Validity of the Kelvin equation and the equation-of-state-with-capillary-pressure model for the phase behavior of a pure component under nanoconfinement

2020 ◽  
Vol 226 ◽  
pp. 115839 ◽  
Author(s):  
Yingnan Wang ◽  
Nadia Shardt ◽  
Chang Lu ◽  
Huazhou Li ◽  
Janet A.W. Elliott ◽  
...  
Keyword(s):  
Equation Of State ◽  
Phase Behavior ◽  
Capillary Pressure ◽  
Pure Component ◽  
Kelvin Equation

scholarly journals Revisiting Kelvin equation and Peng–Robinson equation of state for accurate modeling of hydrocarbon phase behavior in nano capillaries

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ilyas Al-Kindi ◽  
Tayfun Babadagli
Keyword(s):  
Experimental Data ◽  
Surface Tension ◽  
Equation Of State ◽  
Phase Behavior ◽  
Pore Radius ◽  
Microfluidic Chips ◽  
Tight Sandstone ◽  
Kelvin Equation ◽  
Rock Samples ◽  
Robinson Equation

AbstractThe thermodynamics of fluids in confined (capillary) media is different from the bulk conditions due to the effects of the surface tension, wettability, and pore radius as described by the classical Kelvin equation. This study provides experimental data showing the deviation of propane vapour pressures in capillary media from the bulk conditions. Comparisons were also made with the vapour pressures calculated by the Peng–Robinson equation-of-state (PR-EOS). While the propane vapour pressures measured using synthetic capillary medium models (Hele–Shaw cells and microfluidic chips) were comparable with those measured at bulk conditions, the measured vapour pressures in the rock samples (sandstone, limestone, tight sandstone, and shale) were 15% (on average) less than those modelled by PR-EOS.

A New Approach for Determining Equation-of-State Parameters Using Phase Equilibria Data

1966 ◽  
Vol 6 (04) ◽  
pp. 363-371 ◽  
Author(s):  
K.E. Starling
Keyword(s):  
Equation Of State ◽  
Phase Equilibria ◽  
Phase Behavior ◽  
Equilibrium Phase ◽  
Pure Component ◽  
Hydrocarbon Mixtures ◽  
New Approach ◽  
Pvt Data ◽  
Condensate Reservoir ◽  
Phase Data

Abstract Phase equilibria data were used to develop an equation-of-state correlation for complex hydrocarbon mixtures, thereby circumventing difficulties associated with use of pressure-volume-temperature data. Equilibrium phase data for two condensate reservoir fluids were used to determine equation-of-state parameters for hydrocarbons as heavy as C22H46 in a modified form of the Benedict-Webb-Rubin equation of state. Comparative tests of K-values from the resultant correlation were made with data for condensate reservoir, separator and gas plant absorber mixtures. Generally, for temperatures above 0F and computed liquid densities below 0.55 lb-mole/cu ft, the modified BWR equation predicted K-values in close agreement with the experimental data. Introduction Accurate predictions of thermodynamic behavior for complex hydrocarbon mixtures are necessary for many calculations k the petroleum industry. Because of the relatively high cost of extensive experimental data, many correlations for prediction of phase behavior have been developed. Some of these, such as the correlation of K-values presented in the NGAA Equilibrium Ratio Data Book, are totally empirical. Others, such as the Benedict-Webb-Rubin (BWR) equation-of-state method, are semitheoretical. Unfortunately, published correlation methods often do not accurately predict the phase behavior of complex hydrocarbon mixtures, principally because of inadequate representation of the effects of components heavier than decane. This paper presents a new approach to this problem in which basic equation-of-state relations including heavy hydrocarbon effects are applied. Equilibrium phase data for two condensate reservoir fluids containing hydrocarbons as heavy as C22H46 are used to correlate component K-values. The BWR equation was chosen as the prototype equation of state for this study because of its proven capability for accurately predicting phase behavior and thermodynamic properties of light-hydrocarbon mixtures. Research was directed toward development of BWR parameters for the heavy hydrocarbons and modifications of the mathematical form of the BWR equation for application to complex hydrocarbon mixtures. The new equation-of-state approach presented differs considerably from previous methods in that phase equilibria rather than PVT data are used for determination of equation-of-state parameters. It is an explicit approach since the parameters are determined directly from mixture data. As such, it does not encounter problems inherent in the implicit method used by Benedict, Webb and Rubin and numerous other investigators-one in which mixture parameters were postulated to be functions of the pure component parameters. The pure component BWR parameters, in turn, were determined from experimental PVT data. This method has been limited to mixtures containing components lighter than decane because of lack of vapor phase PVT data. Studies have been reported in which BWR parameters have been determined explicitly from PVT data for binary mixtures. However, since small concentrations of heavier components have only a minor effect on PVT behavior, it is doubtful that these explicit methods would yield useful results for condensate systems. Ellington and Eakin have shown that the accuracy of K-values predicted by an equation of state developed from mixture PVT data probably would be more than an order of magnitude lower than the accuracy of the PVT data. On the other hand an equation of state utilizing parameters developed from phase equilibria data should predict K-values with accuracy comparable to be accuracy of the experimental phase compositions. This work applies this explicit approach with the objective of improving hydrocarbon mixture phase behavior predictions. SPEJ P. 363ˆ

scholarly journals On Using the BMCSL Equation of State to Renormalize the Onsager Theory Approach to Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 846
Author(s):  
Donya Ohadi ◽  
David S. Corti ◽  
Mark J. Uline
Keyword(s):  
Equation Of State ◽  
Second Virial Coefficient ◽  
Virial Coefficients ◽  
Pure Component ◽  
Excluded Volume ◽  
Theory Approach ◽  
Prolate Spheroidal ◽  
Empirical Correction ◽  
Prolate Spheroids ◽  
Onsager Theory

Modifications to the traditional Onsager theory for modeling isotropic–nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee–Parsons resummation term. The Lee–Parsons resummation term uses the Carnahan–Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager’s original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee–Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublík–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state.

scholarly journals Pore-Scale Simulation of Confined Phase Behavior with Pore Size Distribution and Its Effects on Shale Oil Production

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1315
Author(s):  
Jingwei Huang ◽  
Hongsheng Wang
Keyword(s):  
Phase Equilibrium ◽  
Equation Of State ◽  
Pore Size Distribution ◽  
Phase Behavior ◽  
Pore Size ◽  
Size Distribution ◽  
Critical Role ◽  
Shale Oil ◽  
Pore Scale ◽  
Modified Equation

Confined phase behavior plays a critical role in predicting production from shale reservoirs. In this work, a pseudo-potential lattice Boltzmann method is applied to directly model the phase equilibrium of fluids in nanopores. First, vapor-liquid equilibrium is simulated by capturing the sudden jump on simulated adsorption isotherms in a capillary tube. In addition, effect of pore size distribution on phase equilibrium is evaluated by using a bundle of capillary tubes of various sizes. Simulated coexistence curves indicate that an effective pore size can be used to account for the effects of pore size distribution on confined phase behavior. With simulated coexistence curves from pore-scale simulation, a modified equation of state is built and applied to model the thermodynamic phase diagram of shale oil. Shifted critical properties and suppressed bubble points are observed when effects of confinement is considered. The compositional simulation shows that both predicted oil and gas production will be higher if the modified equation of state is implemented. Results are compared with those using methods of capillary pressure and critical shift.

The statistical thermodynamics of solutions of non-spherical molecules. I. The thermodynamic functions

1955 ◽  
Vol 229 (1177) ◽  
pp. 271-280 ◽  
Keyword(s):  
Carbon Tetrachloride ◽  
Equation Of State ◽  
Thermodynamic Functions ◽  
Statistical Thermodynamics ◽  
Intermolecular Forces ◽  
Pure Component ◽  
Experimental Results ◽  
Thermodynamics Of Solutions ◽  
Theory And Experiment

The perturbation treatment of the orientational forces between non-spherical molecules proposed by Cook & Rowlinson (1953) is extended to mixtures by using the theory of solutions put forward by Longuet-Higgins (1951). The thermodynamic functions and the equation of state of such mixtures are expressed in terms of the intermolecular forces and the properties of one pure component. Expressions are derived for the excess (or non-ideal) thermodynamic functions which are compared with the experimental results on the four solutions, benzene+ cyclohexane , benzene+carbon tetrachloride, benzene + ethylene dychloride, and cyclohexane + carbon tetrachloride. The agreement between theory and experiment is improved by taking account of the orientational forces.

scholarly journals Curvature-Based Equation of State for Microemulsion-Phase Behavior

SPE Journal ◽  
2018 ◽  
Vol 24 (02) ◽  
pp. 647-659 ◽  
Author(s):  
V. A. Torrealba ◽  
R. T. Johns ◽  
H.. Hoteit
Keyword(s):  
Equation Of State ◽  
Phase Behavior ◽  
Oil Recovery ◽  
Industrial Applications ◽  
Data Availability ◽  
Behavior Modeling ◽  
Average Curvature ◽  
Wide Range ◽  
Definition Of ◽  
Spheroidal Geometry

Summary An accurate description of the microemulsion-phase behavior is critical for many industrial applications, including surfactant flooding in enhanced oil recovery (EOR). Recent phase-behavior models have assumed constant-shaped micelles, typically spherical, using net-average curvature (NAC), which is not consistent with scattering and microscopy experiments that suggest changes in shapes of the continuous and discontinuous domains. On the basis of the strong evidence of varying micellar shape, principal micellar curves were used recently to model interfacial tensions (IFTs). Huh's scaling equation (Huh 1979) also was coupled to this IFT model to generate phase-behavior estimates, but without accounting for the micellar shape. In this paper, we present a novel microemulsion-phase-behavior equation of state (EoS) that accounts for changing micellar curvatures under the assumption of a general-prolate spheroidal geometry, instead of through Huh's equation. This new EoS improves phase-behavior-modeling capabilities and eliminates the use of NAC in favor of a more-physical definition of characteristic length. Our new EoS can be used to fit and predict microemulsion-phase behavior irrespective of IFT-data availability. For the cases considered, the new EoS agrees well with experimental data for scans in both salinity and composition. The model also predicts phase-behavior data for a wide range of temperature and pressure, and it is validated against dynamic scattering experiments to show the physical significance of the approach.

Thermodynamic Analysis of Phase Behavior at High Capillary Pressure

SPE Journal ◽  
2018 ◽  
Vol 23 (06) ◽  
pp. 1977-1990 ◽  
Author(s):  
Mohsen Rezaveisi ◽  
Kamy Sepehrnoori ◽  
Gary A. Pope ◽  
Russell T. Johns
Keyword(s):  
Phase Behavior ◽  
Capillary Pressure ◽  
Thermodynamic Analysis ◽  
Phase Stability ◽  
Tangent Plane ◽  
General Purpose ◽  
Distance Method ◽  
Capillary Equilibrium ◽  
Production Behavior ◽  
Reservoir Simulator

Summary High capillary pressure has a significant effect on the phase behavior of fluid mixtures. The capillary pressure is high in unconventional reservoirs because of the small pores in the rock, so understanding the effect of capillary pressure on phase behavior is necessary for reliable modeling of unconventional shale-gas and tight-oil reservoirs. As the main finding of this paper, first we show that the tangent-plane-distance method cannot be used to determine phase stability and present a rigorous thermodynamic analysis of the problem of phase stability with capillary pressure. Second, we demonstrate that there is a maximum capillary pressure (Pcmax) where calculation of capillary equilibrium using bulk-phase thermodynamics is possible and derive the necessary equations to obtain this maximum capillary pressure. We also briefly discuss the implementation of the capillary equilibrium in a general-purpose compositional reservoir simulator. Two simulation case studies for synthetic gas condensate reservoirs were performed to illustrate the influence of capillary pressure on production behavior for the fluids studied.

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