Compressibility of Nanoconfined Fluids: Relating Atomistic Modeling - PowerPoint PPT Presentation

Compressibility of Nanoconfined Fluids: Relating Atomistic Modeling to Ultrasonic Experiments Gennady Gor Department of Chemical and Materials Engineering New Jersey Institute of Technology Newark, NJ, USA E-mail: gor@njit.edu Web: http://porousmaterials.net G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 1 / 22

Acknowledgments Nick Corrente Max Maximov BS (2019) 4th year Ph.D. Currently: Ph.D. student student at Rutgers Prof. Boris Gurevich Chris Dobrzanski Geophysics Ph.D. (2020) Curtin University, Currently: NJIT Australia G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 2 / 22

Motivation & Potential Industrial Needs ExxonMobil Research & Engineering Company Industrial need: exploration and development of unconventional hydrocarbons (shale gas, shale oil) One of the key difference with conventional hydrocarbons Nanoporous system with hydrocarbons in adsorbed state Loucks, R. G.; Reed, R. M.; Ruppel, S. C. & Jarvie, D. M. J. Sediment. Res. , 2009, 79, 848-861. G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 3 / 22

Wave Propagation in an Elastic Medium Seismic waves – characterization of geological formations Sonic/utrasonic waves – characterization of rock samples Longitudinal waves ↔ longitudinal modulus M M = ρv 2 (1) M Transverse waves ↔ shear modulus G G = ρv 2 (2) G G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 4 / 22 Image from https://chrisplouffe.com

Properties of Fluid-Saturated Porous Media K = M − 4 3 G (3) K = f ( K s , K 0 , K f ) (4) G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 5 / 22

Properties of Composite and its Constituents Fluid does not affect the shear modulus G f = 0 ⇒ G = G 0 Gassmann’s equation (low frequency limit of Biot’s theory): � 2 � 1 − K 0 K s K = K 0 + , (5) K f + (1 − φ ) φ − K 0 K s K 2 s Experimentally measured quantity: the longitudinal modulus M ( K s − K 0 ) 2 K f M = M 0 + . (6) φK 2 s + [(1 − φ ) K s − K 0 ] K f Derived for “classical” macroporous media (Gassmann, 1951) Does it work for nanoporous media? Gassmann, F. ¨ Uber die Elastizit¨ at por¨ oser Medien Viertel. Naturforsch. Ges. Z¨ urich , 1951, 96, 1-23 Biot, M. A. J. Acoust. Soc. Am. , 1956, 28, 168-178 G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 6 / 22

Experiments on Saturated Nanoporous Media Gas adsorption + Ultrasound on Nanoporous Vycor glass Oscilloscope p T t m Pulse Modulator Receiver Schematic for the experimental setup from: Warner, K. L.; Beamish, J. R. J. Appl. Phys. 1988, 63, 4372-4376. Dobrzanski, C. D.; Gurevich, B.; Gor, G. Y. Appl. Phys. Rev. , 2020, submitted G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 7 / 22

Experimental Data: Density and Velocities (N 2 at 77 K) 0 . 04 Volumetric 0 . 005 Volumetric 0 . 03 0 . 004 n/m [mol / g] 0 . 02 0 . 003 ∆ G/G 0 0 . 002 0 . 01 0 . 001 0 . 00 0 . 000 0 . 00 0 . 25 0 . 50 0 . 75 1 . 00 − 0 . 01 p/p 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 p/p 0 0 . 04 Longitudinal Ultrasonic 1 . 00 Transverse Volumetric 0 . 03 0 . 98 ∆ M/M 0 0 . 02 v/v 0 0 . 96 0 . 01 0 . 00 0 . 94 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 − 0 . 01 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 p/p 0 p/p 0 Warner, K. L.; Beamish, J. R. J. Appl. Phys. 1988, 63, 4372-4376. G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 8 / 22

Experimental Data: Other Fluids Argon at 87 K Hexane at 298 K 0 . 06 expt. adsorption 18 . 0 7 . 4 expt. desorption Longitudinal Modulus M (GPa) Shear Modulus G (GPa) 17 . 8 7 . 2 0 . 04 ∆ M/M 0 17 . 6 7 . 0 0 . 02 17 . 4 6 . 8 17 . 2 6 . 6 0 . 00 17 . 0 6 . 4 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 p/p 0 16 . 8 6 . 2 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 Relative Pressure p/p 0 Shear modulus does not appreciably change Longitudinal modulus changes at capillary condensation and continues to change beyond it Page, J.H., Liu, J., Abeles, B., Herbolzheimer, E., Deckman, H.W. and Weitz, D.A., Phys. Rev. E , 1995, 52(3), 2763. Schappert, K. and Pelster, R., EPL (Europhysics Letters) , 2014, 105(5), 56001. G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 9 / 22

Experimental Data vs Gassmann Equation K 0 , K s , K bulk , φ → K or M f 0 . 04 Ultrasonic Volumetric 0 . 03 Bulk ∆ M/M 0 0 . 02 0 . 01 0 . 00 − 0 . 01 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 p/p 0 G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 10 / 22

Experimental Data vs Gassmann Equation Argon at 87 K Hexane at 298 K expt. adsorption expt. adsorption 18 . 0 expt. desorption expt. desorption Longitudinal Modulus M (GPa) Longitudinal Modulus M (GPa) 20 . 2 K f (0) , K s (EMT) K f (0) , K s (EMT) 17 . 8 K f (0) , K s (AD) K f (0) , K s (AD) 20 . 0 17 . 6 19 . 8 17 . 4 19 . 6 17 . 2 19 . 4 17 . 0 19 . 2 19 . 0 16 . 8 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 Relative Pressure p/p 0 Relative Pressure p/p 0 The modulus changes with the vapor pressure p Even at p = p 0 the modulus of saturated sample differs from the modulus of the bulk-fluid saturated sample Page, J.H., Liu, J., Abeles, B., Herbolzheimer, E., Deckman, H.W. and Weitz, D.A., Phys. Rev. E , 1995, 52(3), 2763. Schappert, K. and Pelster, R., EPL (Europhysics Letters) , 2014, 105(5), 56001. G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 11 / 22

Calculating Fluid Modulus from Molecular Simulation Bulk (adiabatic) modulus and isothermal modulus: K f = γK T f Isothermal modulus and isothermal compressibility: K T f = 1 /β T Isothermal compressibility (definition): β T ≡ − 1 � ∂V � V ∂P T,N Fluctuations of number of particles in the grand canonical ensemble ( µ , V , T ) β T = V � δN 2 � k B T � N � 2 Bratko, D.; Curtis, R.; Blanch, D.; and Prausnitz, J. J. Chem. Phys. 2001, 115, 3873-3877. Coasne, B.; Czwartos, J.; Sliwinska-Bartkowiak, M.; Gubbins, K. E. J. Phys. Chem. B , 2009, 113, 13874. Strekalova, E.G., Mazza, M.G., Stanley, H.E. and Franzese, G., Phys. Rev. Lett. , 2011, 106(14), 145701. G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 12 / 22

Calculating Fluid Modulus from Molecular Simulation Lennard-Jones nitrogen, spherical silica pores, T = 77 K, LJ solid-fluid interactions, integrated spherical potential Monte Carlo in the grand canonical ensemble (GCMC) 10 9 equilibration moves, then 3-5 series of 5 × 10 9 moves n s , nm − 2 Interaction σ , nm ǫ/k B , K r cut , σ ff N 2 -N 2 0.36154 101.5 - 5.0 SiO 2 -N 2 0.317 147.3 15.3 - Allen, M. P . & Tildesley, D. J. Computer simulation of liquids. 1987. New York: Oxford, 385. Norman, G. & Filinov, V. High Temp. , 1969, 7, 216 Rasmussen, C. J.; Vishnyakov, A.; Thommes, M.; Smarsly, B. M.; Kleitz, F.; Neimark, A. V. Langmuir 2010, 26, 10147-10157 G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 13 / 22

Results: Adsorption Isotherms 0.8 0.6 2 nm n ∗ 0.4 3 nm 4 nm 5 nm 0.2 6 nm 7 nm 8 nm 0 0 0.2 0.4 0.6 0.8 1 p/p 0 Maximov, M. A.; Gor, G. Y. Langmuir , 2018, 34 (51), 15650-15657 & 2020, 36 (17), 4853-4854 G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 14 / 22

Results: Modulus Isotherms 2 nm (Eq.8) 4 nm (Eq.8) 6 nm (Eq.8) 8 nm (Eq.8) 2 nm (Eq.10) 4 nm (Eq.10) 6 nm (Eq.10) 8 nm (Eq.10) 3 nm (Eq.8) 5 nm (Eq.8) 7 nm (Eq.8) Bulk 3 nm (Eq.10) 5 nm (Eq.10) 7 nm (Eq.10) 1 . 0 f (GPa) 0 . 8 0 . 6 K T 0 . 4 0 . 2 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 p/p 0 G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 15 / 22

Results: Modulus vs Laplace Pressure 2 nm 4 nm 6 nm 8 nm 3 nm 5 nm 7 nm 1 . 0 0 . 8 f (GPa) 0 . 6 K T 0 . 4 0 . 2 − 30 − 20 − 10 0 P L (MPa) � p P L = R g T � log (7) Laplace pressure: V l p 0 G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 16 / 22

Results: Comparison with Experiment 0 . 04 Ultrasonic Volumetric 0 . 03 Theory (GCMC 8 nm) ∆ M/M 0 0 . 02 0 . 01 0 . 00 − 0 . 01 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 p/p 0 Maximov, M. A.; Gor, G. Y. Langmuir , 2018, 34 (51), 15650-15657 & 2020, 36 (17), 4853-4854 G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 17 / 22

Experimental Data vs Gassmann Equation Argon at 87 K Hexane at 298 K expt. adsorption expt. adsorption 18 . 0 Longitudinal Modulus M (GPa) expt. desorption Longitudinal Modulus M (GPa) expt. desorption 20 . 2 K f ( P f ) , K s (EMT) K f ( P f ) , K s (EMT) 17 . 8 K f ( P f ) , K s (AD) K f ( P f ) , K s (AD) 20 . 0 17 . 6 19 . 8 17 . 4 19 . 6 17 . 2 19 . 4 17 . 0 19 . 2 19 . 0 16 . 8 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 Relative Pressure p/p 0 Relative Pressure p/p 0 Gassmann equation is applicable to nanoporous media The fluid modulus K f has to be corrected for confined effects Gor, G. Y. & Gurevich, B. Geophys. Res. Lett. , 2018, 45, 146-155 G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 18 / 22

Results: Modulus vs Pore Size d ext (nm) 10.0 5.0 3.3 2.5 2.0 1.7 1 . 2 Bulk 1 . 0 GCMC f (GPa) 0 . 8 0 . 6 K T 0 . 4 0 . 2 0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 1 /d ext (nm − 1 ) Modulus of confined nitrogen is a linear function of reciprocal pore size Modulus in small pores is higher than in bulk by a factor of three G. Gor (NJIT) Compressibility of Confined Fluids 8/06/2020 19 / 22