Particle number balance approach for simulation of a multi-chamber fluidized bed urea granulator; Modeling and validation H. Nemati a, ⁎, S.A. Shekoohi b a Department of Mechanics, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran b HAMPA Energy Engineering and Design Company, Shiraz, Iran abstract article info Article history: Received 30 October 2019 Received in revised form 7 April 2020 Accepted 3 May 2020 Available online 06 May 2020 In the present work, a model was proposed to simulate the growth in an industrial multi-chamber fluidized bed granulator under steady-state condition. To simulate the growth, it was assumed the coating is the only growth mechanism. Mass balance, as well as particle number balance (PNB), was considered in the simulation. Despite previous works, it was not assumed that particles in each chamber are at the same age. Consequently, the growth was simulated along the granulator length, from its beginning to the end. In this model, most of the influencing parameters are collected in one parameter called C 1 . Using finite difference method, equations were solved and results were compared with samples from an industrial granulator and very good agreements were observed. Sensitivity of the product normalized mass density function to the parameter C 1 was also studied. It was found that for a specific inlet seeds diameter distribution, d 50 of the product is not a linear function of C 1 . © 2020 Elsevier B.V. All rights reserved. Keywords: Urea granulation Multi-chamber Fluidized bed Population balance Particle number balance 1. Introduction The fertilizer industry plays an important role in providing food throughout the world and its importance in human survival may not be ignored. No doubt that the world cannot be fed without the wide- spread use of fertilizers. Among all different types of fertilizers, urea fer- tilizer is widely consumed. Its high nitrogen content (46%), ease of use and flexibility in combination with other types of fertilizers, make urea as one of the most widely used fertilizers in the world. More than 40% of all food grown in the world is fertilized by urea [1]. Global urea supply is estimated at 179,000 tons in 2014 [2]. Global fertilizer demand is expected to continue growing moderately in 2018–2019 due to prospects for persisting low-to-medium interna- tional crop prices [3]. It is predicted that global fertilizer demand will be slightly below 200,0000 tons in 2022–2023 [3]. There are many urea fertilizer plants in operation and many others are under construc- tion. So, in this competitive market, improving knowledge of the urea granulation plants is very valuable. In a urea granulation plant, a granulator is a crucial part. An indus- trial granulator utilizes the fluidized bed to carry growing seeds. Urea granules are fluidized by flowing air while the small urea seeds are fed continuously into the granulator. Meanwhile, molten urea is sprayed onto these seeds. The deposition of tiny urea drops onto the surface of the seed grows granules continuously up to the end of a granulator. A schematic of an industrial fluidized bed urea granulator is repre- sented in Fig. 1. The urea granulator has an enormous structure. The length of this granulator is 16.1 m, its width is 4.85 m and the granulator height is more than 4 m. Furthermore, it can produce around 217 tons/h urea granules. The small seeds, usually around 2 mm in diameter with the rate of 83.15 tons/h are fed into the granulator at its beginning. Flu- idization air inside a duct is also injected through a perforated plate at the bottom of the granulator. This air fluidizes urea granules and con- veys them out. Moreover, the air mixes the granules well and removes the dust toward the exhaust window at the top of the granulator. Sev- eral sprays are distributed uniformly at the bottom of the granulator. The molten urea is sprayed over the surface of seeds and grows them, uniformly. The grown granules get dry and cooled gradually in the granulator. Homogeneity of particle size distribution is defined by two parame- ters: d 50 and span of the particle size distribution [4]. d 50 indicates the mass weighted average of particle diameter [5]. Marketable granules shall meet a specific particle size distribution. So, the product particles shall be later sieved to remove, the out of range granules. The larger granules will be crushed and the smaller granules will be stored to be used later as seeds. So, to have a competitive unit, the product unifor- mity should be guaranteed [6,7]. However, as it may be clear, the oper- ation of a granulator is very stochastic, complicated and unpredictable. Due to this complexity, it is easy to find granulators work with the ca- pacity less than their nominal capacity which results in high recycle ra- tios and overloading other process units [8–10]. In the fluidized bed granulator study, different methods may be used to simulate a granulator such as CFD or DEM-CFD [11–14], or using Powder Technology 369 (2020) 96–105 ⁎ Corresponding author. E-mail address: H.Nemati@miau.ac.ir (H. Nemati). https://doi.org/10.1016/j.powtec.2020.05.010 0032-5910/© 2020 Elsevier B.V. All rights reserved. Contents lists available at ScienceDirect Powder Technology journal homepage: www.elsevier.com/locate/powtec