Computers and Chemical Engineering 25 (2001) 1661 – 1673 A disjunctive programming approach for the optimal design of reactive distillation columns Jennifer R. Jackson, Ignacio E. Grossmann * Department of Chemical Engineering, Carnegie Mellon Uniersity, Pittsburgh, PA15213, USA Received 31 January 2001; received in revised form 3 August 2001; accepted 6 August 2001 Abstract A generalized disjunctive programming formulation is presented for the optimal design of reactive distillation columns using tray-by-tray, phase equilibrium and kinetic based models. The proposed formulation uses disjunctions for conditional trays to apply the MESH and reaction kinetics equations for only the selected trays in order to reduce the size of the nonlinear programming subproblems. Solution of the model yields the optimal feed tray locations, number of trays, reaction zones, and operating and design parameters. The disjunctive program is solved using a logic-based outer-approximation algorithm where the MILP master problem is based on the big-M formulation of disjunctions, and where a special initialization scheme is used to reduce the number of initial NLP subproblems that need to be solved. Two examples are presented that include reactive distillation for the metathesis reaction of 2-pentene and for the production of ethylene glycol. The results show that the proposed method can effectively handle these difficult nonlinear optimization problems. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: Reactive distillation; Disjunctive programming; Optimal distillation column design Nomenclature The continuous ariables for the model constraints are defined as follows : molar feed flow of component i on tray k F k i DIS total molar flow of distillate total molar flow of bottoms BOT total number of trays NT STG k counter for the existence of a tray LIQ k total molar flow of liquid out of tray k total molar flow of vapor out of tray k VAP k molar liquid flow of component i out of tray k L k i V k i molar vapor flow of component i out of tray k H k height of tray k liquid mole fraction of component i out of tray k x k i vapor mole fraction of component i out of tray k y k i  boil-up fraction reflux fraction R reboiler heat load QB www.elsevier.com/locate/compchemeng * Corresponding author. Tel.: +1-412-268-2230; fax: +1-412-268-7139. E-mail address: grossmann@cmu.edu (I.E. Grossmann). 0098-1354/01/$ - see front matter © 2001 Elsevier Science Ltd. All rights reserved. PII:S0098-1354(01)00730-X