(171d) An Efficient and Reliable Numerical Method for Computing Coupled Multicomponent Fluxes for Complex Mixtures across Asymmetric Membranes

Dylan Weber¹, Ronita Mathias¹, Ryan Lively¹, Chau-Chyun Chen², Joseph Scott^1†

1 Department of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

2 Department of Chemical Engineering, Texas Tech University, Lubbock, TX, 79409, USA.

Corresponding author; Email: joseph.scott@chbe.gatech.edu

Abstract

Membranes offer a promising means to intensify many industrial separation processes that are currently achieved using distillation and other thermal separation technologies. Historically, key limitations in the design and synthesis of high-performance membrane materials has posed the most significant barrier to the adoption of membrane processes in industry. However, with steady improvements in membrane material properties and module construction, the lack of reliable membrane modeling and simulation tools is emerging as a major barrier in its own right. In particular, widespread industrial adoption of membrane processes as an alternative to conventional thermal separations is unlikely to occur in the absence of (i) reliable predictive models for membrane performance when confronted with complex multicomponent streams, (ii) methods and databases for parameterizing such models using pure component data and limited multicomponent measurements, and (iii) efficient and reliable numerical solution methods that are compatible with standard process flowsheeting software and enable technoeconomic comparison of membrane and non-membrane processes on a consistent basis.

In this presentation, we will describe a novel numerical solution procedure for computing transmembrane fluxes for non-ideal multicomponent mixtures in contact with an asymmetric membrane. Numerous relevant applications of membrane separations such as water purification, carbon capture, hydrogen separation, olefin/paraffin separation, and benzene derivative concentration include process streams that are multicomponent nonideal mixtures. Along with that there are many different types of membrane material being used. From highly selective zeolites, carbon nanotubes, ionic polymers, mixed-matrix MOF and polymeric, graphene-oxide, and specialty polymers. Many of the current approaches for industrial practice adopt the permeability and linear driving force model to describe permeation across the selective layer. These models are applicable in many cases where the sorption is ideal and uncoupled transport can be assumed. However, this explanation of the system when trying to model many nonideal components and interacting permeants is not correct. That is why our group is looking to employ a feasible rigorous solution of the Maxwell-Stefan equations to describe the multicomponent mass transport. Past contributions from experts in these equations such as Rajamani Krishna, Benny Freeman, or Pavel Izák employ approximate solutions by evaluating terms at average compositions, assume the permeate composition is zero to allow for an approximate solution, or use finite differences to approximate the differential terms. These studies are also restricted to a ternary system with two permeates and a membrane phase. No work has been done to have an effective and reliable numerical method for a system with any number of components.

As a brief overview, the Maxwell-Stefan (MS) approach towards mass-transport is based on irreversible thermodynamics by balancing the driving forces any component from a mixture experienced in the form of the chemical potential with the collective friction forces experienced by transporting with other components in the mixture. The Maxwell-Stefan diffusivities can be physically interpreted as the inverse friction or drag coefficients of a binary interaction between two permeating molecules or the permeant and the membrane phase. The main advantages of this transport model compared to the Fickian model is the incorporation of driving forces other than a concentration gradient, but namely MS diffusivities are not dependent on the system and are an intrinsic property of the binary component or membrane pair. Note, these diffusivities can still be functions of temperature, pressure, and composition. The difference is the general applicability from single or binary permeation data to the multicomponent system with many nonidealities accounted for. Then with the nature of many nonidealities, there are many problems in solving such systems of equations. The problems associated with the complete solution of the set of MS equations are the numerical methods associated with solving the matrix formulation of the set of coupled ordinary differential equations. Our research goal is to provide a working rigorous solution method that converges to physically meaningful solutions with only feed stream inputs, a thermodynamic activity model with required parameters, and single component membrane diffusivities (in some cases binary component diffusivities). This will provide a working toolset for the practicing chemical engineer to design these systems without having to be an expert in the underlying transport equations and allow for rapid plant design prototyping and screening of various process units. In this work we consider the Maxwell-Stefan as the general transport model, and the multicomponent Flory-Huggins equation to describe the activity of the permeants in the polymer phase. The interesting note is this contribution is applicable to any membrane system that can be described by the Maxwell-Stefan equations.