Gas-side mass transfer coefficient of a laboratory column equipped with one sieve tray
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1 Gas-side mass transer coeicient o a laoratory column equipped with one sieve tray Zhivko Ivanov, Zhelcho Steanov, Bogdan Bogdanov Astract: The inluence o plate geometry on the characteristics o luid low and mass transer in a laoratory column was experimentally examined using dierent inary lends. The volumetric gas-liquid mass transer coeicient depends on the properties o the luid, the hydrodynamic regime, and the coniguration o the gas liquid contacting device. Prediction o mass transer coeicient is an important part o gas liquid contactor design. The individual terms in volumetric mass transer coeicients are diicult to measure directly. The aim o this work is experimental study o the kinetic coeicients in distillation o the inary lends in laoratory column at conditions near to model o ideal mixture or liquid phase and ideal displacement or vapour phase. ey words: distillation, mass transer coeicient, tray column INTRODUCTION The inluence o plate geometry on the characteristics o luid low and mass transer in a laoratory column was experimentally examined using dierent inary lends. The volumetric gas-liquid mass transer coeicient depends on the properties o the luid, the hydrodynamic regime, and the coniguration o the gas liquid contacting device. The intensity o interacial mass transer is characterized y the volumetric mass transer coeicient ( a) and determines the amount o gas transerred rom ules into the liquid phase. Bule size is an important design parameter which has a strong inluence on the hydrodynamic ehaviour and on the volumetric mass transer coeicients [1]. Prediction o mass transer coeicient is an important part o gas liquid contactor design. The individual terms in volumetric mass transer coeicients are diicult to measure directly. MATERIALS AND METHODS For direct measurement o overall point eiciency is to make use o the glass la column is complicated-modiication o Oldershaw with take outward overlows [2]. The column has one sieve plate with ollow geometric characteristics: diameter 32mm, numer o the openings-44, diameters o which is 1.1mm. The height o the overlow is 12mm. The overall point eiciency, which takes into account eects o mass transer on tray and in the settling zone, is deined as [3]: ( y n y n 1 ) E = * (1) ( y y ) n 1 Once the point eiciency has een deduced rom the oregoing relationships it can e re-cast in the orm o transer units: N = ln(1 E ) (2) Mass transer eectiveness in gas liquid contactors is most oten expressed y means o the volumetric mass transer coeicient ( a). This may e correlated, or example, with power input per unit volume and gas supericial velocity, ut the resulting correlations do not achieve any degree o generality. Too many phenomena contriute to the values o the ilm coeicient, k and o the speciic area a and their comined eect cannot easily e predicted. Separation o k and a in the volumetric mass transer coeicient is thus a irst step or a etter understanding o the underlying phenomena [4]. The overall volumetric gas-phase mass transer coeicient, a, is calculated rom the ollowing equation,
2 G a u ρ N G G = (3) h M The a value can e predicted i one knows how to estimate the vapour-side mass transer coeicient and the interacial area a, individually. The pure mass transer coeicient is ound through ollowing depends: ' M =, (4) ρg Where: a =, (5) a In order to calculate the volumetric gas-side mass transer coeicient a, one also needs to know how to calculate the speciic interacial area, a. The ormula or its calculation depends on the ule shape [5]:. S a = (6) Au. The surace area S o an ellipsoidal ule can e calculated as ollows [6]: 2 2 l h 1 ( 1+ e) S = π 1+ ln (7) 2 l 2e ( 1 e) Where, the eccentricity e is h e = 1 l 2 The ule ormation requency (numer o ules ormed at the oriice per unit o time) is expressed as: Q (8) G = (9) V The oth asic parameters gas-side mass transer coeicient a and speciic interacial area a depend on the ule diameter [7]: d = 3 g. σ. μ. ρ. ρ. u (10) S L L G G Bule shape, motion and any tendency or the interace to ripple, luctuate or otherwise deorm are all related to the ule size. In turn, ule size is determined y the physical characteristics o the system and operating conditions. Equation implies that the ule size decreases with the increase o oth supericial gas velocity and gas density [5]. The ule diameter is needed also or the calculation o the ule rise velocity: 2σ gds u = + (11) ρl. ds 2 This equation along with equation (10) was also used to calculate the ule Reynolds numer Re needed or estimation o oth ule length l and height h
3 Terasaka derived the ollowing equations or calculating the ellipsoidal ule length and height [8]: d S l = (12) Ta h = 1.3. ds. Ta (13) The ule rise velocity u and oth the ule length l and height h o an ellipsoidal ule take part in the calculation o the rate o surace ormation R s : R s ( l h) l + h = π + u (14) 2 8 Under the examined operating conditions the classical penetration theory cannot e applied successully or the sake o ( ) prediction since this model is explicitly valid only or rigid spherical ules. For all other ule shapes (ellipsoidal in our case) some correction term is needed since the theoretically calculated ( ) values are somewhat inlated and that is why some mitigation will relect to a greater extent the reality. In the case o stripping o caron dioxide rom the aqueous solution with air, has introduced the correction actor to the classical penetration theory to account or the ellipsoidal shape o ules. [9]: 4DR L s = C (15) π S Where the correction actor is C = 683d (16) S EXPERIMENTAL RESULTS Figure 1 shows the proile o the gas-side mass transer coeicient as a unction o the supericial gas velocity otained y experimental and theoretical methods. It is to e noted that the mixture Methanol-Ethanol the maximum dierence etween calculated and experimentally otained Higie values o the coeicients is no more than 14-15%, or mixture o Propanol-Water this dierence is even smaller than 7%. This can e seen even etter in Figure 2, where this comparison is made. Fig.1. Eect o gas velocity and gas-side mass transer coeicient
4 Fig.2. Comparison etween experimental Figure 2 shows that the theoretical reasonale agreement with the experimental results equation (4). ' values and calculated values calculated y equation (15) values are in CONCLUSIONS The classical penetration theory is applicale or predicting gas-side mass transer coeicient measured in methanol-ethanol and propanol-water, in a laoratory column with one sieve tray under atmospheric pressure. NOMENCLATURE A cross-sectional area o the column, [m 2 ] A speciic interacial area, [m 2 /m 3 ] d s sauter mean ule diameter, [m] E overall point eiciency, [%] e ule eccentricity ule ormation requency, [s -1 ] c correction actor g gravitational acceleration, [m.s -1 ] h aerated liquid height, [m] h height o an ellipsoidal ule, [m] gas-side mass transer coeicient, [m.s -1 ] a overal mass transer coeicient, [kmol/m 3.s] l length o an ellipsoidal ule, [m] M molecular weight, [kg/kmol] N numer o overall vapour phase transer units R s surace ormation, [m 2.s -1 ] S ule surace, [m 2 ] u G supericial gas velocity, [m.s -1 ] u ule rise velocity, [m.s -1 ] gas viscosity, [Pa.s] μ G μ L liquid viscosity, [Pa.s] ρ G gas density, [kg.m -3 ] ρ L liquid density, [kg.m -3 ] σ surace tension, [N.m -1 ]
5 4 g. μl Morton numer Mo = 3 ρσ l. ds. u. ρl Bule Reynolds numer Re = μl 0.23 Tadaki numer Ta = Re. Mo REFERENCES 1. Nedelchev, S., U. Jordan, Correction o the Penetration Theory Applied or Prediction o Mass Transer Coeicients in a High-Pressure Bule Column Operated with Gasoline and Toluene, Journal o Chemical Engineering o Japan, 2003, Vol. 36, 5, p Biddulph, M. W., M. A. alassi, A New Column or Measurement o Multicomponent Distillation Design Eiciencies, Trancaction o the Institution o Chemical Engineers, 1990, Vol. 68, Part A, p Chen, G. X.,. T. Chuang, Prediction o Point Eiciency or Sieve Trays in Distillation, Industrial & Engineering Chemistry Research, 1993, Vol. 32, 4, p oichi, A., Mass Transer From Fundamentals to Modern Industrial Application, Wiley-VCH, Weinheim, Nedelchev, S., U. Jordan, A New Correction Factor or Theoretical Prediction o Mass Transer Coeicients in Bule Columns, Journal o Chemical Engineering o Japan, 2006, Vol. 39, 12, p Fan, L. S.,. Tsuchiya, Bule Wake Dynamics in Liquids and Liquid-Solid Suspensions, Butterworth-Heinemann Series in Chemical Engineering, Stoneham, U.S.A, Wilkinson, P. M., H. Haringa, Mass Transer and Bule size in a Bule Column under Pressure, Chem Eng Sci, 1994, Vol. 49, 9, p Terasaka,., Y. Inoue, M. akizaki and M. Niwa, Simultaneous Measurement o 3- Dimensional Shape and Behavior o Single Bule in Liquid Using Laser Sensors, Journal o Chemical Engineering o Japan, 2004, Vol.37, p Miller, D. N.; Scale-up o Agitated vessels gas-liquid mass transer, AIChE J., 1974, 20, Aout the authors: Dipl. Eng. Zhivko Ivanov, Departments o Chemical Engineering Pro. Assen Zlatarov University, Burgas, jijo23@av.g Assoc. Pro. PhD Zhelcho Steanov, Departments o Chemical Engineering Pro. Assen Zlatarov University, Burgas, zhsteanov@av.g Pro. PhD Bogdan Bogdanov, vice Rector Pro. Assen Zlatarov University, Burgas ogdanov_@av.g Acknowledgement The authors would like to acknowledge or the inancial support provided y Bulgarian Ministry o Education and Science, Fund Scientiic Investigations Докладът е рецензиран
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