Comparison of Peng-Robinson Equation of State With Capillary Pressure Model With Engineering Density-Functional Theory in Describing the Phase Behavior of Confined Hydrocarbons
- Yueliang Liu (University of Alberta) | Zhehui Jin (University of Alberta) | Huazhou Andy Li (University of Alberta)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- October 2018
- Document Type
- Journal Paper
- 1,784 - 1,797
- 2018.Society of Petroleum Engineers
- Molecular modeling, density functional theory, phase behavior in nanopores, Hydrocarbons, equation of state
- 14 in the last 30 days
- 344 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
The Peng-Robinson equation of state (PR-EOS) (Robinson and Peng 1978) with capillary effect has been used extensively to describe the phase behavior of hydrocarbons under nanoconfinement in shale reservoirs. In nanopores, surface adsorption may be significant, and molecular distribution is heterogeneous. Although the PR-EOS cannot consider these effects, statistical thermodynamic approaches such as density-functional theory (DFT) can explicitly consider the intermolecular and fluid/surface interactions. In this work, we compare the phase behavior of pure hydrocarbons and mixtures in nanopores from the PR-EOS with capillary effect and engineering DFT. We apply the Young-Laplace (YL) equation, assuming zero contact angle to calculate the capillary pressure in the PR-EOS with capillary effect. On the other hand, we extend the PR-EOS to inhomogeneous conditions with weighted-density approximation (WDA) in engineering DFT.
For pure components, both approaches predict that the dewpoint temperature increases in hydrocarbon-wet nanopores. Although engineering DFT predicts that the confined dewpoint temperature approaches bulk saturation point when pore size approaches 30 nm, the saturation point obtained from the PR-EOS with capillary effect approaches bulk only when the pore size is as large as 1000 nm. With engineering DFT, the critical points in nanopores deviate from those in bulk, but no change is observed from the PR-EOS with capillary-effect model. The difference on the dewpoint temperature between the PR-EOS with capillary effect and engineering DFT decreases as the system pressure approaches the critical pressure. At low-pressure conditions, the PR-EOS with capillary-effect model becomes unreliable.
For binary mixtures, both approaches predict that the lower dewpoint decreases and the upper dewpoint increases. More interestingly, phase transition can still occur when the system temperature is higher than the bulk cricondentherm point. Engineering DFT predicts that the confined lower dewpoint approaches bulk when pore size approaches 20 nm, whereas the dewpoint obtained from the PR-EOS with capillary effect approaches bulk only when the pore size is as large as 100 nm. This work illustrates that assuming homogeneous distributions in nanopores may not be appropriate to predict the phase behavior of hydrocarbons under nanoconfinement.
|File Size||1 MB||Number of Pages||14|
Alfi, M., Nasrabadi, H., and Banerjee, D. 2016. Experimental Investigation of Confinement Effect on Phase Behavior of Hexane, Heptane, and Octane Using Lab-on-a-Chip Technology. Fluid Phase Equilibria 423: 25–33. https://doi.org/10.1016/j.fluid.2016.04.017.
Alharthy, N. S., Nguyen, T., Teklu, T. et al. 2013. Multiphase Compositional Modeling in Small-Scale Pores of Unconventional Shale Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–2 October. SPE-166306-MS. https://doi.org/10.2118/166306-MS.
Balbuena, P. B. and Gubbins, K. E. 1993. Theoretical Interpretation of Adsorption Behavior of Simple Fluids in Slit Pores. Langmuir 9 (7): 1801–1814. https://doi.org/10.1021/la00031a031.
Basaldella, E. I., Tara, J. C., Armenta, G. A. et al. 2007. Cu/SBA-15 as Adsorbent for Propane/Propylene Separation. Journal of Porous Materials 14 (3): 273––278. https://doi.org/10.1007/s10934-006-9062-6.
Bruot, N. and Caupin, F. 2016. Curvature Dependence of the Liquid-Vapor Surface Tension Beyond the Tolman Approximation. Physical Review Letters 116: 056102. https://doi.org/10.1103/PhysRevLett.116.056102.
Bui, K. and Akkutlu, I. Y. 2015. Nanopore Wall Effect on Surface Tension of Methane. Molecular Physics 113 (22): 3506–3513. https://doi.org/10.1080/00268976/2015.1037369.
Cabral, V. F., Alfradique, M. F., Tavares, F. W. et al. 2005. Thermodynamic Equilibrium of Adsorbed Phases. Fluid Phase Equilibria 233 (1): 66–72. https://doi.org/10.1016/j.fluid.2005.04.013.
Cervilla, A., Corma, A., Fornes, V. et al. 1994. Intercalation of [MoVIO2 (O2CC (S) Ph2) 2] 2-in a Zn (II)-Al (III) Layered Double Hydroxide Host: A Strategy for the Heterogeneous Catalysis of the Air Oxidation of Thiols. Journal of the American Chemical Society 116 (4): 1595–1596. https://doi.org/10.1021/ja00083a065.
Civan, F., Devegowda, D., and Sigal, R. 2012. Theoretical Fundamentals, Critical Issues, and Adequate Formulation of Effective Shale Gas and Condensate Reservoir Simulation. AIP Conference Proc. 1453 (1): 155–160. https://doi.org/10.1063/1.4711168.
de Boer, J. H. and Lippens, B. C. 1964. Studies on Pore Systems in Catalysts II. The Shapes of Pores in Aluminum Oxide Systems. Journal of Catalysis 3 (1): 38–43. https://doi.org/10.1016/0021-9517(64)90090-9.
Devegowda, D., Sapmanee, K., Civan, F. et al. 2012. Phase Behavior of Gas Condensates in Shales Due to Pore Proximity Effects: Implications for Transport Reserves and Well Productivity. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8–10 October. SPE-160099-MS. https://doi.org/10.2118/160099-MS.
Didar, B. R. and Akkutlu, I. Y. 2013. Pore-size Dependence of Fluid Phase Behavior and Properties in Organic-Rich Shale Reservoirs. Presented at the SPE International Symposium on Oilfield Chemistry. The Woodlands, Texas, 8–10 April. SPE-164099-MS. https://doi.org/10.2118/164099-MS.
Ebner, C., Saam, W. F., and Stroud, D. 1976. Density-Functional Theory of Simple Classical Fluids. I. Surfaces. Physical Review A 14 (6): 2264–2273. https://doi.org/10.1103/PhysRevA.19.856.
Ebner, C. and Saam, W. F. 1977. New Phase-Transition Phenomena in Thin Argon Films. Physical Review Letters 38 (25): 1486–1489. https://doi.org/10.1103/PhysRevLett.38.1486.
Fan, C., Do, D. D., and Nicholson, D. 2011. On the Cavitation and Pore Blocking in Slit-Shaped Ink-Bottle Pores. Langmuir 27 (7): 3511–3526. https://doi.org/10.1021/la104279v.
Gasparik, M., Ghanizadeh, A., Gensterblum, Y. et al. 2012. The Methane Storage Capacity of Black Shales. Presented at the 3rd EAGE Shale Workshop, Shale Physics and Shale Chemistry, Barcelona, Spain, 23–25 January. https://doi.org/10.3997/2214-4609.2014.3944.
Gelb, L. D., Gubbins, K. E., Radhakrishnan, R. et al. 1999. Phase Separation in Confined Systems. Reports on Progress in Physics 62 (12): 1573–1659. https://doi.org/10.1088/0034-4885/62/12/201.
Jhaveri, B. S. and Youngren, G. K. 1988. Three-Parameter Modification of the Peng-Robinson Equation of State to Improve Volumetric Predictions. SPE Res Eng 3 (3): 1033–1040. SPE-13118-PA. https://doi.org/10.2118/13118-PA.
Jin, L., Ma, Y., and Jamili, A. 2013. Investigating the Effect of Pore Proximity on Phase Behavior and Fluid Properties in Shale Formations. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–2 October. SPE-166192-MS. https://doi.org/10.2118/166192-MS.
Jin, B. and Nasrabadi, H. 2016. Phase Behavior of Multi-Component Hydrocarbon Systems in Nano-Pores Using Gauge-GCMC Molecular Simulation. Fluid Phase Equilibria 425: 324–334. https://doi.org/10.1016/j.fluid.2016.06.018.
Jin, Z. and Firoozabadi, A. 2016a. Thermodynamic Modeling of Phase Behavior in Shale Media. SPE J. 21 (1): 190–207. SPE-176015-PA. https://doi.org/10.2118/176015-PA.
Jin, Z. and Firoozabadi, A. 2016b. Phase Behavior and Flow in Shale Nanopores From Molecular Simulations. Fluid Phase Equilibria 430: 156–168. https://doi.org/10.1016/j.fluid.2016.09.011.
Jin, B., Bi, R., and Nasrabadi, H. 2017. Molecular Simulation of the Pore Size Distribution Effect on Phase Behavior of Methane Confined in Nanopores. Fluid Phase Equilibria 452: 94–102. https://doi.org/10.1016/j.fluid.2017.08.017.
Jin, Z. 2018. Bubble/Dew Point and Hysteresis of Hydrocarbons in Nanopores From Molecular Perspective. Fluid Phase Equilibria 458 (February): 177–185. https://doi.org/10.1016/j.fluid.2017.11.022.
Klomkliang, N., Do, D. D., and Nicholson, D. 2013. On the Hysteresis Loop and Equilibrium Transition in Slit-Shaped Ink-Bottle Pores. Adsorption 19 (6): 1273–1290. https://doi.org/10.1007/s10450-013-9569-5.
Li, Z. and Firoozabadi, A. 2009. Interfacial Tension of Nonassociating Pure Substances and Binary Mixtures by Density Functional Theory Combined With Peng–Robinson Equation of State. Journal of Chemical Physics 130 (15): 154108. https://doi.org/10.1063/1.3100237.
Li, Z., Jin, Z. and Firoozabadi, A. 2014. Phase Behavior and Adsorption of Pure Substances and Mixtures and Characterization in Nanopore Structures by Density Functional Theory. SPE J. 19 (6): 1096–1109. SPE-169819-PA. https://doi.org/10.2118/169819-PA.
Luo, S., Lutkenhaus, J. L., and Nasrabadi, H. 2018. Use of Differential Scanning Calorimetry to Study Phase Behavior of Hydrocarbon Mixtures in Nano-Scale Porous Media. Journal of Petroleum Science and Engineering 163: 731–738. https://doi.org/10.1016/j.petrol.2016.12.019.
Luo, S., Nasrabadi, H., and Lutkenhaus, J. L. 2016a. Effect of Confinement on the Bubble Points of Hydrocarbons in Nanoporous Media. AIChE Journal 62 (5): 1772–1780. https://doi.org/10.1002/aic.15154.
Luo, S., Lutkenhaus, J. L., and Nasrabadi, H. 2016b. Confinement-Induced Supercriticality and Phase Equilibria of Hydrocarbons in Nanopores. Langmuir 32 (44): 11506–11513. https://doi.org/10.1021/acs.langmuir.6b03177.
Luo, S., Lutkenhaus, J. L., and Nasrabadi, H. 2017. Multi-Scale Fluid Phase Behavior Simulation in Shale Reservoirs by a Pore-Size-Dependent Equation of State. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 9–11 October. SPE-187422-MS. https://doi.org/10.2118/187422-MS.
National Institute of Standards and Technology (NIST). 2017. Thermophysical Properties of Fluid Systems, NIST Chemistry WebBook, SRD 69. http://webbook.nist.gov/chemistry/fluid.
Neimark, A. V. and Vishnyakov, A. 2000. Gauge Cell Method for Simulation Studies of Phase Transitions in Confined Systems. Physical Review E 62 (4): 4611–4622. https://doi.org/10.1103/PhysRevE62.4611.
Nojabaei, B., Johns, R. T., and Chu, L. 2013. Effect of Capillary Pressure on Phase Behavior in Tight Rocks and Shales. SPE Res Eval & Eng 16 (3): 281–289. SPE-159258-PA. https://doi.org/10.2118/159258-PA.
Parsa, E., Yin, X., and Ozkan, E. 2015. Direct Observation of the Impact of Nanopore Confinement on Petroleum Gas Condensation. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 28–30 September. SPE-175118-MS. https://doi.org/10.2118/175118-MS.
Robinson, D. B. and Peng, D-Y. 1978. The Characterization of the Heptanes and Heavier Fractions for the GPA Peng-Robinson Programs. Research Report RR-28, Gas Processors Association, Tulsa.
Robinson, D. B., Peng, D-Y., and Chung, S. Y. K. 1985. The Development of the Peng-Robinson Equation and Its Application to Phase Equilibrium in a System Containing Methanol. Fluid Phase Equilibria 24 (1–2): 25–41. https://doi.org/10.1016/0378-3812(85)87035-7.
Rosenfeld, Y. 1989. Free-Energy Model for the Inhomogeneous Hard-Sphere Fluid Mixture and Density-Functional Theory of Freezing. Physical Review Letters 63 (9): 980–983. https://doi.org/10.1103/PhysRevLett.63.980.
Rowlinson, J. S. and Widom, B. 1982. Molecular Theory of Capillarity. Oxford, UK: Clarendon.
Rowlinson, J. S. and Swinton, F. L. 1982. Liquids and Liquid Mixtures. London, UK: Butterworth.
Sandoval, D. R., Yan, W., Michelsen, M. L. et al. 2016. The Phase Envelope of Multicomponent Mixtures in the Presence of a Capillary Pressure Difference. Industrial & Engineering Chemistry Research 55 (22): 6530–6538. https://doi.org/10.1021/acs.iecr.6b00972.
Santiso, E. and Firoozabadi, A. 2006. Curvature Dependency of Surface Tension in Multicomponent Systems. AIChE Journal 52 (1): 311–322. https://doi.org/10.1002/aic.10588.
Sapmanee, K. 2011. Effects of Pore Proximity on Behavior and Production Prediction of Gas/Condensate. University of Oklahoma.
Sing, K. S. W., Everett, D. H., Haul, R. A. W. et al. 2008. Reporting Physisorption Data for Gas/Solid Systems. In Handbook of Heterogeneous Catalysis. Wiley-VCH Verlag GmbH & Co. KGaA.
Singh, J. K. and Kwak, S. K. 2007. Surface Tension and Vapor-Liquid Phase Coexistence of Confined Square-Well Fluid. The Journal of Chemical Physics 126 (2): 024702. https://doi.org/10.1063/1.2424460.
Singh, S. K., Sinha, A., Deo, G. et al. 2009. Vapor-Liquid Phase Coexistence, Critical Properties, and Surface Tension of Confined Alkanes. The Journal of Physical Chemistry C 113 (17): 7170–7180. https://doi.org/10.1021/jp8073915.
Steele, W. A. 1973. The Physical Interaction of Gases With Crystalline Solids: I. Gas-Solid Energies and Properties of Isolated Adsorbed Atoms. Surface Science 36 (1): 317–352. https://doi.org/10.1016/0039-6028(73)90264-1.
Tan, S. P. and Piri, M. 2015. Equation-of-State Modeling of Confined-Fluid Phase Equilibria in Nanopores. Fluid Phase Equilibria 393: 48–63. https://dx.doi.org/10.1016/j.fluid.2015.02.028.
Travalloni, L., Castier, M., Tavares, F. W. et al. 2010a. Thermodynamic Modeling of Confined Fluids Using an Extension of the Generalized Van Der Waals Theory. Chemical Engineering Science 65 (10): 3088–3099. https://doi.org/10.1016/j.ces.2010.01.032.
Travalloni, L., Castier, M., Tavares, F. W. et al. 2010b. Critical Behavior of Pure Confined Fluids From an Extension of the Van Der Waals Equation of State. The Journal of Supercritical Fluids 55 (2): 455–461. https://doi.org/10.1016/j.supflu.2010.09.008.
Volzone, C. 2007. Retention of Pollutant Gases: Comparison Between Clay Minerals and Their Modified Products. Applied Clay Science 36 (1–3): 191–196. https://doi.org/10.1016/j.clay.2006.06.013.
Walton, J. P. R. B. and Quirke, N. 1989. Capillary Condensation: A Molecular Simulation Study. Molecular Simulation 2 (46): 361–391. https://doi.org/10.1080/08927028908034611.
Wang, L., Yin, X., Neeves, K. B. et al. 2016. Effect of Pore-Size Distribution on Phase Transition of Hydrocarbon Mixtures in Nanoporous Media. SPE J. 21 (6): 1981–1995. SPE-170894-PA. https://doi.org/10.2118/170894-PA.
Weinaug, C. F. and Katz, D. L. 1943. Surface Tensions of Methane-Propane Mixtures. Industrial & Engineering Chemistry 35 (2): 239–246. https://doi.org/10.1021/ie50398a028.
Wongkoblap, A., Do, D. D., Birkett, G. et al. 2011. A Critical Assessment of Capillary Condensation and Evaporation Equations: A Computer Simulation Study. Journal of Colloid and Interface Science 356 (2): 672–680. https://doi.org/10.1016/j.jcis.2011.01.074.
Zhang, Y., Civan, F., Devegowda, D. et al. 2013. Improved Prediction of Multi-Component Hydrocarbon Fluid Properties in Organic Rich Shale Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–2 October. SPE-166290-MS. https://doi.org/10.2118/166290-MS.
Zhong, J., Zandavi, S. H., Li, H. et al. 2017. Condensation in One-Dimensional Dead-End Nanochannels. ACS Nano 11 (1): 304–313. https://doi.10.1021/acsnano.6b05666.