scholarly journals A two-dimensional population balance model for cell growth including multiple uptake systems

2018 ◽  
Vol 132 ◽  
pp. 966-981 ◽  
Author(s):  
V. Quedeville ◽  
H. Ouazaite ◽  
B. Polizzi ◽  
R.O. Fox ◽  
P. Villedieu ◽  
...  
Keyword(s):  
Cell Growth ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
Two Dimensional

Two-dimensional population balance model with breakage of high aspect ratio crystals for batch crystallization

2008 ◽  
Vol 63 (12) ◽  
pp. 3271-3278 ◽  
Author(s):  
Kazuhiro Sato ◽  
Hidetada Nagai ◽  
Kazuhiro Hasegawa ◽  
Kunihiko Tomori ◽  
H.J.M. Kramer ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
Two Dimensional ◽  
Batch Crystallization

scholarly journals Comparison of One Dimensional and Two Dimensional Population Balance Model for Optimization of a Crystallization Process

2021 ◽  
Author(s):  
Tamar Rosenbaum ◽  
Victoria Mbachu ◽  
Niall Mitchell ◽  
John Gamble ◽  
Patricia Cho ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Crystallization Process ◽  
Population Balance ◽  
Seed Morphology ◽  
Balance Model ◽  
Population Balance Model ◽  
Two Dimensional ◽  
Population Balance Modeling ◽  
One Dimensional ◽  
The Impact

In this work, the advantage of two-dimensional population balance modeling (2D PBM) for a needle-shaped API is highlighted by comparing the one-dimensional population balance model (1D PBM) developed for an antisolvent crystallization with the 2D PBM. The API utilized for this work had extremely slow desupersaturation, and was not able to achieve solubility concentration despite a ~50 h seed bed age. While the 1D PBM is useful in optimizing the crystallization process to enhance desupersaturation, it is unable to match the particle size quantiles well. 2D PBM was necessary to probe the impact of crystallization process parameters on particle aspect ratio (AR). Simulations utilizing the 2D PBM indicated that regardless of antisolvent addition rate or seed morphology, the final material would still be high aspect ratio. This knowledge saved the investment of much time and efforts in trying to minimize particle AR with changes in crystallization processing parameters alone.

scholarly journals Study on the regional characteristics during foam flooding by population balance model

2020 ◽  
pp. 014459872098361
Author(s):  
Zhongbao Wu ◽  
Qingjun Du ◽  
Bei Wei ◽  
Jian Hou
Keyword(s):  
Numerical Simulation ◽  
Simulation Model ◽  
Oil Recovery ◽  
Population Balance ◽  
Growth Zone ◽  
Balance Model ◽  
Population Balance Model ◽  
Liquid Ratio ◽  
One Dimensional ◽  
Foam Flooding

Foam flooding is an effective method for enhancing oil recovery in high water-cut reservoirs and unconventional reservoirs. It is a dynamic process that includes foam generation and coalescence when foam flows through porous media. In this study, a foam flooding simulation model was established based on the population balance model. The stabilizing effect of the polymer and the coalescence characteristics when foam encounters oil were considered. The numerical simulation model was fitted and verified through a one-dimensional displacement experiment. The pressure difference across the sand pack in single foam flooding and polymer-enhanced foam flooding both agree well with the simulation results. Based on the numerical simulation, the foam distribution characteristics in different cases were studied. The results show that there are three zones during foam flooding: the foam growth zone, stable zone, and decay zone. These characteristics are mainly influenced by the adsorption of surfactant, the gas–liquid ratio, the injection rate, and the injection scheme. The oil recovery of polymer-enhanced foam flooding is estimated to be 5.85% more than that of single foam flooding. Moreover, the growth zone and decay zone in three dimensions are considerably wider than in the one-dimensional model. In addition, the slug volume influences the oil recovery the most in the foam enhanced foam flooding, followed by the oil viscosity and gas-liquid ratio. The established model can describe the dynamic change process of foam, and can thus track the foam distribution underground and aid in optimization of the injection strategies during foam flooding.

Population balance model for solid state sintering II. Grain growth

2001 ◽  
Vol 27 (1) ◽  
pp. 63-71 ◽  
Author(s):  
S Sivakumar ◽  
Manjunath Subbanna ◽  
Satyam S Sahay ◽  
Vijay Ramakrishnan ◽  
P.C Kapur ◽  
...  
Keyword(s):  
Solid State ◽  
Grain Growth ◽  
Population Balance ◽  
Balance Model ◽  
Population Balance Model ◽  
Solid State Sintering
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