(258b) Optimization of Produced Water Networks for Critical Mineral Recovery Integrated to Doe’S Produced Water Optimization Framework Pareto

Rare earth elements (e.g., yttrium) and critical materials (e.g., lithium) are crucial for manufacturing electronics, pharmaceuticals, batteries, renewable energy generators, and more. Establishing a viable domestic rare earth element and critical mineral (REE-CM) supply chain is a critical concern of multiple U.S. agencies. Wastewater streams in oil/gas production (i.e., produced water) can contain appreciable concentrations of CMs (e.g., lithium) which presents an opportunity for domestic sourcing of lithium that may also better incentivize the costly treatment of produced water [1]. Designing and operating produced water networks to recover lithium while satisfying a variety of other operational constraints results in nonconvex mixed-integer nonlinear programs (MINLP) that readily become intractable for real-world sized networks.

Optimizing produced water network operations that rigorously track lithium composition shares some key elements with the multiperiod blending problem (MPBP) which has been well-studied in the literature [2]. MPBPs seek to maximize the profit of a mixing operation where sources with given flow and composition are blended in pools to satisfy a demand with dynamic quantity and quality requirements [3]. In a produced water context, both production and completion pads can be thought of as sources that provide the network with produced water with known dynamic flows and compositions. Similarly, potential lithium recovery companies demand produced water that satisfies certain composition requirements to facilitate economical mineral recovery.

Multiperiod blending problems are traditionally modelled as nonconvex MINLPs which are computationally challenging to solve and require the use of global optimization techniques [4]. Nonlinearities arise as bilinear (nonconvex) terms in a mass balance that are needed to track species compositions in streams and inventories throughout the network [5]. Furthermore, discrete decisions arise to determine the existence of a given flow at a certain time period which is required to enforce a minimum flow constraint, required in networks with large infrastructures such as the ones existing in oil and gas [3].

To address these challenges, several approaches have been proposed in the literature such as discretization [6] or using convex envelopes [7], and we refer the reader to the work made by Floudas and Misener for a more extensive literature survey [8]. One of the most promising approaches is a two-stage decomposition based on generalized disjunctive programming (GDP) proposed by Lotero et al. [3]. This decomposition is based on the fact that mixing, and therefore bilinear balances, need to be considered only when a tank is being charged. Therefore, by determining whether tanks are charging or discharging in a mixed-integer linear programming (MILP) upper-level problem, the size and the number of bilinear terms is reduced improving the computational performance. However, the solution approach proposed by Lotero et al. does not allow a tank to be charged and discharged at the same time period [3] nevertheless, this case can occur in produced water networks. Furthermore, in previous work, it has been shown that the decomposition from Lotero et al. can fail to solve case studies arising from lithium recovery efficiently if applied directly as proposed [3].

There are several characteristics of produced water network optimization that further compound the complexity in comparison to traditional MPBPs. Strategic (i.e., design) decisions such as treatment technology location/sizing, pipeline expansions, and storage location/sizing are essential [9]. Moreover, there are complicating operational considerations such as reversible flows, completion pad oil wells which dynamically switch from sinks to sources, and consideration of multiple constituents/qualities (e.g., lithium and salinity) with interconnected treatment sites and reuse options.

The PARETO framework (Produced Water Application for Beneficial Reuse, Environmental Impact and Treatment Optimization) is a software package to identify cost-effective and environmentally sustainable produced water management, treatment and reuse solutions[9]. The three-year project for the development of PARETO was launched by the National Energy Technology Laboratory (NETL) in cooperation with the Lawrence Berkeley National Laboratory (LBNL). This software package includes a common interface for problem specification, models for produced water networks piping and equipment, and optimization formulations for both strategic and operational decisions. In this work, we have collaborated on the development and integration of GDP and MINLP formulations that leverage network analysis to solve the problem of optimal management of produced water considering recovery of critical minerals. Our formulations and solution approaches focus on achieving scalable solutions for large network models.

Specifically, we explore special properties within the produced water networks to remove unnecessary bilinear terms and exploit the unique structure of dynamic relationships to improve the formulation tractability. The structure of this improved formulation enables us to study tailored decomposition techniques that significantly improve computational performance. This leverages recent developments in nested disjunction modeling to create smaller problems with tighter relaxations to speed up the solution time [10]. We demonstrate the merits of our approach via several representative case studies for produced water network operation/design that incorporates lithium recovery.

Acknowledgements

We gratefully acknowledge support from the U.S. Department of Energy, Office of Fossil Energy and Carbon Management, through the Environmental Prudent Stewardship Program.

Disclaimers

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 its employees, makes any warranty, expressor 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.

References

[1] Can Sener, S. E., Thomas, V. M., Hogan, D. E., Maier, R. M., Carbajales-Dale, M., Barton, M. D., ... & Amy, G. L., “Recovery of critical metals from aqueous sources.” ACS sustainable chemistry & engineering, 9(35), 11616-11634, 2021.

[2] D. Ovalle, J. L. Pulsipher, C. Gomez, J. M. Gomez, C. D. Laird, M. G. Drouven and I. E. Grossmann, “Study of Different Formulations for the Multiperiod Blending Problem Applied to Lithium Recovery from Produced Water”, Accepted to 33^rd ESCAPE, 2023.