(479d) Multiscale Modeling of Chemical Fractionation Using Reverse Osmosis

Increasing the energy efficiency of chemicals separations is critical to the deep decarbonization of industrial products ranging from polymers and pharmaceuticals to solvents and biofuels. Separation and purification accounts for over 40% of the energy consumed in the production of key chemicals and up to 70% of the production cost for biobased chemicals and fuels.^1,2 Thermal distillation forms an integral part of many chemical separations, separating mixtures by the volatility of their constituent components. Although widely used, distillation can be energy intensive, requiring large amounts of heat to drive vaporization and accounting for 10-15% of global energy consumption.³

Membrane-based processes, such as reverse osmosis (RO), separate mixtures based on the size and charge of their constituent components, rather than their volatility. RO utilizes hydraulic pressure to create a chemical potential gradient to drive permeation through a selective membrane, splitting the feed into high and low permeability fractions. By avoiding the energy intensive vapor-liquid phase change, RO can drastically reduce the energy footprint of chemical separations.^4,5 Developing reliable thermodynamic models combined with a thorough understanding of transmembrane mass transport phenomena can accelerate future membrane and process design.

In this investigation, we develop multiscale modeling tools to study the fractionation of mixed xylenes; a multicomponent mixture of isomers ortho-, meta-, para-xylene, and ethylbenzene; using nanoporous nanosheet membranes. Separating ethylbenzene and para-xylene from mixed xylenes mixtures is an essential step in the production of polystyrene and polyethylene terephthalate, respectively, which account for 14% of global polymer production.⁶ However, due to their similar boiling points, the separation of mixed xylene isomers using distillation is prohibitively energy intensive.

We begin by performing all-atom molecular dynamics (MD) simulations in LAMMPS to study the impact of isomer and pore geometry on the transmembrane permeation of ortho-, meta-, para-xylene, and ethylbenzene through multilayered nanoporous graphene as a function of pore size and thickness. Permeation rates from MD simulations are used to inform modifications to the Sampson and Dagan models for Stokes flow through a circular orifice, accounting for continuum breakdown as pore radius approaches molecular radius (< 0.5 nm).^7–9 The modified Sampson-Dagan model captures the impact of both entrance and exit resistances, which are dominant for transport through thin nanopores, and frictional resistance that play an important role in thicker pores.

We then extend our continuum-atomistic framework using the Maxwell-Stefan equations for multicomponent transport to capture the selective transmembrane permeation of mixtures. The modified Navier-Stokes Maxwell-Stefan (NSMS) formulation is used to demonstrate the permeability-selectivity tradeoff for multicomponent mixtures with selectivity increasing rapidly as pore size is reduced while permeability increases proportionally to the cube of pore radius. Finally, we build module- and cascade-scale models for the fractionation of mixtures of mixed xylenes into their four constituent components. By integrating our transmembrane transport expressions over finite membrane area, we highlight the importance of variations in feed flow rate and composition module-averaged permeation and selectivity. Multi-module system-scale optimization is then performed to maximize energy efficiency subject to product purity and membrane area constraints. We conclude by exploring the potential for electrically powered and modular membrane systems to efficiently fractionate multicomponent chemical mixtures and demonstrating how membrane properties impact process-scale performance.

References:

1 S. Jones, E. Tan, J. B. Dunn and L. Valentino, Bioprocessing Separations Consortium Three-Year Overview: Technical Advances, Process Economics Influence, and State of the Science, Bioprocessing Separations Consortium, U.S. Department of Energy, 2020.

2 S. Brueske, C. Kramer and A. Fisher, Bandwidth Study on Energy Use and Potential Energy Saving Opportunities in U.S. Chemical Manufacturing, U.S. Department of Energy, 2015.

3 D. S. Sholl and R. P. Lively, Nature, 2016, 532, 435–437.

4 D.-Y. Koh, B. A. McCool, H. W. Deckman and R. P. Lively, Science, 2016, 353, 804–807.

5 K. A. Thompson, R. Mathias, D. Kim, J. Kim, N. Rangnekar, J. R. Johnson, S. J. Hoy, I. Bechis, A. Tarzia, K. E. Jelfs, B. A. McCool, A. G. Livingston, R. P. Lively and M. G. Finn, Science, 2020, 369, 310–315.

6 R. Geyer, J. R. Jambeck and K. L. Law, Sci. Adv., 2017, 3, 1–5.

7 R. A. Sampson, Philos. Trans. R. Soc. Lond. A, 1891, 182, 449–518.

8 Z. Dagan, S. Weinbaum and R. Pfeffer, J. Fluid Mech., 1982, 115, 505–523.

9 M. Heiranian, A. Taqieddin and N. R. Aluru, Phys. Rev. Res., 2020, 2, 043153.