In this work, we present the modeling, optimization, and conceptual design of a dividing wall column for the separation of four products, commonly referred to in the literature as a Kaibel column, by implementing three different formulations: an NLP, an MINLP, and a GDP formulation. For its solution, we propose a rigorous tray-by-tray model and compared it to results from a commercial software, followed by its reformulation to include a mixed-integer nonlinear programming and a general disjunctive programming formulation to respond to the conceptual design problem attached to these complex configurations. Considering the proposed rigorous model and the two formulations, the Kaibel column is solved, obtaining four high-purity products and new optimal tray locations for the feed and two side product streams, when the mixed-integer nonlinear programming formulation is applied. The use of these optimally located side streams showed reductions in the energy consumption when compared to cases were non-optimal fixed tray locations are used. When the general disjunctive programming problem was solved, the minimum number of trays needed in the main column and dividing wall are obtained, showing a great reduction of the remixing effects in the Kaibel column, and with that, a more energy efficient configuration. The models were coded in Pyomo using the solver IPOPT for the solution of the nonlinear programming problem, the solver Bonmin for the solution of the mixed-integer nonlinear programming problem, and GDPopt for the solution of the general disjunctive programming optimization problem. (C) 2019 Elsevier Ltd. All rights reserved.