(377b) Finding Globally Optimal Minimum Heat Duty for Multicomponent Distillation Sequences
We seek to identify an array of energy-efficient distillation sequences among the hundreds of possible configurations. Towards this end, we minimize, for each configuration, the heat duty requirement which is proportional to its total vapor duty requirement. Since the total vapor duty requirement can be easily computed from the stream flow rates using Underwood's equations, the goal is then to identify the optimal stream flow rates. In prior work, the ?minimum? heat duty of a multicomponent distillation sequence has often been found by minimizing the heat duties of individual distillation columns in a sequential manner. With this approach, one assumes the validity of transition (preferred) split calculations and as a result no optimization is required. We show that, although this technique yields the minimum heat for certain multicomponent distillation sequences, this is not the case for all the sequences. Furthermore, the approach does not extend to distillation sequences with side draw streams and thermally coupled streams. Therefore, in general, the analytical solution approach via transition split calculations falls short and the use of optimization techniques is necessary to identify the correct stream flow rates.
In this work, we formulate the problem of identifying the optimal stream flow rates as a mathematical program. The nonlinearity inherent in the Underwood's equations makes it challenging to identify the globally optimal values for the stream rates quickly and necessitates the use of nonlinear programming (NLP) techniques for its solution.
We address the challenge by first reformulating the nonlinear program using bilinear and fractional expressions. Then, we use the branch-and-bound algorithm to identify the globally optimal stream flow rates. We use physical insights to improve the convergence of the algorithm. As a consequence, we provide a list of the entire set of distillation configurations ordered according to their vapor duty requirement thereby making it possible to identify energy-efficient configurations.