Process simulation convergence methods

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. 

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. 

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). 

Modern process simulators (e.g. Aspen-Plus from AspenTech or ChemGad from Chemstations) simultaneously solve the MESH equations using algorithms based on Newton-Raphson methods (Gmehling and Brehm, 1996). However, for highly non-ideal or complex systems, modifications have been developed to enhance convergence behavior. 

Emphasis is placed in this chapter on the usage of process simulators to carry out the optimization simultaneously with converging the recycle loops and/or decision variables. To do the optimization efficiently, simulators use one of three methods (1) successive linear programming (SLP), (2) successive quadratic programming (SQP), and (3) generalized reduced gradient (GRG). Emphasis in this chapter is placed on SQP, used by ASPEN PLUS and HYSYS.Plant. GRG, which is used by CHEMCAD, is not discussed here, but is covered by Edgar et al. (2001). 

At this point, we would use these tenperatures to determine new K values and then repeat the matrix calculation and bubble-point calculations. To speed convergence, process simulators use more advanced methods for determining the next set of tenperatures (see Section 6.6V Obviously, with this amount of effort we would prefer to use a process simulator to solve the problem (see Problem 6.G1T The process simulator results for tenperature are generally higher than the tenperatures calculated in this exanple after one iteration except for Stage 1, which has a calculated tenperature that is too high. Also, since this system does not follow CMO, there is considerable variation in the flow rates. 

A number of methods to make the convergence schemes more stable have been developed and are employed in commercial process simulators. As a result, commercial simulators are quite robust, particularly if an appropriate method (bubble-point, sum-rates or Naphtali-Sandholm) is chosen and a good first guess has been used, although they occasionally still have difficulty converging. When there is a convergence difficulty, first check that the basic solution approach chosen appears to be appropriate. 

This appendix follows the instructions in the appendices to Chapters 2 and 6. Although the Aspen Plus simulator is referred to, other process simulators can be used. The three problems in this appendix all employ recycle streams in distillation columns. The procedures shown here to obtain convergence are all forms of stream tearing. Since these are not the only methods that will work, you are encouraged to experiment with other approaches. If problems persist while running the simulator, see Appendix A Aspen Plus Separations Troubleshooting Guide, at the end of the book. 

As a process simulator, we used Aspen HYSYS (see Figure 8.15). In all the scenarios, as initial values, we use the stream values obtained when the simulation is done in open loop. Moreover, instead of using the simnlator tools for converging the system (the recycle unit operation in HYSYS), we connect the simulator with external modules developed in MATLAB . In that way, we have a complete control over the numerical methods used for converging the system. In all the cases, a termination tolerance is eqnal to 10 , using a norm 1. 

Special attention was paid to the role of recycle streams in obtaining converged solutions, and methods to help convergence were discussed. The selection of thermodynamic models and their importance were discussed in depth. Finally, a case study for the toluene hydrodealkylation process given in Chapter 1 was given and the required data to complete a process simulation were presented. 

The simulation of an electronegative gas discharge converges much more slowly than that of an electropositive discharge. This is mainly caused by tbe slow evolution of the negative-ion density, which depends only on attachment (to create negative ions) and ion-ion recombination (to annihilate negative ions), both processes with a very small cross section. In addition to the common procedures adopted in the literature [222, 223, 272, 273], such as the null collision method, and different superparticle sizes and time steps for different types of particle, two other procedures were used to speed up the calculation [224]. 

But, computational difficulties can arise due to the iterative methods used to solve recycle problems and obtain convergence. A major limitation of modular-sequential simulators is the inability to simulate the dynamic, time dependent, behaviour of a process. 

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