The Pinch Diagram

CHAPTER THREE Synthesis of mass exchange networks 

Mass of pollutant lost from the ith rich stream 

Once again, the vertical scale is only relative and any stream can be moved up or down on the diagram. A convenient way of vertically placing each arrow is lo 

both composite streams are plotted on the same diagcam (Fig. 3.7). On this diagram, thermodynamic feasibility of mass exchange is guaranteed when the lean composite stream is always above the waste composite stream. This is equivalent to ensuring that at any mass-exchange level (which corresponds to a horizontal line), the composition of the lean conqwsite stream is located to the left of the waste composite stream, asserting thermodynamic feasibility. Therefore, 

Equation (3.5) can be used to establish a one-to-one correspondence among all composition scales for which mass exchange is feasible. Since most environmental applications involve dilute systems, one can assume that these systems behave ideally. Hence, the transfer of the pollutant is indifferent to the existence of other species in the waste stream. In other words, even if two waste streams contain species that are not identical, but share the same composition of a particular pollutant, the equilibrium composition of the pollutant in an MSA will be the same for both waste streams. Hence, a single composition scale, y, can be used to represent the concentration of the pollutant in any waste stream. Next, (3.5) can be employed to generate Ns scales for the MSAs. For a given set of corresponding composition scales y,x, X2. xj. it is thermodynamically and practically feasible to transfer the pollutant from any waste stream to any MSA. In addition, it is also feasible to transfer the pollutant from any waste stream of a composition y/ to any MSA which has a composition less than the xy obtained from (3.5b). 

Mass of pollutant lost from the ith rich stream MRi=Gi(yf-yl), i = 1,2. Nr. 

a global representation of all process lean streams is developed as a lean composite stream. First, we establish Ns/ lean composition scales (one for each process MSA) that are in one-to-one coirespondence with the rich scale according to the method outlined in Section 3.5. Next, the mass of pollutant that can be gained by each process MSA is plotted vei us the composition scale of that MSA. Hence, each i xx ess MSA is represented as an arrow extending between supply and target compositions (see Fig. 3.5 for a two-MSA example). Ihe vertical distance between the arrow head and tail is given by 

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On the pinch diagram, the vertical overlap between the two composite streams represents the maximum amount of the pollutant that can be transfeired from the waste streams to the process MSAs. It is referred to as the integrated mass... 

Interpreting results of the pinch diagram As can be seen from Fig. 3.12, the pinch is located at the corresponding mole fractions (y,Xi.jc ) - (0.(K)10, 0.0030, 0.0010). The excess capacity of the process MSAs is 1.4 x lO" kg mol benzene/s and cannot be used because of thermodynamic and practical-feasibility limitations. This excess can be eliminated by reducing the outlet compositions and/or flowrates of the process MSAs. Since the inlet composition of S2 corresponds to a mole fraction of 0.0015 on the y scale, the waste load immediately... 

Figure 3.12 The pinch diagram for the benzene recovery example (x i = 2 = 0.001).

It is worth noting that there is no need to optimize over ei- As previously shown, when 2 was set equal to its lowest permissible value (0.(X)1), S was selected as the optimal process MSA above the pinch. On the pinch diagram, as increases, S2 moves to the right, and the same arguments for selecting Si over S2 remain valid. 

Optimizing the use of flie external MSA The pinch diagram (Fig. 3.12) demonstrates that below the pinch, the load of the waste stream has to be removed by the external MSA, S3. This renders the remainder of this example identical to Example 2.2. ThereftKc, the optimal flowrate of S3 is 0.0234 kg mol/s and the optimal outlet composition of S3 is 0.(X)85. Furthermore, the minimum total annualized cost of the benzene recovery system is 41,560/yr (see Fig. 2.13). 

So far, an MOC solution has been identified through a two-stage process. First, the use of process MSAs is maximized by constructing the pinch diagram with the lean composite stream composed of process MSAs only. In the second stage, the external MSAs are screened to remove the remaining load at minimum cost. 

Suppose that the process does not have any process MSAs. How can a lean composite line be developed The following shortcut method can be employed to construct the pinch diagram for external MSAs. A more rigorous method is presented in Chapter Six. 

Filture 3.18b Constructing the pinch diagram for external MSAs. 

Use the pinch diagram to determine the minimum operating cost of the MEN. 

Figure 3.19b The pinch diagram for the toluene-removal example.

Using the pinch diagram with si = 2 = 0.0001, find the minimum cost of MSAs required to handle the desulfurization of R and R2. Where is the pinch located ... 

In order to synthesize an optimal MEN for intercepting the off-gas condensate, we constnict the pinch diagram as shown in Fig. 4.9. Since the three MSA s lie completely to the left of the rich stream, they are all thermodynamically feasible. Hence, we choose the one with the least cost ( /kg NH3 removed) namely the resin. The annual operating cost for removing ammonia using the resin is ... 

MltUmum Utility Targets Using the Pinch Diagram... 

The objective of this case study is to use heat integration via the pinch diagram to reduce this operating cost. A value of Ar" " = 10 K. 

Solution Figures 9.6-9.8 illustrate the hot composite stream, the cold composite stream and the pinch diagram, respectively. As can be seen from Fig. 9.8, the two composite streams touch at 310 K on the hot scale (300 K on the cold scale). The minimum heating and cooling utilities are 2,620 and 50 kW, respectively, leading to an annual operating cost of... 

Once the minimum utility cost has been identified, tradeoffs between operating and fixed costs must be established. This step is undertaken iteratively. For given values of minimum approach temperatures, the pinch diagram is used to obtain minimum cooling cost and outlet gas temperature. By ccmducting enthalpy balance around each unit, intermediate temperatures and exchanger sizing can be determined. Hence, one can evaluate the fixed cost of the system. Next, the minimum approach temperatures are altered, until the minimum TAC is identified. 

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