A fully reliable and efficient adaptive control methodology has been long awaited in industry due to the time-varying nature of industrial plants. This paper demonstrates that this kind of adaptive solution is now available and simple to apply by presenting the first application of a methodology called Adaptive Predictive Expert (ADEX) Control in a petrochemical production unit. A description of the plant and the ADEX solution is followed by a comparative analysis of the results obtained with those of the existing conventional PID control. The objectives of the application involving the naphtha splitter at the Puertollano Refinery of Repsol were to establish the viability of ADEX in this environment, increase the quality of the naphtha products by achieving closer compliance with desired specification and maximizing the economic yield. To achieve these objectives it was necessary to enhance the stability of the naphtha splitter by improving control of the principal variables and eliminating a degree of interaction between them which was causing a resonance problem in the column. The application of the ADEX system confirm its viability, demonstrated a marked increase in column stability, significant improvements in levels of control and the elimination of the resonance problems