Page 267 - Design and Operation of Heat Exchangers and their Networks
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256   Design and operation of heat exchangers and their networks


             In the pinch design method, Δt min is an important parameter for the bal-
          ance between the investment costs and utility costs. A large value of Δt min
          would decrease the investment costs but increase the utility costs and vice
          versa. Furthermore, the pinch position could also change with Δt min . The
          value of Δt min can be optimized by taking the total costs of the network
          as the objective function.
             The pinch design method focuses on the matches of streams near the
          pinch because at that point, the temperature difference is the minimum.
          For the matches away from the pinch, the earlier rules must not be fulfilled.
          In some cases, there might be multiple pinches or no pinch. A detailed
          description of the pinch design method can be found in Linnhoff et al.
          (1982).


             Example 6.4 Pinch method for H2C2_175R.
             We take the problem data of H2C2_175R (Ravagnani et al., 2005. See
             Table 6.3) as an example to illustrate how to design the network with
             the pinch technology (Luo and Roetzel, 2010, 2013). The problem deals
             with two hot streams (N h ¼2) and two cold streams (N c ¼2). Let
             Δt min ¼5K, it is easy to calculate the problem table by Eqs. (6.63)–
             (6.70), which gives the pinch position at t h ¼125°C, Q HU,min ¼200kW,
             Q CU,min ¼120kW. Other results are given in Table 6.4. The composite
             curves are shown in Fig. 6.3. The detailed calculation procedure can be
             found in the MatLab code for Example 6.4 in Appendix.
                To design the network, we divide the problem into two parts at the
             pinch, as is shown in Fig. 6.4. In the part above the pinch, there is only
                                                           _
             one match: H1C1, that is, N h ¼N c ¼1 with C H1 ¼ 10 kW/K,
              _
             C C1 ¼ 20 kW/K; therefore, Eqs. (6.74), (6.76) are fulfilled, and no
             splitting is necessary.
                In the part below the pinch, N h ¼N c ¼2, which meets the rule (6.75).
             We would like to choose the matches H1C1 and H2C2 due to their


          Table 6.3 Problem data for H2C2_175R (Ravagnani et al., 2005).
                                                         2
                                        _
          Stream    T in (°C)  T out (°C)  C (kW/K)  α (kW/m K)  Cost ($/kWyr)
          H1        175      45         10         2.615
          H2        125      65         40         1.333
          C1        20       155        20         0.917
          C2        40       112        15         0.166
          HU        180      179                   5            110
          CU        15       25                    2.5          10
                                               2
          Heat exchanger cost¼1200A 0.57 $/yr (A in m )
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