Modelling fluid phase equilibria in the binary system trifluoromethane + 1-phenylpropane

Asphaltene is a group of complex compounds commonly present in reservoir fluids, especially in viscous oils. It is conceivable that asphaltene strongly interacts with water through hydrogen bonding, affecting phase behavior of water/oil mixtures with/without forming an asphaltene-rich phase. Modeling of these polar components in reservoir fluids is challenging with cubic equations of state (EOS) due to the size-symmetricity and self- and cross-associations of asphaltene and water. In this research, the cubic-plus-association (CPA) EOS is applied to represent complex multiphase behavior associated with water and asphaltene. Asphaltene-containing heavy oils are characterized by the CPA EOS with four pseudo components (asphaltene and the other three pseudo components) based on their experimental data. Asphaltene is the only associating component in the oil models. Then, multiphase behavior data for mixtures of water with each of these oils are represented by the CPA EOS. Calculated phase behavior by the CPA EOS models is compared with experimental data and also with the Peng-Robinson EOS for several cases. This paper also presents a new correlation for binary interaction parameters (BIPs) for water with n-alkanes for the CPA EOS on the basis of experimental data for three-phase coexistence for water/n-alkane binaries (Brunner 1990). In case studies, the CPA EOS is shown to be able to represent multiphase behavior for water/oil mixtures with up to four equilibrium phases: asphaltene-rich, solvent-rich, aqueous, and vapor phases. In particular, the CPA EOS is successfully applied to bitumen/water mixtures, involving asphaltene-water emulsion, water solubility in bitumen, and their continuous transition with varying temperature. Furthermore, results show that the CPA EOS can reasonably represent the multiphase data measured for a n-butane/bitumen/water mixture that were not accurately correlated with the PR EOS in the literature. Modeling an asphaltene-rich phase in several cases is possible only with consideration of the water-asphaltene interaction, which is worth the additional complexities of the CPA EOS in comparison with the PR EOS.

Equations of state are widely used in compositional simulation to predict phase distribution and composition, which in turn facilitates prediction of compositionally dependent properties such as density, viscosity, interfacial tension, and enthalpy. A well-known problem confronted with naturally occuring hydrocarbon systems is characterization of the high molecular weight fraction (usually C7 +). The high molecular weight fraction must be split into an optimum number of pseudo-components each having a prescribed set of critical properties and interaction coefficients. Since procedures for doing this are largely empirical, typical equation of state packages must be tuned to available experimental data. Often available experimental data are limited in scope, or the ultimate simulation involves significant changes in temperature, pressure or composition. In each situation, tuned pseudo-component critical properties and/ or interaction parameters will manifest important temperature, pressure, and composition dependencies. Thus, a versatile phase description can effectively be ensured if tuning is automated internally within the equation of state package. In this paper, a methodology for achieving this task is described. First, the heavy fraction is split into a defined number of pseudo-components and starting values of binary interaction parameters and critical properties are obtained by using readily available correlations in the literature and/or mixing rules. Then, a linear optimization technique (two-phase method) is adopted for non-linear applications by using iterative techniques (iterative variables being pseudo-component binary interaction coefficients with CH4 and pseudo-component critical properties). Tuned sets of binary interaction parameters and critical properties of pseudo-components for a cubic equation of state are generated by using experimental depletion curves. As the computation progresses the tuned set replaces the default set to achieve further improvements. The success of this linear optimization routine is demonstrated for different reservoir oils.

In this work experimental vapor-liquid equilibrium (VLE) data and three-phase vapor-liquid-liquid equilibrium (VLLE) data are presented for the carbon dioxide + 1-decanol system. The VLE data were measured at five temperatures, (303.2, 308.2, 323.2, 333.2, and 343.2) K, and pressures up to 16 MPa. The VLLE data cover pressure-temperature (P-T) values from 289 K and 5 MPa to the upper critical end point (UCEP). We have used two models to represent the complex fluid phase behavior (P-T critical curve, VLLE line, and VLE isotherms) of the carbon dioxide + 1-decanol system: the cubic general equation of state (GEOS) and Peng-Robinson (PR) equation in conjunction with van der Waals two parameters conventional mixing rules (2PCMR). A correlation method involving temperature-dependent interaction parameters and a semipredictive approach with independent temperature interaction parameters have been used. Comparisons with experimental data reported in this work and available in the literature indicate that the topology of fluid phase behavior is satisfactorily given by the semipredictive procedure both for the critical line and in subcritical region, considering the relative simple used cubic equations of state.

Representation of solid-supercritical fluid phase equilibria using cubic equations of state

A local composition extension of the van der Waals mixing rule for PR cubic equation of state

This paper presents an approach for predicting the solubility of hydrogen in hydrocarbons using a cubic equation of state. Because the α function from the Soave−Redlich−Kwong and Peng−Robinson equations of state is inadequate at temperatures far above the critical temperature, the binary interaction parameters required for hydrogen−hydrocarbon systems using these equations are typically large and strongly dependent on the temperature. An approach is proposed for developing a temperature-dependent α function for hydrogen which minimizes the need for interaction parameters. The minimization of the values of the binary interaction parameters between hydrogen and heavy hydrocarbons is desirable because this produces better predictions when the binary interaction parameters are not known and are set to zero. A universal procedure is also presented for interconverting the binary interaction parameters between the new hydrogen α function developed in this work and the traditional Soave α function or any other type of α function.

Hydrogen solubility in bio-based furfural and furfuryl alcohol at elevated temperatures and pressures relevant for hydrodeoxygenation

In this study using Equation of State/ Helmholtz excess energy function, EOS/AE, two new local composition-Equation-of State mixing rules, LCEOS1 and LCEOS2 were developed in which the energy interaction parameters were expressed in terms of attractive and repulsive parameters of the cubic equation of state. The EOS/AE models are applied for equilibrium calculation of natural gas that consists of light to heavy hydrocarbons with water and acid gases, i.e. H2S and CO2. Applying these new mixing rules, the bubble point pressure and vapor phase compositions at high pressure were simulated. The binary interaction parameters and a lumped nonrandomness parameter for the binary systems containing CO2, H2S, H2O, CH4, C2H6, EG, TEG were obtained. Using the binary parameters, solubility of CH4 and C2H6 in ternary systems CH4+EG+H2O and C2H6+EG+H2O were predicted, respectively. A comparison of these two new mixing rules with experimental data showed that both LCEOS1 and LCEOS2 demonstrated high accuracy.

A three-parameter cubic equation of state for prediction of thermodynamic properties of fluids

The purpose of this paper is to compare three thermodynamic models to correlate the phase behavior of the highly polar system: carbon dioxide +1-heptanol. These three models rely either on the Peng–Robinson (PR) or on the Soave–Redlich–Kwong (SRK) equations of state and are all coupled with classical van der Waals one-fluid mixing rules. For the two first models, noted SRK/2PCMR and PR/2PCMR, where 2PCMR means two-parameter conventional mixing rule, a single set of temperature-independent binary parameters (kij and lij) was considered. The third model is the well-established PPR78 model also based on the PR equation of state (1978 version). In such a model, lij = 0 but the second binary interaction parameter (kij) is temperature-dependent and predicted by a group-contribution method. All available literature data in a wide range of pressures and temperatures and the global phase equilibrium diagram of the system were calculated with the three aforementioned models. Although the models used are simple, they are able to represent reasonably well the complex phase behavior of the system studied in this work.

In modern versions of cubic equations of state (EoS), the mixing rules for EoS parameters are derived from an activity coefficient model using either the Huron-Vidal or the Zero Reference Pressure (ZRP) approach. As it is a fact that Wilson's activity coefficient model cannot predict liquid-liquid equilibria (LLE), this article attempts to answer the question: if Wilson's model is coupled with a cubic EoS, is the resulting model capable of predicting LLE?This question is actually becoming increasingly important as recent EoS rely on such a coupling (e.g., the tc-PR EoS). We show that although Wilson's model is mathematically unable to predict instable liquid phases, this is not true for Wilson-EoS models (i.e., EoS incorporating Wilson's model). However, it is also shown that the capacity of Wilson-EoS to predict LLE depends not only on the approach chosen (Huron-Vidal or ZRP) but also on mixture characteristics (such as the ratio of covolumes, the ratio of critical attractive parameters, the binary interaction parameters etc.).

Improving the prediction of elemental sulfur solubility in sour gas mixtures by modifying cubic equations of state

Measurement and calculation of solubility of quinine in supercritical carbon dioxide

An analytical and consistent delumping procedure is implemented for fluids of petroleum interest containing water, non-hydrocarbon gases (such as N2, CO2, and H2S) and hydrocarbon (HC) compounds. Two sorts of difficulties are associated with these fluids: they often exhibit three or more equilibrium phases, and their thermodynamics cannot be described by conventional cubic equations of state (EoS). In this work, the Søreide-Whitson modification of the Peng-Robinson EoS, in which different binary interaction parameters are used in the aqueous and non-aqueous phases, is used. The method is successfully tested on two cases in the two- and three-phase regions: one synthetic HC/N2/CO2/H2O fluid and a “real” water/reservoir fluid.

Saturation densities of new refrigerant mixtures: Densité de saturation de nouveaux mélanges frigorigènes