(111a) Rate-Based Column Simulation in the Complex Domain

The models used by engineers to simulate and design distillation and related column operations consist of large numbers of non-linear algebraic equations. Chemical engineers have been developing computer-based methods to solve these equations since the 1950s. Only limited progress has been made in the last 25 years or so, however, probably due largely to the widespread availability of mostly reliable commercial simulation programs.

Our experience, however, is that engineers are always pushing for improvements in process design and operation and this now is leading to increasing stress on the computational methods used to solve column models and an increasing rate at which simulations fail.

One of the most interesting and original innovations in process simulation was proposed by Angelo Lucia in the early 1990s; carry out the computations in the complex domain. The advantages of doing so were demonstrated in a series of papers written by Lucia and his coworkers (which, full disclosure, occasionally included the second author of this paper) (see references for details). The disadvantage includes increased computational time, and moderately increased effort required in programming the model.

Taylor et al. (1996) took Lucia’s original idea and used it to equilibrium-stage column simulation problems. Among other findings was the fact that for some cases there exist complex domain solutions to the model equations. More importantly, it was demonstrated that otherwise difficult cases could be solved easily while using the complex domain and that the solution could still be mathematically real and, therefore, physically realizable as well.

That paper and the thesis by K. Achuthan on which it was based presented solutions for only 3 columns and all were done using equilibrium stage models. No other examples were attempted at that time, or, so far as we know, since.

More recently, rate-based or non-equilibrium stage models have become quite widely used and sometimes they pose significant convergence difficulties, most particularly at high pressure, a situation we encounter more and more frequently. However, until now, nobody, to the best of our knowledge, has attempted to solve the non-equilibrium stage model in the complex domain, despite the considerable promise that such a method can offer.

This changes now; we have made a version of the simulation program ChemSep to conduct column simulation problems in the complex domain. In particular, we use a complex domain code to solve rate-based column models. This paper outlines the techniques and demonstrates that solutions can be obtained significantly more easily under some circumstances where computations carried out in the real-domain experience considerable difficulty.

References

1. Lucia, A., Guo, X., & Wang, X. (1993). Process simulation in the complex domain. AIChE journal, 39(3), 461-470.
2. Taylor, R., Kooijman, H. A., & Hung, J. S. (1994). A second generation nonequilibrium model for computer simulation of multicomponent separation processes. Computers & chemical engineering, 18(3), 205-217.
3. Taylor, R., Achuthan, K., & Lucia, A. (1996). Complex domain distillation calculations. Computers & chemical engineering, 20(1), 93-111.
4. Lucia, A., & Taylor, R. (1992). Complex iterative solutions to process model equations. Computers & chemical engineering, 16, S387-S394.