This study considers the Nonlinear Autoregressive eXogenous Neural Net model (NARX NN) based real-time optimization (RTO) for industrial-scale air & gas compression system in a commercial terephthalic acid manufacturing plant. NARX model is constructed to consider time-dependent system characteristics using actual plant operation data. The prediction performance is improved by extracting the thermodynamic characteristics of the chemical process as a feature of this model. And a systematic RTO method is suggested for calculating an optimal operating condition of compression system by recursively updating the NARX model. The performance of the proposed NARX model and RTO methodology is exemplified with a virtual plant that simulates the onsite commercial plant with 99.6% accuracy. NARX with feature extraction model reduces mean squared prediction error with the actual plant data 43.5% compared to that of the simple feed-forward multi-perceptron neural networks. The proposed RTO method suggests optimal operating conditions that reduce power consumption 4%.