Converging the Flowsheet

The fresh feed is 0.06kmol/s with a composition of 84mol% ethanol and 16mol% water. Essentially, all the ethanol must come out in the bottoms B1 from the first column. So in the setup of this column, a bottoms flow rate is fixed at (0.06)(0.84) = 0.0504 kmol/s. This column only has one degree of freedom because it has no condenser or internal reflux. The organic reflux will eventually be adjusted to achieve the desired purity of the ethanol bottoms product (99.92 mol% ethanol). Note that both benzene and water can appear in the bottoms as impurities. 

The first guesses of the compositions of the recycle and reflux are inserted in the Input of these streams. First guesses of reflux and recycle flow rates are made of 0.12 and 0.06 kmoFs, respectively. The simulation is run giving a bottoms composition of 21 mol% benzene and 7 X 10 mol% water in the first column. The water is driven overhead, but there is too much 

TABLE 5.1 Effect of Changing Reflux Elow Rate 

Reflux (kmol/s) Bottoms Composition (mol% B) Bottoms Composition (mol% W) Notes 

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From a simulation point of view, the two thermal couples introduce two recycles.. In this case, recycles introduces two complications 1. Good initial values are needed to converge the flowsheet, and 2. The time to converge the flowsheet considerably increases. It would be possible to decompose the system in individual columns and develop a kriging for each column, but the dimensionality of the kriging model would be larger, because we would have to deal with the recycles explicitly. Therefore, it is better to keep the divided wall column as an entity that can be efficiently substituted by a kriging metamodel. 

Partially converge the flowsheet, a less stringent recycle tolerance, for the intermediate adjusted variable values. 

This process has the particularity of the recycle. To help converge the flowsheet, it is convenient to tear the recycle stream and compute the exit of compressor 10 as a product and a new feed so that the systems are initialized (see Figure 8.42). 

The presence of inerts in the ternary systems requires a different method for converging the flowsheet. The impurity levels in both the bottoms and distillate streams are not known and change as design parameters change. The bottoms, which are 98 mol% C, can have impurities of any of the other three components A, I, or B. The distillate, which is mostly I, can have impurities of either A or B. 

The older modular simulation mode, on the other hand, is more common in commerical applications. Here process equations are organized within their particular unit operation. Solution methods that apply to a particular unit operation solve the unit model and pass the resulting stream information to the next unit. Thus, the unit operation represents a procedure or module in the overall flowsheet calculation. These calculations continue from unit to unit, with recycle streams in the process updated and converged with new unit information. Consequently, the flow of information in the simulation systems is often analogous to the flow of material in the actual process. Unlike equation-oriented simulators, modular simulators solve smaller sets of equations, and the solution procedure can be tailored for the particular unit operation. However, because the equations are embedded within procedures, it becomes difficult to provide problem specifications where the information flow does not parallel that of the flowsheet. The earliest modular simulators (the sequential modular type) accommodated these specifications, as well as complex recycle loops, through inefficient iterative procedures. The more recent simultaneous modular simulators now have efficient convergence capabilities for handling multiple recycles and nonconventional problem specifications in a coordinated manner. 

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... 

At this point all the units in the flowsheet are installed and converged. The last issue is to converge the recycle stream. The initial guessed values are adjusted to be close to the calculated values of flow and composition leaving the split S1. When these two streams are fairly close, the source of the recycle stream is defined as the split SI and the recycle stream is defined as a Tear stream. The flowsheet did not converge when the default convergence method... 

Wegstein) was used. Switching to the Broyden method successfully converged to flowsheet. Figure 6.97 gives the temperature and composition profiles in the two reactors. 

Process design for continuous processes is carried out mostly using steady-state simulators. In steady-state process simulation, individual process units or entire floivsheets are calculated, such that there are no time deviations of variables and parameters. Most of the steady-state floivsheet simulators use a sequential modular approach in which the flowsheet is broken into small units. Since each unit is solved separately, the flowsheet is worked through sequentially and iteration is continued until the entire flowsheet is converged. Another way to solve the flowsheet is to use the equation oriented approach, where the flowsheet is handled as a large set of equations, which are solved simultaneously. 

As a final step, the binary ethanol-water underflow from the second column may be opportunistically separated to produce a pure water underflow and a composition close to the original feed to which it also may be recycled. The amount of extractive entrainer must now be readjusted because of the increased amount of feed to the first column, but iteration shows that the flowsheet structure generated remains unchanged and has converged. The tasks specified accomplish the composition goals, producing pure water and pure ethanol. The entrainer remains totally within the system. The subsequent integration into equipment involves three columns and one decanter (Fig. 29). 

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. 

For a sequential-modular simulation program to be able to solve a flowsheet with a recycle, the design engineer needs to provide an initial estimate of a stream somewhere in the recycle loop. This is known as a tear stream, as the loop is torn at that point. The program can then solve and update the tear stream values with a new estimate. The procedure is repeated until the difference between values at each iteration becomes less than a specified tolerance, at which point the flowsheet is said to be converged to a solution. 

The choice of tear stream can have a significant impact on the rate of convergence. For example, if the process of Figure 4.39 were modeled with a yield-shift reactor, then tearing the flowsheet at stream 5 would probably give faster convergence. Some of the simulation programs automatically identify the best tear stream. 

If one or more unit operations have been given infeasible specifications, then the flowsheet will never converge. This problem also occurs with multicomponent distillation columns, particularly when purity specifications or flow rate specifications are used, or when nonadjacent key components are chosen. A quick manual mass balance around the column can usually determine whether the specifications are feasible. Remember that all the components in the feed must exit the column somewhere. The use of recovery specifications is usually more robust, but care is still needed to make sure that the reflux ratio and number of trays are greater than the minimum required. A similar problem is encountered in recycle loops if a component accumulates because of the separation specifications that have been set. Adding a purge stream usually solves this problem. 

Start by converging a simulation of the flowsheet. This helps the designer detect errors, ensures that specifications are feasible, and provides good estimates for tear streams. 

Alternatively, closed-form model representations require a modular simulation approach, where each closed-form model is computed using the internal solver of the software tool the model is implemented in. The algorithm sets the model inputs, performs control over the simulation, and retrieves the outputs of each model through the commonly defined interface of the closed-form model representation, independently of the specific implementation. These outputs are propagated to the inputs of downstream units, and the simulation continues until all the units are computed. If the flowsheet contains recycles, an iterative strategy is performed until convergence of the flowsheet variables in tear streams is achieved. 

In the CRC scenario (cf. Sect. 1.2), CHEOPS [409], described in Subsect. 5.3.5, is used for the simulation of the overall PA6 production process. CHEOPS uses different existing simulation tools to carry out the overall process simulation by an a-posteriori runtime integration approach. The task of CHEOPS is to perform all partial simulations, each with the appropriate tool, to exchange simulation results between them, and to converge recycle streams which may occur in the flowsheet. 

Unit models are written to calculate output stream values, given input stream values and unit parameters. The recycle stream values are then calculated and checked against the estimated values for that iteration. If they agree within a tolerance, then the flowsheet has converged. This procedure is called tearing a recycle stream. The important questions for this approach are... 

For a design problem, converge the entire flowsheet (close all the recycles) for every intermediate value of the adjust variable. This is very expensive computationally and is a major drawback to the sequential modular approach. Alternative and sometimes faster approaches include... 

The simulation is successful when the convergence criteria are fulfilled both at the flowsheet and units level. The user should pay particular attention to convergence history for troubles shootings. Here the steps involved are ... 

The analysis of the computational sequence is recommended, even if this is found automatically. Selecting tear streams before key units, as reactors and separators, avoid severe failure and accelerate the flowsheet convergence. 

Degrees of freedom analysis is necessary but insufficient in converging a simulation. It is obvious that the number of specifications must match the available DOF s. Normally DOF analysis is done automatically. However, the specifications must be feasible not only at the unit s level, but also for the flowsheet as a whole. From this point of view some common mistakes could be identified as, (1) inconsistent specifications, or (2) interdependent specifications. 

Figure 3.31 displays a generic reactor/separator flowsheet. The reaction is bimolecular of type A+B -> P. Study the convergence properties of the flowsheet with respect to specifications for individual units. 

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-... 

Extract difficult units and make them converge separately. Generally, isolate convergence problems and treat it outside the flowsheet. 

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