Solvent extraction (SX) is an industry standard separation process to effectively separate and purify CM and REE extracted from a variety of feedstocks [2, 3, 4]. The design of SX separation sequencing is challenging and relies significantly on domain knowledge to identify the optimal configuration that uses the least number of stages while maximizing the separation between the REEs. The design or selection of solvent mixtures is also difficult because of the underlying complex chemical mechanisms and interactions between the metals and extractants. Additionally, the optimal flowsheet configuration may not be obvious, the separation is significantly impacted by both the pH and the extractant used, and many stages may be needed to achieve a desired split for REEs that have similar chemical properties. There is an urgent need for computational tools to automate the design process for CM and REE recovery, which are generalizable to a variety of feedstocks and solvents. This can be addressed using a conceptual design approach, which screens the system-level perspective to establish an initial configuration that will be used later in the detailed design phase [5].
We propose a novel superstructure optimization formulation to determine the optimal flowsheet configuration and operating pH alongside extractant selection for the separation process. We employ a discretization approach to address the nonlinearity arising from equilibrium expressions and pH dependence. We develop a generalized disjunctive programming (GDP) formulation that embeds hierarchical modeling decisions and logic into a nested structure to account for the existence of the stage, as well as pH and extractant selection. Furthermore, using Pyomo.GDP we can transform the GDP using Big-M into a mixed-integer quadratically constrained program that is compatible with the Gurobi solver to guarantee global optimality [6]. After completing the sharp separation configuration, we investigate how the computational time scales with increasing configuration size, specifically the total number of stages. Our future work will focus on exploring expanded superstructures to identify the optimal pathway for multicomponent separation sequencing.
Acknowledgements: This effort was funded by the U.S. Department of Energy’s Process Optimization and Modeling for Minerals Sustainability (PrOMMiS) Initiative, supported by the Office of Fossil Energy and Carbon Management’s Office of Resource Sustainability.
Disclaimer: This project was funded by the United States Department of Energy, National Energy Technology Laboratory, in part, through a support contract. Neither the United States Government nor any agency thereof, nor any of their employees, nor the support contractor, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof, or any of their contractors.
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