Showing papers on "Population balance equation published in 1999"
TL;DR: In this paper, the authors developed a new methodology to analyse breakage and coalescence phenomena in bubble columns, and detailed measurements of the bubble-size distribution and the development of population balance equation (PBE) model were carried out.
113 citations
TL;DR: This mechanistic/semiempirical approach to fluid-bed agglomeration fosters an environment for process scaleup by eliminating specific equipment and process variable constraints to focus on the underlying mechanisms for proper scale-up procedures.
Abstract: Many agrochemicals are formulated as water dispersive granules through agglomeration, beginning with a fine powder (∼1 μm) and ending with granules on the order of 500 μm. Powders are charged into a granulation system with a liquid binding agent, and granules are subsequently grown to an appropriate size. Granulation in fluid beds is presented using a mass conserving discretized population balance equation. Coalesce kernels governing the rate and extent of granulation are assumed dependent on the Stokes number, which is indirectly linked to important process variables (air and binder flow rate, bed charge, bed geometry) such that the physical processes governing particle coalescence and rebound are correlated to process variables. A new coalescence kernel is proposed based on physical insight, simplicity, and deterministic equivalent modeling to account for uncertainty. This kernel is based on a Stokes number method where uncertainty in the Stokes number is characterized by polynomial chaos expansions. The magnitude of the coalescence kernel is proportional to the probability of the distribution of Stokes number exceeding a critical value. This mechanistic/semiempirical approach to fluid-bed agglomeration fosters an environment for process scaleup by eliminating specific equipment and process variable constraints to focus on the underlying mechanisms for proper scale-up procedures. Model predictions using this new kernel are then compared to experimental pilot-plant observations.
70 citations
TL;DR: In this article, a droplet population balance model is used to simulate the hydrodynamic behavior of solvent extraction columns in order to reduce the effort invested in experimental scale-up.
Abstract: A droplet population balance model is used to simulate the hydrodynamic behaviour of solvent extraction columns. This model describes the axial change of local column hold-up and local droplet size distributions caused by basic phenomena such as droplet rise, axial dispersion, and droplet break-up and coalescence. In order to reduce the effort invested in experimental scale-up, single droplet experiments were performed in small-scale laboratory devices. A Rotating Disc Contactor (RDC) with 5 compartments was used for this purpose. The single droplet movement is investigated by using a light source to reproduce the three dimensional particle trajectories on a two-dimensional screen. The resulting pictures are analysed by digital image processing. The experiments were performed for different droplet sizes under different agitation and throughput conditions. Droplet rise is found to slow down with increasing agitation whereas higher continuous phase throughput shows only a weak influence on the relative rising velocity. Simultaneously the axial dispersion coefficient decreases at higher agitation and continuous phase flow rates. Based on these single droplet parameters, the population balance equation is solved numerically for a RDC column using a Galerkin method.
19 citations
TL;DR: In this article, a simple theoretical analysis concerning the steady-state particle size distribution in combined aggregation-fragmentation processes is presented, where the general conditions are provided for this distribution to exhibit self-similar behaviour.
10 citations
TL;DR: In this article, a new effective nuclei concept for a simplified approach to the analysis of batch crystallization with agglomeration is proposed, where small-sized crystals could combine with both large-sized and each other.
Abstract: A new “effective nuclei” concept for a simplified approach to the analysis of batch crystallization with agglomeration is proposed. The new effective-nuclei concept comes from agglomeration characteristics observed experimentally in a batch crystallizer. Small-sized crystals could combine with both large-sized crystals and each other. Agglomeration among large-sized crystals can be neglected. From these experimental results, new effective nuclei are defined as crystals at a size-boundary between small-sized crystals and large-4sized crystals. By taking into account only large-sized crystals in formulating population balance equation, the agglomeration term can be omitted. The analytical solution of the population balance equation is induced for an ideal batch-cooling case (constant supersaturation and constant effective growth rate of crystal). The solution explains measured data well.
2 citations