  Innovative membrane technologies optimally integrated into large separation
process plants are essential for economical water treatment and disposal.
However, the mass transport through membranes is commonly described by
nonlinear differential-algebraic mechanistic models at the nano-scale, while
the process and its economics range up to large-scale. Thus, the optimal design
of membranes in process plants requires decision making across multiple scales,
which is not tractable using standard tools. In this work, we embed artificial
neural networks~(ANNs) as surrogate models in the deterministic global
optimization to bridge the gap of scales. This methodology allows for
deterministic global optimization of membrane processes with accurate transport
models -- avoiding the utilization of inaccurate approximations through
heuristics or short-cut models. The ANNs are trained based on data generated by
a one-dimensional extended Nernst-Planck ion transport model and extended to a
more accurate two-dimensional distribution of the membrane module, that
captures the filtration-related decreasing retention of salt. We simultaneously
design the membrane and plant layout yielding optimal membrane module synthesis
properties along with the optimal plant design for multiple objectives, feed
concentrations, filtration stages, and salt mixtures. The developed process
models and the optimization solver are available open-source, enabling
computational resource-efficient multi-scale optimization in membrane science.
