Fiber energy efficiency Part I: Extended entropy model

This is the first in a series of papers presenting the development of a comprehensive multiscale model with focus on fiber energy efficiency in thermo mechanical pulp processes. The fiber energy efficiency is related to the defibration and fibrillation work obtained when fibers and fiber bundles interact with the refining bars. The fiber energy efficiency differs from the total refining energy efficiency which includes the thermodynamical work as well. Extracting defibration and fibrillation work along the radius in the refining zone gives information valuable for fiber development studies. Models for this process must handle physical variables as well as machine specific parameters at different scales. To span the material and energy balances, spatial measurements from the refining zone must be available. In this paper, measurements of temperature profile and plate gaps from a full-scale CD-refiner are considered as model inputs together with a number of process variables. This enables the distributed consistency in the refining zone as well as the split of the total work between the flat zone and the CD-zone to be derived. As the temperature profile and the plate gap are available in the flat zone and the CD-zone at different process conditions it is also shown that the distributed pulp dynamic viscosity can be obtained. This is normally unknown in refining processes but certainly useful for all fluid dynamic models describing the bar-to-fiber interactions. Finally, it is shown that the inclusion of the machine parameters will be vital to get good estimates of the refining conditions and especially the split between the thermodynamical work and the defibration/fibrillation work