  Generalized disjunctive programming (GDP) models with bilinear and concave
constraints, often seen in water network design, are challenging optimization
problems. This work proposes quadratic and piecewise linear approximations for
nonlinear terms to reformulate GDP models into quadratic GDP (QGDP) models that
suitable solvers may solve more efficiently. We illustrate the benefits of the
quadratic reformulation with a water treatment network design problem in which
nonconvexities arise from bilinear terms in the mixers' mass balances and
concave investment cost functions of treatment units. Given the similarities
with water network design problems, we suggest quadratic approximation for the
GDP model for the optimal design of a large-scale reverse electrodialysis (RED)
process. This power technology can recover energy from salinity differences
between by-product streams of the water sector, such as desalination brine
mixed with regenerated wastewater effluents. The solver Gurobi excels in
handling QGDP problems, but weighing the problem's precision and tractability
balance is crucial. The piecewise linear approximation yields more accurate,
yet larger QGDP models that may require longer optimization times in
large-scale process synthesis problems.
