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

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.

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

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

One of the most challenging aspects of using a Van der Waals type equation of state for mixtures is determining the appropriate expressions for the coefficients a (attractive parameter) and b (covolume) involved in this equation. It has been 45 years since Huron and Vidal first proposed the “EoS/ g E ” advanced mixing rules. By equating under infinite reference pressure, the mathematical expression of the excess Gibbs energy g E derived from an equation of state, to the same quantity issued from an explicit activity coefficient model, they deduced an expression for the ratio a / b . A decade after Huron and Vidal’s initial proposal, building upon the original proposal, Michelsen subsequently derived the “zero reference pressure” (ZRP) approach and proposed the approximate ZRP mixing rules MHV1 and MHV2. Throughout the 1990′s and 2000′s, the Huron-Vidal and ZRP approaches were subject, often empirically, to multiple revisions in order to remedy some of their well identified shortcomings. It would appear that the debates surrounding advanced mixing rules are now over, with the latest conclusions proposed in the 2000s enjoying a degree of consensus. The objective of this article is to reopen the debate in light of the scientific insights gained from our recent research on advanced mixing rules for cubic equations of state. The concept of deriving mixing rules by equating the excess Gibbs energy expressed from an equation of state to the same quantity expressed from an activity coefficient model (this equality is called a “ matching equation” ) was undoubtedly an appealing one. However, experience has shown that such a matching equation is not without its limitations, particularly due to the lack of sufficient constraints. We have reached the conclusion that the only way to derive advanced mixing rules that are free from shortcomings is to ensure that not only are the complete expressions of g E from an equation of state and from an activity coefficient model equal but also that the three separate contributions that make it up (i.e., combinatorial, residual and the product of the pressure by the excess volume P · v E ) are equal. As discussed in this paper, achieving this objective is challenging and we conclude that the best and unique solution for developing safe mixing rules is to modify the matching equation proposed by Huron-Vidal and Michelsen and to only equate the residual contributions. Based on this observation, we demonstrate how the demonstrations of the ZRP and HV mixing rules can be reworked to arrive at a unique and universal (independent of the reference pressure) mixing rule, called UHVM (Unified Huron Vidal Michelsen) mixing rule. We hope that this result will encourage new thinking on mixing rules for cubic equations.

The effects of the simple composition‐dependent combining rules (conventional, Adachi‐Sugie and van Laar‐Stryjek‐Vera‐type) and Huron‐Vidal‐NRTL mixing rules and different cubic equations of state (Redlich‐Kwong, Soave‐Redlich‐Kwong, Peng‐Robinson and Peng‐Robinson‐Stryjek‐Vera) on excess molar volume correlation are examined. The results obtained for some asymmetric non‐ideal mixtures indicate very good agreement between correlated and experimental data in all cases when Huron‐Vidal‐NRTL mixing rules are coupled with the Peng‐Robinson‐Stryjek‐Vera equation of state.

Measurement and calculation of solubility of quinine in supercritical carbon dioxide

The ability of different thermodynamic models to predict the phase behaviour of carbon dioxide (1) + 1,2-dimethoxyethane (2) binary system is tested. The model chosen is the General Equation of State (GEOS) coupled with classical van der Waals mixing rules (two-parameter conventional mixing rule, 2PCMR). Comparisons were made with the GEOS3C, Soave-Redlich-Kwong (SRK), and Peng-Robinson (PR) cubic equations of state (EoS) too. A single set of binary parameters for each model was used to predict correctly the global phase behaviour of the system.

Thermodynamic calculation of supercritical-fluid equilibria: New mixing rules for equations of state

A comparative performance evaluation of cubic equations of state for predicting the compositional distribution of hydrate inhibitors in reservoir fluid systems

Liquid activity coefficient model for CEOS/ AE mixing rules

PVT and Phase Behaviour of Petroleum Reservoir Fluids

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.

The paper presents results from vapour-liquid equilibrium experiments simulating gas injection processes, using 25-component fluids as black and volatile oils. Gases were added to the oil to approach the system to the critical point (miscibility) and the volume, density and compositions of equilibrated phases were measured at various levels of pressure and added gases. The measured near miscibility data as well as pertinent literature data have been used to evaluate the reliability of EOS modelling. It is shown that whilst certain EOS are capable of predicting the phase behaviour at these conditions, others, including some widely used equations, can give unreliable results. The predicted volumes of equilibrated phases are shown to be particularly inaccurate with deviations over 100%. A volume translation method, based on equilibrium ratios, has been proposed to improve the predicted phase density for mixtures near critical point. The significance of input compositional and volumetric data for accurate phase behaviour prediction near miscibility is demonstrated.

Prediction of multicomponent phase behavior of CO2-expanded liquids using CEoS/GE models and comparison with experimental data

Prediction of CO2 solubility in bitumen using the cubic-plus-association equation of state (CPA-EoS)