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Stock Flow Modelling

Stock Flow Modelling

Gary M. Scott, Ph.D.

Faculty of Paper and Bioprocess Engineering
Empire State Paper Research Institute

State University of New York, College of Environmental Science and Forestry


Stock preparation systems for recycled paper and machine approach systems need to be designed to produce a high quality, uniform product from a source that has highly varying properties. In addition, water use and losses must be carefully monitored to properly use the natural resources and protect the environment. Process models are a useful tool for analyzing and optimizing stock preparation systems. However, many models only account for the bulk flows of the components in the system and do not consider the dynamic nature of the process. This work would extend some of these concepts to include these ideas. For example, the fiber fraction can be treated as a distribution based on the fiber length, diameter, coarseness, or composition. The contaminant concentration can be expressed as a function of both the particle size and density.

Modelling of the size distributions of the flow of the components is important because the efficiencies of the unit op-erations depend on these parameters. Modelling in this manner allows the sys-tems to be designed to remove certain sizes of particles. The model can also be used to evaluate an existing process if the distribution of contaminants in the feedstock should change over time. Dynamic modelling demonstrates the effect of disturbances on the system. Because of the multiple recycle loops in these systems, disturbances may take a great deal of time to work their way through the system. By changing the configuration, the effect of these disturbances may be reduced. Furthermore, different control schemes can be implemented and evaluated in the modelling system.

Current Work

Our initial work will be to investigate statistical techniques for the analysis of fiber length distributions such as those obtained from a Kajaani Fiber Length Analyzer. Statistical analysis of distributions is well developed for normal (bell-curve) distributions; however, fiber lengths area typically not normally distributed. For this work, appropriate transforms for the fiber length distributions to normal distributions will need to be developed. In the case of mechanical pulps, the lognormal distribution is often appropriate as has been discussed in the literature. After transformation, methods will be developed to statisti-cally analyze the distributions using the large body of statistical knowledge built up around normal distributions. These distributions will them be used as the basis of future process models or in statistical process control applications. A better understanding of the fiber length distributions will aid in the prediction of the resulting paper properties from pulp characteristics.

Continuing work work begin building dynamic models of recycling and papermaking systems. The unit operations of the system would be modelled as input-output blocks that are dynamic in nature. That is, they would allow for time varying input and outputs. For recycling systems, some of the important unit operations to be modelled include dilution, mixing, holding tanks, and the various separation processes such as screens, cleaners, washers, and flotation cells. The mathematical structure of these operations would be based on literature models of the processes. Alternatively, empirical models could be developed for specific pieces of separation equipment. These unit operations could then be combined into flowsheets for the modelling of entire systems.

The major objectives of this research are:

  1. to develop statistical analysis techniques for the components of stock flow systems;
  2. to develop process models that are dynamic in nature in order to investigate the effect of disturbances in fiber quality and contaminant levels on the final product and water loops of the process;
  3. to develop process models that include distributions of the various components based on properties important to that component;
  4. to incorporate these models into control algorithms for pulp and paper operations.


Mr. Vincent Barber
Graduate Student
Empire State Paper Research Institute
SUNY-College of Environmental Science and Forestry
Syracuse, NY

Key Publications

  1. Scott, Gary M. (1995). "Distribution Modelling of Stock Preparation Systems for Recycled Fibers," In Proceedings of the 1995 Tappi Recycling Symposium , Atlanta, GA: Tappi Press. pp. 327-334. (PDF)

Copyright 2001, Gary M. Scott. All rights reserved.