Flowsheeting calculation sequence

Both sequential and simultaneous calculational sequences have been proposed for the modular approach as well as the equation-oriented approach. Either the program and/or the user must select the decision variables for recycle and provide estimates of certain stream values to make sure that covergence of the calculations occurs, especially in a process with many recycle streams. Reviews by Evans and Rosen point out many of the problems and practices pertaining to flowsheeting. 

From a computational viewpoint, the presence of recycle streams is one of the major impedements in the sequential solution of a flowsheeting problem. Without recycle streams, the flow of information would proceed in a forward direction, and the calculational sequence for the modules could easily be determined from the precedence order analysis outlined above. With recycle streams present, large groups of modules have to be solved simultaneously, defeating the concept of a sequential solution module by module. For example, in Fig. 5.14, you cannot make a material balance on the reactor without knowing the information in stream S6, but you have to carry out the computations for the cooler module first to evaluate S6, which in turn depends on the separator module, which in turn depends on the reactor module. Partitioning will identify those collections of modules that have to be solved simultaneously (termed maximal cyclical subsystems or irreducible nets). 

Again, we propose for each unit correct specifications, but we would like to know if these are feasible for the whole flowsheet. The recycle tear stream is cut in two parts, 8 and 9. The calculation sequence is Mixer, Reactor, Flash, and Splitter. We denote with Fh and Fm the partial flow rates of hydrogen and methane in the stream 9. After one pass through the calculation sequence, the partial flow rates of the components in the stream 8 will change. The convergence is obtained when the difference in the component flow rates of the streams 8 and 9 becomes smaller than an error. Consider nd... 

We may proceed with a somewhat complicated flowsheet. Suppose that an exit stream of the unit e will be sent back to the unit b (Fig. 3.33c). A new loop is created, including the units b, c, d, e, nested with the previous loop a, b, c, d. If the stream 7 is selected as a new tear stream, the simulation of the flowsheet can be done in a single calculation sequence, as follows (convergence unit (tear streams 5, 7)-a-b-c-d-... 

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...

Note that this is the calculation sequence prepared by ASPEN PLUS. Alternatively, when the user prefers to provide guesses for the two recycle streams, S5 and SIO, the simulation flowsheet in Figure 4.12c is utilized. To accomplish this in ASPEN PLUS, select Convergence from the Data pulldown menu. Then, select Tear which produces the Tear Streams... 

A more complex flowsheet, which contains three recycle loops, is shown in Figure 4.13a. Two calculation sequences are illustrated in Figure 4.13b and 4.13c. These involve the minimum number of tear streams, S5 and S8, and result in the following ouq>ut from ASPEN PLUS ... 

You are given the feed stream and fraction purged in the splitter. Prepare a simulation flowsheet and, when applicable, show the calculation sequence prepared by the process simulator (if using ASPEN PLUS, complete SEQUENCE USED... 

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. 

A computational sequence for modular flowsheeting. Initial values of both recycles are guessed, then the modules are solved in the order 1, 2, 3, 4, 5, and 6. Calculated values for recycle streams S9 and S10 are compared with guessed values in a convergence block, and unless the difference is less than some prescribed tolerance, another iteration takes place with the calculated values, or estimates based on them, forming the new initial guessed values of the recycle streams. 

Modular simulators are frequently constructed on three levels. The lowest level consists of thermodynamics and other physical property relations that are accessed frequently for a large number of flowsheeting utilities (flash calculations, enthalpy balances, etc.). The next level consists of unit operations models as described above. The highest level then deals with the sequencing and convergence of the flowsheet models. Here, simultaneous... 

In a sequential-modular program, the executive program sets up the flowsheet sequence, identifies the recycle loops, and controls the unit operation calculations, while interacting with the unit operations library, physical property data bank, and the other subroutines. The executive program also contains procedures for the optimum ordering of the calculations and routines to promote convergence. 

Sets of linear and/or nonlinear equations can be solved simultaneously using an appropriate computer code (see Table L.l) by one of the methods described in Appendix L. Equation-based flowsheeting codes pertaining to chemical engineering can be used for the same purpose. The latter have some advantages in that the physical property data needed for the coefficients in the equations are transparently transmitted from a data base at the proper time in the sequence of calculations. 

Using the flowsheet simulators, design calculations are needed to estimate the reflux ratio and the theoretical tray requirements for the two towers in each of the sequences. In ASPEN PLUS, this is accomplished with the DSTWU subroutine, which is described in the module ASPEN — Separators Distillation FUG Shortcut Design on the multimedia CD-ROM. 

The method of dynamic programming synthesizes the optimal sequence starting from its end. Therefore, expenditures Su should be determined without calculation of the previous part of the flowsheet. For this purpose, it is necessary to determine the composition of feeding of colunm IJJi.. It can be done easily, if it is accepted that each product of separation sequence i contains as impurity components only adjacent components i -1) and i +1) (i.e., the set permissible concentrations of impurity components) ... 

After identification of several preferable sequences, choosing among the optimum sequences, taking into consideration possible thermodinamic improvements and thermal integration of columns, arises. This task is similar to the synthesis of separation flowsheets of zeotropic mixtures (see Section 8.3), and it should be solved by the same methods (i.e., by means of comparative estimation of expenditures on separation). The methods of design calculation, described in Chapters 5 7 for the modes of minimum reflux and reflux bigger than minimum, have to be used for this purpose. In contrast to zeotropic mixtures, the set of alternative preferable sequences for azeotropic mixtures that sharply decreases the volume of necessary calculation is much smaller. 

To achieve this, use a calculator block. This block will take the flow rate of methanol in the stripper bottoms and add enough makeup methanol to ensure that the combined total adds to 22,300 kmol/h. First, create a Calculator block and place it anywhere on the flowsheet. Inside the block, you must first define the parameters, which are the data collected from the simulation. In this case, we want the molar flow rate of methanol in the stripper bottoms product, which you can specify with the Edit/ View declarations button (see Figure 16b). If this is given parameter number one, it means that in the calculator code, it can be obtained with the expression P(l). Then, in the Stream Sequence tab, you must specifically state the order in which streams should be accessed by your calculator code. In this case, select the stripper bottoms stream first, then the makeup methanol stream second (where the results will be stored). Finally, in the procedure text box, add the actual code, which sets the methanol flow rate appropriately (see Figure 16b) ... 

Executive program (flowsheet solver) The heart of any process simulator and controls the sequence of the calculations and the overall convergence of the simulation... 

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