Supercomputing and machine learning-aided optimal design of high permeability seawater reverse osmosis membrane systems

Holomorphic embedding method for large-scale reverse osmosis desalination optimization

Large-scale optimal design problems involving nonlinear differential equations are widely applied in modeling such as craft manufacturing, chemical engineering and energy engineering. Herein we propose a fast and flexible holomorphic embedding-based method to solve nonlinear differential equations quickly, and further apply it to handle the industrial application of reverse osmosis desalination. Without solving nonlinear differential equations at each discrete point by a traditional small-step iteration approach, the proposed method determines the solution through an approximation function or approximant within segmented computational domain independently. The results of solving more than 11 million of nonlinear differential equations with various design parameters for the reverse osmosis desalination process indicate that the fast and flexible holomorphic embedding-based method is six-fold faster than several typical solvers in computational efficiency with the same level of accuracy. The proposed computational method in this work has great application potential in engineering design.

A rapid-convergent particle swarm optimization approach for multiscale design of high-permeance seawater reverse osmosis systems

Directly solving sophisticated partial differential equation constrained optimization problems is not only extremely time-consuming, but also very hard to find unique optimal solutions. Here, we propose stable and efficient surrogate models for seawater reverse osmosis desalination processes that enable thorough quantitative description of hydrodynamics and local transport characteristics in narrow flow channels. Without iteratively solving complex multi-physics simulation problem taking several hours, the proposed multi-scale design optimization framework significantly reduces the problem complexity by computing the surrogate models in seconds. Moreover, a fast-converging active subspace particle swarm optimization framework is proposed to address the optimal design problem. Compared to the standard particle swarm optimization algorithm, the proposed method enhances the average optimum by 14% and the standard deviation of optimum results for multiple runs is reduced by no less than ten times. The optimized desalination system achieves 9% reduction on energy consumption and 30% improvement on water production efficiency.

Impact of temperature and forward osmosis membrane properties on the concentration polarization and specific energy consumption of hybrid desalination system

This study investigates how temperature and forward osmosis (FO) membrane properties, such as water permeability (A), solute permeability (B), and structural parameter (S), affect the specific energy consumption (SEC) of forward osmosis-reverse osmosis system. The results show that further SEC reduction beyond the water permeability of 3 LMH bar-1 is limited owing to high concentration polarization (CP). Increasing S by 10-fold increases FO recovery by 177.6%, causing SEC decreases by 33.6%. However, membrane with smaller S also increases external CP. To reduce SEC, future work should emphasize mixing strategies to reduce external CP. Furthermore, increasing the temperature from 10 to 40 °C can reduce SEC by 14.3%, highlighting the energy-saving potential of temperature-elevated systems. The factorial design indicates that at a lower temperature, increasing A and decreasing S have a more significant impact on reducing SEC. This underlines the importance of developing advanced FO membranes, particularly for lower-temperature processes.

Multiscale Analysis of Permeable and Impermeable Wall Models for Seawater Reverse Osmosis Desalination

In recent years, high permeability membranes (HPMs) have attracted wide attention in seawater reverse osmosis (SWRO) desalination. However, the limitation of hydrodynamics and mass transfer characteristics for conventional spiral wound modules defeats the advantage of HPMs. Feed spacer design is one of the effective ways to improve module performance by enhancing permeation flux and mitigating membrane fouling. Herein, we propose a multiscale modeling framework that integrates a three-dimensional multi-physics model with a permeable wall and an impermeable wall, respectively, at a sub-millimeter scale and a system-level model at a meter scale. Using the proposed solution framework, a thorough quantitative analysis at different scales is conducted and it indicates that the average errors of the friction coefficient and the Sherwood number using the impermeable wall model are less than 2% and 9%, respectively, for commercial SWRO membrane (water permeability 1 L m−2 h−1 bar−1) and HPMs (3 L m−2 h−1 bar−1, 5 L m−2 h−1 bar−1 and 10 L m−2 h−1 bar−1) systems, compared to the predictions using the permeable wall model. Using both the permeable and impermeable wall models, the system-level simulations, e.g., specific energy consumption, average permeation flux, and the maximum concentration polarization factor at the system inlet are basically the same (error < 2%), while the impermeable wall model has a significant advantage in computational efficiency. The multiscale framework coupling the impermeable wall model can be used to guide the efficient and accurate optimal spacer design and system design for HPMs using, e.g., a machine learning approach.