**Effect of FCC Catalyst Fines
Particle Distribution on Stack Opacity**

By Ronald G. McClung

This article is the third in a series dealing with quantification of FCC physical property effects on emissions measurements. The two previous Catalyst Reports dealt with stack emissions as affected by density in cyclone operation, and opacity as affected by fresh catalyst density and attrition index.

This Catalyst Report deals with the much more complex issue of fines particle size distribution effect on stack opacity.

**Background**

In the previous Catalyst Report, the attrition index as measured by two different methods was shown to have the single largest impact on opacity measurement for a fixed particle size distribution (PSD).

The particle sizes most adversely impacting opacity are in the 0.2 to 1 micron range as illustrated in Figure 1 for a commercial fines sample of average particle size 9.2 microns. This data supports the previous conclusion that the particle sizes most significantly affecting opacity are products of catalyst attrition. The information simply does not exist or is very limited regarding the interrelationship of actual stack losses and the particle size distribution of those losses. Part of the reason for this lack of information is the primary emphasis on total stack emissions when sampling stack gases as opposed to obtaining PSD's on the sampled material.

Nonetheless, the opacity model used in the just prior Catalyst Report and various commercial fines analysis will allow quantifying of fines PSD using a key simplifying assumption— the attrition tendency of the cataIyst will be assumed constant for all PSD's studied.

**Opacity**

By way of review, the equation giving stack opacity as a function of FCC physical properties is given in Table 1.

The parameters x_{i} and d_{i}
can be obtained from commercial fines particle size distribution
data. The more complex Q_{E} function is pictured in
Figure 2 and requires some very difficult calculations using
complex variables, Bessel functions of different orders, and
their corresponding first derivatives. Fortunately, values of the
"Extinction Function" are available in tabulated
form(Ref. 1) and these will be used in subsequent calculations.
Figure 2 provides an interesting picture of light behavior as it
passes through a stream containing small solid particles. The
phenomenon pictured is one of a light beam reflected off
particles of various sizes and onto others, eventually expending
its kinetic energy after many particle collisions.

**Calculation of PSD Effect**

**Model Input Data**

The data required for x_{i}
and d_{i} is taken from 12 commercial fines samples
illustrated in Figure 3. Given the broad range of these samples,
they very likely are representative of both normal and abnormal
final cyclone or precipitator operation. Nonetheless, in the
course of this article, the analytical technique will be used on
all fines samples for illustrative purposes. The
"conclusions" section will deal with the issue of which
samples are the most representative of stack emissions.

There are a number of equations commonly used to define particle size distribution for mixed solid particles(Ref. 2). The most common distribution used in connection with FCC fresh and E-CAT is the log-normal distribution. However, for the commercial fines data of Figure 2, such distribution does not apply. The commercial data fit best a Gaudin-Schuhmann distribution form. The equations fitting this distribution and data are given in Table 2.

**Light Extinction Coefficient**

The parameters needed for calculation of are wavelength of incident light, , refractive index, m, and the particle size distributions given in the previous sections.

As noted in the previous Catalyst Report, the transmitted wavelength band for an opacity meter is 400-700 nanometers (0.4 to 0.7 microns). However, the maximum meter response occurs in the 500-600 nanometer range. As a consequence for the purposes of this article, a single wavelength of 550 nanometers will be used. The refractive index varies with particle light absorption and reflection characteristics. For FCC catalyst, a value of m = 1.5 is used, a typical value for small white particles(Ref. 3).

Using the particle size
distributions, equations and tabulated values of Q_{E},
the light extinction coefficient can be calculated. Representative values of Q_{E}
are given in Table 3 for illustrative purposes only. Values of for the four average
particle sizes of Figure 3 are listed in Table 4.

**Conclusions**

The effect on opacity of particle size distribution is illustrated in Figure 4 using average particle size as the plotted parameter.

The base case for this figure is:

Note that for a significant range of average particle sizes (4 to 11 microns) the opacity changes less than 3%. Above 11 microns (the two curves representing an APS of 15.1 and 21.9), there is a more substantial decline of opacity due to the presence of lower percentages of finer particles, as illustrated in Table 5.

In addition, given the significant amounts of 30+ or 40+ micron material in each of these coarser samples (see Figure 5), the other two curves (APS = 4.0 and 9.2 microns) would seem more likely to represent a stack fines distribution during proper final cyclone or precipitator operation.

In summary, FCC physical properties affecting opacity in decreasing order of importance are as follows:

**References**

1. Penndorf, Rudolph B., New Tables of Mie Scattering Functions for Spherical Particles, Geophysics Research Directorate, Air Force Cambridge Research Center, Bedford, Mass., 1956

2. Yu, A.B. and Standish, N., "A Study of Particle Size Distributions", Powder Technology, vol. 62. Pp. 101-118, 1990

3. Wolbach, C. Dean, "Approximations to Discrepancies Between Visual and Instrument Opacity Readings for Submission Material", Environmental Science and Technology, Vol. 8, No. 5, May 1974, pp. 458-459