Fluid Dynamics and Mass Transfer in the Total Capacity Range of Packed Columns up to the Flood Point

Transcription

1 Chem. ng. Tehnol. 18 (1995) Fluid Dynamis and Mass Transfer in the Total Capaity Range of Paked Columns up to the Flood Point R. Billet and M. Shultes" Up to now, the only equations that were known for alulating mass transfer during twophase ounterurrent flow in paked olumns were those that apply to the range extending up to the loading point. The gas and liquid streams flow separately through the olumn below but not above this point. Above it, the shear stress in the gas stream supports an inreasing quantity of liquid in the olumn, with the result that the liquid holdup greatly inreases. Finally, at the flood point, the liquid aumulates to suh an extent that olumn instability ours. Mass transfer in this upper loading range an be desribed if these fluid dynami relationships are taken into onsideration. The algorithm that is presented here for its predition is based on theoretial and experimental studies. 1 Fluid Dynamis A model that desribes the fluid dynami relationships in paked olumns with ounterurrent flow of the gas and liquid phases was developed in a previous work by Billet 31. It allows the flow onditions to be desribed UP to the flood point. The assumption made was that the void fration in a bed of paking ould be represented by a multipliity of vertial hannels through whih the liquid flows downwards in the form of a film ounterurrent to the asending gas stream. This model also permits mass transfer in the loading range up to the flood point to be determined. If a gas flows ounterurrent to a liquid film and the inertia fores are negleted, the shear and gravity fores at the surfae of the film s = so, as defined by q. (l), are in equilibrium with the shear fores t in the gas stream in aordane with q. (2)'), ds = e'g It follows from this that the loal veloity lz,s is given by and the average effetive liquid veloity in the film lz, by 1 = s ~ so s=o =soi The loading point in twophase ounterurrent flow is reahed whenever the gas veloity is just so high that ii,s beomes zero at the surfae of the film s = so. In view of this fat, q. (5) an be derived from the void fration, the speifi surfae a of the bed of paking, and the liquid holdup h, = sou orresponding to the gas veloity at the loading point u ~, The ~. term vs for the resistane fator in q. (5) is desribed by q. (6); and that for the liquid holdup h,s by q. (7). In the derivation of lq. (5), the terms uv = ziv(&k) and u = ah were introdued to allow for the fundamental relationship between the superfiial gas and liquid veloities uv and u and the figures obtained for the average effetive gas and liquid veloities iiv and ii from qs (3) and (4)[2 51. (3) where u,s is the loal liquid veloity in the film, q is the dynami visosity of the liquid, Q is the density of the liquid, g is the aeleration due to gravity, uv is the average effetive gas veloity, ev is the gas density, and (v is the resistane fator for twophase flow. 1 WS * Prof. Dr.Ing. R. Billet and Dr.Ing. M. Shultes, Ruhr University Bohum, UniversitatsstraBe 1, D4630 Bohum. 1)ist of symbols at the end of the paper. The onstant for the speifi paking Cs and the exponent ns in q. (6) depend on the mass flow rate / V and density 0 VCH Verlagsgeseilshaft mbh, D69451 Weinheim, /95/ I $OO+,1'0

2 372 Chem. ng. Tehnol. 18 (1995) &/e ratios, in aordane with qs (8) and (9); and numerial values of Cs for the pakings investigated are If 4 $>0,4: listed in Table 1 [4, 51. v Q If fi $.4: n, = ; Cs from Table 1 (8) n, = ; Cs = CS,T~~. 1 (:) (9) Table la. Charateristi data and onstants for dumped pakings. Dumped pakings Pall ring Ralu flow Ralu ring NOR PAC ring Hiflow ring Clitsh ring Clitsh CMR ring TOPPak ring Rashig ring VSP ring nvi Pa ring Bialeki ring Tellerette Hakette Raflux ring Berl saddle DINPAK Cerami Cerami Ah Cerami Cerami No. 2 hydr '0 hydr. s PMK 30 P 1.5" 1.5" T 1.O' 0.5" ( , I

3 Chem. ng. Tehnol. 18 (2995) Table 1 b. Charateristi data and onstants for regular pakings. Regular pakings Size N a & CS Fl, CV [mml [1/m3] [m2/m'] [m3/m3] Pall ring Cerami Bialeki ring Ralu pak YC Mellapak 2 Y Gempak A2T Impulse paking 2 Cerami 100 h4ontz paking Meral B B uroform PN Above the loading point, the shear stress in the ounterurrent gas stream arrests the downward flow of the liquid film, with the result that the liquid holdup rapidly inreases, as is illustrated in Fig. 1, whih was ompiled from experimental results. It an be seen from this diagram that the urves drawn through the plotted points beome vertial at the flood point, and the ondition duv/dh = 0 an thus be formulated. Another boundary ondition at the flood point, i.e. du/dh = 0, an be dedued from Fig. 2, whih shows the results of studies on the hange in liquid holdup with inrease in the liquid load. These onditions allow qs (10) and (1 1) to be derived for the gas and liquid veloities at the flood point u ~, and ~ I u,f~; and q. (12) for the liquid holdup h,fi if the /V ratio is onstant [3 51. The resistane fator at the flood point vf an be desribed by qs (13)(15) in analogy to the loading point, although the effet of the visosity ratio q/qv is less. One again, the onstant CFI for the speifi paking an be obtained from Table 1 [4, 51. If 4 Jes0.4: nf1 = ; CFI from Table 1 (14) " 10 " s. A= 0 _ 10 3 F C I GCS veio ry uv[m/sj Fig. 1. iquid holdup as a funtion of speifi gas veloity for various liquid load?. The liquid holdup at the flood point h,f1 must be determined by iteration from q. (12) for the mass flow ratio /Vthat relates to the problem in question. In this ase, the only values of physial signifiane are those in the ~/35h~,~~s:~ range. The example given in Fig 3 for the alulation of liquid holdup by means of q. (1 2) applies to a mm plasti Pall ring and an airlwater system. It an be seen that h,fi is only slightly greater than &/3 over a wide range and does not inrease signifiantly until the liquid load exeeds 200 m3/m2 h. 2 Mass Transfer The authors' omprehensive studies on mass transfer in paked olumns have revealed that the volumetri mass transfer oeffiients on the gas and liquid sides /"~a~h and

4 374 Chem. ng. Tehnol. 18 (1995) r 20. m = % a 2 quid and the gas, V and vg are the kinemati visosities of the liquid and the gas, and aph/u is the effetive area, as desribed by q. (20), of the phase boundary available for mass transfer expressed in terms of the area of the unwetted paking [6, 9, 10).. 0 " a a C !z I iquid lood u [m3/rnz/hl Fig.2. iquid holdup as a funtion of liquid load for onstant gas veloity. mm Pait ring, plostt. 0=220 m2/m3. =O.~ m3/m3 Airlwaler, 1 bar, 293 K The height of a olumn is the produt of the height of an overall transfer unit HTUov and the number of overall transfer units NTUov on the gas side (q. (21)). The NTUov an be alulated from the equilibrium urve, the operating harateristis, and the olumn inlet and outlet onentrations; and the HTUoV, from the height of transfer units on the gas and liquid sides HTUv and HTU, and the stripping fator 1 (q. (22)). The latter is the ratio of the slope of the equilibrium urve inyx to the molar liquid/gas flow ratio /V. H = HTUov NTUov (21) HTUov = HTUv + J. HTU, =,&aph an best be desribed by qs (16) and (17) up to the loading point. The liquid holdup h, as desribed by q. (18), is inluded in the equations, beause it is not a funtion of the gas veloity up to the loading point, i.e. h~ = h ~, as ~ desribed, by q. (7) 12, 6, 9, 10, 1 I], qs (16) and (1 7) for &aph and &aph were derived from physial onsiderations, and their validity has been onfirmed in absorption, desorption, and retifiation studies. q. (20) is valid for systems in whih the surfae tension o remains approximately onstant during mass transfer or for systems in whih the surfae tension of the liquid film inreases along the length traversed in the olumn. If, however, the surfae tension of the film dereases along the downward path in the olumn, vorties will our at the phase interfae and thus redue the area of the phase boundary. This ase is referred to as a negative system. Mass transfer experiments in retifiation have demonstrated that allowane an be made for the resulting additional effet on the area of the phase boundary by means of the Marangoni number, as indiated by qs (23) (). A relationship for the area of the phase boundary is thus obtained (q. (26)) P, 101. (1 7) do, Ax da XX* HTU (23) Ma= = l (18) dx D V a du D v a HTUo HTU HTUv X = I= (24) where C and Cv are onstants for speifi pakings, HTU~ HTUov l+x values of whih are listed in Table 1, dh is the hydrauli diameter, as defined by q. (19), D and DV are the diffusion oeffiients for the omponents transferred in the li V Mev vy6 ~Y3a"" 1 &'4 x = m YX C, Mv e v;"~ D;12 g'16 ( h)1'2 u;'~ ()

5 Chem. ng. Tehnol. 18 (1995) Table 2. Capaity range and test failities. oading/flood point Mass transfer Gas apaity fator F v[ m1/2kg1/2si I iquid load u [m3/m2h] 4.88 i iquid density e [kg/m31 7i t 1237 Kinemati visosity of liquid v [m2/s] x lo Surfae tension of liquid u [kg/s2] x lo i 74.0 Diffusion oeffiient in liquid D, [m2/s] x lo9 1.04t6. Gas density ev [kg/m t 4.93 Kinemati visosity of gas vv [m2/s1 x lo Diffusion oeffiient in gas D, [m2/s] x lo6 3.70t87.4 Investigated systems neg. (ys. q. (20) (1 2.4~ 1041MaIo.5) (26) The term da,/dx in q. (23) desribes the differential hange in surfae tension with the liquid onentration x; and the term Ax, the driving onentration differene from the liquid bulk to the phase boundary. The differene Ax is generally unknown; but, if the operating harateristi and equilibrium urve are known, it an be obtained from the overall differene (xx *) and the distribution of the resistane to mass transfer HTU,/HTU, (qs (24) and ()). This is illustrated in Fig. 4, whih shows an xy diagram for the separation of a mixture by retifiation. A detailed example is given in Refs [7, 91. The gas stream exerts a strong effet on the liquid holdup above the loading point. Previous evaluations have revealed that the inrease in h with the gas load, as represented in Fig. 1, an be expressed by q. (27) [8, 1 I]. The liquid holdup h,s up to the loading point an be alulated from q. (18); and that at the flood point h,f1 from q. (12). A hange in film flow within the range above the loading point leads not only to an inrease in the liquid holdup but also to an enlargement of the phase boundary. It IS evident from observations at high gas loads in paked olumns that, as the gas veloity inreases, the film undulates or individual droplets are detahed from it in the one layer of paking and regained by it in the overlying layer. Sine no results of phase boundary measurements in this loading range have yet been published, it is assumed that, in analogy to q. (27), the area of the phase boundary, as defined by q. (28), tends towards a maximum at the flood point. (2) aph Ph,S I t:f1 2,s) (28) a U The area of the phase boundary up to the loading point, expressed in terms of the area of the paking Q, is independent of the gas veloity, i.e. aph = +h,s and an be alulated from q. (20) or, if the system is negative, from q. (26). The enlargement of the phase boundary and the inrease in liquid holdup above the loading point are aompanied by bakmixing of the liquid aused by entrainment of liquid droplets in the gas stream. The shear stress in the ounterurrent gas stream thus redues the average effetive veloity of the liquid film. q. (4) desribes the redution of the average effetive liquid veloity R, with inrease in gas load in the range between the loading and flood points in twophase ounterurrent flow. If the liquid holdup is introdued into this equation, q. (29) will be obtained. 13 v 1 Oiagonol I I 1 I X* XPh XO Mole fration in liquid Fig. 4. yxonentration diagram to desribe the overall onentration differene (xx*) from equilibrium and operating lines for determination of the Marangoni number, f. q. (23). It an be seen that allowane must be made for the hange in liquid holdup and in the resistane fator in alulating the average liquid veloity U above the loading point. q. (29) also indiates that the gas veloity Uv redues the effetive liquid veloity. For the determination of u above the loading point, an empirial equation (q. (30)) an be taken that desribes in general the derease in U in the uv 2 uv,s range and ontains the loaddependent quantities A and B.

6 I 376 Chem. ng. Tehnol. 18 (1995) The average effetive liquid veloity up to the loading point is given by Q = u/h. Afterwards, it progressively dereases with an inrease in the gas load until the flood point is reahed, when it attains a value of zero as a result of strong bakmixing. q. (31) follows from these boundary onditions. (The exponent n is obtained from mass transfer experiments.) " I _4 & Z 0 2 f I= 3 =J g + II 2? = I I I I 1 I I I I I I I I I I I II 1 a, D z 5 Gas opaity fator FV [in "' kgi''s~'1 Fig. 6. xperimental and alulated speifi effiieny NTUov/H for absorption as a funtion of gas apaity fator. In the determination of the volumetri mass transfer oeffiient on the liquid side, allowane must be made in aordane with q. (32) for the hange in the average effetive liquid load. The volumetri mass transfer oeffiient on the gas side an be alulated by q. (33) with the liquid holdup determined from q. (27). v). 3.. r k a.or l : ;j k,,= 3 & 1 + n s ; Gas apaity fator FV lm''2 ky"*.s'] Fig. 7. xperimental and alulated speifi effiieny NTU,/H for desorption as a funtion of gas apaity fator. al =. 5 5 mrn Hiflowring plasli Chlarobenzenelethvlbenzene. 0,=67 mbar. /V=l (33) Typial results of mass transfer measurements inluding those performed at high olumn loads are shown in Fig. 5 for the vauum retifiation of a hlorobenzene/ethylbenzene mixture; in Fig. 6, for the absorption of ammonia from air in water; and in Fig. 7, for the desorption of arbon dioxide from water in air. Fig. 5 is harateristi for retifiation: above the loading point, the speifi effiieny NTUoV/H initially inreases until a maximum is attained and then dereases rapidly. In the absorption studies illustrated in Fig. 6, the speifi number of transfer units dereases with the gas load and also passes through a minimum, after whih it inreases. In the desorption of arbon dioxide (Fig. 7), the gas load does not exert any effet at first on the speifi effiieny NTU,/H, beause the OJ 5 z Vopour opoity fator FV lm"2 kgli2 s'i Fig. 5. xperimental and alulated speifi effiieny NTUov/H for retifiation under total reflux. resistane to mass transfer is entirely on the liquid side. It is only above the loading point that NTU/H inreases. Curves alulated from the above equations have been inluded in Figs 5 7. A balane that was made to minimize the differene between the experimental and alulated results yielded a value of n = 2 for the exponent n in q. (31) and demonstrated that the area of the phase boundary at the flood point ould be desribed by q. (34), %Q!=7 U (zi)0.56 ~ "Ph,S = 10.5 (2),S a 0.56 dh) 0.5 R~ 0.2 ~ ~ 0. F~ 7,0.45 5,S s (34) where o is the surfae tension of the system and ow is the referene value of surfae tension for water at 20 "C. As an be seen from Figs 5 7, the values alulated from this funtion agree well with the experimental results. It is also evident that retifiation represented the only ase in whih the flood point load was attained experimentally. As a onsequene of pronouned bakmixing, the average effetive liquid veloity U beomes zero at the flood point. The signifiane of this for mass transfer at the flood point is that the volumetri mass transfer oeffiient on the liquid side also tends to zero and that the height of a transfer unit on the gas side, as defined by q. (22), beomes infinitely large or NTUov/H beomes infinitely small. The absorption and desorption alulations reveal that a limit is imposed on the inrease in NTUoV/H or NTU/H

7 Chem. ng. Tehnol. 18 (1995) in the upper loading range and that, here too, the separation effiieny dereases onsiderably at the flood point. It an be derived from Figs 6 and 7 that the flood point was not reahed in the absorption and desorption experiments. It is evident that many fators affet mass transfer between the phase above the loading point. The greatly enlarged phase boundary in the upper loading range favours mass transfer on both the liquid and gas sides. ikewise, the inrease in the liquid holdup leads to higher effetive gas veloities, with the result that the volumetri mass transfer oeffiient on the gas side beomes greater. Both these fators initially give rise to an inrease in the separation effiieny of the equipment. It is only when the loads are lose to the flood point that the liquid bakmixing brought about by entrained droplets events an influene on mass transfer that is suffiiently strong to overompensate the effets mentioned and to ause a rapid derease in separation effiieny after the maximum has been passed [l I]. 3 Conlusions quations for the determination of the loading and flood points were derived from a fluid dynamis model that desribes twophase ounterurrent flow in paked olumns in the loading range up to the flood point. It was demonstrated that mass transfer alulations must allow for the ontinuous derease in the average effetive liquid load at gas veloities above the loading point. In the upper loading range, both the liquid holdup and the area of the phase boundary inrease and attain a maximum at the flood point. It has been demonstrated that the values alulated from these equations losely agree with the results of retifiation, absorption and desorption experiments performed in the total apaity range. All that is required for prediting performane are the properties of the phases, the loading parameters, and the data presented in Table 1 on speifi types of paking. Reeived: Deember 5, 1994 [CT718] mny n N NTUo S U U U,S uv 4 v V X Y Greek symbols Subsripts F1 0 Ph S S V W Dimension less n um bers Referenes slope of the equilibrium line exponent paking density overall number of transfer units film thikness superfiial liquid load average effetive liquid veloity loal liquid veloity superfiial gas or vapour veloity average effetive gas or vapour veloity molar flow of gas or vapour mass flow of gas or vapour mole fration in liquid phase mole fration in gas or vaponr phase mass transfer oeffiient void fration dynami visosity stripping fator kinemati visosity density surfae tension shear stress resistane oeffiient flood point liquid surfae interfaial loading point film thikness vapour water Froude number of liquid Marangoni number Reynolds number of liquid Weber number of liquid Symbols used U aph C dh ds D FV g H h HTU HTU, k0 M surfae area per unit paked volume interfaial area per unit paked volume onstant hydrauli diameter olumn diameter diffusion oeffiient vapour or gas apaity fator gravitational onstant height liquid holdup height of a mass transfer unit overall height of a mass transfer unit overall mass transfer oeffiient molar flow of liquid mass flow of liquid moleular weight [l] Billet, R., Industrielle Destillation, Verlag Chemie, Weinheim [2] Billet, R., Festshrift der Fakultat fur Mashinenhau, Ruhr Universitat Bohum 1983, pp [3] Billet, R., I. Chern.. Symp. Ser. No. 104 (1987) pp. A171 A182. [4] Billet, R., Shultes, M., I. Chem.. Symp. Ser. No. 104 (1987) pp. B5 B266. [5] Billet, R., Chem. ng. Tehnol. 1Z (1988) pp [6] Billet, R., Fat. Si. Tehnol. 92 (1990) pp [7] Billet, R., Shultes M., Beitrage zur Verfahrens und Umweltfehnik, RuhrUniversitat Bohum 1991, pp [8] Billet, R., Shultes, M., Chem. ng. Tehnol. 14 (1991) pp [9] Billet, R., Shultes, M., Chem. ng. Tehnol. 16 (1993) pp [lo] Shultes, M., Ph. D. Thesis, RuhrUniversitat Bohum [ll] Billet, R., Paked Towers, VCH Verlagsgesellshaft, Weinheim 1995.

8 = 378 Chem. ng. Tehnol. I8 (1995) Appendix less than 0.4 the exponent n, is given by Numerial xample Absorption of ammonia from 10 m3/h air with water at temperature of C under normal pressure in a paked olumn filled with mm plasti Hiflow rings. The molar flow ratio of liquidlgas is 1.2 and the absorption olumn should operate at 80% of the apaity at the flood point. The physial properties of gadliquidsystem Moleular weight of gas Mv = kg/kmol Moleular weight of liquid M = 18 kg/kmol Density of gas ev= 1.187kg/m 3 Density of liquid e = 998 kg/m3 Visosity of gas qv = x kg/ms Visosity of liquid q = x kg/ms Diffusion oeffiient in gas DV = 24.9 x m2/s Diffusion oeffiient in liquid D, = 2.01 x m2/s Surfae tension of liquids q = 72.14~ kg/s2 Phase equilibrium of gasliquid inyx = 0.95 system rs = x 2*8942 [ 17805(%%)'i2(l8.75~ = h,s = x lop uv,s () = = 'I2 6.9 [ x lop3 1 / x (0.326)= The harateristi paking data and onstants: Total surfae area per unit a = m2/m3 volume Relative void fration = 0.9 m3/m3 Constants Cs = CF1= C, CV = Operation data: Volume stream of gas P = 10 m3/h Molar flow ratio /V= 1.2 Speifi gas veloity UV = 0.8 uv,fi The molar and mass flow of air and water is alulated by: m3 kg V= = kg/h h m3 m kg/m3 v= 10 = kmol/h h kg/kmol kmol = 1.2 V= = kmol/h h kmol kg = ~ kg/h h kmol The olumn apaity at the loading point uv,s follows from qs (5) (9) with the resistane fator ws and the liquid holdup h.s. The liquid load u,s is a funtion of gas veloity uv,s for onstant mass flow ratio /V U,S = ~ _ uv, s _ By iteration uv,s is alulated: uv,s = m/s The gas veloity at flood point UV,FI follows from qs (10) (15) with the resistane fator vfi and the liquid holdup h,fi. For the above determined flow parameter of 0.026<0.4 the exponent nfl is given by ~ /1.187\1'2/o.998x 0.212(0.194) = ~ = ( 998 ) (18.75~ 1 ht,f1(3 h ~,q 0.9) = 0*998x I2x X uv, FI For a flow parameter ( 998 \'I2 x.. (1.187)

9 uv, = Chem. ng. Tehnol. 18 (1995) The iquid load u ~ is again, ~ a funtion ~ of the gas veloity u ~ for, the ~ mass ~ flow ratio /V. U,FI = I F1 Iteration gives the veloites at the flood point: uv,fi = m/s U,FI = x lod3 m3/m2s The absorption olumn should operate at of the apaity at the flood point uv = 0.8 UV,F~ = m/s = m/s U = uv = 2.49~ The olumn diameter is then obtained ds = d = d /3600 m3/m2s = 0.44 m n QV uv K The liquid holdup at the loading and flood point for operating onditions are 0.998~ 2.49~ h;,q (3 h~,~10.9) = 1 x l2X 9.81 X = By iteration the liquid holdup at the flood point is alulated for the boundary ondition: e/3 < h,f, < h ~ ~1, = (2.49X 10~)~ x ( )0 45 = The speifi interfaial area +h/a q. (28). _ 0.4+(3.90.4) () =0.668 a follows then from Above the loading point, the effetive liquid veloity ti is redued in form of q. (31) 8, = 2.49 x [l ( )] = m/s whih effets the liquid side volumetri mass transfer oeffiient in form of q. (32).,8 ffph = / x = 9.51 x x ( ) 2 The gas side volumetri mass transfer oeffiient is alulated from q. (33) /2 pv aph = x x ( ) I87 ( ~ \ I l/s (18.75~ 106/1.187 ) I = 9.01 l/s 24.9 x so that the liquid holdup h follows from q. (27). The heights of liquid and gas side mass transfer units are (:::::> then h~ = ( ) = u 2.49~10~ HTU = ~ = m p aph 9.51 x The speifi interfaial area at the loading and flood point for operating onditions is aiuiated with the hydrauli HTUv uv = = m diameter of the paking dh PVuPh 9*01 d h = 0.U316m I 1.5 ( )0.5 a 2.49~ x 103/ whih give the following height of an overall gas side mass transfer unit with the stripping fator A x A= myx 0.95 = /V 75.18/62.65 ( (2.49~ 103) HTUov = HTUv + A HTU = = 0.512m.