Multidimensional Population Balance Model Development and Validation of a Reactive Detergent Granulation Process Anwesha Chaudhury, † Ashutosh Tamrakar, † Marek Schö ngut, ‡ David Smrc ̌ ka, ‡ Frantis ̌ ek S ̌ tě pa ́ nek, ‡ and Rohit Ramachandran* ,† † Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, 98 Brett Road, Piscataway, New Jersey 08854, United States ‡ Department of Chemical Engineering, Institute of Chemical Technology, Prague, Technicka 5, 166 28 Prague 6, Czech Republic ABSTRACT: Reactive granulation is a complex process which brings about a physical and chemical change in the raw materials. It is extensively used for the production of detergents through the “dry neutralization” reaction. In this paper, the dynamics of the reactive granulation process is captured using a coupled multidimensional population balance model (PBM) for the size enlargement and a diffusion-reaction (DR) equation for the kinetics of the reaction. This framework can capture the experimental observations that have also been reported in Schö ngut et al. (Ind. Eng. Chem. Res. 2011, 50, 11576). There are a few empirical parameters involved in the modeling framework for which a dynamic sensitivity analysis was employed to shortlist the parametric quantities that have the largest influence on the critical quality attributes. The model is calibrated against experimental results via the Nelder-Mead simplex algorithm for estimating the empirical parameters, and the model predictions were compared with experimental results. Both the parameter estimation and prediction results showed good agreement with the experimental results. The development in terms of a comprehensive mathematical model and the results as presented in this paper suggest the ability of this approach to make suitable model predictions which can significantly reduce the number of experimental trials required for process optimization and control. ■ INTRODUCTION AND OBJECTIVES Granulation is an important unit operation that is ubiquitous in various industries (e.g., food industry, pharmaceutical industry, detergents) that involves the processing of particulate matter. It improves powder flowability, minimizes segregation, and also controls the dissolution of any active ingredient. The process of reactive granulation is relevant to the production of detergents and depicts the formation of a new compound along with the particle design process. Typically, one or more of the com- ponents participating in the reaction acts as the binder and allows the process of agglomeration and growth of primary particles into granules. Granulation by itself is a highly complex process; 2 however, when it is coupled with the accompanying reaction, the complexity of the problem is further increased. For instance, the binder properties are significantly modified with the progress of the reaction, thus making the granulation tougher to control. Studies have shown that adopting a model based systems approach can enable various industries to move to a more sustainable position. 3 This approach requires gaining in-depth knowledge about the process in order to develop models which could enable the a priori prediction of the pro- cess outcome. The model based approach significantly aids with alleviating the inefficient operation of a process and enables the optimization of a process with minimal experimental trials. During the reactive granulation of detergents, the anionic surfactant compound, sodium dodecyl-benzenesulfonate (NaLAS, where LAS stands for linear alkylbenzenesulfonate), which contributes to the cleansing action of detergents, is produced by a dry neutralization reaction. Dodecyl-benzene- sulfonic acid (HLAS) which is a mixture of C 10 -C 13 isomers is neutralized by a sodium salt or sodium base. The resultant product from the reaction, NaLAS (the sodium salt), is widely used due to its cleansing properties, favorable cost/performance ratio, and environmental friendliness. 4 The reaction showing the formation of NaLAS can be written as ⏟ ⏟ + → + +     2HLAS (l) Na CO (s) 2 NaLAS (s) H O(l) CO (g) (A) 2 3 (B) (C) 2 (D) 2 (E) The reactants in this system comprise the viscous acid, HLAS, and the base in its solid form, Na 2 CO 3 ; the resulting re- action is thus called dry neutralization. NaLAS is a hygroscopic semisolid substance which forms a liquid crystalline phase with water and can be considered as the solid form of the binder. For the purpose of modeling, in this work, NaLAS is however con- sidered as a highly viscous liquid. At the industrial scale, the dry neutralization reaction is carried out via granulation by spraying the acid on a fluidized or mechanically agitated powder bed of Na 2 CO 3 particles. A stoichiometric excess of sodium carbonate, which also acts as the detergent builder, is typically used in order to maximize the conversion. 5 With the progress of the reaction, a product layer, known as the passivation layer, is formed around the Na 2 CO 3 particle which aids in the agglomeration of particles by forming strong liquid bridges which bind primary particles together to form agglomerates (Figure 1). The viscosity of the product layer changes as the reaction proceeds 6 and thus the strength of the liquid bridges binding the particles together also changes. Because dry Received: August 29, 2014 Revised: December 28, 2014 Accepted: December 28, 2014 Published: December 28, 2014 Article pubs.acs.org/IECR © 2014 American Chemical Society 842 DOI: 10.1021/ie503203z Ind. Eng. Chem. Res. 2015, 54, 842-857