Fugacity Coefficient

2016 ◽  
Author(s):  
Heinz Gamsjäger ◽  
John W. Lorimer ◽  
Pirketta Scharlin ◽  
David G. Shaw
Keyword(s):  
Fugacity Coefficient

A Proxy Peng-Robinson EOS for Efficient Modeling of Phase Behavior

2021 ◽  
Author(s):  
Mark Zhao ◽  
Ryosuke Okuno
Keyword(s):  
Phase Behavior ◽  
Computational Cost ◽  
Training Data ◽  
Petroleum Engineering ◽  
Fugacity Coefficient ◽  
Fugacity Model ◽  
Proxy Model ◽  
Reservoir Conditions ◽  
Fugacity Coefficients ◽  
Proxy Models

Abstract Equation-of-state (EOS) compositional simulation is commonly used to model the interplay between phase behavior and fluid flow for various reservoir and surface processes. Because of its computational cost, however, there is a critical need for efficient phase-behavior calculations using an EOS. The objective of this research was to develop a proxy model for fugacity coefficient based on the Peng-Robinson EOS for rapid multiphase flash in compositional flow simulation. The proxy model as implemented in this research is to bypass the calculations of fugacity coefficients when the Peng-Robinson EOS has only one root, which is often the case at reservoir conditions. The proxy fugacity model was trained by artificial neural networks (ANN) with over 30 million fugacity coefficients based on the Peng-Robinson EOS. It accurately predicts the Peng- Robinson fugacity coefficient by using four parameters: Am, Bm, Bi, and ΣxiAij. Since these scalar parameters are general, not specific to particular compositions, pressures, and temperatures, the proxy model is applicable to petroleum engineering applications as equally as the original Peng-Robinson EOS. The proxy model is applied to multiphase flash calculations (phase-split and stability), where the cubic equation solutions and fugacity coefficient calculations are bypassed when the Peng-Robinson EOS has one root. The original fugacity coefficient is analytically calculated when the EOS has more than one root, but this occurs only occasionally at reservoir conditions. A case study shows the proxy fugacity model gave a speed-up factor of 3.4% in comparison to the conventional EOS calculation. Case studies also demonstrate accurate multiphase flash results (stability and phase split) and interchangeable proxy models for different fluid cases with different (numbers of) components. This is possible because it predicts the Peng-Robinson fugacity in the variable space that is not specific to composition, temperature, and pressure. For the same reason, non-zero binary iteration parameters do not impair the applicability, accuracy, robustness, and efficiency of the model. As the proxy models are specific to individual components, a combination of proxy models can be used to model for any mixture of components. Tuning of training hyperparameters and training data sampling method helped reduce the mean absolute percent error to less than 0.1% in the ANN modeling. To the best of our knowledge, this is the first generalized proxy model of the Peng-Robinson fugacity that is applicable to any mixture. The proposed model retains the conventional flash iteration, the convergence robustness, and the option of manual parameter tuning for fluid characterization.

Gaseous Solutions

1993 ◽  
Author(s):  
Greg M. Anderson ◽  
David A. Crerar
Keyword(s):  
Equations Of State ◽  
Intermolecular Forces ◽  
Point Of View ◽  
Alternative Methods ◽  
Gaseous Species ◽  
Fugacity Coefficient ◽  
Ideal Gases ◽  
Component Systems ◽  
Liquid Solutions ◽  
History Of

The procedures described in Chapter 15 are well suited to solid and liquid solutions and could also be applied to gases, but in fact, other approaches are generally used. The main reason for this is partly historical; much work was done early in the history of physical chemistry on the behavior of gases, and these methods have continued to evolve to the present day. We have also just seen that the Margules equations become very unwieldy with multi-component systems. Because true gases are completely miscible, natural gases often contain many different components, so the Margules approach is not very suitable. Unfortunately, the most successful alternative methods described in this section are also quite unwieldy; however, they do not become much more complicated for multi-component gases than they are for the pure gases themselves, and this is a definite advantage. We have seen that with real, non-ideal gases, all the thermodynamic properties are described if we know the T, P, and the fugacity coefficient. For gaseous solutions, the fugacity coefficient for each component generally depends on the concentrations and types of other gaseous species in the same mixture. All gases, whether pure or multi-component, should approach ideality at higher T and lower P; conversely, non-ideality is most pronounced in dense, low-temperature gases where intermolecular forces are strongest. The challenge here is to find an equation of state that can adequately cover this range of conditions for gases of many different constituents. In the following discussion we first briefly outline some of the equations of state used to describe pure gases. We will introduce these from the molecular point of view since this helps understand the physical basis (and limitations) of each model. Each of these equations of state can then be applied to mixtures of gases using a set of rules which we describe at the end of this section.

Computation of Temperature-Pressure Phase Diagrams of High-Pressure Nitrides

2006 ◽  
Vol 987 ◽  
Author(s):  
Peter Kroll
Keyword(s):  
High Pressure ◽  
High Temperature ◽  
Phase Diagrams ◽  
Noble Metal ◽  
Lower Boundary ◽  
Explicit Scheme ◽  
First Principle ◽  
Fugacity Coefficient ◽  
Pressure Phase ◽  
High Temperature High Pressure

AbstractWe propose an explicit scheme to include the fugacity of nitrogen in computations of phase diagrams of nitride compounds at high-temperature/high-pressure conditions. The assessment is based on available thermochemical data and two kind of extrapolating functions to provide upper and lower boundary for the fugacity coefficient as a funtion of p and T. The procedure is applied to investigate the synthesis of novel nitrides of tantalum, tungsten, and platinum. The combination of first-principle and thermochemical calculations let us predict the synthesis of a new high-pressure phase of Ta3N5 at about 27 GPa. Synthesis of WN2 becomes feasible at about 45 GPa. We furthermore explain why the synthesis of the noble metal subnitride, PtN2, occurs at about 40 GPa, and why PtN is not accessible in high-pressure experiments.

A generalized treatment of cubic equations of state

1989 ◽  
Vol 54 (11) ◽  
pp. 2879-2895
Author(s):  
Vladimír Míka
Keyword(s):  
Equations Of State ◽  
Compressibility Factor ◽  
Fugacity Coefficient

From the formula proposed for the van Waals type equations of state, general expressions for the compressibility factor, the departure functions and the fugacity coefficient are derived. Easy construction of the formula needed is possible for any of the equations listed in the paper. The method is applicable to other equations of this type.

scholarly journals Liquid balance - steam for methanol mixing - Benzen using the Peng Robinson and Van-Laar models

Respuestas ◽  
2019 ◽  
Vol 24 (1) ◽  
pp. 34-41
Author(s):  
Miguel Fernando Palencia Muñoz ◽  
Natalia Prieto-Jiménez ◽  
Germán González Silva
Keyword(s):  
Experimental Data ◽  
Binary System ◽  
Activity Coefficient ◽  
Liquid Mixture ◽  
Theoretical Data ◽  
Dew Point ◽  
Bubble Point ◽  
Fugacity Coefficient ◽  
Cubic Equation

This paper is related to the procedure for calculating curves dew point and bubble point of a binary system, consisting of the methanol and benzene mixture to 45°C, using the Peng-Robinson cubic equation to calculate the fugacity coefficient of gas i in the mixture, and Van Laar model to calculate the activity coefficient of component i in the liquid mixture. Then a comparison between the theoretical data with the experimental data and later with the commercial simulator Hysys-Aspen, which applies the model of Wilson. The simulation was validated with experimental data,in addition to comparing the results with a commercial simulator.

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