(71h) Modeling of Falling Film Absorber

Exchange of material between a gas and a liquid plays a very important role in many chemical processes. This transfer forms the basis of distillation, absorption and humidification. In these cases there is a physical transfer of material across the phase boundary controlled by the physical properties of the system.

Falling film gas absorption, in particular, is a very common phenomenon to be encountered in industrial operations specifically in exothermic gas-liquid reactions such as chlorination, sulphonation and nitration etc. in detergent and wetting/dispersing agent industries, polymerization units, fermentation processes and waste disposal systems.

Absorption of a gas in a falling liquid film may take place with or without reaction. The reactant gas absorbs at the liquid interface due to diffusion perpendicular to the direction of liquid flow. Previous mathematical models for falling film reactors in the field of sulphonation reaction have been proposed by Johnson and Crynes (1974), Davis et al. (1979), Mann et al. (1977), Gutierrez et al. (1988) and Dabir et al. (1996). Bhattacharya et al. (1987) and Nielsen and Villadsen et al. (1983) studied the gas absorption for chlorination reactions. All these studies predict chemical conversion and interfacial temperatures as the most important variable in product yield and product quality.

The aim of the present work is to develop mathematical models for the falling film reactor, which can be used for laminar and turbulent films. The coupled partial differential equations, which describe the mass and heat transfer in the liquid for first and second order reactions are solved by finite difference backward implicit scheme wherein the tridiagonal matrix of order (M x M) was transformed into TDM ( M x 3) using Srivastava's (1983) subroutine. This saves a lot of computer processing time and storage memory. FORTRAN programming language is used for numerical solution. The performance of the model is examined for chlorination of decane and sulphonation of dodecylbenzene.

The model predicts concentration of gas and liquid reactants and temperature in a constant liquid film thickness at various axial and radial distances. The results have been compared with the published work for the first order reaction. It has been observed that this model suits well with the published work but was found highly sensitive to parameters like Thiele modulus and Lewis numbers. Oscillations were obtained for a very narrow range of parameters, so to avoid this non-reliability; parameters (Thiele modulus (F) Arrhenius paramter (g_R) and Biot number for mass transfer (Bi_M) were optimized using Genetic Algorithm (GA)(Deb (2002)) . The parameters were varied in the range of 0.35-0.6 for F , 30-40 for g_R and 1.0-7.0 for Bi_M based on the sensitivity analysis. The final results obtained using GA code for the parameters F , g_R and Bi_M were 0.598, 39.355 and 7.0 respectively. Effect of Thiele modulus and Arrhenius parameter on concentration and temperature profiles has also been incorporated. Variation of Thiele modulus shows that reaction is diffusion-controlled.

The model has also been extended for turbulent flow and varying film thickness. The effect of wavy film flow was considered by using eddy diffusivity parameter in the model. The eddy diffusivity model proposed by Lamourelle and Sandall (1972) for the outer region modified by van Driest Model (1956) for the region near the wall have been used. Effects of interfacial drag at the gas liquid interface and the gas phase heat and mass transfer resistances have been also considered. The equations were solved to predict conversion, liquid film thickness, liquid velocity and temperature of liquid film along the radial and axial direction. The results were compared with the published data and were found to be in good agreement.

Keywords: Falling film reactor, Gas absorption, Coupled equations, Backward implicit scheme

References [1] Bhattacharya, A., Gholap, R.V. & Chaudhari, R.V.,Canadian J. Chem. Eng. 66 (1988) 599-604. [2] Dabir, B., Riazi, M.R. & Davoudirad, H.R.,Chem. Eng. Sci. 51 (1996) 2553-2558. [3] Davis, E.J., Ouwerkerk, M.V. & Venkatesh, S., Chem Eng. Sci. 34 (1979) 539-550. [4] Deb, K., Optimization for Engineering Design- Algorithms and Examples; Prentic of India, New Delhi (2002). [5] Gutierrez, J., Mans, C. & Costa, J., Ind. Eng. Chem. Res. 27 (1988) 1701-1707. [6] Johnson, G.R. & Crynes, B.L., Ind. Eng. Chem., Process Des. Develop.13 (1974) 6-14. [7] Lamourelle, A.P. and Sandall, O.C. Chem. Eng. Sci., 27 (1972) 1035-1043. [8] Mann, R. & Moyes, H., AIChE J. 23 (1977) 17-23. [9] M.R. Riazi & A. Faghri, AIChE J. 31 (12) (1985) 1967-1972. [10] Nielsen, P.H. & Villadsen, J., Chem. Eng. Sci., 38 (1983) 1439-1454. [11] Srivastava, V.K., Ph.D. Thesis, University of Wales, Swansea, UK (1983). [12] Van Driest, E.R., J.Aero. Sci. 23 (1956) 1007-1015.