UBC Theses and Dissertations
The permeability and compressibility of semi-dilute pulp fibre suspensions : inversely solving the governing PDE of sedimentation Young, Edmond Wai Keung
This thesis discusses the development of a numerical tool for studying the permeability and compressibility of pulp fibres in sedimentation. The purpose is to determine the functional relationships of permeability and compressibility in the semi-dilute concentration regime of pulp suspensions. The first step in the approach to developing this numerical tool involves performing settling tests and obtaining experimental data by positron emission tomography (PET). By radioactively labelling select fibres, the mobility of certain fibre fractions can be detected using PET and changes in concentration throughout the settling suspensions can be shown over time. These results can be summarized into concentration profiles that represent a snapshot of the settling fraction at one instant in time. The next step is to obtain corresponding theoretical concentration profiles by numerical simulation. The settling process of a suspension in a vertical column is governed by a time-dependent one-dimensional partial differential equation. This PDE is derived by assuming the suspension is a superimposed continuous porous medium governed by permeability and compressibility functions that describe the physical behaviour of the suspension. The PDE can be solved numerically by suitable discretization of the spatial domain and stable advancement of the time-dependent solution. Once solved, the solution to the settling process can again be represented by a series of concentration profiles. Since the PDE is governed by permeability and compressibility functions, a good match between experimental and theoretical concentration profiles reveals the correct functions for a given fibre fraction within the suspension. For known functional forms of permeability and compressibility, this reduces to a parameter fitting exercise. The optimal set of parameters is found by numerically comparing the match between results using the sum-of-squares method to measure overall discrepancy. Final comparison be tween experimental and numerical profiles reveals a good fit between results and shows that the parameter fitting procedure is successful in determining the desired functions of permeability and compressibility.
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