Measuring the particle size of a known distribution using the focused beam reflectance measurement technique
Introduction
Accurate particle size analysis is a key to study hydrate formation from a water-in-oil (W/O) emulsion. During the hydrate formation process it is proposed that two main phenomena occur in which size information is important: (1) water droplets in the emulsion crystallize to form hydrate shells (the inner core of the shells being unconverted water), and (2) these shells aggregate to form larger hydrate agglomerates (Palermo et al., 2005, Turner, 2005). For more information about hydrate formation and agglomeration the reader is referred to Sloan and Koh (2008). Two particle size measurement techniques have been implemented to investigate hydrate growth and agglomeration: a focused beam reflectance measurement (FBRM) probe and a particle video microscope (PVM) probe. The purpose of this study is to determine how well the FBRM can measure the original water droplet size in the emulsion, detect hydrate nucleation and agglomeration, and measure the actual agglomerate size, including the measurement of a potential bimodal distribution between distinct particles and large agglomerates.
The FBRM probe used in this study is a Mettler–Toledo Lasentec D600X particle size analyzer. A Class I, 3 mW laser with wavelength 791.8 nm (near infrared) is transmitted through fiber-optics to the probe tip. A rotating optical lens at the probe tip deflects the laser as shown in Fig. 1a. When the probe is inserted into a system of droplets or particles, the laser emitted is reflected if it scans across the surface of a particle, as shown in Fig. 1b. The probe measures the reflectance time and determines the chord length by the product of the time and the laser scan speed (scan speed in this work is 4 m/s, but it can range from 2 to 16 m/s). For more information on the probe and the technique the reader is referred to the FBRM Hardware Manual (Mettler–Toledo Lasentec®, 2001).
Previous studies have focused on evaluating the chord length distribution measured using the FBRM technique compared with alternative sizing techniques, such as laser diffraction and microscopy (Heath et al., 2002, Li et al., 2005; Pons et al., 2006). A complementary particle size analyzer, the PVM, also from Mettler–Toledo Lasentec, was used in this work. The PVM device was installed in the same thermostated reaction vessel with the FBRM probe at a orientation (for experimental set-up see description below and Fig. 5). Unlike most alternative measurement techniques, the PVM can be used simultaneously with the FBRM. The PVM consists of six lasers which illuminate a small area in front of the probe face (Fig. 2a). The probe records digital images of the illuminated area with a field of view of . Droplets and particles larger than can be clearly identified and measured from the PVM images in these experiments; below this size scale, it can be difficult to distinguish individual drops (Fig. 2b). For more information on the probe and the technique the reader is referred to the PVM User Manual (Mettler–Toledo Lasentec®, 2002).
Li et al. (2005) compared the FBRM technique with three alternative sizing techniques, including laser diffraction (using a Mastersizer S), ultrasonic attenuation, and image analysis of microscope photographs. Their study concluded that the chord length distribution (CLD) measured by the FBRM technique is complex, depending on not just the size distribution of the particles but also on the optical properties and shape, especially for very small particles where backscattering becomes important. A similar study by Heath et al. (2002) analyzed the effects on the measured FBRM CLD of weighting the distribution, adjusting the focal point, and varying the agitation speed, the particle properties, and the suspension volume fraction. Heath et al. (2002) concluded that the mean of square-weighted chord lengths, for objects in the size range of , compares well with the actual mean droplet diameter obtained using other (conventional) sizing techniques. They also suggest applying length and cube weightings to better model smaller and larger particles, respectively. Work by Pons et al. (2006) also helped to elucidate the relationships between particle size, shape, and the CLD in order to make the best use of data from the FBRM distributions. In the work of both Heath et al. (2002) and Pons et al. (2002) a linear relationship was reported between the median size of the sieve used to obtain the particles studied and the mean chord length found using the FBRM.
The FBRM probe measures chord lengths, grouped in a chord length distribution, rather than the actual sizes (i.e. diameters); thus the CLD must be transformed into a particle size distribution (PSD) to model the actual surface area for hydrate formation. The subject of transforming or unfolding a CLD into a PSD has gained much attention, and multiple mathematical unfolding techniques exist to translate the CLD into its corresponding PSD (Langston et al., 2001, Ruf et al., 2000, Wynn, 2003).
The ability of the FBRM measurement to characterize particle size is of interest in this work and not the unfolding method; thus the direct approach is applied and compared with the measured FBRM CLD. The measured PSD acquired from analysis of the PVM images or by microscopy is used to create an appropriate CLD. The calculated CLD (from the measured PSD) can then be compared with the CLD measured with the FBRM probe. The mathematical expression for a chord length distribution for spherical particles is given in Eq. (1) (Ruf et al., 2000). A theoretical chord length distribution for each system was generated by inputting the measured particle size distribution into Eq. (1):where is a chord length, is the actual particle diameter, and is the relative probability of obtaining a chord given the diameter .
Known size distributions in the size ranges (small), (medium), and (large) were used to investigate the effects of the experimental conditions and fluid properties on the FBRM results for unimodal distributions. Three bimodal distributions were also studied using the FBRM and PVM to identify system behavior when two distinct (though perhaps overlapping) distributions are present in the system. Using the FBRM to distinguish bimodal systems is invaluable for monitoring agglomerating or flocculating systems where individual droplets or particles agglomerate while some droplets or particles remain dispersed. For example, a bimodal distribution may appear during hydrate formation and agglomeration if large aggregates in the system co-exist with unconverted droplets and singular hydrate particles. The PVM probe provides a visual confirmation of the bimodal dispersion.
Two FBRM probe adjustments were considered for this study: changes to the focal point setting and to the electronics discrimination setting. The focal point of the FBRM laser can be adjusted into the fluid or inside the probe with the standard FBRM focal point position being (Mettler–Toledo Lasentec®, 2004). The standard focal point setting was used at all times unless otherwise noted. Heath et al. (2002) explored the impact of the focal point position on the FBRM measurements, observing that adjusting the focal point more into the fluid increased the number of measured longer chords due to larger particles being less able to approach the measurement window.
The electronics setting can be switched during operation between the fine and the coarse discrimination settings. Turner (2005) suggested that the coarse setting would be “more sensitive to agglomerate sizes than primary particle sizes” compared to the fine setting, bypassing less detectable edges. Heath et al. (2002) also suggest using the coarse setting for flocculated systems. The fine setting was used in these experiments unless noted.
Section snippets
Experimental procedure
Trelleborg Fillite cenospheres were used for all unimodal and bimodal distribution experiments. Cenospheres are hollow microspheres of low density commonly used as fillers in emulsions, epoxies, cements, etc. These alumino-silicate spheres have low oil adsorption and low reactivity, making them ideal for particle size analysis (Trelleborg, 2007). The cenospheres were sieved to make the three standard distribution group sizes: small, medium, and large.
Images of these
Single size distributions
A comparison of the particle size distribution from the PVM and the chord length distribution using the FBRM probe is given in Fig. 6. It is interesting to note that the FBRM chord length cumulative distribution extends well beyond the size of the particles actually in the system for the two smaller distributions. Chords should be a fraction of the particle size; hence, there should be no chords above the maximum particle diameter in the system. Additionally, the small size end of the FBRM-CLD
Conclusions
The applicability of the FBRM probe for typical measurements of emulsion and hydrate characterization has been studied. FBRM measurements tested include droplet and agglomerate size, the detection of hydrate nucleation, and the response to a potential bimodal system. It was found that the FBRM can precisely detect system changes, such as hydrate or ice nucleation, or the introduction of a different particle size. However, certain limitations exist in using the FBRM: (1) the measured chord
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