Page 232 - Membranes for Industrial Wastewater Recovery and Re-Use

System design aids 201

Programming
The solution of a water demand problem based on pinch methodology essentially
has two components: a proper routine that formulates the problem and accounts
for the superstructure and a robust optimisation package to solve the highly non-
linear equations. Optimisation demands the solution of highly non-linear
equations. Indeed, the pinch problem is fundamentally non-linear with discrete
decisions (complexity, number of connections, etc.), generally demanding
solution by MINLP algorithms (Mixed-Integer Non-Linear Programming). For
WaterTargetIE' it can be observed that in running the optimisation procedure,
GAMS (General Algebraic Modeling System: GAMS, 2002) is called upon as a
solver. The commercial solvers used are OSL (MILP) and MINOS (NLP), whereas
the algorithm used to solve the MINLP is proprietary. As for Water, the problem
is decomposed into a linear approximation (NIILP) followed by a non-linear
(NLP) solver. Gianadda et al. (2002) use the UMIST approach, breaking down the
problem into a MILP followed by NLP using CONOPT as the solver to deal with
the NLP problem. The optimisation problem has been solved by Ullmer et al.
(2002) by using a MINLP algorithm developed by Lassahn and Gruhn (2002).
XPRESS-MP@ solves the MILP problem: the remaining NLP problem is solved by
LSGRG2B'. At the Rzeszow University of Technology (Poland) an adaptive
random search (ARS) optimisation method was developed to design the optimal
wastewater reuse network containing a small or medium number of water-using
processes (Poplewski et al., 2002). To overcome the limited number of processes,
further investigations are planned. Shafiei et al. (2002) propose an alternative
approach by coupling genetic algorithms with mathematical programming and
evaluating the solutions obtained by process simulation.
Solving the highly non-linear problem forces the user, and thus the software
developer, to carefully examine the solution to ensure that the solution provided
is not a local but a global minimum. However, due to the non-linearity there is no
guarantee the solution is a global one. Using many different initial conditions
appropriate to the system being examined and searching the optimum value is
an indication of how well the global optimum has been reached. The process of
thoroughly checking this often makes the calculation lengthy, especially when
many contaminants, regeneration techniques and constraints are considered.
The software should indicate whether a local, a presumed global or no optimum
has been reached.

4.2.6 Case study: water pinch and implementation of regeneration techniques
As already stated, water pinch is a mcthodology to determine the minimum
water usage as an overall target and, as such, does not take into account the
minimum total cost and compliance with effluent discharge consents. A case
study is presented where a water network is determined, achieving minimum
water usage at minimum total cost. The example is based on the WaterTarget ''
software package, this being a package that allows a total system design to be
developed, including compliance with the final effluent discharge limits. The
theory behind the methodology incorporating regeneration techniques and final