Abstract
A population balance equation was solved by combining the Lax-Wendroff and Crank-Nicholson methods. The population balance was used in the simulation of an evaporative cooling crystallizer with fines dissolution. The stability of the method, along with that of the Lax-Wendroff and Crank-Nicholson methods alone, was compared under different operating and initial conditions. When tested under conditions of uninterrupted growth to steady state, it was found that the three methods produced virtually identical final crystal size distributions (CSDs), though the Lax-Wendroff and Crank-Nicholson methods showed some oscillatory behaviour early on. Under dissolution conditions, only the combined Lax-Wendroff/Crank-Nicholson method proposed in this paper produced a population density that steadily reduced to zero. The Lax-Wendroff method became unstable, while the Crank-Nicholson method became extremely oscillatory. Under dynamic conditions, both the Lax-Wendroff and Crank-Nicholson methods showed some oscillations that did not affect the ultimate CSD. The combined Lax-Wendroff/Crank-Nicholson method showed no oscillations in any case, producing smooth dynamic and steady state CSDs.
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