A novel distribution rate predicting method of dense medium cyclone in the Taixi coal preparation plant

International Journal of Mineral Processing 142 (2015) 51–55

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International Journal of Mineral Processing journal homepage: www.elsevier.com/locate/ijminpro

A novel distribution rate predicting method of dense medium cyclone in the Taixi coal preparation plant Dongyang Dou a,b,⁎, Jianguo Yang c,⁎⁎, Jiongtian Liu c, Hongfang Zhang d a

Key Laboratory of Coal Processing and Efficient Utilization of Ministry of Education, China University of Mining and Technology, Xuzhou 221116, PR China School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, PR China National Engineering Research Center of Coal Preparation and Purification, China University of Mining and Technology, Xuzhou 221116, PR China d Finlay Coal Processing Engineering & Technology (Beijing) PTY. LTD, Beijing 100004, PR China b c

a r t i c l e

i n f o

Article history: Received 26 November 2014 Received in revised form 20 April 2015 Accepted 22 April 2015 Available online 24 April 2015 Keywords: Modeling Dense medium cyclone Coal cleaning Distribution rate Prediction

a b s t r a c t To predict real-time distribution curve of dense medium cyclone in the Taixi coal preparation plant, a new method based on field data was presented. A group of uniformly designed single machine checks (sampling test of a dense medium cyclone) were carried out for modeling field operating parameters and distribution curve indexes. Then three real-time indexes could be predicted by onsite sensor values, and the present distribution curve model was able to be calculated. Predicting part of the method was also compared with the usual approximate formula method based on the proposed models. The models were proved to be acceptable as the RMS accuracy reached 0.73%, 0.77%, and 0.90% respectively in the training set and 0.76%, 0.63%, and 0.51% for the test example. The predicting results were also verified to be better and more reasonable than the approximate formula method. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Dense medium cyclone (DMC) is one of the most important cleaning units in coal washery. It essentially separates coal particles in the light of their differences in density, and is capable of realizing sharp separations and heavy loads at the same time (Holtham, 2006). Although DMC research has made a tremendous development in the last four decades focusing on size design (Wang et al., 2011; Magwai and Bosman, 2008; Chen et al., 2012) and flow field (Narasimha et al., 2006; Wang et al., 2009; Chu et al., 2012), their industrial model study based on field data is hardly reported. However, a factory study of DMC is considered as significant as those above in the laboratory, it can improve productivity on site, and tends to be more and more attractive nowadays. For example, experience-driven models for the density components of raw coal, the float-and-sink data composition, and the expression of distribution curves were built by analyzing a month comprehensive material of float-and-sink tests of raw coal (Wang et al., 2012). A coal preparation plant in Zonguldak was optimized by equalization of incremental product quality method which maximizes plant yield with a given ash requirement based on float-sink data (Cebeci and Ulusoy, 2013). ⁎ Corresponding author at: Key Laboratory of Coal Processing and Efficient Utilization of Ministry of Education, China University of Mining and Technology, Xuzhou 221116, PR China. ⁎⁎ Corresponding author. E-mail addresses: [email protected] (D. Dou), [email protected] (J. Yang).

http://dx.doi.org/10.1016/j.minpro.2015.04.015 0301-7516/© 2015 Elsevier B.V. All rights reserved.

Once an industrial DMC goes into operation, both the body sizes and process flow are fixed, therefore, operating parameters are the only practical element affecting the separating performance or product quality when the properties of the raw coal do not change significantly with time. However, it is quite surprising that — to our knowledge — there is little literature studying the models between the operating conditions and DMC indexes on the basis of field data. There are two bottlenecks restricting the development of integrated automation in DMC processes. The first is the fast gauging of raw coal material. There seems to be two approaches solving this bottleneck. 1) analyzing a month comprehensive material of float-and-sink tests of raw coal to make an estimation (Wang et al., 2012). 2) real-time prediction by image analysis (Zhang et al., 2012, 2013a,b, 2014a,b). The second is the field models of separation indexes e.g. distribution curves (rates). Usually, the separation indexes of DMCs cannot be monitored directly. Therefore, soft sensor modeling is adopted. A soft sensor comprises a group of measurement signals and a model to estimate an immeasurable parameter. Soft sensors can thus provide a tool for supporting or replacing the potentially difficult and expensive measurements. It has been used successfully in measuring the coal moisture (Zeng et al., 2015) and particle size in a grinding process (Pani and Mohanta, 2014). In this paper, a new soft sensor modeling method for predicting realtime distribution curve of dense medium cyclone in the Taixi coal preparation plant by field operating parameters was proposed. A group of

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D. Dou et al. / International Journal of Mineral Processing 142 (2015) 51–55

Table 1 U6(32 × 21).

Table 2 U12(42 × 32).

No.

Factor 1

Factor 2

Factor 3

1 2 3 4 5 6

1 1 2 2 3 3

1 2 3 1 2 3

1 2 1 2 1 2

specially designed single machine checks were carried out for modeling field operating parameters and distribution curve indexes. Then realtime indexes could be predicted by onsite sensor values, and the present distribution curve model was able to be calculated. An additional experiment was arranged for testing the method and illustrating the prediction process. Based on the models, the method was also compared with the approximate formula method. 2. Soft sensor modeling of DMC

No.

1 2 3 4 5 6 7 8 9 10 11 12

Uniform design (UD) is established on the uniform distribution in number theory. Following UD, experiment points are scattered uniformly within the factor range for obtaining more information by less experiments. UD just takes into account uniform, so the points have a better representative. As orthogonal design, UD provides various experimental tables for users. For example, U6(32 × 21) with multiple levels is given in Table 1. It can arrange two three-level factors and another twolevel factor in six experiments (Liang et al., 2001; Song et al., 2012). It is believed that for experiments with too many parameters or expensive costs, UD may be preferred. 2.2. Modified single machine check Raw coal, clean coal, middings and gangue are sampled simultaneously from a three product dense medium cyclone. It lasts 20 min continuously, during which the values of sensors are recorded once a minute. The averages of each sensor values are documented to represent the work conditions of the time. Then, sample quartering is employed locally to cut down each sample to about 80 kg first. The four samples are transported to a laboratory for further sample splitting to 30 kg each and then float-sink tests are carried out. Finally,

first-stage cyclone

Fig. 1. Three-product cyclone in Taixi plant.

p

kg/L

MPa

r t/h

1.600 1.570 1.520 1.570 1.520 1.620 1.520 1.570 1.600 1.620 1.600 1.620

0.800 0.800 0.650 0.750 0.700 0.800 0.650 0.750 0.700 0.700 0.750 0.650

0.265 0.255 0.275 0.265 0.255 0.275 0.255 0.275 0.265 0.255 0.275 0.265

400 350 300 300 400 350 350 300 400 400 350 300

100 þl 1 þ eð−m⋅ðx−nÞÞ

ð1Þ

where x indicates the density level, f(x) indicates the distribution rates, and l, m, and n are constant coefficients. The least square model identification method is utilized to reckon the above coefficients by the float-sink test data, and the partition curve can be got. 3. Distribution curve prediction on field parameters 3.1. Selecting field parameters Four factors, i.e. density of dense medium suspension (d), content of magnetic substance (c), inlet pressure of dense medium suspension (p) and coal feed rate (r) are selected as our field parameters because they are common, indispensable measuring variables in usual DMC circuits. They are also primary process parameters manipulated by workers in the factory and affect the running performance of DMC significantly. 3.2. Predicting distribution curve To rebuild the distribution curve model as shown in Eq. (1), three points are needed for coefficients l, m, and n. On the basis of two wellknown performance characteristics of DMC i.e. the actual separation

Table 3 Actual UD table. No.

second-stage cyclone

c

kg/L

the distribution rates of each density level can be computed according to the Grumbrech method (Lu, 2005). To plot a partition curve, the modified logistic model is adopted (Dou et al., 2015), f ðxÞ ¼

2.1. Uniform design

d

1 2 3 4 5 6 7 8 9 10 11 12

d

c

p

r

kg/L

kg/L

MPa

t/h

1.609 1.593 1.524 1.577 1.522 1.614 1.517 1.574 1.617 1.616 1.596 1.631

0.803 0.761 0.655 0.682 0.617 0.863 0.623 0.734 0.663 0.838 0.798 0.936

0.257 0.251 0.272 0.266 0.258 0.274 0.261 0.281 0.264 0.256 0.278 0.261

412 350 337 330 403 327 392 340 415 455 283 398

D. Dou et al. / International Journal of Mineral Processing 142 (2015) 51–55

53

Table 4 Example result of float-sink test. Density grade

Raw coal

Clean coal

Middings

Gangue

Weight

Yield

Weight

Yield

Weight

Yield

Weight

Yield

kg/L

kg

%

kg

%

kg

%

kg

%

b1.4 1.4–1.5 1.5–1.6 1.6–1.7 1.7–1.8 1.8–1.9 1.9–2.0 N2.0 Sum

11.80 7.18 1.00 0.57 0.45 0.18 0.30 6.86 28.33

41.652 25.344 3.512 2.012 1.571 0.635 1.059 24.215 100.000

15.54 12.44 2.45 0.68 0.82 0.09 0.01 0.09 32.11

48.396 38.742 7.630 2.118 2.554 0.265 0.030 0.266 100.000

0.37 0.23 0.06 0.04 0.36 3.26 3.72 9.89 17.93

2.064 1.255 0.335 0.251 2.008 18.182 20.747 55.159 100.000

0.00 0.00 0.00 0.00 0.00 0.00 0.19 31.78 31.97

0.000 0.000 0.000 0.000 0.000 0.000 0.579 99.421 100.000

δ75 ¼ f 3 ðd; c; p; r Þ

Table 5 Example distribution rate. Density grade

Distribution rate

kg/L

%

1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.3

0.04 0.03 0.04 0.11 0.70 38.22 92.47 99.14

ð4Þ

where f1, f2, and f3 indicate a polynomial of d, c, p, and r respectively. The models are data-driven models depending on single machine checks following UD. For predicting real-time distribution curves in daily production, δ25, δ50, and δ75 will be calculated by Eqs. (2), (3) and (4) respectively on the four sensor values first. After that, the partition curve model expressed in Eq. (1) can be determined by solving an equation set using three points (δ25, 25), (δ50, 50), and (δ75, 75) and thus the present distribution curve is able to be acquired. 4. Application

density and the probable error, distribution curve index δ25, δ50, and δ75 are selected from the obtained curve, where δ25 indicates the corresponding density to the distribution rates of 25% on the curve, and the others are similar. According to the curve points and corresponding work conditions, δ25, δ50, and δ75 are able to be modeled on the four selected parameters above by regression, δ25 ¼ f 1 ðd; c; p; r Þ

ð2Þ

δ50 ¼ f 2 ðd; c; p; r Þ

ð3Þ

100 90

The non-pressure-feeding DMC typed 3GDMC1300/920 as shown in Fig. 1 in the Taixi coal preparation plant of Ningxia province processed 80–0.5 mm anthracite coal. Coal property of the feedings was smooth and relatively steady. Only the first stage of the DMC was studied. The model number of the sensors used for monitoring d, c, p, and r were LH101, FT2007, KC-3851 and KXHC-0.3/9 respectively. The common scope of each parameter was 1.520–1.620 kg/L for d, 0.650–0.800 kg/L for c, 0.255–0.275 MPa for p and 300–400 t/h for r. They were all the show value of sensors. Four levels for d and c and three levels for p and r were selected, so the UD table U12(42 × 32) was adopted to reduce the number of experiments due to the huge workload of a single machine check. Single machine checks were carried out twelve times, once a day and before daily production. Another one was arranged for testing. In each experiment, the DMC circuit was manipulated to make the sensor values approximate to the corresponding row of Table 2, and after 0.5 h, as the process was stable, modified single machine check started. There existed some differences between Table 2 and the actual

Distribution rate(%)

80 70

Table 6 UD experiment results.

60

No.

50 40 30 20 10 0

1.4

1.6

1.8

2

Density(kg/L) Fig. 2. Example distribution curve.

2.2

2.4

2.6

1 2 3 4 5 6 7 8 9 10 11 12

δ25

δ50

δ75

kg/L

kg/L

kg/L

1.8308 1.7808 1.7246 1.7236 1.6705 1.8619 1.6889 1.7751 1.7836 1.8882 1.7723 1.9184

1.8659 1.8312 1.7525 1.7549 1.7081 1.9058 1.7374 1.7984 1.8120 1.9335 1.8098 1.9550

1.9011 1.8816 1.7804 1.7863 1.7457 1.9497 1.7858 1.8212 1.8404 1.9787 1.8473 1.9916

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D. Dou et al. / International Journal of Mineral Processing 142 (2015) 51–55

Table 7 Relative error of training set. No.

1

2

3

4

5

6

7

8

9

10

11

12

RMS

δ25 (%) δ50 (%) δ75 (%)

−0.47 −0.78 −1.06

0.60 0.67 0.71

1.59 1.18 0.79

−0.23 −0.49 −0.75

−1.25 −1.35 −1.43

0.49 0.91 1.32

−0.08 0.47 1.00

−0.15 −0.34 −0.53

0.34 0.39 0.45

0.31 0.57 0.82

−1.07 −0.84 −0.62

−0.12 −0.46 −0.79

0.73 0.77 0.90

executing table as shown in Table 3. Because of the complicacy and operability in a real plant, it was accredited on the whole. Take single machine check under the first condition in Table 3 (No. 1) for example, where the original data of float-sink test were given in Table 4, based on which, the distribution rate could be calculated using the Grumbrech method as shown in Table 5. Then, the distribution curve which was described in Fig. 2 was obtained by parameter identification of Eq. (1). Thus, values of δ25, δ50, and δ75 could be got. They were 1.8308 kg/L, 1.8659 kg/L and 1.9011 kg/L respectively. Finally, all the 12 experiment results were listed in Table 6. Using the linear regression method, models of δ25, δ50, and δ75 could be built given in Eqs. (5)–(7). Table 7 showed the relative error of the models' predicting value in the training set, where RMS indicated root mean square of the 12 errors. δ25 ¼ 0:06969 þ 0:50287⋅d þ 0:54320⋅c þ 1:23502⋅p þ 0:00050⋅r

ð5Þ

δ50 ¼ 0:45350 þ 0:40538⋅d þ 0:59438⋅c þ 0:45311⋅p þ 0:00044⋅r

ð6Þ

δ75 ¼ 0:83992 þ 0:30906⋅d þ 0:64528⋅c−0:34251⋅p þ 0:00037⋅r

ð7Þ

Another single machine check was carried out for testing the models, the details were shown in Table 8. The predicting values and relative errors were given in Table 9. This testing record was also used for illustrating how to realize a real-time prediction of distribution rate in a real plant. To predict the real-time distribution rate, field operating parameters were gathered first by sensors, for example, d, c, p, and r in Table 8 were got, and immediate predicting value of δ25, δ50, and δ75 could be calculated according to Eqs. (5)–(7). Then, three points i.e. (1.7426, 25), (1.7731, 50) and (1.8035, 75) were offered to Eq. (1) for solving the unknown parameters l, m and n. Finally, m = 36.07965, n = 1.77325, and l = 0.13530. Thus, the present predicting curve model was able to be established. It was described in Fig. 3. By the way, the last point was a little over 100% on axis y, it was then limited to 100% according to general knowledge. Absolute errors between the predicting rate and actual distribution rate were listed in Table 10. From Table 9, the predicting actual separation density δp and the probable error Ep could be obtained,

based on which the approximate formula method (AFM) was able to be adopted to predict the distribution rate too. δp ¼ δ50 ¼ 1:7731kg=L

ð8Þ

δ75 −δ25 ¼ 0:0305 2

ð9Þ

Ep ¼

Absolute errors between the AFM and actual distribution rate were listed in Table 11 for comparison. The first four values of AFM were negative, so they were modified to 0. The last two were greater than 100, so they were limited to 100 too. The modification to AFM result was greater than that of our predicting method, thus it seemed less reasonable. The average absolute value of error in Table 10 was 1.75% while the one in Table 11 was 1.83%. It could be found that the accuracy of the proposed predicting method was a little better than the AFM. However, the accuracy gap was not significant as their foundations, i.e. Eqs. (5)–(7) and (8) and (9), were indeed the same, which were both obtained by our soft sensor modeling method. 5. Conclusions The method is a data-driven method which relies on factory data. UD makes the times of single machine check as less as possible. The models are proved to be acceptable as the RMS accuracy reaches 0.73%, 0.77%, and 0.90% respectively in the training set and 0.76%, 0.63%, and 0.51% for the test example. Although the predicting distribution curve seems to be close to the actual one, the maximum absolute error between the predicting rate and actual distribution rate is 9.7% in 1.75 kg/L grade due to the abrupt slope in the middle of the curve. However, it is verified to be better and more reasonable than the usual approximate formula method. The method provides one of the most significant foundations of advanced process control in coal separating plants such as parameter optimization, product prediction, feedforward control, and operating simulation. 100 predicting curve actual curve original test data

90 80

Table 8 A test experiment result.

1

70

d

c

p

r

δ25

δ50

δ75

kg/L

kg/L

MPa

t/h

kg/L

kg/L

kg/L

1.564

0.622

0.261

450

1.7295

1.7620

1.7944

Distribution rate(%)

No.

60 50 40 30

Table 9 A test experiment result.

20

Model

Predicting value

Relative error

kg/L

%

δ25 δ50 δ75

1.7426 1.7731 1.8035

−0.76% −0.63% −0.51%

10 0

1.4

1.6

1.8 2 Density(kg/L)

2.2

Fig. 3. The predicting distribution curve.

2.4

2.6

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References

Table 10 Error between the predicting and actual distribution rate. Density grade

Actual distribution rate

Predicting distribution rate

Absolute error

kg/L

%

%

%

1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.3

0.09 0.11 0.19 2.14 40.01 95.31 97.86 99.84

0.14 0.14 0.17 1.29 30.31 94.23 99.97 100.00

−0.05 −0.03 0.02 0.85 9.70 1.08 −2.11 −0.16

Table 11 Error between the approximate formula method and actual distribution rate. Density grade

Actual distribution rate

AFM distribution rate

Absolute error

kg/L

%

%

%

1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.3

0.09 0.11 0.19 2.14 40.01 95.31 97.86 99.84

0 0 0 0 30.44 95.58 100 100

0.09 0.11 0.19 2.14 9.57 −0.27 −2.14 −0.16

Acknowledgment The authors would like to thank the Natural Science Foundation of Jiangsu Province (No. BK20140211), the Fundamental Research Funds for the Central Universities (No. 2013QNB06), the National Natural Science Foundation of China (No. 51374207) and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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