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Cryogenic air separation plants that produce argon in addition to oxygen and nitrogen use two heat-integrated distillation columns and a side rectifier. The dynamics of the side rectifier are very slow because of three factors:  the large number of separation stages, the small amount of argon in the air feed, and the high product purity. Currently, when the plant shuts down, the liquid inventory in the argon column drains into the upper (low-pressure) column. A normal start-up takes about 10 h to achieve argon product purity. The start-up time can be reduced significantly by using storage vessels to collect the liquid that drains from the argon column upon shutdown and reintroducing the liquid during the subsequent start-up. Compared to a 10 h start-up time with no collection points, the time required to achieve argon product purity is reduced to 3.35 h by using 2 collection points and is reduced to 2.23 h by using 6 collection points.

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Model quality is a key factor that affects the control performance of model predictive control. In this paper, a new closed-loop model assessment approach is proposed to assess model deficiency from routine closed-loop data. The proposed model quality index is a minimum variance benchmark for the model residuals obtainable from closed-loop data. From the feedback invariant principle the disturbance innovations at current instance are shown to be unaffected by the controller even if it is a nonlinear time-varying controller. Then it is shown that the disturbance innovations sequence can be estimated from closed loop data by an orthogonal projection of the current output onto the space spanned by past outputs, inputs or setpoints. With the disturbance innovations as the benchmark, a model quality index is developed by using the ratio of a quadratic form of model residuals and that of the estimated disturbance innovations. The effectiveness of the proposed methods is shown by simulation results.

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