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the cascade analysis technique (Manan, Foo, and Tan, 2004), and the
source CC (Bandyopadhyay, Ghanekar, and Pillai, 2006). Once the
flow-rate targets have been identified, numerous techniques can be
used to design a water network that achieves those targets. The works
just cited were developed for continuous processes, but there have
been several reported efforts to apply Water Pinch Analysis to batch
processes; these include the works of Wang and Smith (1995), Liu,
Yuan, and Luo (2007), Foo et al. (2006), and Majozi, Brouckaert, and
Buckley (2006).

5.4 Flow-Rate Targeting with the Material
Recovery Pinch Diagram
This section illustrates the targeting technique of Material Recovery
Pinch diagram—MRPD (El-Halwagi, Gabriel, and Harell, 2003;
Prakash and Shenoy, 2005). Constructing an MRPD requires knowledge
about the material flow rates and loads of each process sink and
source. Given this information, one may construct an MRPD as
follows:

1. Arrange the individual water sources (SRi) and demands
(SKj) into two lists, in ascending order of concentration
level (C).
2. For each source and demand, calculate the load given by the
product of its flow rate and concentration level (i.e., F × C).
3. Plot the cumulative sources and demands, on a diagram of
load versus cumulative flow rate, in ascending order of their
concentration levels to form the sink and source CCs. In
order to render the problem feasible, the cumulative water
source CC must lie below the cumulative water demand CC,
ensuring that the water purity requirements are satisfied.
4. For pure fresh resources (zero concentration of impurities),
the sink and source CCs are separated horizontally until
they barely touch—with the source composite lying below
and to the right of the sink composite—as shown in
Figure 5.3(a).
5. For impure fresh resources, the source CC is shifted along an
impure fresh locus until it lies below and to the right of the
sink CC; this is shown in Figure 5.3(b).
The overlap area of the sink and source CCs represents the
maximum recovery among all sink and source streams within the
network. The point where the two composites touch is called
the Material Recovery Pinch, which is the bottleneck for maximum
recovery. The segment where the sink CC extends to the left of the