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118 Cha p te r F i v e

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and wastewater amounts are calculated to be 96 m and 84 m ,
respectively (these values are given by the sum of the individual
water flows).
For this case study, three assumptions are made in order to
simplify the analysis:
1. The batch process is operated repeatedly on a yearly basis.
Therefore, the process behaves as if it is operated in
continuous mode. It has been shown elsewhere (Foo, Manan,
and Tan, 2005) that a repeated batch operation achieves the
same flow targets as for equivalent continuous operation.
2. An unlimited water storage tank is always available. Thus, water
can be stored for later use.
3. Water recovery is always carried out between two consecutive
batches. In other words, water sources in an earlier batch will
be sent to water storage tanks before being reused or recycled
to the water sinks of the next batch operation. A similar
assumption was made in the paper by Shoaib and colleagues
(2008).

Given these assumptions, any established targeting technique for
continuous processes can be used to identify rigorous water targets
for the case study. For purposes of this example, the MRPD is used.
The MRPD is illustrated in Figure 5.4(a), and the network that
achieves the MRPD-derived water targets is shown in Figure 5.4(b).
As shown in the figure, the minimum freshwater demand (F ) is
FW
determined to be 35 m ; the wastewater flow (FWW), 23 m . When
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compared with the total water flow prior to water recovery, this
represents a significant reduction of 63.5 and 72.6 percent for
freshwater and wastewater, respectively.

5.6 Water Minimization via Mathematical Optimization

5.6.1 Introduction to Mathematical Optimization
Besides Water Pinch Analysis, water minimization problems have
also been solved using mathematical optimization techniques.
Various mathematical optimization approaches have been developed
to complement Water Pinch Analysis in dealing with more complex
problems—for example, multicontaminant systems (Takama et al.,
1980; Alva-Argáez, Kokossis, and Smith, 1998; Huang et al., 1999);
complex operational constraints, which include limiting the number
of pipeline connections (Hul et al., 2007); and forbidden/compulsory
matches between water-using processes (Bagajewicz and Savelski,
2001; Kim and Smith, 2004; Li and Chang, 2006). New research results