Phase equilibrium calculations in shale gas reservoirs

Tao Zhang, Yiteng Li, Shuyu Sun

Abstract view|494|times       PDF download|201|times


Compositional multiphase flow in subsurface porous media is becoming increasingly attractive due to issues related with enhanced oil recovery, CO2 sequestration and the urgent need for development in unconventional oil/gas reservoirs. One key effort to construct the mathematical model governing the compositional flow is to determine the phase compositions of the fluid mixture, and then calculate other related physical properties. In this paper, recent progress on phase equilibrium calculations in unconventional reservoirs has been reviewed and concluded with authors’ own analysis, especially focusing on the special mechanisms involved. Phase equilibrium calculation is the main approach to investigate phase behaviors, which could be conducted using different variable specifications, such as the NPT flash and NVT flash. Recently, diffuse interface models, which have been proved to possess a high consistency with thermodynamic laws, have been introduced in the phase equilibrium calculation, incorporating the realistic equation of state (EOS), e.g. Peng-Robinson EOS. In the NVT flash, the Helmholtz free energy is minimized instead of the Gibbs free energy used in NPT flash, and this thermodynamic state function is decomposed into two terms using the convex-concave splitting technique. A semi-implicit numerical scheme is applied to the dynamic model, which ensures the thermodynamic stability and then preserves the fast convergence property. A positive definite coefficient matrix is designed to meet the Onsager reciprocal principle so as to keep the entropy increasing property in the presence of capillary pressure, which is required by the second law of thermodynamics. The robustness of the proposed algorithm is demonstrated by using two numerical examples, one of which has up to seven components. In the complex fluid mixture, special phenomena could be captured from the global minimum of tangent plane distance functions and the phase envelope. It can be found that the boundary between the single-phase and vapor-liquid two phase regions shifts in the presence of capillary pressure, and then the area of each region changes accordingly. Furthermore, the effect of the nanopore size distribution on the phase behavior has been analyzed and a multi-scale scheme is presented based on literature reviews. Fluid properties including swelling factor, criticality, bubble point and volumetrics have been investigated thoroughly by comparing with the bulk fluid flow in a free channel.

Cited as: Zhang, T., Li, Y., Sun, S. Phase equilibrium calculations in shale gas reservoirs. Capillarity, 2019, 2(1): 8-16, doi: 10.26804/capi.2019.01.02


Phase equilibrium, flash calculation, shale gas, capillary effect, confinement

Full Text:



Alharthy, N.S., Nguyen, T., Teklu, T.W., et al. Multiphase compositional modeling in small-scale pores of unconventional shale reservoirs. Paper SPE 166306 Presented at SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, USA, 30 September-2 October, 2013.

Barbosa, G.D., Travalloni, L., Castier, M., et al. Extending an equation of state to confined fluids with basis on molecular simulations. Chem. Eng. Sci. 2016, 153: 212- 220.

Chareonsuppanimit, P., Mohammad, S.A., Robinson Jr, R.L., et al. High-pressure adsorption of gases on shales: Measurements and modeling. Int. J. Coal Geol. 2012, 95: 34-46.

Devegowda, D., Sapmanee, K., Civan, F., et al. Phase behavior of gas condensates in shales due to pore proximity effects: Implications for transport, reserves and well productivity. Paper SPE 160099 Presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 8-10 October, 2012.

Dong, X., Liu, H., Hou, J., et al. Phase equilibria of confined fluids in nanopores of tight and shale rocks considering the effect of capillary pressure and adsorption film. Ind. Eng. Chem. Res. 2016, 55(3): 798-811.

Hartman, R.C., Ambrose, R.J., Akkutlu, I.Y., et al. Shale gas-in-place calculations part II-multicomponent gas adsorption effects. Paper SPE 144097 Presented at North American Unconventional Gas Conference and Exhibition, The Woodlands, Texas, USA, 14-16 June, 2011.

Islam, A.W., Patzek, T.W., Sun, A.Y. Thermodynamics phase changes of nanopore fluids. J. Nat. Gas Sci. Eng. 2015, 25: 134-139.

Jin, B., Bi, R., Nasrabadi, H. Molecular simulation of the pore size distribution effect on phase behavior of methane confined in nanopores. Fluid Phase Equilibr. 2017, 452: 94-102.

Jin, B., Nasrabadi, H. Phase behavior of multi-component hydrocarbon systems in nano-pores using gauge-GCMC molecular simulation. Fluid Phase Equilibr. 2016, 425: 324-334.

Jin, B., Nasrabadi, H. Phase behavior in shale organic and inorganic nanopores from molecular simulation. SPE Reserv. Eval. Eng. 2018, 21(3): 626-637.

Jin, Z., Firoozabadi, A. Thermodynamic modeling of phase behavior in shale media. SPE J. 2016, 21(1): 190-207.

King, G.R. Material-balance techniques for coal-seam and devonian shale gas reservoirs with limited water influx. SPE Reserv. Eval. Eng. 1993, 8(1): 67-72.

Li, Y., Kou, J., Sun, S. Thermodynamically stable two-phase equilibrium calculation of hydrocarbon mixtures with capillary pressure. Ind. Eng. Chem. Res. 2018, 57(50): 17276-17288.

Li, Z., Cao, D.,Wu, J. Layering, condensation, and evaporation of short chains in narrow slit pores. J. Chem. Phys. 2005, 122(22): 224701.

Lu, X.C., Li, F.C., Watson, A.T. Adsorption studies of atural gas storage in Devonian shales. SPE Form. Eval. 1995, 10(2): 109-113.

Luo, S., Jin, B., Lutkenhaus, J.L., et al. A novel pore-sizedependent equation of state for modeling fluid phase behavior in nanopores. Fluid Phase Equilibr. 2019, 498: 72-85.

Luo, S., Lutkenhaus, J.L., Nasrabadi, H. Experimental study of confinement effect on hydrocarbon phase behavior in nano-scale porous media using differential scanning calorimetry. Paper SPE 175095 Presented at SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, Houston, Texas, USA, 28-30 September, 2015.

Luo, S., Lutkenhaus, J.L., Nasrabadi, H. Confinement-induced supercriticality and phase equilibria of hydrocarbons in nanopores. Langmuir 2016, 32(44): 11506-11513.

Luo, S., Lutkenhaus, J.L., Nasrabadi, H. Multi-scale fluid phase behavior simulation in shale reservoirs by a poresize- dependent equation of state. Paper SPE 187422 Presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 9-11 October, 2017.

Nojabaei, B., Johns, R.T., Chu, L. Effect of capillary pressure on phase behavior in tight rocks and shales. SPE Reserv. Eval. Eng. 2013, 16(3): 281-289.

Tan, S.P., Piri, M. Equation-of-state modeling of confinedfluid phase equilibria in nanopores. Fluid Phase Equilibr. 2015, 393: 48-63.

Thommes, M., K¨ohn, R., Fr¨oba, M. Sorption and pore condensation behavior of pure fluids in mesoporous MCM-48 silica, MCM-41 silica, SBA-15 silica and controlled-pore glass at temperatures above and below the bulk triple point. Appl. Surf. Sci. 2002, 196(1-4): 239-249.

Travalloni, L., Castier, M., Tavares, F.W., et al. Thermodynamic modeling of confined fluids using an extension of the generalized van der Waals theory. Chem. Eng. Sci. 2010, 65(10): 3088-3099.

Trens, P., Tanchoux, N., Papineschi, P.M., et al. Confinements effects in MCM-41-type materials: Comparison of the energetics of n-hexane and 1-hexene adsorption. Microporous Mesoporous Mat. 2005, 86(1-3): 354-363.

Walton, J.P.R.B., Quirke, N.P.R.B. Capillary condensation: a molecular simulation study. Mol. Simulat. 1989, 2(4-6): 361-391.

Wang, L., Parsa, E., Gao, Y., et al. Experimental study and modeling of the effect of nanoconfinement on hydrocarbon phase behavior in unconventional reservoirs. Paper SPE 169581 Presented at SPE Western North American and Rocky Mountain Joint Meeting, Denver, Colorado, 17-18 April, 2014.

Wu, K., Li, X., Wang, C. Model for surface diffusion of adsorbed gas in nanopores of shale gas reservoirs. Ind. Eng. Chem. Res. 2015, 54(12): 3225-3236.

Zhang, X., Wang, W. Square-well fluids in confined space with discretely attractive wall-fluid potentials: Critical point shift. Phys. Rev. E 2006, 74(6): 062601.

Zhong, D.L., Li, Z., Lu, Y.Y., et al. Phase equilibrium data of gas hydrates formed from a CO2+ CH4 gas mixture in the presence of tetrahydrofuran. J. Chem. Eng. Data 2014, 59(12): 4110-4117.

Zhu, H.Y., Ni, L.A., Lu, G.Q. A pore-size-dependent equation of state for multilayer adsorption in cylindrical mesopores. Langmuir 1999, 15(10): 3632-3641.


  • There are currently no refbacks.

Copyright (c) 2019 The Author(s)

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright ©2018. All Rights Reserved