The processing of solids of changing size in bubbling fluidized beds

Levenspiel, Octave; Kunii, Daizō; Fitzgerald, T. J.

doi:10.1016/0032-5910(68)80043-9

Cited by 73 publications

(41 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Most, if not all, practical dissolution processes involve solids consisting of a wide range or distribution of particle sizes. Particle size distributions also have a significant effect on other processes that are of importance to chemical engineers: crystallization (Randolph and Larson,197 l), fluidized-bed reactors (Levenspiel et al, 1968), and combustion (Dickinson and Marshall, 1968). Use of models based on a concept of average size, while simple, can lead to grievous errors in predicting the dissolution behavior, and they can be avoided through the use of the population balance method presented here.…”

Section: Introductionmentioning

confidence: 97%

Population balance modeling of the dissolution of polydisperse solids: Rate limiting regimes

LeBlanc

Fogler

1987

AIChE Journal

View full text Add to dashboard Cite

Significant errors can result in modeling dissolution processes if the polydispersity of the solid particles is ignored and the sample is treated as a collection of monodisperse spheres having the average size of the mixture. Population balance modeling provides an effective analytical means of predicting the effect of polydispersity on a wide variety of heterogeneous reaction systems including dissolution processes.

show abstract

Section: Introductionmentioning

confidence: 97%

Population balance modeling of the dissolution of polydisperse solids: Rate limiting regimes

LeBlanc

Fogler

1987

AIChE Journal

View full text Add to dashboard Cite

show abstract

“…3 shows the graphic solution, including the particle scale, of η p = f(η ph , M in,0 , Da pin,0 , n) given in Eq. (36). The solution Fig.…”

Section: Solution For Cgsrmentioning

confidence: 99%

“…Also, all particles are assumed to enter with the same conversion x c0 . The treatment follows the procedure developed by [36]. The present approach, however, expresses the equations in extent of conversion instead of time or particle size [37,10].…”

Section: Fb Reactor Modelling For Ncgsrmentioning

confidence: 99%

See 1 more Smart Citation

Gas–solid conversion in fluidised bed reactors

Gómez–Barea

Leckner

Santana

et al. 2008

Chemical Engineering Journal

View full text Add to dashboard Cite

A simplified model for gas-solid reactions in fluidised bed (FB) is proposed. Such models already exist for catalytic gas-solid reactions (CGSRs), providing general description of the system in terms of main governing parameters. Expansion of this approach to non-catalytic gas-solid reactions (NCGSRs) is difficult, because the solid reactant takes part in the reaction. Therefore, FB reactor models for NCGSR are usually devised only for specific cases, and a general analysis has not been presented up to date. The present model allows analysis of different types of NCGSR in a generalised way, handling catalytic reactions as a particular, simpler, case. It is shown that the reactor behaviour can be described by three governing dimensionless parameters. Two additional parameters, quantifying the importance of diffusion effects in single particles are also identified, and their impact on reactor behaviour is analysed. Possible simplifications are explored. Model limitations, that is, assumption of isothermal bed and particle and the occurrence of only one reaction, are discussed. Examples are outlined to show the applicability of the method.

show abstract

“…In this example, we consider the optimal estimation of PSD as it changes with time in a fluidized bed. In a solids processing fluidized bed (Levenspiel et al, 1968;Weimer and Clough, 1980), a diagram of which is shown in Figure 3, fresh particles of known PSD, p,(r), are fed at a constant rate to a fluidized bed with a E D , pb(r,r). They are discharged either by an overflow pipe or by entrainment via the fluidization gas.…”

Section: Psd In a Fluidized Bedmentioning

confidence: 99%

Comparison of linear distributed‐parameter filters to lumped approximants

Cooper¹,

Ramirez²,

Clough³

1986

AIChE Journal

View full text Add to dashboard Cite

Optimal distributed-parameter filters are commonly implemented using approximating lumped Kalman filtering theory. The effect of such an approximation is investigated. A theoretical development shows that there is a loss in the spatial noise correlation for the lumped approximants. Two numerical examples of engineering significance illustrate that one result of this loss is slower filter convergence for the lumped approximants relative to the full distributed-parameter filters. D. J. COOPER W. F. RAMIREZ and D. E. CLOUGH Department of Chemical EngineeringUniversity of Colorado Boulder, CO 80309 SCOPESimplifying approximations are often made when designing a distributed-parameter filter for real-time implementation. Early lumping is one simplifying approximation that is commonly employed. Lumping (spatial discretization) is a process that must occur at some point during filter development so that the equations can be programmed for digital computation. Lumping can occur at several points in the filter development. The earlier that lumping occurs, the more simplifying the effect. At one extreme, early lumping involves discretizing the state model partial differential equations and approximating them as a system of ordinary differential equations. Application of optimal filtering theory to the system of ordinary differential equations results in a lumped Kalman filter that approximates the distributed-parameter filter. This is in contrast to late lumping, at the other extreme, where the full distributed-parameter filter partial differential equations are derived before they are lumped for numerical computation.Advantages of early lumping include being able to use simpler theoretical and numerical methods for filter design and implementation. Also, the early lumped filtering algorithm requires less computation for filter equation solution, so less computer resources are used when on-line. The early lumping approximation does have negative consequences, however.In this work, we present a side-by-side comparison of early lumping vs. late lumping as applied to the least-squares filtering of linear distributed-parameter systems. This investigation includes a general theoretical formalization that is applicable to such lumping methods as finite differencing, eigenfunction expansion, orthogonal collocation, and Galerkin's method. The results of the theoretical investigation are illustrated by means of two numerical examples. The first example considers the optimal estimation of dynamic temperature distributions in a heated bar. The second example considers the optimal estimation of dynamic particle-size distributions (PSD) in a fluidized bed. CONCLUSIONS AND SIGNIFICANCEThe early lumping approximation results in a loss in the spatial noise correlation that is associated with distributed-parameter systems. This spatial noise correlation is preserved in the late-lumped distributed filter.In a spatially correlated system, an occurrence at one location will directly affect neighboring locations. The early lumping approximation...

show abstract

The processing of solids of changing size in bubbling fluidized beds

Cited by 73 publications

References 4 publications

Population balance modeling of the dissolution of polydisperse solids: Rate limiting regimes

Population balance modeling of the dissolution of polydisperse solids: Rate limiting regimes

Gas–solid conversion in fluidised bed reactors

Comparison of linear distributed‐parameter filters to lumped approximants

Contact Info

Product

Resources

About