Integrated modeling methodology for ash agglomeration in poly-disperse fluidized beds using particle population framework
Graphical abstract
Introduction
Prediction of the kinetics of agglomerate growth is critical for several industries that use fluidized beds to alter the particle size in industrial unit operations such as granulation and pelletization to improve powder flow characteristics and handling., sintering of ores, briquetting and many similar processes. It is also critical in the pharmaceutical industry. On the other hand, the process of agglomerate growth is undesirable in the combustion and gasification of carbonaceous materials for energy production applications as it causes deposition and defluidization causing operational issues. For an improved understanding of the effects of particle properties and operating conditions on agglomeration, mathematical models to predict the rate of agglomeration can be useful to industrial operations using fluid bed processes.
Prior research in the development of mathematical models for this application is limited and hence the model has been developed based on concepts that have been previously applied to granulation in the pharmaceutical and fertilizer industry. A critical review of the available models to predict kinetics of particle growth conducted by us [1] discussed the significance of heterogeneities in chemical composition and particle physics that exist at the particle-level in the fluidized bed combustion and gasification industry. The available agglomeration models were based on either the effect of chemistry-based parameters or physics-based hydrodynamics. The interdependency between these chemistry- and physics-based parameters makes it more complicated to predict their combined effect on fluidized bed ash agglomeration. In previous work [2,3], we have studied the effect of particle chemical composition on the initiation of agglomeration using FactSage and experimental analysis of fuel particle classes that are rich in specific mineral matter. Additionally, heterogeneities arise in particle physics as well, due to the distribution of particle sizes and the resulting collision velocities and collision frequencies. Starting from a population balance equation, This paper focusses on the development of a modeling methodology to predict agglomeration in fluidized bed combustors and gasifiers by combining the chemistry-based parameters such as heterogeneity in the ash composition that forms the binder, and granular-physics (collision frequency).
Previous studies reported in the literature, have estimated values of the physics-based, hydrodynamic parameters such as collision frequency specifically for the case under study and assumed them as constant throughout the process or have made approximations which make them adequate for comparative purposes alone and restricts their use to a given particle-binder system [4,5]. The models have also used several empirical parameters such as the adhesiveness co-efficient and empirical constants for dispersion and wetting as in the development of coalescence kernels that are system-specific [6,7]. Thielmann et al. [4] acknowledged the dependence of collision frequency on granular temperatures and system hydrodynamics. Although collision frequency is needed to translate iteration counts into real time, since their study used one specific solid material, their model was based only on iteration counts, which was sufficient for making comparisons within the specific system. However, it is difficult to extend that assumption to an ash agglomeration prediction model due to heterogeneities in bed solids in the fluidized bed combustion or gasification systems. The majority of the experimental correlations developed and used in the literature [7,8] focus on systems that have mono-sized particles. Cryer [9] incorporated a variation in particle collision velocity using an uncertainty calculated with polynomial chaos functions. He superimposed this uncertainty onto an assumed, normal distribution of the collision velocity. Since there size distributions of bed particles in gasification and combustion systems, leading to non-normal distributions of collision velocities and collision frequencies, the present study targeted the incorporation of such non-uniformities into the model. So far population balance equations have used empirical coalescence kernels to determine the growth kinetics. The effect of parameters such as liquid binder properties and its distribution on the particle surface are then determined from limited, select experimentation. The determination of such relationships is complicated for fluidized bed combustion and gasification systems due to the distributive nature of bed solids properties.
In this paper, a modeling methodology for agglomeration prediction, that considers both the particle chemical composition and particle hydrodynamics, is presented. This paper presents the first part of the work undertaken, the model development methodology. A subsequent publication will discuss the detailed application and validation efforts of the model.
Section snippets
Research objectives
The specific research objectives of the work reported in this paper are as follows-
- •
From a population balance equation, develop a unified mathematical modeling methodology that combines the effects of physics- and chemistry-based
parameters on fluidized bed ash agglomeration,
- •
Account for the effect of particle class-level heterogeneity in ash chemical composition in this model, and
- •
Develop a method to calculate and use a distribution of collision frequencies in fluidized beds, corresponding to a
The population balance equation
The model development process begins from consideration of the population balance Eq. A generalized version of this equation is shown below in Eq. (1) [10].
V represents the control volume, and (x,r) represents particle properties and position. Y(r,t) is vector which represents a continuous phase in which the particles are distributed. Finally, f(x,r,t) is the average number of particles defined by (x,r) in the phase Y(r,t), and h(x,r,Y,t) represents the
Results and discussion
The following results show the effect of incorporation of slag amount from FactSage and collision frequency distribution from CFD simulations on agglomeration. They also demonstrate that using the methodology developed, the rate of agglomerate growth can be modeled at the particle-level, as a combined effect of the chemical and physical properties of the particle and binder system.
Applicability and industrial impact of modeling methodology developed
The modeling methodology developed is based on particle-particle collisions and hence can be adapted for the development of particle growth models in fluidized bed combustion, gasification and related processes involving controlled increase in particle size. The model extends modeling capabilities that were previously used in the granulation industry to poly-disperse systems with heterogeneities in particle chemical composition, temperature and collision frequencies. In the gasification and
Conclusions
Penn State has developed a modeling methodology to predict the growth rate of ash agglomerates in fluidized bed combustion and gasification systems. The model being developed uses a population balance model framework to consider binary particle collisions, facilitating the incorporation of particle-level variation in collision frequency, particle wetness and slag formation tendencies that depend on chemical composition. The Stokes' criterion is used to test for particle stickiness based on
List of symbols
- Symbol
Definition (Units (SI))
- W
Weight of bulk coal (kg)
- wi
Fraction of ith gravity-separated coal fraction
- wsl
Attribute tracked fraction of slag to solid ash
- ai
Ash content of ith gravity-separated fraction
- mij
Mass of particle in interval i, j (kg)
- di
Diameter of particle in interval i, j (M)
- ρ i,j
Density of particle in interval i, j (kg/m3)
- Vi,j
Volume of particle in interval i, j (m3)
- St
Stokes' number for a collision
- uc
Collision velocity (m/s)
- μ
Viscosity of binder (Pa.s)
- D
Reduced diameter of colliding
Declaration of Competing Interest
The authors have no conflicts of interest to declare that are relevant to the content of this article.
Acknowledgments
This study was partially funded by National Energy Technology Laboratory/US Department of Energy under Award # DE-FE0026825.
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