Influence of the Estimation Procedure on the Accuracy and Precision of Aluminum Trihydroxide Crystallization Kinetics from Dynamic Data

Li, Tian S.; Livk, Iztok; Ilievski, Dean

doi:10.1021/ie0102145

Cited by 16 publications

(20 citation statements)

References 26 publications

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“…The thickness of the latest growth layers in both Figs. 1a and 1b are consistent with those determined from the measured growth kinetics using the kinetics estimation techniques reported Li et al [6].…”

Section: Internal Structuresupporting

confidence: 90%

Studies into the Internal Structure of Gibbsite Agglomerates

Ilievski

Austin

Whittington³

2003

Chem Eng & Technol

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This paper outlines techniques that have been developed or adapted to characterise the internal structure of gibbsite agglomerates and their application to selected laboratory gibbsite sample. The specific structural properties investigated include the quantification of gibbsite voidage (Floc Density Analyser), determination of relative changes in gibbsite crystal orientation (Raman spectroscopy and electron backscattered diffraction) and location of the cement binding agglomerated gibbsite particles (Raman spectroscopy, charge contrast and orientation contrast imaging). This paper also describes the use of Kikuchi patterns for investigating crystal orientation at a point and as a tool to assess if a particle is a single crystal or an agglomerate or a multi-fold twin.

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Section: Internal Structuresupporting

confidence: 90%

Studies into the Internal Structure of Gibbsite Agglomerates

Ilievski

Austin

Whittington³

2003

Chem Eng & Technol

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“…Our multiple characteristic time optimal control problem is to choose a control function u(t), a system parameter ζ ∈ [−1, 1], and observation times 4,7] and τ 3 ∈ [8, 9] so that (28) is minimized subject to the dynamics (23)- (26), the terminal state constraint (27), and…”

Section: Example 1 (Optimal Observation Times)mentioning

confidence: 99%

“…The problem of choosing values for these unknown parameters in such a way that the solution of the dynamic model will best fit experimental data at a set of sample points can be formulated as an optimal parameter selection problem with the objective function depending on many characteristic times. This technique has recently been applied to the study of crystallization processes; see Livk, Pohar & Ilievski (1999) and Li, Livk & Ilievski (2001), for example. However, finite difference approximations are often employed to generate the gradients required by the underlying optimization procedure.…”

Section: Introductionmentioning

confidence: 99%

Optimal control problems with multiple characteristic time points in the objective and constraints

2008

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In this paper, we develop a computational method for a class of optimal control problems where the objective and constraint functionals depend on two or more discrete time points. These time points can be either fixed or variable. Using the control parametrization technique and a time scaling transformation, this type of optimal control problem is approximated by a sequence of approximate optimal parameter selection problems. Each of these approximate problems can be viewed as a finite dimensional optimization problem. New gradient formulae for the cost and constraint functions are derived. With these gradient formulae, standard gradient-based optimization methods can be applied to solve each approximate optimal parameter selection problem. For illustration, two numerical examples are solved.

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“…The parameters for the kinetics expressions, e.g., Eqs. (7)± (10), were obtained by fitting to the estimates of b, G and B u , which were obtained using experimental data and the kinetics estimation procedures described in [21]. The bulk-averaged shear rates were used in the onecompartment model.…”

Section: Modeling the Uniformly-mixed Gibbsite Crystallizermentioning

confidence: 99%

Dynamic Compartmental Models of Uniformly‐Mixed and Inhomogeneously‐Mixed Gibbsite Crystallizers

Livk

Lane

et al. 2003

Chem Eng & Technol

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The use of simple compartmentalized population balance (PB) models was investigated for describing the crystal size distributions (CSD) of two different laboratory batch gibbsite crystallizers, one uniformly-mixed and the other inhomogeneously-mixed with respect to particulate phase. The compartments were selected on the basis of the shear rate and solids concentration distribution maps generated by the computational fluid dynamics (CFD). In the inhomogeneouslymixed case, the CSD predicted by the compartmental model was highly sensitive to the relationship between the agglomeration kernel and shear rate used to describe the local agglomeration rate. This observation is consistent with recent findings reported in the literature that to correctly account for the agglomeration process in crystallizers its kinetic formulation should be based on the local rather than the volume-averaged properties.

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Influence of the Estimation Procedure on the Accuracy and Precision of Aluminum Trihydroxide Crystallization Kinetics from Dynamic Data

Cited by 16 publications

References 26 publications

Studies into the Internal Structure of Gibbsite Agglomerates

Studies into the Internal Structure of Gibbsite Agglomerates

Optimal control problems with multiple characteristic time points in the objective and constraints

Dynamic Compartmental Models of Uniformly‐Mixed and Inhomogeneously‐Mixed Gibbsite Crystallizers

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