Abstract
In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the efficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.
Highlights
Population balance models (PBMs) show a significant role in different areas of science and engineering
The Quadrature Method of Moments (QMOM) for solving the governed models was first introduced by McGraw [12]
The moment-generating function was used to convert the governing partial differential equation moment-generating function was used to The convert the governing partial differential equation into aThe system of ordinary differential equations
Summary
Population balance models (PBMs) show a significant role in different areas of science and engineering These models have numerous applications in high-energy physics, geophysics, biophysics, meteorology, pharmacy, food science, chromatography, chemical engineering, civil engineering, and environmental engineering. The Quadrature Method of Moments (QMOM) for solving the governed models was first introduced by McGraw [12]. Qamar et al [13] introduced an alternative QMOM for solving length-based batch crystallization models telling crystals nucleation, size-dependent growth, aggregation, breakage, and dissolution of small nuclei below certain critical size. The QMOM is used to solve volume-based batch crystallization models with fines dissolution. Orthogonal polynomials, taken from the lower-order moments, are used to find the quadrature points and weights. The mathematical outcomes of QMOM are compared with the analytical outcomes that are accessible in literature
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