(120c) A Fresh Look at Underwood's Method

Energy consumption in the chemical and petrochemical industries is dominated by distillation. However, distillation is still the most versatile means of separation and will continue to be used in some capacity to address a wide variety of separation needs. With the rising cost of energy, there is renewed interest in the design and/or retrofit of energy efficient processes so that the end products are more cost effective.

Despite its limitations, Underwood's method remains a widely used tool for determining minimum energy needs in distillation ? largely because it is straightforward and gives good results in many situations. Recently our group has introduced a new methodology ? the concept of the shortest stripping line ? to determine minimum energy requirements for multicomponent separations involving ideal, nonideal, azeotropic and reactive mixtures. This new methodology can also determine minimum energy consumption for multi-unit processes like hybrid separations (e.g., distillation plus extraction) or reaction/separation/recycle.

This presentation centers on Underwood's method and its relationship to the concept of shortest stripping lines. In particular, the shortest stripping line approach is further extended for analyzing the sensitivities of column composition profiles, and in turn energy requirements, to distillation product compositions. Since Underwood's method is a group method and does not involve rigorous mass balance calculations, it cannot be used for this type of analysis. It is also well known that methods like the boundary value methods of Doherty and co-workers can show strong sensitivy to product compositions ? especially with regard to components present in trace amounts. As a result, feasibility difficulties can arise and marked differences in calculated energy use can result in boundary value methods. It is thereofre desirable to develop a method that finds the best product compositions so that the desired separation is met and minimum energy is used.

In this work, a methodology that combines a robust optimization technique with the shortest stripping line approach is proposed to address the problem of sensitivity of column composition profiles and energy requirements to specified product compositions. The overall strategy, which can be applied to mixtures with any number of components, involves two levels of optimization. In the inner loop, product compositions consistent with the desired separation are used as optimization variables to ensure feasibility while the stripping or reboil ratio is used as the optimization variable in the outer loop to minimize the associated energy requirements. A terrain-following method, which has also been developed in our group, is used for solving the resulting nonlinear programming problems. This two-level optimization methodology is applied to a variety of multicomponent distillations and detailed numerical results are presented to illustrate the robustness of our approach. These numerical results clearly show that our two-level optimization approach can be used to reliably find the best combination of components in the products so that the desired separation requires minimum energy and to quantify the relative sensitivities of column profiles to product compositions. Our numerical results are also compared and contrasted to results from Underwood's method.