been established. For ternary systems containing two associating polymers in athermal solvent, simple analytical formula has been obtained for the location of the upper critical consolute point in the long chain limit. Possible types of phase behavior (sol–sol, sol–gel, gel–gel) have been discussed.

Effect of Asphaltene Structure on Association and Aggregation Using Molecular Dynamics

The aggregation of asphaltenes has been established for decades by numerous experimental techniques; however, very few studies have been performed on the association free energy and asphaltene aggregation in solvents. The lack of reliable and coherent data on the free energy of association and aggregation size of asphaltene has imposed severe limitations on the thermodynamic modeling of asphaltene phase behavior. Current thermodynamic models either consider asphaltenes as non-associating components or use fitting parameters to characterize the association. In this work, the relations between Gibbs free energy of asphaltene association and asphaltene molecular structure are studied using molecular dynamics (MD). The free energy of association is computed from the potential of mean force profile along the separation distance between the centers of mass of two asphaltene molecules using the umbrella sampling technique in the GROMACS simulation package. The average aggregation number for asphaltene nanoaggregates and clusters is also calculated through MD simulations of 36 asphaltene molecules in toluene and heptane in order to estimate the effects of association free energy and steric repulsion on the aggregation behavior of asphaltenes. Our simulation results confirm that the interactions between aromatic cores of asphaltene molecules are the major driving force for association as the energy of association increases substantially with the number of aromatic rings. Moreover, heteroatoms attached to the aromatic cores have much more influence on the association free energy than to ones attached to the aliphatic chains. The length and number of aliphatic chains do not seem to have a noticeable effect on asphaltene dimerization; however, they have a profound effect on asphaltene aggregation size since steric repulsion can prevent asphaltenes from forming T-shape configurations and therefore decrease the aggregation size of asphaltenes significantly. Our MD simulation results show for the first time asphaltene precipitation in heptane as an explicit solvent, and predict three distinct stages of aggregation (nanoaggregation, clustering, and flocculation) as proposed by the modified Yen model. Finally, the association free energy for asphaltenes in heptane is higher than that in toluene, which is consistent with asphaltene aggregate sizes obtained from MD simulations.

Hyperbranched Polymers in a Supercritical Fluid: Recent Progress on Phase Behavior and Modeling

Abstract: The advent of new chemistries has led to the creation of well-defined, novel polymer architectures. Due to their unique structures, hyperbranched polymers are receiving more and more attention and widely applied in various fields in the past two decades. In spite of their increasingly mature applications, some fundamental properties of star polymers are still lacking, such as their solubility behavior in different solvents, especially at high pressures. On the other hand, supercritical fluids (SCF) are ideal environmentally preferable solvents for polymer processing. This article intends to review the recent progress on the experimental determination and modeling of phase behavior of hyperbranched polymer systems, especially hyperbranched polymers in SCF. Following a brief description of the definition, properties, and applications of hyperbranched polymers, a detailed overview will be presented on the recent studies on phase behavior of hyperbranched polymer systems. Emphasis will be laid on the high-pressure phase behavior of polymers in SCF. Different models proposed by previous researchers will be then compared for the purpose of accurately predicting the phase equilibrium data. Finally current challenges will be discussed for future work.