Real-Time Modelling of Dynamic Behaviour for Clinker Rotary Kilns: *Learning from Experiment and Theory*

ABSTRACT

The authors’ objective is to estimate a dynamic behaviour of Clinker Rotary Kiln when the state variables of the process can be measured only at a few locations. These variables (gas, clinker temperatures and clinker mass distributions) are elaborated with the help of heat, pressure and mass balance partial differential equations. The resulting state model, decomposed into five phenomenological zones of CRK, is used as a first step to define a set of Basic Operating Functions. A second step is used to identify a set of Operating Functions. These OFs have also been decomposed into longitudinal distributions of CRK to replace the constant, unknown or unmeasured parameters. Based on the feature of each zone, the OFs are obtained by solving the steady-state model using the standard Newton-Raphson procedure. The CRK is thus characterized by the state variables and intelligent software of the Numerical Estimated Operating Functions and method is proposed to reevaluate the set of the state variables, in adequate space step-size. Consequently, the state variables profiles are linked with the corresponding OFs, which have a direct influence on submitted disturbances for calibration.

The authors’ objective is to estimate a dynamic behaviour of Clinker Rotary Kiln when the state variables of the process can be measured only at a few locations. These variables (gas, clinker temperatures and clinker mass distributions) are elaborated with the help of heat, pressure and mass balance partial differential equations. The resulting state model, decomposed into five phenomenological zones of CRK, is used as a first step to define a set of Basic Operating Functions. A second step is used to identify a set of Operating Functions. These OFs have also been decomposed into longitudinal distributions of CRK to replace the constant, unknown or unmeasured parameters. Based on the feature of each zone, the OFs are obtained by solving the steady-state model using the standard Newton-Raphson procedure. The CRK is thus characterized by the state variables and intelligent software of the Numerical Estimated Operating Functions and method is proposed to reevaluate the set of the state variables, in adequate space step-size. Consequently, the state variables profiles are linked with the corresponding OFs, which have a direct influence on submitted disturbances for calibration.

Cite this paper

Stanislaw, T. and N’zi, Y. (2014) Real-Time Modelling of Dynamic Behaviour for Clinker Rotary Kilns:*Learning from Experiment and Theory*. *Advances in Pure Mathematics*, **4**, 550-565. doi: 10.4236/apm.2014.410064.

Stanislaw, T. and N’zi, Y. (2014) Real-Time Modelling of Dynamic Behaviour for Clinker Rotary Kilns:

References

[1] Spang, H.A. (1972) Adynamic Model of a Cement Kilns. Automatica, 8, 309-323.

http://dx.doi.org/10.1016/0005-1098(72)90050-7

[2] Bouge, R.H. (1947) The Chemistry of Portland Cement. The Maple Press Company, New York.

[3] Martins, M.A., Oliveira, M.A. and Franca, L.S. (2002) Modeling and Simulation of Limestone Calcinations in Rotary Kilns, Part 1: Pilot kIln, Part 2: Industrial Rotary Kiln. ZKG International, 4-5, 74-87.

[4] Guruz, H.K. and Bac, N. (1981) Mathematical Modeling of Rotary Cement Kilns by the Zone Method. The Canadian Journal of Chemical Engineering, 59, 540-548.

http://dx.doi.org/10.1016/0005-1098(72)90050-7

[5] Mastorakos, E., Massias, A., Tsakiroglou, C. D., Goussis, C., Burganos, V. and Payatakes, A.C. (1999) CFD Predictions for Cement kilns Including Flame Modelling, Heat Transfer and Clinker Chemistry. Applied Mathematical Modelling, 23, 57-76. http://dx.doi.org/10.1016/S0307-904X(98)10053-7

[6] Gorog, J.P., Brimacombe, J.P. and Adams, T.N. (1981) Radiative Heat Transfer in Rotary Kilns. Metallurgical and Materials Transactions B, 12, 55-70.

[7] Barr, P.V., Brimacombe, J.K. and Watkinson, A.P. (1989) A Heat-Transfer Model for the Rotary Kiln, Part 2: Development of the Cross Section Model. Metallurgical and Materials Transactions B, 20, 403-419.

[8] Gorog, J.P., Adams, T.N. and Brimacombe, J.K. (1983) Heat Transfer from Flames in a Rotary Kiln. Metallurgical and Materials Transactions B, 14, 411-424.

[9] Tarasiewicz, S., Gille, J.C., Léger, F. and Vidal, P. (1994) Modelling and Simulation of Complex Mechanical Systems with Applications to a Steam-Generating System, Part 1: Mathematical Modeling. International Journal of Systems Science, 25, 2393-2402. http://dx.doi.org/10.1080/00207729408949360

[10] Tarasiewicz, S., Vidal, P., Léger, F. and Gille, J.C. (1994) Modelling and Simulation of Complex Mechanical Systems with Applications to a Steam-Generating System, Part 2: Numerical Simulation. International Journal of Systems Science, 25, 2403-2416. http://dx.doi.org/10.1080/00207729408949361

[11] Tarasiewicz, S., Charette, A. and Bui, R.T. (1983) Modeling the Direct Continuous Dryer. Proceedings of the 14th Annual Pittsburgh Conference, Pittsburgh, 569-580.

[12] Shahriari, K. and Tarasiewicz, S. (2011) Modeling of a Clinker Rotary Kiln Using Operating Functions Concept. The Canadian Journal of Chemical Engineering, 89, 345-359. http://dx.doi.org/10.1002/cjce.20398

[13] Incropera, F.P. and DeWitt, D.P. (2007) Fundamentals of Heat and Mass Transfer. 6th Edition, John Wiley & Sons, USA.

[14] Sonntag, R.-E. and Borgnakke, C. (2007) Introduction to Engineering Thermodynamics. 2nd Edition, John Wiley & Sons, USA.

[15] Hauser, A. and Walther, T. (1998) Temperature Measurement on Rotary Kiln and Clinker Coolers for Process Control. International Cement Journal, 1-3.

[16] Tarasiewicz, S. and Ding, F. (1998) Multilevel Control to Complex Systems. Proceeding of the Advances in Systems, Signals, Controls and Computers, Durban, 22-24 September 1998, 437-441.

[17] Tarasiewicz, S. and Shahriari, K. (2008) Operating Functions Approach to Model Heat Exchange in a Clinker Rotary Kiln: Case Study for Initial and Boundary Conditions. Technical Report, LACM-Laval University, CRIB-Laval University and Lafarge North America Inc., QC, Canada, 1-37.

[1] Spang, H.A. (1972) Adynamic Model of a Cement Kilns. Automatica, 8, 309-323.

http://dx.doi.org/10.1016/0005-1098(72)90050-7

[2] Bouge, R.H. (1947) The Chemistry of Portland Cement. The Maple Press Company, New York.

[3] Martins, M.A., Oliveira, M.A. and Franca, L.S. (2002) Modeling and Simulation of Limestone Calcinations in Rotary Kilns, Part 1: Pilot kIln, Part 2: Industrial Rotary Kiln. ZKG International, 4-5, 74-87.

[4] Guruz, H.K. and Bac, N. (1981) Mathematical Modeling of Rotary Cement Kilns by the Zone Method. The Canadian Journal of Chemical Engineering, 59, 540-548.

http://dx.doi.org/10.1016/0005-1098(72)90050-7

[5] Mastorakos, E., Massias, A., Tsakiroglou, C. D., Goussis, C., Burganos, V. and Payatakes, A.C. (1999) CFD Predictions for Cement kilns Including Flame Modelling, Heat Transfer and Clinker Chemistry. Applied Mathematical Modelling, 23, 57-76. http://dx.doi.org/10.1016/S0307-904X(98)10053-7

[6] Gorog, J.P., Brimacombe, J.P. and Adams, T.N. (1981) Radiative Heat Transfer in Rotary Kilns. Metallurgical and Materials Transactions B, 12, 55-70.

[7] Barr, P.V., Brimacombe, J.K. and Watkinson, A.P. (1989) A Heat-Transfer Model for the Rotary Kiln, Part 2: Development of the Cross Section Model. Metallurgical and Materials Transactions B, 20, 403-419.

[8] Gorog, J.P., Adams, T.N. and Brimacombe, J.K. (1983) Heat Transfer from Flames in a Rotary Kiln. Metallurgical and Materials Transactions B, 14, 411-424.

[9] Tarasiewicz, S., Gille, J.C., Léger, F. and Vidal, P. (1994) Modelling and Simulation of Complex Mechanical Systems with Applications to a Steam-Generating System, Part 1: Mathematical Modeling. International Journal of Systems Science, 25, 2393-2402. http://dx.doi.org/10.1080/00207729408949360

[10] Tarasiewicz, S., Vidal, P., Léger, F. and Gille, J.C. (1994) Modelling and Simulation of Complex Mechanical Systems with Applications to a Steam-Generating System, Part 2: Numerical Simulation. International Journal of Systems Science, 25, 2403-2416. http://dx.doi.org/10.1080/00207729408949361

[11] Tarasiewicz, S., Charette, A. and Bui, R.T. (1983) Modeling the Direct Continuous Dryer. Proceedings of the 14th Annual Pittsburgh Conference, Pittsburgh, 569-580.

[12] Shahriari, K. and Tarasiewicz, S. (2011) Modeling of a Clinker Rotary Kiln Using Operating Functions Concept. The Canadian Journal of Chemical Engineering, 89, 345-359. http://dx.doi.org/10.1002/cjce.20398

[13] Incropera, F.P. and DeWitt, D.P. (2007) Fundamentals of Heat and Mass Transfer. 6th Edition, John Wiley & Sons, USA.

[14] Sonntag, R.-E. and Borgnakke, C. (2007) Introduction to Engineering Thermodynamics. 2nd Edition, John Wiley & Sons, USA.

[15] Hauser, A. and Walther, T. (1998) Temperature Measurement on Rotary Kiln and Clinker Coolers for Process Control. International Cement Journal, 1-3.

[16] Tarasiewicz, S. and Ding, F. (1998) Multilevel Control to Complex Systems. Proceeding of the Advances in Systems, Signals, Controls and Computers, Durban, 22-24 September 1998, 437-441.

[17] Tarasiewicz, S. and Shahriari, K. (2008) Operating Functions Approach to Model Heat Exchange in a Clinker Rotary Kiln: Case Study for Initial and Boundary Conditions. Technical Report, LACM-Laval University, CRIB-Laval University and Lafarge North America Inc., QC, Canada, 1-37.