(347f) Trust Region Formulations for Integrating Treatment in Produced Water Networks

Currently, the U.S. produces approximately 55 million barrels of produced water containing high concentrations of dissolved solids from oil and gas wells every day. Since natural gas is critical for U.S. electrification of the industry and net zero emission plans, this number is projected to increase in the next decade as we complete more and more wells. Currently, produced water can be (1) reused at another well for completion operations, (2) disposed at an injection site, or (3) treated for beneficial reuse (i.e., recovery of precious metals, treated water for irrigation, etc.). Produced water treatment (i.e., thermal or mechanical separation) is needed to enable beneficial reuse. However, the application of established desalination technologies to produced water has not yet been tested, and their economic potential must be studied. Mathematical models for the design and operation of produced water network problems with reduced order treatment models have been studied (Drouven et al., 2022; Oke et al., 2019). These studies indicate that the integration of water treatment into produced water networks to make strategic and operational decisions is pivotal for optimal design and operation of the produced water networks. Detailed produced water treatment models for shale gas flowback have been developed (Onishi et al., 2017). However, since the detailed water treatment models are challenging nonlinear programs (NLPs) with mass, energy balances, and some non-linear thermodynamic properties, the full network problem with rigorous treatment models has not yet been solved. Integrating these models directly into a network optimization problem, which can be modeled as a quadratically constrained program (QCP), poses significant computational challenges.

In this work we build a framework for integrating detailed treatment models with the produced water network models to support PARETO’s strategic and operational decision-making framework. We propose to build on the trust region filter framework (Eason & Biegler, 2016) in order to integrate the treatment NLP with the QCP of the network model. This framework relies on constructing a reduced order split-fraction based model of the treatment units. We then decompose the problem into a trust region subproblem consisting of the QCP network, which contains a reduced order treatment model, and which is updated in every step using zero and first order updates from the “truth model” of the detailed treatment units.

To demonstrate the potential of this approach, we show how a produced water network with the embedded detailed treatment model leads to an intractable optimization problem, while the trust region-based decomposition converges with few iterations and function evaluations. This approach allows us to integrate complex treatment models into the network problem by keeping the detailed treatment model separate from the network optimization problem. We also demonstrate the scalability of this approach on real-world produced water networks from the Permian and Appalachian basins taken from the PARETO (Drouven et al., 2022) network library.

The talk will describe our suite of treatment models built in Pyomo (Bynum et al., 2021), the details of our implementation in the PARETO software framework, details of the trust region filter algorithm tailored to the integrated network problem, and provide a detailed presentation of results for various network instances.

Disclaimer

This project was funded by the U.S. Department of Energy, National Energy Technology Laboratory an agency of the United States Government, through a site support contract. Neither the United States Government nor any agency thereof, nor any of its employees, nor the support contractor, nor any of their 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.

Acknowledgements

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

References

Bynum, M. L., Hackebeil, G. A., Hart, W. E., Laird, C. D., Nicholson, B. L., Siirola, J. D., Watson, J.-P., & Woodruff, D. L. (2021). Pyomo–optimization modeling in python (Third, Vol. 67). Springer Science & Business Media.

Drouven, M. G., Caldéron, A. J., Zamarripa, M. A., & Beattie, K. (2022). PARETO: An open-source produced water optimization framework. Optimization and Engineering. https://doi.org/10.1007/s11081-022-09773-w

Eason, J. P., & Biegler, L. T. (2016). A trust region filter method for glass box/black box optimization. AIChE Journal, 62(9), 3124–3136. https://doi.org/10.1002/aic.15325

Oke, D., Mukherjee, R., Sengupta, D., Majozi, T., & El-Halwagi, M. M. (2019). Optimization of water-energy nexus in shale gas exploration: From production to transmission. Energy, 183, 651–669. https://doi.org/10.1016/j.energy.2019.06.104

Onishi, V. C., Carrero-Parreño, A., Reyes-Labarta, J. A., Ruiz-Femenia, R., Salcedo-Díaz, R., Fraga, E. S., & Caballero, J. A. (2017). Shale gas flowback water desalination: Single vs multiple-effect evaporation with vapor recompression cycle and thermal integration. Desalination, 404, 230–248. https://doi.org/10.1016/j.desal.2016.11.003