(734g) Finite Element Modeling and Optimization of Heat Exchangers

The rise in energy demand throughout the globe calls for
more energy efficient design using process intensification techniques. These
designs require solving complicated steady state models describing the physical
phenomenon happening inside the system. One of the most important and
well-researched aspects of chemical plant design are heat exchangers, yet these
are currently designed under the assumption that the physical properties of the
streams remain constant inside the heat exchanger. This assumption breaks down
significantly under phase change as liquid and vapor phase properties vary
drastically and non-smoothly. Lack of a priori knowledge of where the
phase transition occurs inside the heat exchanger posts a serious problem for
the solution algorithms. This complexity is compensated by adding safety
factors that lead to inefficient and over-design of heat exchangers thus
decreasing the energy efficiency of the whole process.

In this work, a new optimization framework for heat
exchanger design is presented that can solve the difficulty of non-smooth
nature resulting from phase change inside the heat exchanger. With this in
mind, we describe a discretized finite element structure [1], which can be used
as a candidate heat exchanger model for large-scale process design problems
including phase change. We model the non-smooth nature of phase-change using
complementarity constraints [3] that are relaxed and solved iteratively until
an acceptable tolerance level is achieved. The discontinuity in heat transfer
coefficient arising from the huge difference in latent and sensible heat
transfer is described by a smooth approximation. We apply the proposed model by
designing heat exchangers in a single-stage and multi-stage Vapor Compression
Refrigeration (VCR) cycle with R-152a (1,1-Difluoroethane) as the refrigerant.
The VCR cycle subject to complementarity and process constraints with around
4000 variables and constraints is modeled as a non-linear program (NLP) in AMPL
and solved using IPOPT [2]. The intricacies of the model along with initialization
and the results from the optimization will be presented. Extensions to modeling
the system dynamics and solving it using optimization solvers will be
discussed.

[1] Ravikumaur, S.G., Seetharamu, K.N. and Aswatha Narayana,
P.A., Finite element analysis of shell and tube heat exchanger, International
Communications in Heat and Mass Transfer, Volume 15, Issue 2, Pages
151-163,(1986)

[2] Wächter Andreas, Biegler L.T., On the implementation of
an interior-point filter line-search algorithm for large-scale nonlinear
programming, Mathematical Programming, Volume 106, Issue1, Pages 25-57,(2006)

[3] B.T. Baumrucker, L.T. Biegler, MPEC strategies for
optimization of a class of hybrid dynamic systems, Journal of Process Control,
Volume 19, Issue 8, Pages 1248-1256(2009)