# Spectral Solutions of a Combined Multifluid--population Balance ModelDescribing Bubbly Flow - A Numerical Study of weighted Residual Methods

### Hugo A. Jakobsen, Jannike Solsvik

#### Abstract

Fluid particle breakage and coalescence phenomena are important for optimal operation for industrial process units like the bobble column reactors. The population balance equation (PBE) can be applied to describe the evolution of populations of countable entities such as the bubbles in the bubble column. In recent literature, the least-squares methods has been adopted for the approximate solution of population balance (PB) models. Adopting a weighted residual method such as the least-squares method, the distribution function resolved instead of obtaining only a few moments of the distribution function. The performance of the least-squares method for PB problems should be compared to other techniques in the family of weighted residual methods. The aim of the present study is to evaluate the orthogonal collocation, tau and last-squares methods for the solution of a combined multifluid-PB model describing bubbly flows.

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#### Paper Citation

#### in Harvard Style

Jakobsen H. and Solsvik J. (2013). **Spectral Solutions of a Combined Multifluid--population Balance ModelDescribing Bubbly Flow - A Numerical Study of weighted Residual Methods** . In *Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,* ISBN 978-989-8565-69-3, pages 102-107. DOI: 10.5220/0004477401020107

#### in Bibtex Style

@conference{simultech13,

author={Hugo A. Jakobsen and Jannike Solsvik},

title={Spectral Solutions of a Combined Multifluid--population Balance ModelDescribing Bubbly Flow - A Numerical Study of weighted Residual Methods},

booktitle={Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,},

year={2013},

pages={102-107},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0004477401020107},

isbn={978-989-8565-69-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SIMULTECH,

TI - Spectral Solutions of a Combined Multifluid--population Balance ModelDescribing Bubbly Flow - A Numerical Study of weighted Residual Methods

SN - 978-989-8565-69-3

AU - Jakobsen H.

AU - Solsvik J.

PY - 2013

SP - 102

EP - 107

DO - 10.5220/0004477401020107