A lumped parameter model of an industrial HDPE reactor is presented. Discontinuity in the mode of operation makes either a set of 15 DAEs or a set of 12 DAEs applicable to this system at any instant. The reactor switches back and forth from one model to another reaching a time averaged steady state. The DAEs are integrated by DASSL. Using the Box-Complex procedure, the sum of squares of errors between plant data and model prediction is minimised and the model tuned. The tuned parameters agree with the literature values. Sensitivity analysis of the model shows that manipulation of pressure will yield a faster change in the reactor conditions as compared to manipulating the catalyst feed rate.