A generalized, steady-state model is proposed for predicting brightness and/or bleach consumption during chlorine dioxide brightening (D1 and D2) for softwood pulps treated with chlorine dioxide delignification sequences. The model is adapted from the D1 hardwood model of McDonough and co-workers, which related chlorine dioxide consumption to brightness gains with three tunable parameters. Literature data from various Elemental Chlorine-Free (ECF) bleaching studies were analyzed to find generalized relationships for the models' parameters. Data analysis revealed that the ultimate brightness limits for both D1 and D2 models, at excessively high bleach charges, was ～92% ISO. Another parameter for the D1 model was found to be a linear function of extracted kappa number, whereas for the D2 model, the parameter was a linear function of pre-D2 brightness. The third equation parameter for the D1 and D2 models was found to be a function of the other two parameters and the entering brightness value. The generalized brightening models predict D1 brightness to ±1% ISO units and D2 brightness to ±0.3% ISO units for a given amount of chlorine dioxide consumed. These relatively simple brightening models, which have a minimum number of equation parameters, can used in conjunction with other bleaching delignification models to simulate chemical consumption for a given ECF sequence.
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