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Development of a particle size distribution measurement method at high temperature


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Powder Technology 180 (2008) 190 – 195 www.elsevier.com/locate/powtec

Development of a particle size distribution measurement m

ethod at high temperature by use of classification during sampling
Hirofumi Tsuji a,?, Hisao Makino a , Hideto Yoshida b
a b

Energy Engineering Research Laboratory, Central Research Institute of Electric Power Industry, 2-6-1 Nagasaka, Yokosuka 240-0196, Japan Department of Chemical Engineering, Faculty of Engineering, Hiroshima University, 1-4-1 Kagamiyama, Higashi-Hiroshima 739-8527, Japan Received 14 February 2006; accepted 22 February 2007 Available online 1 March 2007

Abstract Dust removal at high temperature is a vital technology for advanced coal utilizing technologies. Particle size distribution measurements are very important for evaluation of the performance of the dust removal equipment. The cascade impactor like Andersen stack sampler (A.S.S.) is now widely used for the measurement of dust. Particulate matters, such as fly ash, become melting particles at high temperature. It, however, is impossible to apply A.S.S. to melting particles. The authors have developed a particle size distribution measurement method by use of classification during particle sampling, which is available for melting particles. The method is applied to the dust emitted from pulverized coal combustion, and the result is compared with a conventional method. The advanced coal utilizing technologies involve lots of coal treating processes, such as pressurized combustion, gasification, etc., which emit many kinds of dusts. It, therefore, is very important to improve the new method to accurately measure wide size distribution. The optimization of operating conditions of the new method is one of the measures of the improvement. The influence of operating conditions of the method on the measurement accuracy is also investigated. The method has a sufficient accuracy for dust with wide size distribution. ? 2007 Elsevier B.V. All rights reserved.
Keywords: Particle size distribution; Measurement; Anisokinetic sampling; Backward sampling; Classification

1. Introduction Coal is an important energy resource for electricity supply because its reserve is more abundant than those of other fossil fuels. Combined cycle power generation systems such as pressurized fluidized bed combustion combined cycle (PFBC), integrated coal gasification combined cycle (IGCC) and integrated coal gasification and fuel cell combined cycle (IGFC) are now attracting attention for more efficient use of coal. For these systems, dust removal at high temperature is a vital technology. The particle size distribution measurements in gas flow are very important to evaluate the performance of dust removal equipment. In particular, the measurement of aerodynamic size is indispensable for such an evaluation. Particulate matters, such as fly ash, become melting particles at high temperature. It is very difficult to measure the particle size distribution of melting particles using a cascade impactor like
? Corresponding author. Tel.: +81 46 856 2121; fax: +81 46 857 5829. E-mail address: tsuji@criepi.denken.or.jp (H. Tsuji). 0032-5910/$ - see front matter ? 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2007.02.019

A.S.S., which is one of the most well-known methods for particle size distribution. Some methods based on optical techniques have been developed recently. These methods may be applied to melting particles at high temperature, but it is extremely difficult to apply these to full-scale units, and these cannot measure aerodynamic size. The authors proposed a particle size distribution measurement method by use of classification during particle sampling [1]. Anisokinetic sampling and backward sampling, in which the sampling probe is aligned at 180° to the main flow, are used for particle classification in this method. This method enables the measurement of particle size distribution of melting particles and droplets, because particles are classified during the sampling and a classifier such as a cascade impactor is not used in this method. The new method is firstly applied to the dust in the exhaust gas from a pulverized coal combustion test furnace. The result is compared with the value obtained by a conventional method, and the possibility of the new method is investigated. The advanced coal utilizing technologies involve lots of coal treating processes, such as pressurized combustion, gasification,

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etc., which emit many kinds of dusts. It, therefore, is very important to improve the new method to accurately measure wide size distribution. The optimization of operating conditions of the new method is one of the measures of the improvement. To elucidate the applicability of the new method to wide size distribution, a numerical experiment is also carried out by numerical generated data on a computer. These show that the new method has a sufficient accuracy for dust with wide size distribution. 2. Principle of the measurement method for particle size distribution 2.1. Classification characteristics Classification of particles by anisokinetic sampling and backward sampling is used in the new method. There are some studies on sampling deviation based on classification during anisokinetic sampling [2–6]. These found that the particle concentration in the sampling probe changes with the Stokes number and velocity ratio (main flow velocity U0/sampling velocity U ). Davies [2] showed that concentration ratio, which is the ratio of the measured particle concentration C to the particle concentration in the main flow C0 for monodispersed particles has a linear relation with the velocity ratio U0/U as follows. & ' C Sk ?x? U0 0: 5 ?1? ? ? C0 Sk ?x? ? 0:5 U Sk ?x? ? 0:5
p 0 Here, Sk ?x? ? 9 lDs is the Stokes number, x is the particle size, U0 is the main flow velocity and U is the sampling velocity. The authors numerically and experimentally investigated particle classification by backward sampling and found that the concentration ratio (particle concentration in the probe C/particle concentration in main flow C0) is determined by the Stokes number and the ratio of main flow velocity to sampling velocity [7,8]. This investigation led to the following equation, which gives the relationship between them.

Fig. 1. Classification ratio of anisokinetic sampling and concentration ratio of backward sampling.

Fig. 1 shows the classification ratio for anisokinetic sampling Ce and the concentration ratio for backward sampling, C/C0. The classification ratio for anisokinetic sampling changes sharply for Sk = 0.1–10. This means that particles of Sk = 0.1– 10 can be classified by anisokinetic sampling. The concentration ratio for backward sampling changes sharply for Sk = 0.03– 0.5, which shows that particle classification can be performed by backward sampling for particles of Sk = 0.03–0.5. Therefore, particles of Sk = 0.03–10 can be classified by combining anisokinetic sampling with backward sampling. 2.2. Procedure of the measurement method The concentration ratio of polydispersed particles with size distribution f (x) for anisokinetic sampling can be derived from Eq. (1) as follows. ' Z & ? C U0 l Sk ?x? ? f ?x?dx ? U Z 0 & Sk ?x? ? 0:5 C0 ' l 0:5 f ? x ? dx ? 4? ? Sk ?x? ? 0:5 0 ?/C ?0 is the concentration ratio of polydispersed Here, C particles with size distribution. This equation shows that there ?/ C ?0 and U0/U. Eq. (4) also exists a linear relationship between C can be expressed as ? C U0 ? ?1?A?: ?A ? U C0 ? 5?

q U x2

& ' C U0 ? exp ?5:09 Sk ?x? C0 U

?2?

The particle size distribution measurement method proposed by the authors uses Eqs. (1) and (2). It is very difficult to directly compare Eqs. (1) and (2). Because Eq. (2) shows that the concentration ratio C/C0 for backward sampling becomes 1 for Sk = 0 and becomes 0 for Sk = ∞, and the concentration ratio for anisokinetic sampling becomes 1 for Sk = 0 and becomes U0/U for Sk = ∞. The authors accordingly introduce the classification ratio Ce for anisokinetic sampling.   Ce ?  
C C C0 w? l ? C0 U0 C U ? C0 U0 U ?1

The slope “A” in Eq. (5) can be determined experimentally. The next equation is derived from Eqs. (4) and (5). Z A?
0 l

C C C0 w ? l ? C0 w? 0

 

?

?

0: 5 Sk ?x? ? 0:5

Sk ?x? f ?x?dx Sk ?x? ? 0:5

? 6?

?3?

When polydispersed particles with size distribution f (x) are aspirated on backward sampling with sampling velocity Ui, the

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H. Tsuji et al. / Powder Technology 180 (2008) 190–195

Fig. 2. Pulverized coal combustion test facility and details of test section.

concentration ratio for backward sampling is expressed as follows. & '   Z l ? C U0 exp ?5:09 Sk ?x? f ?x?dx ?7? P ? Ui C0 i 0 Here, suffix i denotes each sampling velocity. The mathematical forms of Eqs. (6) and (7) are the same. Then, Eqs. (6) and (7) can be expressed as Z l gi ? k i ? x ? f ? x ? dx ; ?8?
0

where g1 ? A; k1 ?x? Sk ?x? ?for anisokinetic sampling? ? Sk ?x? ? 0:5 & '   ? C U0 gi ? P ; ki ?x? ? exp ?5:09 Sk ?x? Ui C0 i ?i ? 2; 3; 4? ?for backward sampling?: ?9?

of the furnace and the details of the test section. Pulverized coal of 40 μm in mass median size was fed into the furnace using two table feeders. Particle sampling was carried out in the test section, located just before the bag filter. Temperature in the test section is approximately 250 °C. Fig. 3 shows the sampling probe employed in the experiment. Silica fiber filters with a diameter of 50 mm were used to collect dust particles. The particles were aspirated both in anisokinetic sampling and in backward sampling. The concentration ratios for anisokinetic sampling and backward sampling were defined as the ratio of the particle concentration measured to that measured by isokinetic sampling. Furthermore, dust particles were isokinetically sampled and introduced into an A.S.S.

?10?

gi is obtained experimentally and ki(x) can be easily calculated. Therefore, the unknown quantity in Eq. (8) is only the size distribution f (x). ki(x) is called the response function. The authors apply the Twomey algorithm [9] to obtain f (x) using the above equation. 3. Experimental A pulverized coal combustion test furnace (coal feed rate; 100 kg/h) was used in the experiment. Fig. 2 shows a schematic

Fig. 3. Sampling probe used in the experiments.

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4. Results and discussion 4.1. Comparison of the measurement accuracy of the new method with that of a cascade impactor The sampling probes with inner diameters of 6 mm were used to anisokinetic sampling and backward sampling of the dust from the exhaust gas of the pulverized coal combustion test furnace. The ratios of main flow velocity to sampling velocity, U0/Ui were set at 1/1.0, 1/1.75 and 1/2.5 on backward sampling. ?/ C ?0) in Eq. (7) were The values of “A” defined in Eq. (5) and (C experimentally determined. Particle size distribution f (x) was calculated by the procedure shown in Section 2.2. Fig. 4 shows two particle size distributions measured by the new method and A.S.S. The dust has a peak at 5 μm in the size distribution. The results obtained by these two methods are not perfectly in agreement, because the result of A.S.S. is affected by the reentrainment of particles on plates and deposition of particles on the wall. Furthermore, the result of the new method is also affected by the measurement errors of concentration ratio. However, the particle size distributions obtained by these two methods briefly agree. It is elucidated that the new method has sufficient applicability as a measurement method for dust emitted from pulverized coal combustion.

Table 1 Operating conditions of the new method on the numerical experiment Case 1 Main flow velocity [m/s] Particle density [kg/m3] Sampling probe inner diameter [mm] U0/U for backward sampling 10 2200 6 1/1.0, 1/1.75, 1/2.5 Case 2

10 1/0.360, 1/0.630, 1/0.900

4.2. Improvement of the measurement accuracy by optimizing the operating conditions There are various kinds of dusts in the advanced coal utilizing technologies. It, therefore, is very important to improve the new method to accurately measure wide size distribution. The optimization of operating conditions of the new method is one of the measures of the improvement. To elucidate the applicability of the method to wide size distribution, a numerical experiment was also carried out by numerical generated data on a computer. Two operating conditions were set in the numerical experiment as shown in Table 1. Main flow velocity and particle density were respectively 10 m/s and 2200 kg/m3 for the two cases. The sampling probe inner diameter of Case 1 was 6 mm, and that of Case 2 was 10 mm. The ratios of main flow velocity to sampling velocity U0/Ui (i = 2, 3, 4) on backward sampling were set at 1/1.0, 1/1.75 ?and 1/2.5 for ? Case 1. The 2 on backward authors set sampling flow rates ? k D s U i 4 sampling for Ds = 6 mm and Ds = 10 mm to the same value. The

Fig. 4. Particle size distributions of dust by the new method and A.S.S.

Fig. 5. Response functions of the new method.

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Table 2 Assumed size distributions for numerical experiment Size distribution function Distribution 1 Distribution 2

Mixture of two lognormals Median size x50 Geometric standard deviation σg Mass fraction 1 2.5 0.5 10 0.5 0.5 0.5 20 0.5

ratios of main flow velocity to sampling velocity U0/Ui for Case 2 were, then, 1/0.360, 1/0.630 and 1/0.900. Fig. 5 shows the response functions of the two cases. There are differences between the response functions of the two cases. In particular, the regions, where the response functions change drastically, are different in the two cases. Fig. 5 suggests that measurement accuracy of Case 2 is better than that of Case 1 for the wide size distribution, because the response function in Case 1 changes sharply for particles of x = 1–10 μm and that in Case 2 changes sharply for particles of x = 0.5–20 μm. The authors assumed two size distributions for the numerical experiment. Table 2 shows the size distributions. In both cases, the mixture of two lognormal size distributions was assumed. The size distribution of Distribution 1 is wider than that of Distribution 2. The g1 in Eq. (9) and gi (i = 2, 3, 4) in Eq. (10) were calculated for both Distribution 1 and 2. Particle size distributions were determined from these values and response functions ki(x) (i = 1, 2, 3, 4) by use of the procedure shown in Section 2.2. Fig. 6 shows the result for Distribution 1. The difference of the size distributions between Case 1 and Case 2 is very small, and these distributions are quite close to the true distribution. The result for Distribution 2 is shown in Fig. 7. There are differences between the true distribution and the size distribution estimated in Case 1. On the other hand, the size distribution in Case 2 is closer to the true. As mentioned before, this is attributed to the fact that the region, where the response function changes drastically, in Case 2 is wider than that in Case 1. By altering the operating conditions, the new method is able to

Fig. 7. Particle size distributions estimated in Cases 1 and 2, and true distribution (mixture of two lognormal distributions; peak1: 0.5 microns, peak2: 20 microns).

measure the wide size distribution. It is considered that the new method has a sufficient accuracy for dust with wide size distribution. 5. Conclusions A particle size distribution measurement method by use of classification during particle sampling was applied to dust emitted from pulverized coal combustion, and the result was compared with the value measured by a conventional method. A numerical experiment was also carried out by numerical generated data on a computer to elucidate the applicability of the method to wide size distribution. The following results are obtained. (1) The size distribution obtained by the new method almost agrees with the result by a conventional method. It is elucidated that the new method has sufficient applicability as a measurement method for dust emitted from pulverized coal combustion. (2) By altering the operating conditions of the new method, it is possible to change the response function. This change in response function affects the measurement accuracy of the method. As the operating conditions are optimized, the method is able to measure wide size distribution. Nomenclature A Value defined by Eq. (5) [–] C Measured particle concentration of monodispersed particles [kg/m3] ? C Measured particle concentration of polydispersed particles [kg/m3] C0 Particle concentration of monodispersed particles in main flow [kg/m3] ?0 C Particle concentration of polydispersed particles in main flow [kg/m3] Ds Sampling probe diameter [m] f ( x) Particle size distribution [–/m] gi Value defined by Eqs. (9) and (10) [–]

Fig. 6. Particle size distributions estimated in Cases 1 and 2, and true distribution (mixture of two lognormal distributions; peak1: 1 micron, peak2: 10 microns).

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ki ( x) Sk U, Ui U0 x σg μ ρp

function of x defined by Eqs. (9) and (10) [–] Stokes number [–] Sampling velocity [m/s] Main flow velocity [m/s] Particle size [m] Geometric standard deviation of lognormal distribution [–] Gas viscosity [Pa s] Particle density [kg/m3]

References
[1] H. Tsuji, H. Makino, H. Yoshida, Advanced measurement methods for particle size distribution by means of backward sampling, J. Soc. Powder Technol., Jpn. 36 (1999) 810–818. [2] C.N. Davies, The entry of aerosols into sampling tubes and heads, Br. J. Appl. Phys. 2 (1968) 921–932.

[3] H.H. Watson, Errors due to anisokinetic sampling of aerosols, Am. Ind. Hyg. Assoc., Q. 15 (1954) 21–25. [4] S. Badzioch, Collection of gas-borne dust particles by means of an aspirated sampling nozzle, Br. J. Appl. Phys. 10 (1959) 26–32. [5] S.P. Beyaev, L.M. Levin, Investigation of Aerosol aspiration by photographing particle tracks under flash illumination, J. Aerosol Sci. 3 (1972) 127–140. [6] S.P. Beyaev, L.M. Levin, Techniques for collection of representative aerosol samples, J. Aerosol Sci. 5 (1974) 325–338. [7] H. Tsuji, H. Makino, H. Yoshida, F. Ogino, T. Inamuro, I. Fujita, Particle classification in gas–particle flow by means of backward sampling, Kagaku Kogaku Ronbunshu 25 (1999) 780–788. [8] H. Tsuji, H. Makino, H. Yoshida, Classification and collection of fine particles by means of backward sampling, Powder Technol. 118 (2001) 45–52. [9] S. Twomey, Comparison of constrained linear inversion and an iterative nonlinear algorithm applied to the indirect estimation of particle size distributions, J. Comput. Phys. 18 (1975) 188–200.


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