Structural and Practical Identifiability of a dynamic gas-liquid film model.
Advancing the chemical engineering fundamentals
Multifase Flows - III (T2-5c)
Keywords: model identifiability, gas-liquid mass transfer coefficient
The mathematical models used to describe the gas-liquid mass-transfer processes usually have two spatial-temporal scales which refer to the physical mass-transfer itself at the gas-liquid interface level, i.e. the microscopic model, and the modelling of the reactor configuration which considers the mixing processes and the chemicals distribution in the whole volume of the reactor, i.e. the macroscopic model. The system has been modelled considering the liquid and the gas phase in well mixed flow regime with a global second order irreversible chemical reaction. To describe the mass-transfer phenomenon at the gas-liquid interface level, chemical reactions and diffusive mass transport have been considered simultaneously in the liquid film. The identifiability analysis based on similarity transformation approach [1,2] shows that the simultaneous measurement of concentrations in the liquid and the gas phase is required for the parameter determination. Furthermore, model parameters like the diffusion coefficients, the specific interfacial area or the film thickness cannot be uncoupled from other parameters, but the kinetic rate constants could be identified in the fast or slow chemical regimes [3]. The structural identifiability analysis of the model without chemical reaction and using the macroscopic concentrations at the gas and liquid phase shows that the identifiable parameters of the model are the gas hold-up, e, the Henry’s constant, H, the reciprocal of the diffusion time, D/d^2, and the volumetric mass transfer coefficient, kLa.
A procedure for the optimal experimental design is proposed based on the analysis of the Fisher Information Matrix of the model. The analysis concludes that the measure of the dynamics of the concentration just in the liquid phase leads to important systematic errors in the determination of kLa [4]. The proposed model is essentially non-linear and its linearisation reduces to the classical macroscopic model. Both models give a straight line when log(1-C/C*) is plotted vs. t but with different slopes for the same kLa.
The structural and the practical indentifiability analysis of the model allows to define an optimal optimisation algorithm and experimental design for parameter identification.
The authors wish to acknowledge the Ministerio de Educación y Ciencia for the financial support for this work under contract CTQ2006-10783/PPQ (Project DATO3)
1.- Vajda, S.; Godfrey, K. R.; Rabitz, H. Math. Biosc. 1989; 93: 217-248.
2.- Chapman, M. J.; Godfrey, K. R.; Chappell, M. J.; Evans, N. D. Math. Biosc. 2003; 183: 1-14.
3.- J. Navarro-Laboulais, S. C. Cardona, J. I. Torregrosa, A. Abad, and F. López; AIChE J. 2006; 52 (8), 2851-63
4.- J. Navarro-Laboulais, S. C. Cardona, J. I. Torregrosa, A. Abad, and F. López; AIChE J. submitted
Presented Tuesday 18, 08:45 to 09:05, in session Multifase Flows - III (T2-5c).
