Solution of the Population Balance Equation (PBE): An efficient criterion to compare calculated particle size distributions (PSDs) with experimental data given by sieve analysis

PIÑA, JULIANA; SCHBIB, SUSANA NOEMÍ; BUCALÁ, VERÓNICA

Río de Janeiro, Brasil

Congreso; ENPROMER 2005 (4º Congreso de Procesos de Ingeniería del Mercosur); 2005

Universidad Federal de Río de Janeiro

The population balance concepts are of importance to many industrial areas. Particularly for granulation processes, the PBE solution allows to evaluate the PSDs as the particles grow if it is solved simultaneously with the fundamental balance equations of the process responsible of their growth (e.g., chemical vapor deposition, drying). In this work the method of characteristics (MOC) is selected to solve the PBE. MOC involves the movement of the control volume along the particle size coordinate over time. Consequently the initial grid points are shifted to higher values in the size axis as the granulation takes place, i.e. a moving grid is employed in the calculations. The PBE is solved for different growth rates including pure growth and agglomeration mechanisms. A wide range of techniques are used to experimentally determine the PSDs, among them the sieve analysis is the most popular one. Often the same set of sieves is used to measure the PSDs at different operating times; therefore for a batch process the experimental PSDs are based on a fixed size grid. Contradictorily, the calculated PSDs are represented on a moving grid. The challenge that involves the use of MOC, known as adequate to solve the PBE, is the proper comparison between the experimental and calculated data. In this work three criteria are proposed to compare PSDs obtained by numerical solution of the PBE with experimental data given by sieve analysis. The results indicate that one of the three proposed methods can be successfully employed to compare simulated and experimental PSDs of granulation processes. The population balance concepts are of importance to many industrial areas. Particularly for granulation processes, the PBE solution allows to evaluate the PSDs as the particles grow if it is solved simultaneously with the fundamental balance equations of the process responsible of their growth (e.g., chemical vapor deposition, drying). In this work the method of characteristics (MOC) is selected to solve the PBE. MOC involves the movement of the control volume along the particle size coordinate over time. Consequently the initial grid points are shifted to higher values in the size axis as the granulation takes place, i.e. a moving grid is employed in the calculations. The PBE is solved for different growth rates including pure growth and agglomeration mechanisms. A wide range of techniques are used to experimentally determine the PSDs, among them the sieve analysis is the most popular one. Often the same set of sieves is used to measure the PSDs at different operating times; therefore for a batch process the experimental PSDs are based on a fixed size grid. Contradictorily, the calculated PSDs are represented on a moving grid. The challenge that involves the use of MOC, known as adequate to solve the PBE, is the proper comparison between the experimental and calculated data. In this work three criteria are proposed to compare PSDs obtained by numerical solution of the PBE with experimental data given by sieve analysis. The results indicate that one of the three proposed methods can be successfully employed to compare simulated and experimental PSDs of granulation processes. The population balance concepts are of importance to many industrial areas. Particularly for granulation processes, the PBE solution allows to evaluate the PSDs as the particles grow if it is solved simultaneously with the fundamental balance equations of the process responsible of their growth (e.g., chemical vapor deposition, drying). In this work the method of characteristics (MOC) is selected to solve the PBE. MOC involves the movement of the control volume along the particle size coordinate over time. Consequently the initial grid points are shifted to higher values in the size axis as the granulation takes place, i.e. a moving grid is employed in the calculations. The PBE is solved for different growth rates including pure growth and agglomeration mechanisms. A wide range of techniques are used to experimentally determine the PSDs, among them the sieve analysis is the most popular one. Often the same set of sieves is used to measure the PSDs at different operating times; therefore for a batch process the experimental PSDs are based on a fixed size grid. Contradictorily, the calculated PSDs are represented on a moving grid. The challenge that involves the use of MOC, known as adequate to solve the PBE, is the proper comparison between the experimental and calculated data. In this work three criteria are proposed to compare PSDs obtained by numerical solution of the PBE with experimental data given by sieve analysis. The results indicate that one of the three proposed methods can be successfully employed to compare simulated and experimental PSDs of granulation processes. The population balance concepts are of importance to many industrial areas. Particularly for granulation processes, the PBE solution allows to evaluate the PSDs as the particles grow if it is solved simultaneously with the fundamental balance equations of the process responsible of their growth (e.g., chemical vapor deposition, drying). In this work the method of characteristics (MOC) is selected to solve the PBE. MOC involves the movement of the control volume along the particle size coordinate over time. Consequently the initial grid points are shifted to higher values in the size axis as the granulation takes place, i.e. a moving grid is employed in the calculations. The PBE is solved for different growth rates including pure growth and agglomeration mechanisms. A wide range of techniques are used to experimentally determine the PSDs, among them the sieve analysis is the most popular one. Often the same set of sieves is used to measure the PSDs at different operating times; therefore for a batch process the experimental PSDs are based on a fixed size grid. Contradictorily, the calculated PSDs are represented on a moving grid. The challenge that involves the use of MOC, known as adequate to solve the PBE, is the proper comparison between the experimental and calculated data. In this work three criteria are proposed to compare PSDs obtained by numerical solution of the PBE with experimental data given by sieve analysis. The results indicate that one of the three proposed methods can be successfully employed to compare simulated and experimental PSDs of granulation processes. The population balance concepts are of importance to many industrial areas. Particularly for granulation processes, the PBE solution allows to evaluate the PSDs as the particles grow if it is solved simultaneously with the fundamental balance equations of the process responsible of their growth (e.g., chemical vapor deposition, drying). In this work the method of characteristics (MOC) is selected to solve the PBE. MOC involves the movement of the control volume along the particle size coordinate over time. Consequently the initial grid points are shifted to higher values in the size axis as the granulation takes place, i.e. a moving grid is employed in the calculations. The PBE is solved for different growth rates including pure growth and agglomeration mechanisms. A wide range of techniques are used to experimentally determine the PSDs, among them the sieve analysis is the most popular one. Often the same set of sieves is used to measure the PSDs at different operating times; therefore for a batch process the experimental PSDs are based on a fixed size grid. Contradictorily, the calculated PSDs are represented on a moving grid. The challenge that involves the use of MOC, known as adequate to solve the PBE, is the proper comparison between the experimental and calculated data. In this work three criteria are proposed to compare PSDs obtained by numerical solution of the PBE with experimental data given by sieve analysis. The results indicate that one of the three proposed methods can be successfully employed to compare simulated and experimental PSDs of granulation processes. The population balance concepts are of importance to many industrial areas. Particularly for granulation processes, the PBE solution allows to evaluate the PSDs as the particles grow if it is solved simultaneously with the fundamental balance equations of the process responsible of their growth (e.g., chemical vapor deposition, drying). In this work the method of characteristics (MOC) is selected to solve the PBE. MOC involves the movement of the control volume along the particle size coordinate over time. Consequently the initial grid points are shifted to higher values in the size axis as the granulation takes place, i.e. a moving grid is employed in the calculations. The PBE is solved for different growth rates including pure growth and agglomeration mechanisms. A wide range of techniques are used to experimentally determine the PSDs, among them the sieve analysis is the most popular one. Often the same set of sieves is used to measure the PSDs at different operating times; therefore for a batch process the experimental PSDs are based on a fixed size grid. Contradictorily, the calculated PSDs are represented on a moving grid. The challenge that involves the use of MOC, known as adequate to solve the PBE, is the proper comparison between the experimental and calculated data. In this work three criteria are proposed to compare PSDs obtained by numerical solution of the PBE with experimental data given by sieve analysis. The results indicate that one of the three proposed methods can be successfully employed to compare simulated and experimental PSDs of granulation processes. The population balance concepts are of importance to many industrial areas. Particularly for granulation processes, the PBE solution allows to evaluate the PSDs as the particles grow if it is solved simultaneously with the fundamental balance equations of the process responsible of their growth (e.g., chemical vapor deposition, drying). In this work the method of characteristics (MOC) is selected to solve the PBE. MOC involves the movement of the control volume along the particle size coordinate over time. Consequently the initial grid points are shifted to higher values in the size axis as the granulation takes place, i.e. a moving grid is employed in the calculations. The PBE is solved for different growth rates including pure growth and agglomeration mechanisms. A wide range of techniques are used to experimentally determine the PSDs, among them the sieve analysis is the most popular one. Often the same set of sieves is used to measure the PSDs at different operating times; therefore for a batch process the experimental PSDs are based on a fixed size grid. Contradictorily, the calculated PSDs are represented on a moving grid. The challenge that involves the use of MOC, known as adequate to solve the PBE, is the proper comparison between the experimental and calculated data. In this work three criteria are proposed to compare PSDs obtained by numerical solution of the PBE with experimental data given by sieve analysis. The results indicate that one of the three proposed methods can be successfully employed to compare simulated and experimental PSDs of granulation processes. The population balance concepts are of importance to many industrial areas. Particularly for granulation processes, the PBE solution allows to evaluate the PSDs as the particles grow if it is solved simultaneously with the fundamental balance equations of the process responsible of their growth (e.g., chemical vapor deposition, drying). In this work the method of characteristics (MOC) is selected to solve the PBE. MOC involves the movement of the control volume along the particle size coordinate over time. Consequently the initial grid points are shifted to higher values in the size axis as the granulation takes place, i.e. a moving grid is employed in the calculations. The PBE is solved for different growth rates including pure growth and agglomeration mechanisms. A wide range of techniques are used to experimentally determine the PSDs, among them the sieve analysis is the most popular one. Often the same set of sieves is used to measure the PSDs at different operating times; therefore for a batch process the experimental PSDs are based on a fixed size grid. Contradictorily, the calculated PSDs are represented on a moving grid. The challenge that involves the use of MOC, known as adequate to solve the PBE, is the proper comparison between the experimental and calculated data. In this work three criteria are proposed to compare PSDs obtained by numerical solution of the PBE with experimental data given by sieve analysis. The results indicate that one of the three proposed methods can be successfully employed to compare simulated and experimental PSDs of granulation processes.