Kriging modelling applied to the clinker production process

Gladson Euler Lima Júnior1, Ascendino Pereira de Araújo Neto1, Fabricia Araújo Sales1, Gilvan Wanderley Farias Neto1 Danilo Pablo Barros Araújo1,Romildo Pereira Brito1

Federal University of Campina Grande1, Chemical Engineering Department. May, 2019.

Introduction

24 Cement groups (national and international) .

100 plants in operation.

Production capacity of 100 million tonnes yearly.

Search for alternatives for optimization of the clinkerization process.

High fuel consumption; Figure 1 – Cement plants installed in Brazil

2

Introduction

Phenomenological modeling and machine learning techniques.

Variables of different types such as thermal and mechanical.

3

Objectives To perform the analysis and preprocessing of real data of a rotary kiln.

To build a model based on machine learning techniques using the variables of higher degree of coupling with the equipment.

To perform the validation of the generated model.

To optimize the validated model in order to minimize the consumption related to the inputs of the equipment.

4

Methodology

Figure 3 - Rotary kiln model

Inputs Outputs

Inputs

• Calciner fuel (tonnes/h) • Kiln fuel(tonnes/h) • Feed(tonnes/h) • Exhaust Speed(%)

Outputs

• Secondary air temperature(°C) • O2 in the smoking chamber (%) • Engine torque(%) • Free CaO (%) • Smoking chamber temperature(°C)

Figure 2 - Flowchart of applied methodology

(RQ Kernel)

Preprocessing

5

Methodology

Figure 4 – (a)Sampling data to the secondary air temperature;(b)Boxplot technique; (c) Filtered data of secondary air temperature

(a)

(b) (c)

Figure 2 - Flowchart of applied methodology

(RQ Kernel)

Preprocessing

6

Methodology

Figure 5 – (a)Sampling data to the O2 in the smoking chamber ;(b)Enlarged behavior; (c)Filtered data to the O2 in the smoking chamber

(a)

(b) (c)

Figure 2 - Flowchart of applied methodology

(RQ Kernel)

Preprocessing

7

Methodology

𝚼 𝒙 = 𝑯𝜷 + 𝒁(𝒙

Υ 𝑥 = 𝑦(𝑥1 , 𝑦(𝑥2 , … 𝑦(𝑥𝑛 𝑇

𝐻 =

ℎ1 𝑥1 ℎ2 𝑥1 ⋯ ℎ𝑘 𝑥1

ℎ1 𝑥2 ℎ2 𝑥2 ⋯ ℎ𝑘 𝑥2

⋮ ⋮ ⋱ ⋮ ℎ1 𝑥𝑛 ℎ2 𝑥𝑛 ⋯ ℎ𝑘 𝑥𝑛

𝛽 = 𝛽1, 𝛽2, … 𝛽𝑘𝑇

Z 𝑥 = 𝑧(𝑥1 , 𝑧(𝑥2 , … 𝑧(𝑥𝑛 𝑇

𝐶𝑜𝑣 𝑧 𝑥𝑖 , 𝑧 𝑥𝑗 = 𝔼 𝑧 𝑥𝑖 − 𝑚 𝑥𝑖 (𝑧 𝑥𝑗 − 𝑚 𝑥𝑗 = 𝜎2𝐾 𝑘 𝑥𝑖 , 𝑥𝑗 𝜃

𝐾 𝑘 𝑥𝑖 , 𝑥𝑗 𝜃 =

𝑘 𝑥1, 𝑥1 𝜃 𝑘 𝑥1, 𝑥2 𝜃 ⋯ 𝑘 𝑥1, 𝑥𝑛 𝜃

𝑘 𝑥2, 𝑥1 𝜃 𝑘 𝑥2, 𝑥2 𝜃 ⋯ 𝑘 𝑥2, 𝑥𝑛 𝜃 ⋮ ⋮ ⋱ ⋮ 𝑘 𝑥𝑛, 𝑥1 𝜃 𝑘 𝑥𝑛, 𝑥2 𝜃 ⋯ 𝑘 𝑥𝑛, 𝑥𝑛 𝜃

(2)

(1)

(3)

(4)

(5)

(6)

(7)

𝑘 𝑥, 𝑥∗ 𝜃 = 𝜎𝑓2 1 +

𝐷2

2𝛼𝜎𝑙2

−𝛼

(8)

Rational Quadratic Kernel:

Figure 2 - Flowchart of applied methodology

(RQ Kernel)

Preprocessing

8

Variable Mean Values

Calciner fuel (tonnes/h) 15.68

Kiln fuel (tonnes/h) 11.31

Feed (tonnes/h) 399.8

Exhaust Speed (%) 67.7

Secondary air temperature(°C) 1070

O2 in the smoking chamber (%) 4.25

Smoking chamber temperature(°C) 1017

Engine torque(%) 37.9

Free CaO (%) 0.82

Table 1 – Mean of the variables that compose the base case

Methodology

Figure 2 - Flowchart of applied methodology

(RQ Kernel)

Preprocessing

9

Restrictions

Secondary air temperature(°C):

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛(𝑆𝑒𝑐. 𝐴𝑖𝑟𝑇𝑒𝑚𝑝. ≤ 0.05(1070

O2 in the smoking chamber (%):

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛(𝑂2𝑆𝑚𝑜. 𝐶ℎ𝑎𝑚. ≤ 0.05(4.25

𝑓𝐶𝑂𝑀𝑆𝑈𝑀𝑃𝑇𝐼𝑂𝑁 = 𝑉𝐹𝑈𝐸𝐿𝐾𝐼𝐿𝑁+ 𝑉𝐹𝑈𝐸𝐿𝐶𝐴𝐿𝐶𝐼𝑁𝐸𝑅

Objective Function

Smoking chamber temperature(°C):

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛(𝑇𝑒𝑚𝑝𝑆𝑚𝑜.𝐶ℎ𝑎𝑚. ≤ 0.05(1017

Engine torque(%):

𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛(𝐸𝑛𝑔𝑖𝑛𝑒𝑇𝑜𝑟𝑞𝑢𝑒 ≤ 0.05(37.9

Methodology

Free CaO (%):

1.1 ≤ 𝐹𝑟𝑒𝑒𝐶𝑎𝑂 ≤ 1.6 Method

𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒(𝑜𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒, 𝑥0,𝑚𝑒𝑡ℎ𝑜𝑑 = ′𝐶𝑂𝐵𝑌𝐿𝐴′, 𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠 = 𝑐𝑜𝑛𝑠, 𝑜𝑝𝑡𝑖𝑜𝑛𝑠 = {′𝑚𝑎𝑥𝑖𝑡𝑒𝑟′: 5000,′ 𝑐𝑎𝑙𝑡𝑜𝑙′ = 0.002}

(9)

(10)

(11)

(12)

(13)

(14)

Figure 2 - Flowchart of applied methodology

(RQ Kernel)

Preprocessing

10

Validation Results and Discussion

Figure 7 – Histogram for the secondary air temperature error(%)

Figure 6 – Histogram for the secondary air temperature

Figure 8 – Error scattering for the secondary air temperature

11

Secondary air temperature(%)

O2 in the smoking chamber (%)

Smoking chamber temperature(%)

Engine torque (%) Free CaO (%)

Error (%) 1.12 3.67 0.43 1.82 6.59

Results and Discussion Validation

Table 2– Mean Relative Error

Figure 10 – Validation data sampling for the Free CaO Figure 9 – Validation data sampling for the secondary air temperature

12

Optimization

Variable Base Case Optimization Deviation(%)

Calciner fuel (tonnes/h) 15.68 16.05 -

Kiln fuel (tonnes/h) 11.31 8.96 -

Feed (tonnes/h) 399.8 399.8 -

Exhaust Speed (%) 67.7 67.7 -

Secondary air temperature(°C) 1070 1081 0.97

O2 in the smoking chamber (%) 4.25 4.07 4.39

Smoking chamber temperature(°C) 1017 1001 1.64

Engine torque(%) 37.9 39.8 5.02

Free CaO (%) 0.82 1.16 -

Table 3 – Optimization results

Results and Discussion

13

Conclusions

Preprocessing stage.

Construction and validation of the model.

Reduction of 3.2% (1.53 tonnes/h) in fuel consumption.

Industrial reality.

14

Acknowledgements

15

Kriging modelling applied to the clinker production process

Gladson Euler Lima Júnior1, Ascendino Pereira de Araújo Neto1, Fabricia Araújo Sales1, Gilvan Wanderley Farias Neto1 Danilo Pablo Barros Araújo1,Romildo Pereira Brito1

Federal University of Campina Grande1, Chemical Engineering Department. May, 2019.