In this paper, we propose a disjunctive formulation for the simultaneous chemical process optimization and heat integration with unclassified process streams -streams that cannot be classified a priori as hot or cold streams and whose final classification depend on the process operating conditions-, variable inlet and outlet temperatures, variable flow rates, isothermal process streams, and the possibility of using different utilities. The paper also presents an extension to allow area estimation assuming vertical heat transfer. The model takes advantage of the disjunctive formulation of the 'max' operator to explicitly determine all the 'kink' points on the hot and cold balanced composite curves and uses an implicit ordering for determining adjacent points in the balanced composite curves for area estimation. The numerical performance of the proposed approach is illustrated with four case studies. Results show that the novel disjunctive model of the pinch location method has excellent numerical performance, even in large-scale models. (C) 2017 Elsevier Ltd. All rights reserved.