Overall graphical design procedure

For a more general ’k’ contaminants case and many sources available. The ideal case of source allocation depends on the number of contaminants. For 2 contaminants, it should be paired with 2 sources (3 equations: Sink mass balance and both impurity constraints with 3 unknowns: FFw, FSR1, FSR2). For ’k’ contaminants, then pair with ’k’ sources (’k’ equations with ’k’ unknowns). The following Source Allocation Step is presented to identify the optimal source flowrates for a specific sink:
  1. For a specific sink, check whether the Pinch Point occurs at the CCs that correspond to the main limiting contaminant. The main limiting contaminant is the one producing the smallest ratio of sink’s concentration to the maximum source concentration (see Section 2.2.1). If the Pinch is at the limiting contaminant, go to step (vi), else continue to step (ii).
  2. For a sink, if there are ’k’ contaminants, then pair with ’k’ sources that are arranged in the order based on the contaminant cascade that the sink is assigned to.
For example, if SK1 is assigned to contaminant cascade ’A’, then pair with the first ’k’ sources that are arranged with ascending order of concentration ’A’. This is explained in the next point.
Set \(F_{Fw,SK1}\) for contaminant ’k1’ = \(F_{Fw,SK1}\) for contaminant ’k2’ for each binary contaminant pairs minus 1 (kC2 – 1). Determine the flowrates of the first ’k’ sources using Eq(3) by using one of the sources as a reference source.
  1. If one of the source flowrates is determined as negative, this means the scenario where all contaminants have Pinch Points does not exist. If this is the case, repeat the procedures (i) to (iv) for ’k-1’ contaminants. If not, go to step (vi)
  2. Check if the sources flowrates are enough to cover the sink. If one of the sources has not enough flowrates, fully use up the source. Repeat the procedures (i) to (iv) with the next ’k’ sources.
For example, for the 3 contaminants example, if the optimal flowrates of SR1 exceed the available SR1, fully use up SR1 for the sink. Repeat the similar procedures using the next three sources, i.e. SR2, SR3 and SR4.
Repeat procedures (i) to (v) until all sinks are fulfilled
Based on these observations, the following overall design procedures using graphical methodology with Pinch concept are proposed:
  1. Assign the sink to proper contaminant cascade. This can be done by determining the ratio of sink’s concentration to the maximum source concentration (see Section 2.1)
  2. For each sink, determine whether it should be Below or Above the Pinch.
  3. Start the design procedures with the contaminant cascade that contains the sink that has the highest flowrate.
  4. Arrange the sink in the contaminant cascade with ascending order of the concentration of contaminant based on the cascade it has been assigned to.
  5. Perform the Source Allocation Steps for the sinks that are Below the Pinch.
  6. Repeat the procedures (iii) to (v) until the sinks (Below the Pinch) for the next contaminant cascade.
  7. Allocate the remaining sources to the sinks that are Above the Pinch.