(183g) Integrated Membrane Material Design and System Synthesis

Membranes have been recognized as a promising separation technology and a potential alternative for inefficient thermally driven separation processes [1]. Due to its compactness, energy efficiency, scalability, and flexibility, membrane gas separation finds applications not only in conventional industrial gas separations but also in emerging applications such as biogas purification and onboard inert gas generation systems. In most commercial applications, polymeric membranes are chosen due to their inexpensive and scalable production. Unfortunately, polymeric materials demonstrate a trade-off in their permeability and selectivity [2], which becomes an obstacle in separation tasks where both purity and recovery are important. To overcome this obstacle, several permeators can be interconnected forming a system. Consequently, early decisions such as the system structure, operating conditions, and membrane materials greatly affect the final economics of the process.

Membrane system synthesis often relies on sequential design approaches in which the membrane material is chosen a priori while the remaining decisions are determined afterward. However, these approaches may yield suboptimal final designs due to the restricted search space. Alternatively, the process synthesis can be done through a simultaneous approach where decisions such as structure, operating conditions, and material selection are obtained simultaneously by solving an optimization problem. Most studies in this area focused on problems with only binary mixtures, whereas those with multicomponent mixtures were solved using local methods. While solving the synthesis problem using local solvers is generally computationally inexpensive, the solutions are sometimes significantly worse than the global optimal solution [3].

Accordingly, we present a global optimization approach for integrated membrane material design and system synthesis for multicomponent gas mixture separation. We propose a mixed-integer nonlinear programming (MINLP) model to identify the optimal material(s) and system (i.e., configuration, operating pressures, and flowrates). We employ a richly connected superstructure with structural decisions for interconnections between stages (i.e., retentate and permeate recycle streams), the feed stage, and stage-to-product streams to represent numerous distinct configurations. To describe the permeation in the membranes, we use modified versions of previously developed physics-based surrogate models of crossflow and countercurrent flow permeators [4].

When a list of candidate membrane materials is provided, we consider two strategies: (1) single material is used throughout the system, and (2) different materials may be used in the system. To represent permeation in different materials, we introduce binary variables to denote the material selection and use the convex-hull reformulation for the mass transport equations. We also consider property-targeting membranes whose permeances are variable and costs depend on the distance of the permeances from the Robeson trade-off line. These permeances vary within a domain limited by their lower and upper bounds, the trade-off line correlation, and a specified distance from the trade-off line. Finally, we showcase the applicability of our approach through a case study of biogas upgrading.

References

[1] R. W. Baker and B. T. Low, “Gas separation membrane materials: A perspective,” Macromolecules, vol. 47, no. 20, pp. 6999–7013, 2014, doi: 10.1021/ma501488s.

[2] L. M. Robeson, “The upper bound revisited,” Journal of Membrane Science, vol. 320, no. 1–2, pp. 390–400, 2008, doi: 10.1016/j.memsci.2008.04.030.

[3] J. A. C. Velasco, R. T. Gooty, M. Tawarmalani, and R. Agrawal, “Optimal design of membrane cascades for gaseous and liquid mixtures via MINLP,” Journal of Membrane Science, 2021, doi: 10.1016/j.memsci.2021.119514.

[4] G. S. P. Taifan and C. T. Maravelias, “Generalized optimization-based synthesis of membrane systems for multicomponent gas mixture separation,” Chemical Engineering Science, vol. 252, p. 117482, 2022.