Measured Chord Length Distribution Research Articles

In-situ measurement of particle length distribution by FBRM with application to needle- or rod-shape crystallization processes

In this paper, an in-situ measurement method is proposed for detecting needle- or rod-shape particle length distribution (PLD) during a crystallization process, by using the instrument named focused beam reflectance measurement (FBRM). A data pretreatment strategy is firstly presented to modify the measured chord length distribution (CLD) of particles by FBRM for proper analysis, which could guarantee measurement accuracy when the particle length are smaller than 150 μm. Based on the pretreated CLD, a moment conversion algorithm is established for estimating the moments of particle population density, so as to further improve the measurement accuracy for particles possessing larger sizes. Correspondingly, the particle growth-nucleation model parameters are efficiently estimated by using the interior point method (IPM) in combination with the homotopy analysis method (HAM). Then the PLD is reconstructed based on these estimated low-order moments, through a modified cubic-spline interpolation algorithm with variable interpolation grids. Experimental results on the seeded cooling crystallization process of β form L-glutamic acid (LGA) well demonstrate the effectiveness of the proposed method for in-situ measurement.

Bubble size distribution for bubbly-to-slug transition flow in narrow rectangular channel

To thoroughly understand the flow structure evolving characteristics in flow regime transition process from bubbly to slug flow in narrow rectangular channel, bubble size distribution (BSD) are experimentally measured by four-sensor conductivity probes. The results show that the T-location distribution fits the measured chord length distribution best in bubbly-to-slug transition flow and the fitting performance becomes worse in slug flow at high void fraction. To solve the problem, two-group bubble fitting for transition flow is proposed and obtains good performance. Function dependence of bubble coalescence and break-up rate is thoroughly analyzed for the transition flow considering its influence on BSD. According to the function dependence and fitting results, empirical correlations are proposed to predict BSD in bubbly and the transition flow. The evolving characteristics of BSD in transition flow are also discussed based on the trends of adjusted parameters in the predicted BSD.

An artificial neural network model applied to convert sucrose chord length distributions into particle size distributions

Online monitoring of the solid phase in industrial processes of sugar crystallization is still a challenge. Laser backscattering is one of the most promising techniques; however, the measured chord length distribution (CLD) does not have a physical meaning of crystal size. This work converted sucrose CLD measured by an online sensor into particle size distribution (PSD) using an artificial neural network (ANN). CLD and suspension concentration of 116 experiments were the input to the ANN and PSD was its output. The trained ANN exhibited a coefficient of variation between experimental and calculated PSD of 0.998. Data of experimental sucrose crystallization was used to validate the model, resulting in a maximum deviation of 0.090 mm in mean size and 6.16% in the coefficient of variation of distribution. This model may be used to improve both industrial processes (process optimization and control) and laboratory studies (kinetics determination).

Local flow regime and bubble size distribution in the slender particle-containing scrubbing-cooling chamber of an entrained-flow gasifier

A dual-tip conductivity probe was used to measure local radial gas holdups and bubble chord lengths to study the local flow regime and bubble size distribution in a scrubbing-cooling chamber cold model apparatus containing slender particles. The results showed that the cross-section averaging gas holdups with different fiber volume fractions and aspect ratios could be estimated within errors of ±10% using the modified Kataoka-Ishii bubbly flow semi-empirical correlation at superficial gas velocities ranging from 0.074 m/s to 0.37 m/s. The local flow regime map showed that an obvious bubbly flow formed near the inner wall of the liquid bath due to the effect of wall shear stress, while a cap-bubbly flow formed in other annulus regions due to the emergence of cap bubbles. Chord length distributions were transformed into bubble size distributions by decomposing the measured chord length distributions and estimating the bubble shape factors. Bubble size was categorized into two types—small spherical and large non-spherical bubbles—depending on if the equivalent diameter of the bubbles was smaller or larger than 2 mm. Liquid turbulence, shear stress between the fluid and the wall and liquid backmixing were enhanced by increasing the superficial gas velocity, which affected the size distributions of rising and descending bubbles as well as that of bubble populations. The extent of turbulence suppression and “fiber separation walls” varied with the fiber volume fractions, which affected the bubble size distribution in different regions. The fiber number density characterizing the variation of the fiber aspect ratio with different fiber diameter and length was used to study the bubble size distribution. The bubble size distribution at different aspect ratios was affected by interactions among fibers, bubbles, the fluid and the wall.

A new method of relating a chord length distribution to a bubble size distribution for vertical bubbly flows

Measurements of a bubbly flow using an intrusive probe give a set of random chord length values whose distribution differs considerably from the actual bubble size distribution (BSD). Considering the interaction of bubbles in groups of different sizes and shapes with the probe, a new method of relating the measured chord length distribution (CLD) to the BSD is proposed. The CLD is decomposed into simple distributions, which are considered as the CLDs of individual bubble groups and translated into BSDs using a developed analytical transformation. Entire BSD is constructed statistically from the obtained BSDs. The new method is applied to analyzing the CLDs measured by a five-sensor conductivity probe for a vertical bubbly flow in a narrow rectangular channel at different flow conditions. The results show a good agreement between the predicted BSDs and the experimental distributions measured simultaneously by a high-speed video camera. Valuable information on the statistical characteristics estimated from the CLDs and BSDs, including the chord length, bubble size and shape, and bubble population fraction, are evaluated and discussed in detail.

Development of an empirical method relating crystal size distributions and FBRM measurements

The empirical model developed in the present work allows estimation of crystal size distributions from focused beam reflectance measurements (FBRM) of chord length distributions. The model is constructed from purposely varied crystal size distributions and the corresponding measured chord length distributions, which allows construction of a transformation matrix relating the two distributions. Experimental results show advantages over more complex phenomenological models, presumably because the transformation matrix implicitly embodies such phenomena. The ability of the model to address varying crystal concentration and selectively added size fractions is demonstrated with experimental results. Finally, the simplicity of the approach allows rapid (of order 0.1s) estimation of crystal size distributions from FBRM, which is a promising outcome for potentially using the approach in an on-line control scheme.

Study of phosphoric acid crystallization using a focused beam reflectance measurement method

AbstractA way for restoring the crystal size distributions (CSD) from measured chord length distributions (CLD) was reported in this paper. The kinetics of phosphoric acid crystallization process was investigated in cooling mode using focused beam reflectance measurement (FBRM) and digital photo technique. In order to restore the CSD from measured CLD and verify the reliability of FBRM data, digital photo technique in real time and optical microscope were applied in large crystal size and small range, respectively. Results indicated a converting constant A existed between CLD and CSD when crystal growth follows size‐independent growth (Mcabe's ΔL law) law. It was verified by Malvern particles size analysis method. The converting constant A varied with crystal morphology. The crystal growth order increased with the stirring increasing speed during phosphoric acid crystallization process. The trend was especially notable at higher speed situations. It can illustrate that the state of phosphoric acid hemihydrate crystal growth was controlled by both diffusion and surface‐integration with the increasing stirring speed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multivariable real‐time optimal control of a cooling and antisolvent semibatch crystallization process

AbstractThis article presents an experimental study of simultaneous optimization with respect to two variables (cooling rate and flow‐rate of antisolvent) in an offline and online (real‐time) manner on a semibatch crystallizer. The nucleation and growth kinetic parameters of paracetamol in an isopropanol‐water cooling, antisolvent batch crystallizer were estimated by nonlinear regression in terms of the moments of the crystal population density. Moments of crystal population were estimated from the measured chord length distribution, generated by the FBRM®, and the supersaturation was calculated from the measured concentration by attenuated total reflectance‐fourier transform infrared spectroscopy. The results of real‐time optimization showed a substantial improvement of the end of batch properties (the volume‐weighted mean size and yield). For the same objective function, the real‐time optimization method resulted in an increase in the volume‐weighted mean size by ∼100 μm and 15% of theoretical yield compared with the best result obtained in an offline optimization manner. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Kinetics Estimation and Single and Multi-Objective Optimization of a Seeded, Anti-Solvent, Isothermal Batch Crystallizer

The nucleation and growth kinetic parameters of paracetamol in an isopropanol−water antisolvent batch crystallizer were estimated by nonlinear regression in terms of the moments of the crystal population density. The moments were calculated using the measured chord length distribution (CLD) generated by the FBRM. The measured supersaturation by ATR-FTIR spectroscopy was also used to calculate the nucleation and growth rates using power law correlations. Using the estimated kinetic parameters, the crystallization model based on the population and mass balance, was validated using the open-loop experimental particle size distribution and supersaturation results. Subsequently, the solution to the optimal antisolvent flow-rate profiles was obtained by applying nonlinear constrained single- and multiobjective optimization on the validated model. These profiles were implemented on the crystallizer and crystal-size distributions were compared with the open-loop experiments. The bimodality in the particle size distribution (PSD), which was present in the open-loop experiments, was either minimized or completely eliminated with the optimal profile policies. The results of the multiobjective optimization showed an improvement of 27.5 μm and 3% in the volume weighted mean size and yield, respectively, in comparison to the best results obtained from the open-loop experiments.

Analysis of FBRM measurements by means of a 3D optical model

Continuous process monitoring is desirable for many particulate processes such as the crystallization of active pharmaceutical ingredients. Only an in-line measurement technique can achieve such a continuous monitoring. A popular in-line measurement technique, which can be applied without dilution, is the focussed beam reflectance measurement (FBRM). However, FBRM is at this point mainly used for qualitative measurements. The measured chord length distribution is different from a particle size distribution. For a quantitative measurement a sound understanding of the measurement principle is necessary. In this paper, an optical model of the FBRM probe and a three-dimensional simulation of the measurement are presented. A three-dimensional particle field is generated with a Monte-Carlo approach. The back scattered light intensity is calculated as a function of the position of the laser beam with respect to this particle field. A vector of scattering intensities is obtained for a given laser path. This vector is processed with the simulated electronics of the Lasentec FBRM system. The output of this processing step is a chord length distribution which can be compared to the output of the Lasentec FBRM system. Simulation studies with mono-disperse polystyrene particles of different sizes and concentrations are conducted and compared to measurements of a Lasentec D600L FBRM probe. With the presented model yet unexplained massive over-estimation of small particles and concentration-dependent changes in the chord length distribution can be described.

Modeling Focused Beam Reflectance Measurement and its Application to Sizing of Particles of Variable Shape

A model for particle detection in focused beam reflectance measurement is presented in the general case of particles of any convex shape. Shape dependent convolution relationships between measured chord length distribution (CLD), particle size distribution (PSD) and particle mass distribution (PMD) are derived and an explicit formula for the weighting characteristic length is given in terms of particle shape. Based on the derived convolution relationships, equations relating moments of the CLD, PSD and PMD are obtained. Issues related to the definition of particle size of non spherical objects and its connection to the particle sizing technique are discussed. Based on the moment relationships, particle size is defined for focused beam reflectance measurement measurements in terms of a CLD equivalent sphere. CLD and characteristic length for a thin cylinder are obtained analytically and used as simple model in order to illustrate issues in sizing particles of variable shape, General conclusions regarding the role of the weighting characteristic length on the behavior of the measured CLD are drawn.

Comparison of Particle Size Distributions Measured Using Different Techniques

ABSTRACT In this article, particle size distributions (PSDs) measured by different techniques, including image analysis (IA), laser diffraction (LD), ultrasonic attenuation spectroscopy (UAS), and focused-beam reflectance measurement (FBRM), are compared for spherical glass beads and nonspherical silica flakes. It is shown that particle shape strongly affects the results obtained by different techniques. For spheres, the PSDs obtained by IA, LD, and UAS agree well. There is no consistent result among different particle measurement techniques for nonspherical particles. The conversion between PSDs obtained by IA, LD, and UAS has been based on particle shape factors. Caution must be exercised when a measured chord length distribution (CLD) is used to indicate the PSD during a process because the CLD result obtained by FBRM is complex, depending not only on the PSD, but also on particle optical properties and shape.

Determination of non-spherical particle size distribution from chord length measurements. Part 2: Experimental validation

In this paper, the theory on the translation of a measured chord length distribution (CLD) into its particle size distribution (PSD), which was developed in the first part of this study [Li and Wilkinson, 2005. Determination of non-spherical particle size distribution from chord length measurements. Part 1: theoretical analysis. Chemical Engineering Science 60, 3251–3265], has been validated using experimental results. CLDs were measured using the Lasentec focused beam reflectance measurement (FBRM) with three different materials, spherical ceramic beads and non-spherical plasma aluminium and zinc dust particles. Meanwhile, the particle shape and PSD of each material were also investigated by image analysis (IA). Comparison of the retrieved PSDs with the measured PSDs by IA shows that the PSD can be retrieved from a measured CLD successfully using the proposed iterative nonnegative least squares (NNLS) method based on the PSD–CLD model.

Bubble chord length distribution in three-phase fluidized beds

Three ideal bubble chord length distributions have been derived for three different bubble shapes (spherical, ellipsoidal and spherical-cap). The measured chord length distributions in three-phase fluidized beds have been analyzed by the combined bubble length distribution model based on the ellipsoidal and spherical-cap bubble shapes. The combined bubble length distribution predicts well the measured bubble length distribution in three-phase fluidized beds. It has been found that the distribution approaches that for length distribution in three-phase fluidized beds. It has been found that the distribution approaches that for ellipsoidal-shaped bubbles in the bubble-disintegrating regime and that for spherical-cap-shaped bubbles in the bubble-coalescing regime and/or in slug flow regime. The ellipsoidal-bubble fraction increases with increasing liquid velocity and particle size, but decreases with increasing gas velocity and liquid viscosity.