Estimating lags in a kraft mill.

In pulp mills, lags obscure the effect of upstream operations on downstream measurements. Here, we estimate lags in a Canadian pulp mill using autoregressive exogenous (ARX) models. First, we show that ARX models can approximate lags in a process simulation that resembles the liquor storage tanks in pulp mills, a major source of lag in the kraft recovery cycle. Then, we use ARX models to estimate the lagged effect of a change in species pulped on as-fired liquor heating value, viscosity, and boiling point rise. Additionally, we compare the predictions of the ARX models to autoregressive (AR) models and a persistence model. The estimated lags between a change in species and heating value (49 h) and boiling point rise (41 h) agree with a detailed simulation of the mill and are close to estimated hydraulic residence times, suggesting that the liquor tanks exhibit imperfect mixing. A lagged effect of species change on viscosity could not be identified. ARX and AR models produce similar predictions that are slightly better than those of a persistence model. Finally, we show that process measurements upstream of units characterized by large residence times will likely provide little benefit to prediction accuracy.