Cavett problem

One of the basic tools of analysis for tearing is the cycle matrix. This consists of a matrix of streams (the row) and the loop in which they are contained in columns. For example, consider Figure 3 (the Cavett problem). The cycle matrix is found by placing a 1 in the loop column if a stream appears in a loop or 0 if it does not. This is shown in the cycle matrix of Figure 4. The total number of loops in which a stream is included is calculated and placed in the loop total column. We shall use this number later. Note that the loop must pass through a module (node) only once. 

Figure 7. Convergence of the Cavett problem by direct substitution...

Cavett Problem A Benchmark Problem for Testing THE Convergence and Tear Set Selection... 

FIGURE 8.15 Aspen HYSYS implementation of the Cavett problem example of a nonre-dundant and nonminimum tear set. 

Cavett proposed the following problem as a test problem for computer-aided design. Four flash drums are connected as shown in Fig. P5.ll. The temperature in each flash drum is specified, and equilibrium is assumed to be independent of composition so that vapor-liquid equilibrium constants are truly constant. Is the problem properly specified, or do additional variables have to be given If the latter, what should they be The feed is as follows... 

The flowsheet in Fig 3.37 consisting of three nested loops of mixers and flashes, is a standard problem in flowsheeting known as the Cavett s problem (Rosen, 1980). Table 3.9 gives the cycle matrix, where 1 marks each stream included in a recycle loop. For example, the stream Z, appears both in the loops 1 and 3, while the stream Sj only in the loop 3. The last column shows the number of loops tom by each stream, and may be used to evaluate the tearing action. An obvious choice would be to consider three tear streams for three recycles, as for example R Rj, R3, which tom each loop only one. Another choice would be R, Sj, and R3, where Sj would replace Rj. However, it is possible to solve the flowsheet only with two tear streams, as Z, and Zj, now each breaking two loops. Zj may be also replaced by R3 or S3. Hence, several tear sets are... 

In order to illustrate the convergence of the numerical methods discussed earlier and the effect of the set of tear streams on the convergence of the system, we will solve the benchmark problem presented by Cavett [43] (see Figm-e 8.14). This problem represents a typical flowsheet problem for the petroleum industry. It consists of mixers and TP-flash units. The heat exchangers are fictitious unit operations used to modify the P and T conditions to the flash specifications. The problem is interesting because tear stream convergence is not easy and process could be sensitive to changes to the condition of operation. Data for this problem are shown in Table 8.7. 

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