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ii In this thesis we present a collocation method originally developed for minimum reflux calculations which is applicable to the flexible distillation design problem. Solvent recovery plants need to separate a wide range of mixed solvent streams into their pure components. To have a flexible distillation system, single columns must be able to handle multiple separation tasks. We address the design problem of a single flexible column model, successfully designing a column for an azeotropic system with different separation tasks for different feed streams. The collocation model incorporates two variable transformations which enable it to successfully model columns near pinch and columns with very high purities. With this model, the number of trays in each column section is a continuous variable, allowing us to optimize the column size and feed location. We developed the models in the ASCEND system, which we have found to be an excellent environment for model and design algorithm development