Ph.D student Atle Christer Christiansen

Status

I started my doctoral studies in march 1994 under the supervision of Professor Sigurd Skogestad and plan to finish within the end 1997. My doctoral work is financed by the NFR-supported project on computer aided process engineering.

Research area

The working title of my Ph.D. is ``Studies on Dynamics and Control of Integrated Plants'', in which the main objectives and aims are to contribute towards a greater understanding of the dynamic behavior of integrated plants. By integrated plants we understand here processes that are interconnected either in series or in parallel, or simpler processes that involve material recycle or heat integration.

In terms of research activities I finished a paper on dynamics of batch distillation columns with emphasis on parametric sensitivity. We showed that columns operated under high reflux and with mass inputs may become very sensitive to small changes in some operating parameters. The effects may be dramatic if the potential sensitivity is not considered during operation and without proper feedback mechanisms. I also did some work on numerical methods for solving systems of nonlinear algebraic equations (NAE's), in which I compared a homotopy- continuation algorithms with a novel tear and grid method. We addressed some inherent problems that often arise in using homotopy methods, and simple remedies were suggested. We further showed that combining conventional techniques for solving NAE's with the addition of making a grid of the tear variables, offers large savings with respect to both implementation effort and computational cost. The potential benefit in computational efficiency is due to avoiding costly iterative scheme, since it is possible to reduce the systems of NAE's to linear subsets which allows for explicit solutions. I also started working within the promising area of reactive distillation. I've up to the present date considered some simple models in order to explore the steady state behavior of such systems. In the future we will address more rigorous models and also look into designs of more complex columns such as the reactive petlyuk column.

During 1995, I also finished my course work with the completion of the following:

• Multivariable frequency analysis
• Dynamical systems
• Mathematical modelling and model fitting

Activities

• Received a stipend from ``Norges Forskningsraad'', for which I stayed a prolonged period at the University of California at Berkeley, USA, and at the University of Aachen (RWTH), Germany.
• Presented the work on dynamics of batch distillation columns at the HCM workshop in Stuttgart, July 1995, at the NPC Workshop in Aaland, August 1995. The work was also presented by Sigurd Skogestad at the AIChE annual meeting in Miami, November 1995.
• Co-advised the diploma work of Gunnar Østgaard on ``Reactive Distillation''
• Organized the excersizes for the process control course at the Chemical Engineering department
• Organized a project work for the process control course, consisting of ca. 15 example processes in which the students were supposed to (i) Derive dynamic models and comment on the qualitative dynamics (ii) Implement dynamic models in MATLAB for dynamic simulation (iii) Implement simple control strategies (SISO) for simulation in MATLAB

Publications

• Christiansen, A. C., E. W. Jacobsen, J. D. Perkins and S. Skogestad. ``On the Dynamics of Batch Distillation : Parametric Sensitivity in Ideal Binary Columns'', presented at AIChE Annual Meeting 1995, Miami, USA
• Christiansen A. C., J. Morud and S. Skogestad. ``A Comparative Analysis of Numerical Methods for Steady State Analysis : Tear and Grid Approach or Homotopy Continuation''. Unpublished

Plans for 1996

During 1996, I hope to publish at least the work on batch distillation and perhaps the study on numerical methods, in an international journal. I will further continue the work on reactive distillation and in particular establish a rigorous model suitable for studies on dynamics and control. I may also start analyzing the novel concept of reactive petlyuk distillation, for which there at present does not exist any literature. I also plan to spend some time at the Center of Process Systems Engineering at Imperial College in London. The objective of this stay is primarily to learn how to use a computer software tool recently developed at the center, but also to discuss some of the issues of my work with the research groups at the centre.