Frequency Domain Model Simplification of Cumulative Mass Fraction in CMSMPR Crystallizer

Document Type: Research Article

Authors

Chemical Engineering Department, Iran University of Science and Technology (IUST) P.O. Box16846-13114 Tehran, I.R. IRAN

Abstract

In this contribution, linearized dynamic model of Cumulative Mass Fraction (CMF) of Potassium Nitrate-Water Seeded Continues Mixed Suspension Mixed Product Removal (CMSMPR) crystallizer is approximated by a simplified model in frequency domain. Frequency domain model simplification is performed heuristically using the frequency response of the derived linearized models data. However, the CMF frequency response of the original model is obtained versus three input variables encompass seeding mass flow rate, inlet liquid volumetric flow rate and jacket temperature with emphasis on minimum model simplification assumptions. Results show that the simplified CMF frequency response predicts system dynamics and covers all system characteristics as well as the main complex model.

Keywords

Main Subjects


[1] Chiu T., Christofides P.D., Nonlinear Control of Particulate Processes, AIChE J., 45, p. 1279, (1999).

[2] Ramanathan, S., “Control of Quasi Rational Distributed Systems with Examples on Control of Cumulative Mass Fraction of a Particle Size Distribution” Ph.D. Thesis, Michigan University, (1988).

[3] Christofides P.D., Li M., Mädler L., Control of Particulate Processes: Recent Results and Future Challenges, Powder Technol., 175, p. 1 (2007).

[4] Sherwin M.B., Shinnar R., Katz S., Dynamic Behavior of the Well-Mixed lsothermal Crystallizer, AIChE J., 13, p. 1141 (1967).

[5] Randolph A.D., Beckman J.R., Krajevich Z.I., Crystal Size Distribution Dynamics in a Classified Crystallizer Part I. Experimental and Theoretical Study of Cycling in a Potassium Chloride Crystallizer, AIChE J., 23, p. 500 (1977).

[6] Yin Q., Song Y., Wang J., Analyses of Stability and Dynamic Patterns of a Continuous Crystallizer with a Size-Dependent Crystal Growth Rate, Ind. Eng. Chem. Res., 42, p. 630, (2003).

[7] Motz S., Mitrović A., Gilles E.-D., Vollmer U., Raisch, J., Modeling, Simulation and Stabilizing H∞-Control of an Oscillating Continuous Crystallizer with Fines Dissolution, Chem. Eng. Sci., 58, p. 3473 (2003).

[8] Vollmer U., Raisch J., Population Balance Modelling and H∞ Controller Design for a Crystallization Process, Chem. Eng. Sci., 57, p. 4401, (2002)

[9] Lakatos B.G., Blickle T., Nonlinear Dynamics of Isothermal CMSMPR Crystallizer: A Simulation Study, Comput. Chem. Eng., 19, p. 501 (1995).

[10] Moldoványi N., Lakatos B.G., Szeifert F., Model Predictive Control of MSMPR Crystallizers, J.Cryst. Growth, 275, p. 1349 (2005).

[11] Shirvani M., Inagaki M., Shimizu T., Simplification Study on Dynamic Models of Distributed Parameter Systems, AIChE J., 41, p. 2658 (1995).

[12] Shirvani M., Doustary M.A., Shahbaz M., Eksiri Z., Heuristic Process Model Simplification in Frequency Response Domain, Int. J. Eng. Transaction B, 17, p. 19, (2004).

[13] Ramkrishna D., “Population Balances: Theory and Application to Particulate Systems in Engineering”, Academic Press, San Diego, USA, (2000).

[14] Mersmann A., “Crystallization Technology Handbook”, Marcel Dekker Inc., New York, USA, (2001).

[15] Miller M.S., “Modelling and Quality Control Strategies for Batch Cooling Crystallizers” Ph.D. Thesis, Texas University at Austin, USA, (1993).

[16] Rojkowski Z., Initial Condition for Population Balance in an MSMPR Crystallizer, AIChE J., 36, p. 630 (1990).

[17] Gahn C., Mersmann A., Brittle Fracture in Crystallization Processes Part B: Growth of Fragments and Scale-up of Suspension Crystallizers, Chem. Eng. Sci., 54, p.1283 (1999).

[18] Gerstlauer A., Motz S., Mitrović A., Gilles E.-D., Development, Analysis and Validation of Population Models For Continuous and Batch Crystallizers, Chem. Eng. Sci., 57, p. 4311 (2002).

[19] Sun X., Tang H., Dai J., Retrieval of Particle Size Distribution in the Dependent Model Using the Moment Method, Opt. Express, 15, p. 11507 (2007).