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Managers of cement plants are gradually becoming aware of the need for soft sensors in product quality assessment. Cement clinker quality parameters are mostly measured by offline laboratory analysis or by the use of online analyzers. The measurement delay and cost, associated with these methods, are a concern in the cement industry. In this study, a regression-based model was developed to predict the clinker quality parameters as a function of the raw meal quality and the kiln operating variables. This model has mean squared error, coefficient of determination, worst case relative error and variance account for (in external data) given as 8.96 × 10
^{–7}, 0.9999, 2.17% and above 97%, respectively. Thus, it is concluded that the developed model can provide real time estimates of the clinker quality parameters and capture wider ranges of real plant operating conditions from first principle-based cement rotary kiln models. Also, the model developed can be utilized online as soft sensor since they contain only variables that are easily measured online.

Cement plays an important role in the construction industry. It is the principal hydraulic binder, and the major strength-giving and property-controlling component of concrete. The raw materials for cement production are usually quarried from local rocks, crushed, and then heated at temperature in excess of 1000˚C in a rotary kiln to form clinker. The quality of the clinker determines the property (such as compressive strength) of the cement made from it; the basis for this property is reported to be the result of a well-burned clinker with consistent chemical composition and free lime [_{2}S) concentration, tricalcium silicate or alite (C_{3}S) concentration, tricalcium aluminate (C_{3}A) concentration, and tetracalcium aluminoferrite (C_{4}AF) concentration [

To deal with the challenges accompanying the data-driven soft sensors, First Principle Models (FPMs) can be applied. Although several FPMs have been developed for optimization and control of cement rotary kilns, none has been developed for soft sensing of cement clinker quality parameters. First principle models have the advantages of being able to capture the physicochemical behaviour of the rotary kiln and have good extrapolation property. Unfortunately, the existing first principle-based rotary kiln models contain variables that are difficult to measure real time, and also are a system of nonlinear Differential-Algebraic Equations (DAEs) which must be solved numerically. Hence, these FPMs are not in the form suitable for online implementation as soft sensors and so, cannot be applied online in their current forms. Therefore, in this work, a framework was developed for converting the first principle models of cement rotary kiln available in the literature to the form useful for online estimation of cement clinker quality parameters. Soft sensor is needed for online sensing of the clinker compositions coming out of the cement rotary kiln because it can also function as a backup sensor when the hardware sensor (using XRF and/or XRD techniques) is faulty or down for maintenance or replacement [

In the cement manufacturing process, the quality of the clinker exiting the rotary kiln determines the eventual quality of the cement produced. In this study, regression models were developed for online estimation of the clinker quality parameters. Experimental designs were performed to investigate the effect of the process (input) parameters on the clinker quality parameters. Numerical solution of first principle and semi-empirical based cement rotary kiln models was obtained at different operating conditions and the data obtained were used to develop the regression models for online estimation of clinker quality parameters.

Real life data from cement plants are not easily available because, for cement manufacturing companies to gain competitive advantage, they keep their data and experience confidential [

The model for cement rotary kiln (Equations (1)-(14)) used in this study is a collation from the works of Darabi [

The equations that describe the one-dimensional steady-state axial evolution of components involved in the clinker formation are given as Equations (1)-(9) [

Calcium Carbonate (Lime Stone)

Calcium Oxide (Quick lime)

Silicon (IV) Oxide (Silica)

Aluminum Oxide (Alumina)

Iron (III) Oxide

Dicalcium Silicate (Belite)

Tricalcium Silicate (Alite)

Tricalcium Aluminate (C_{3}A)

Tetracalcium Aluminoferrite (C_{4}AF)

The energy balance equations that describe the one-dimensional steady-state axial temperature profiles of the phases involved in clinker formation are given as Equations (10)-(12) [

Gas (Free Board) Phase

Solid (Bed) Phase:

Wall Phase

The residence time and velocity of the solid materials within the rotary kiln are described by Equation (13) Equation (14) [

Velocity of the solid,

Material residence time,

where, the heat transfer coefficients (

The twelve differential-algebraic equations (DAEs) in section 2.1 (from which the regression model was developed) are not in the form suitable for soft sensing of clinker quality parameters. To transform this model to a form suitable for soft sensing of clinker quality parameters, numerical solutions are required.

Mastorakos and Co-workers [

Furthermore, to verify the simulation approach adopted in this work, the operating conditions of a typical industrial plant obtained from [

Having verified the simulation approach adopted in this study, data in the range of the plant’s operating conditions and the values of some process parameters for a typical cement manufacturing plant were obtained from [

With these operating conditions, a central composite response surface design (with 1/2 fraction) was used to generate one hundred and fifty-four (154) data points. These data points were then plugged into the rotary kiln simulation platform to determine the response variables for a combination of the inputs/factors. Furthermore, with the aid of Design Expert 7.0 statistical tool, these 154 data points were then used (after outlying data points had been removed based on the method described in section 2.3.1) to build the regression models.

Outlier DetectionAn outlier is defined as an observation that “appears” to be inconsistent with other observations in the data set [

S/N | Raw Meal Quality | Operating Conditions | Kiln Operating Variables | Operating Conditions |
---|---|---|---|---|

1 | Quick Lime (CaO) | 0.30 - 0.50 | Kiln Feed Rate, | 35 - 45 |

2 | Silicon (IV) Oxide | 0.10 - 0.20 | Feed Inlet Temperature, | 990 - 1120 |

3 | Aluminum Oxide | 0.02 - 0.05 | Fuel Feed Rate, | 1.5 - 1.9 |

4 | Iron (III) Oxide | 0.01 - 0.04 | Mass Flow rate of Air, | 27 - 33 |

such approach is, visual inspection. Although visual inspection alone cannot always identify an outlier and can lead to mislabeling an observation as an outlier. Pani and Co-workers [

In this study, 3δ edit and the Box plot methods were applied to each of the operating (response) variable data set. For the 3δ edit rule, a data set was labeled outlier when the data points were three or more standard deviations from the mean. That is,

While, the Box plot method defines regions (upper and lower fences) in the plot beyond which a data set may be labelled an outlier. These regions are:

Furthermore, the Externally Studentized Residual (ESR) diagnostic platform, of central composite design (CCD in) Design Expert 7.0 software was used to detect and eliminate outliers because it uses the concept of 3δ edit rule, and also handled outliers in all five responses simultaneously contrary to the box-plot method.

Any numerical method that computes an approximate solution, is usually accompanied with some limitations, especially its error. Thus, the uncertainty surrounding the data from which the regression models were built is a function of the error propagation in the numerical technique employed. This error propagation is reported in [

where

Alternatively, according to Söderlind and Arévalo [

This numerical approach converges because

Hence to minimize this error, a very small step size was used for the simulation in this study; though it resulted in a longer computational time.

In the chemical analysis of cement, certain mathematical relations exist between the percentage of lime and the combination of compounds like silica, alumina and iron oxide [

Lime saturation factor (LSF) which is the ratio of the actual amount of lime to the theoretical lime required by the other major oxides in the clinker was calculated using the Equation (21).

Silica Moduli (SM) which gives an idea of the amount of melt phase present in the burning zone of the kiln was calculated from the formula given in Equation (22):

The Alumina Moduli (AM) which determines the composition of liquid phase in the clinker was calculated from the formula given in Equation (23):

These quality parameters did not require formulae for their determination. For instance, free lime (FCaO) is simply the amount of unreacted lime free in the clinker; Alite (C_{3}S) was among the kiln exit compositions.

The regression models (eight (8) input-five (5) response model) were built following the steps (below) in Design Expert 7.0 statistical software.

・ The values of the responses (for each design run) in the simulation platform were copied into the central composite design layout view of the Design Expert software.

・ Each response variable was transformed for cases where the ratio of maximum to minimum response value was above 10. Otherwise, transformation was not necessary.

・ The fit summary environment was viewed to access information about the goodness of fit of the model (such as degree of freedom, F-value, P-value) and the model summary statistics (such as standard deviation,

・ Backward elimination regression (with alpha = 0.05) was employed at model process order (which could be linear, 2FI, quadratic, cubic) for automatic elimination of undesired model terms.

・ Analysis of variance (ANOVA) platform which analyzes the chosen model gave a view of the results of analysis.

・ Diagnostic platform which evaluates the model fit and transformation choice with graphs (such as normal plot, residual vs prediction, etc.) was viewed to make a final choice on the model type.

Finally, the coefficients of the proposed regression model given in Equation (24) were determined from ANOVA using Design Expert 7.0 software.

where R is the estimated response variable (clinker quality parameters, i.e., LSF, SM, AM, etc.); _{2}, Al_{2}O_{3}, Fe_{2}O_{3}, mass flow rate of solid, feed inlet temperature, mass flow rate of fuel and mass flow rate of air);

Two sets of data (interpolation and extrapolation) were obtained through two (2)-level factorial design (Res IV) to evaluate the performance of the model.

New operating conditions for the interpolation test were created and plugged into the simulation platform of the first principle-based rotary kiln model to generate response data for the interpolation test. The lower boundary (LB) of the new operating conditions was 110% LB of the (original) operating conditions used to develop the model while the upper boundary (UB) was 90% UB of the (original) operating conditions. The response data so generated were compared with the model predictions at the same design points.

For the extrapolation test, the lower boundary (LB) of the new operating conditions was 90% LB of the (original) operating conditions that were used to develop the model while the upper boundary (UB) was 110% UB of the (original) operating conditions. These response data were compared with the model predictions at the same design points.

In addition to the statistical criteria outlined in section 2.6, the performance of the model developed in this study was determined by evaluating the percent relative error^{2}) and the mean of squared error (MSE) values produced by each model to the trained data (i.e. data used to build the model) and untrained data (i.e. data different from the model data). The Equations (25)-(27) were used to calculate the above mentioned performance criteria.

where,

Furthermore, analysis of the estimation capability of the developed model was done by computing the variance account for (VAF) values of the model for the unknown (external) data. The VAF values of the model used for predicting the clinker quality parameters were calculated in Microsoft Excel using Equation (28) [

The performance criteria are:

・ Statistically, a good model will have

・ The closer the VAF value is to 100%, the better the model prediction capability [

Response surface model was used to fit the first principle-based cement rotary kiln simulation data generated in this study. The model developed is a second order regression model, presented as Equation (29).

where

where

where

The regression model (29) is a relationship between the clinker quality parameters and the input variables: CaO (A), SiO_{2} (B), Fe_{2}O_{3} (C), Al_{2}O_{3} (D), mass flow rate of solid (E), feed inlet temperature (F), mass flow rate of fuel (G) and mass flow rate of air (H).

The performance of the developed regression model was evaluated by comparing its predictions with the simulated first principle-based cement rotary kiln model under the same input conditions. Moreover, some statistical criteria presented in section (2.10) were used to evaluate the capability of the regression model. The results are as reported in

The estimation capabilities of the developed regression model were evaluated with respect to untrained data obtained from simulation (with 2-factor design interpolation data and extrapolation data) as described in section 2.7.

The interpolation capability of the regression model was tested by evaluating its predictive ability using a set of simulated data different from the ones used to develop the model. The results are as reported in

Quality Parameter | MSE | R^{2} | Relative Error (Worst cases), % |
---|---|---|---|

LSF | 0.0150 | 0.9999 | 1.73 |

SM | 0.0983 | 0.9999 | 1.83 |

AM | 0.0172 | 0.9998 | 2.17 |

FCaO | 0.0044 | 0.9999 | 1.39 |

Alite (C_{3}S) | 8.96E−07 | 0.9999 | 0.0497 |

The extrapolation capacity of the regression model was tested by evaluating its predictive ability using a set of data outside the population of simulation data used to develop the model. The results are as reported in

Quality Parameter | MSE | VAF | Relative Error (Worst cases), % |
---|---|---|---|

LSF | 4.1997 | 99.80 | 5.20 |

SM | 0.09633 | 99.88 | 6.96 |

AM | 0.1544 | 99.92 | 6.66 |

FCaO | 1.7885 | 99.52 | 7.32 |

Alite (C_{3}S) | 0.08526 | 99.72 | 6.6649 |

Quality Parameter | MSE | VAF | Relative Error (Worst cases), % |
---|---|---|---|

LSF | 120.88 | 97.02 | 13.30 |

SM | 465.19 | 98.36 | 14.60 |

AM | 75,557,125.73 | 98.82 | 15.81 |

FCaO | 38.27 | 98.80 | 12.99 |

Alite (C_{3}S) | 1197.74 | 97.74 | 17.59 |

outside the plant’s normal operating conditions the model can handle worst case relative error less than 20%. Practically, this error is reasonable as a 10% deviation may result in out-of-specification production.

The estimation capability of the model is satisfactory having met the performance criteria of a predictive model. Therefore, it can be used for online estimation of clinker quality parameters. In addition, this model produces result real time when the input variables are provided, unlike the theoretical model which requires the investigator to wait for its numerical solution to converge. Hence, it can be concluded that the model has the potential to meet the challenge of (real-time) online measurement of clinker quality parameters, by providing reliable, fast online estimation of clinker quality parameters for high quality cement production.

Online, accurate estimates of clinker quality (in real time) will eliminate additional energy and production cost associated with out-of-specification production. Unfortunately, soft sensors developed in the literature for clinker quality parameters are data driven and custom built. So, if the operating conditions of the plant drift away from the original operating range from which the model was built, a new model must be redeveloped.

In this study, a regression-based model was developed for online prediction of clinker quality parameters. The developed model can provide the plant operators with information on clinker quality, for quick control actions which will eventually lead to product quality improvement. The estimation capability of the developed model was satisfactory based on the statistical criteria: mean squared error, coefficient of determination, worst case relative error and variance account for (in external data) given as 8.96 × 10^{−7}, 0.9999, 2.17% and above 97% respectively. Also, the developed model is robust as it captures wider ranges (within and outside) of the real plant operating conditions. Hence, the developed model can be utilized as soft sensor since it contains only variables that are easily measurable online.

It is recommended (for further study) to use nonlinear techniques to develop models from the first principle- based cement rotary kiln simulation data (solutions).

Nsidibe-Obong Ekpe Moses,Sunday Boladale Alabi, (2016) Predictive Model for Cement Clinker Quality Parameters. Journal of Materials Science and Chemical Engineering,04,84-100. doi: 10.4236/msce.2016.47012