(606h) Mathematical Optimization and Process Intensification of Diafiltration Membrane Systems

Mathematical Optimization and Process Intensification of
Diafiltration Membrane Systems

Elvis A. Eugene, William A. Phillip,
and Alexander W. Dowling

Chemical and Biomolecular Engineering
| University of Notre Dame

Membrane systems are
superior to current separations processes because of lower footprints
(compactness) and lower mass transfer limitations (rapidity) and are therefore
an exciting field of research for sustainable technology [1]. However, there
exists a critical need
to systematically identify the most promising applications for novel membrane
materials and address the gaps in scientific knowledge that most inhibit their
translation to scalable technologies. Diafiltration, a
continuous operating strategy for staged membrane cascades, is one such technology,
but barring a few experimental lab scale demonstrations, has not been
rigorously modeled and analyzed [2]. We present a rigorous superstructure
optimization framework for a continuous diafiltration cascade design and
intensification. In a battery recycling case study, we show how staging in
diafiltration cascades could enable novel membrane separations of lithium and
cobalt [3]. Through sensitivity analysis with the optimization model, we
identify membrane materials property targets. We conclude with ongoing
nonlinear parameter estimation work to assess different transport mechanisms
and interfacial phenomena from dynamic diafiltration experiments.

In diafiltration,
dialysate is strategically added to the feed channel of a membrane module to
offset concentration polarization effects and achieve high purity and recovery
of products [4]-[6]. We present a novel modeling and superstructure
optimization framework to 1) elucidate optimal multi-stage process
configurations with complex recycle strategies and 2) systematically identify property
targets for membrane materials. We present strategies to study several
configurations of a diafiltration process network (e.g., counter-current,
co-current) using superstructure optimization. Our nonlinear optimization model
treats flow and concentration of all streams in the network as decision
variables. We then use the epsilon-constraint method to characterize the Pareto
trade-off set between purity and recovery objectives. Interestingly, we find
distinct regions of the Pareto set with similar recycle strategies but each
with unique flow and concentration profiles. Using an illustrative case study,
we show how novel 3 or 4-stage cascade design recycle strategies with modest
improvements in membrane materials could enable new lithium and cobalt
separations technologies for battery recycling [3]. We also compare our
proposed diafiltration technology with classic process intensification
technologies such as distillation and thereby accentuate the potential for
disruptive membrane-based technologies of the future.

Guided by these
membrane material performance targets, we conclude with some brief remarks
about our ongoing work to elucidate molecular design rules for chemically
selective copolymer membranes. These membranes use chemical factors to selectively
target similarly sized solutes for separation from a feed solution. Batch
diafiltration membrane characterization experiments are inherently dynamic,
with membrane interfaces exposed to a large range of solution compositions. We
propose a dynamic model and parameter estimation approach to quantitatively
compare different membrane-solution thermodynamic models and transport
mechanisms. In particular, we are interested
leveraging optimal design of experiments paradigms to systematically design dynamic
diafiltration experiments which can maximize information gain and better
discriminate between rival models, i.e., proposed transport mechanisms [7]-[8].
We wrap up with some remarks on future opportunities for uncertainty
quantification and systems engineering to guide material discovery and
ultimately realize our vision of integrated engineering frameworks that span molecular
to systems scales.

References:

[1]       Qu, S., Dilenschneider, T., &
Phillip, W. A. Preparation of Chemically-Tailored Copolymer Membranes with
Tunable Ion Transport Properties. ACS Applied Materials and Interfaces 2015, 7, 19746 – 19754.

[2]       Nambiar, A. M.
K., Li, Y., & Zydney, A. L. Countercurrent staged
diafiltration for formulation of high value proteins. Biotechnology and Bioengineering 2018, 115(1), 139–144.

[3]       Eugene, E. A.,
Phillip, W. A., & Dowling, A. W., Material Property Goals to Enable
Continuous Diafiltration Membrane Cascades for Lithium Ion Battery Recycling, Submitted to FOCAPD 2019.

[4]       Cheryan, M. Ultrafiltration and Microfiltration Handbook,
1998.

[5]       Mulder, M. Basic Principles of Membrane Technology, 1998.

[6]       Strathmann, H. Selective removal of heavy metal ions from
aqueous solutions by diafiltration of macromolecular complexes. Separation Science and Technology 1980, 15(4), 1135–1152.

[7]       Franceschini,
G., & Macchietto, S. Model-based design of
experiments for parameter precision: State of the art. Chemical Engineering
Science 2008, 63(19), 4846–4872.

[8]       Laínez-Aguirre, J. M., Mockus,
L., & Reklaitis, G. V. A stochastic programming
approach for the Bayesian experimental design of nonlinear systems. Computers
and Chemical Engineering 2015, 72, 312–324.