Process simulation convergence

Kliesch, H. C., "An Analysis of Steady State Process Simulation Formulation and Convergence", PhD Thesis in Chemical Engineering, Tulane University, 1967. 

Simultaneous Convergence Methods One drawback of some tearing methods is their relatively limited range of application. For example, the BP methods are more successful for distillation, and the SR-type methods are considered better for mixtures that exhibit a wide range of (pure-component) boiling points (see, however, our remarks above on modified BP and SR methods). Other possible drawbacks (at least in some cases) include the number of times physical properties must be evaluated (several times per outer loop iteration) if temperature- and composition-dependent physical properties are used. It is the physical properties calculations that generally dominate the computational cost of chemical process simulation problems. Other problems can arise if any of the iteration loops are hard to converge. 

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. 

The methods used to converge recycle loops in the commercial process simulation programs are similar to the methods described in Section 1.9. Most of the commercial simulation programs include the methods described below. 

If a flowsheet is not converged, or if the process simulation software runs and gives a statement converged with errors, then the results cannot be used for design. The designer must take steps to improve the simulation so that a converged solution can be found. 

When there are multiple recycles present, it is sometimes more effective to solve the model in a simultaneous (equation-oriented) mode rather than in a sequential modular mode. If the simulation problem allows simultaneous solution of the equation set, this can be attempted. If the process is known to contain many recycles, then the designer should anticipate convergence problems and should select a process simulation program that can be run in a simultaneous mode. 

When the values above for nitrous oxide, organic waste, and aqueous waste are entered in the spreadsheet, the mass balance shows 101 MT of product for every 100 MT of feed. This is not perfectly closed but is good enough at this stage in the analysis. The error is most likely in the organic or aqueous waste streams and will have little impact on the economic analysis. This should, of course, be revisited when better process yield data and a converged process simulation are available. 

The use of simulation software to analyze this type of process is illustrated in Example 5, which considers a simplified ternary system for illustration. The simulation of an actual aromatics extraction process is more complex and can exhibit considerable difficulty converging on a solution however. Example 5 illustrates the basic considerations involved in carrying out the calculations. For more detailed discussion of process simulation and optimization methods, see Sei-der, Seader, and Lewin, Product and Process Design Principles Synthesis, Analysis, and Evaluation, 2d ed. (Wiley, 2004) and Turton et al.. Analysis, Synthesis, and Design of Chemical Processes, 2d ed. (Prentice-Hall, 2002). 

Many process simulators use this procedure because it is quite easy to implement. You only need to have a module or subroutine for a mixer, a reactor, and a separator, and the equations for each of these are quite simple. One problem that arises, though, is that the procedure takes many iterations to converge if the conversion is low. And, if there are interlocking recycle streams, convergence may not occur at all. However, it is quite a good scheme, and you can apply it using a spreadsheet. 

When modeling mass transfer equipment, there are two key points to remember (1) thermodynamics is important and (2) convergence is difficult. The corollary is that you have to compare your thermodynamic predictions with experimental data. Also, you may start with ideal thermodynamics and obtain a solution. This solution can then be used as the initial guess when the thermodynamic model is more realistic. Process simulators do not always work, so you need to be flexible about how you approach a problem. 

The inlet stream is compressed to 4000 psi with an isentropic compressor. The stream is mixed with the recycle stream and heated to 900°F, the reactor temperature. In the reactor, there is a pressure drop of 30 psi. The outlet is cooled to 80 F and the liquid and vapor phases are separated. The vapor phase goes to recycle, and 0.01 percent of it is used as purge. A recycle compressor then compresses the rest from 3970 to 4000 psia. In a real process, the heat transfer to preheat the feed to the reactor uses the effluent from the reactor, usually inside the same vessel. In process simulators, though, it is useful to begin as shown in Figure 7.1 to help convergence. NRTL thermodynamics was chosen and is justihed a posteriori. 

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