Recycle convergence

Simultaneous, dynamic simulators require appreciably more computing power than steady-state simulators to solve the thousands of differential equations needed to describe a process, or even a single item of equipment. With the development of fast, powerful computers, this is no longer a restriction. By their nature, simultaneous programs do not experience the problems of recycle convergence inherent in sequential simulators however, as temperature, pressure, and flow rate are not fixed and the input of one unit is not determined by the calculated output from the... 

Note that Figure 4.10a shows the simulation flowsheet with the recycle convergence unit, SOLVEROl, inserted in stream S6. Here, S6 denotes the vector of guesses for the stream variables of the tear stream, and S6 denotes the vector of stream variables after the units in the recycle loop have been simulated. Although the ASPEN PLUS simulation flowsheet in Figure 4.10b does not show SOLVEROl and S6, the user should recognize that they are implemented. The user can supply guesses for S6, or they are supplied by the simulator. 

Figure 4.12a shows a simulation flowsheet with two recycle loops for ASPEN PLUS. Flowsheets for CHEMCAD and PRO/II are identical except for the subroutine (or model) names for the units. Note that no recycle convergence units are shown. This is typical of the simulation flowsheets displayed by most process simulators. The flowsheet for HYSYS.PIant is an exception because the recycle convergence unit(s) are positioned by the user and appear explicitly in the flowsheet. For ASPEN PLUS, CHEMCAD, and PRO/Il, to complete the simulation flowsheet, either one or two convergence units are inserted, as described below. Note that a single convergence unit suffices because stream S6 is common to both loops, as illustrated in Figure 4.12b. Stream S6 is tom into two streams, S6 and S6, with guesses provided for the variables in S6. Since no units are outside of the loops, all units are involved in the iterative loop calculations. The calculation sequence is...

Figure 4.12 Nested recycle loops (a) Incomplete simulation flowsheet (b) simulation flowsheet with a single tear stream and a single recycle convergence unit (c) simulation flowsheet with two tear streams and a single recycle convergence unit (d) simulation flowsheet with two tear streams and two recycle convergence units.

In the previous subsection, the successive substitution and Wegstein methods were introduced as the two methods most commonly implemented in recycle convergence units. Other methods, such as the Newton-Raphson method, Broyden s quasi-Newton method, and the dominant-eigenvalue method, are candidates as well, especially when the equations being solved are highly nonlinear and interdependent. In this subsection, the principal features of all five methods are compared. 

Complete the simulation flowsheets using sequences acceptable to ASPEN PLUS. If any of the streams are tom, your flowsheets should include the recycle convergence units. In you should indicate the calculation sequences. 

When solving a NLP, to optimize a flowsheet, still another alternative exists. In many cases, it is preferable to incorporate the design specifications as equality constraints, i, = 0, as shown in NLP3. Then, it is necessary to remove these design specifications when adding the optimization convergence unit. The latter usually replaces the recycle convergence units in the simulation flowsheet. 

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