FISHERIES AND MARINE SERVICE. distillation

Transcription

1 FISHERIES AND MARINE SERVICE Translatin Series N. 188 Separatin f liqid mixtres by partial distillatin by Dr. -Ing Reinhard Billet Original title:. Frm: Chemie-Ing.-Techn. 29(11): , 1957 Translated by the Translatin Brea( PJW ) Mltilingal Services Divisin Department f the Secretary f State f Canada Department f the Envirnment Fisheries and Marine Service pages typescript

2 498 German PJW Fisheries Research Bard f Canada Translatin f article pblished in "Chemie-Ing.-Techn." 29(11): Separatin f.iqid mixtres by partial distillatin 1 by Dr.-Ing,Reinhard Billet Frm the Institte fr Apparats Cnstrctin and Prcedral Techniqe f the Technical Highschl Karlsrhe. An attempt is being made t shw p the determinative inflences and cnnectins in the decmpsitin f binary mixtres thrgh partial distillatin in the thin-layer vaprizer with rtating installatins. Relatins are given fr the cmptatin and mathematical cmprehensin f the distillatin prcess in the thin-layer vaprizer. The practical applicatin is shwn n an example. The thin-layer vaprizer is sed mre and mre fr small and medim evapratin tasks becase f its advantages ver ther types f vaprizers in the chemical indstry; it is sed fr the distillatin f heatsensitive sbstances which is sally carried t nder vaccm in spite f the shrt time f stay, frther fr the cncentratin f sltins, fr the recvery f slvents, and, finally, fr drying. 1 Dedicated n the ccasin f his 57th birthday t Prf. Dr. Ing. Emil Kirschbam at whse sggestin and with whse spprt the wrk was carried t at the Technical Highschl Karlsrhe. I wish t thank my frmer clleages, Messrs. Dr. Ing. G. Lipphardt and Dipl.-Ing. E. Weiss, fr kindly reading the manscript.

3 -2- The shrt time f stay f the gds in the vaprizer is achieved by the bservance f thin flid films with mechanical means. The tw mst familiar types f cnstrctin are the Lwa and the Sambay thinlayer vaprizers, the peratin and se f which have already been described in detail in ther articles 1) 2). Strctre and manner f peratin are characterized by the fact that the liqid t be vaprized is rnning dwn in a thin film n the inner side f a vertical heating cylinder heated frm the tside, and is kept in rtatin by stirring blades fastened t a shaft. In the Lwa vaprizer the stirring blades are rigidly attached t the skft, the distance t the heating jacket amnting t 1 t 2 mm. This als gives s the thickness f the film. In the Sambay vaprizer, n the ther hand, the stirring blades (wipers) are sspended scillatingly n the shaft, s that the thickness f the flid film is adjsted by itself, depending n the bearing pressre f the blade and als n the viscsity f the biling flid. While the peratinal behavir f these thin-layer vaprizers has already been ascertained by investigatins 1) 2), n cmptatin data is available s far which wld make it pssible t calclate in advance the thin-layer vaprizers. It is the aim f the present article t demnstrate sch a mde f calclatin; in it a thery is develped which gives infrmatin n the cnnectin and the fnctinal dependence f the nmers magnitdes which are f imprtance in the separatin frm the litid mixtres thrgh a cntining distillatin in thin-layer vaprizers. Basic eqatins fr partial separatin f liqids thrgh thin-layer distillatin. In the fllwing demnstratin f the determinative cnnectins n the example f a tw-cmpnent mixtre, mlar nits-are sed fr the sake

4 -3- f expediency. Fr the frmlatin f the eqatins f the mixtre we chse, first f all, tl,f_,.lnst general case accrding t Fig. 1. Alng a heated cylindrical wall mves a thin layer f the liqid mixtre which is t be vaprized; it flws in at the place 1= L at a biling temperatre. Let s assme that the mixtre vapr frmed n the liqid-film layer immediately flws away frm (illegible). If the inner diameter f the heating jacket is designated by d(m), the heattransfer srface falling t the infinitely small length dl amnts t: d f = d YP d..( Em?] (1) If Kkcal/m2h C nw represents the heat-transfer nmber frm the heat medim thrgh the wall t the liqid, the fllwing amnt f heat dq/dz passes hrly per length dl: dq = Kdf I=Kd'iP d (?) kcal/h] (2) sme f this eqatin dz is illegible M where?pc] represents the temperatre gradient between heating medim and the liqid which is t be vaprized. Of the latter this amnt f heat vaprizes at place 1 the infinitely small amnt dd CMl/]h, which can be determined with the aid f the mlar evapratin heat r kcal/ml f the mixtre at biling pint p frm: dd- Kd n d,q [M1/h] (3) r At any arbitrary place 1 t dl flws an amnt f liqid F^Ml/] f a cncentratin- xf C M l - % 2. Alng the infinitely small stretch dl riginates the amnt f vapr dd, determined by Eqatin ( 3), with a cncentratin f xdg [M1-3 at the srface f cntact between the vapr f the mixtre and the liqid. At place 1 than remains an amnt f liqid (F - dd) []Ml/]h with a cntent f a lwer-biling cnstitent, smaller nw^r -b;l'tn^ sc`6^sb^,ce >C n4wa`as i^^ rc,aa^-

5 -4- by dxf, while the amnt f mixtre vapr DI[Ml/h1with xd 51l-17. f the lwer-biling sbstance increases alng d1 by the infinitely small amnt dd Ml/h with an increase f dxd CMl-% in the cncentratin f the lwer-biling sbstance. This prcess i s determined by the qantitative eqatin: FxF W dl) xdg + ( F- dl))-(x F - dxf) (4) frm which we btian by mltiplying t: F xf = ddxdg t FxF - d-1) xf - r dxf t d1) dxf (5) By disregarding the infinitely small magnitdes f the secnd rder dd dxf there fllws the differential eqatin fr the accmlatin d-7)=f dxf xdg - xf (6) The eqating f this relatinship with qatin (3) leads t the dif-^ ferentiàl eqatin F, dxf n xdg - X y M ip d r Ml (7) which expresses mathematically the evapratin prcess at any desired place. Fr the integratin f this eqatin let s assme that the mlar evapratin heats f the tw mixtre cmpnents are eqally large. With a nifrm heating-srface lad the amnt f liqid F then de.creases linearly with a decreasing length 1 and can ths be expressed by a simple analytical expressin as fnctin f 1: hi + rml/h (8a) is eqal t the expressin: K - r -F ^ (8b)

6 -5- if ^^M1/^ represents the amnt f inflw and F CMl/h^ the amnt f discharge. If the qtient F / F is expressed by the qantitative relatin`n1, (9) we may als write fr F as fnctin f 1: F (1 --1,^) F= ^f F ^Ml/^ (1) L By insertin^ this relatix^hip in Eqatin ( 7) we get after crrespnding cnversins: F. (1 -ir^). dxf 1 ^ (11a) d^- ^ +F L '. n ' ^^^ xdg - xf ^ d n, Since the variatin in the heat-transfer nmber k cannt be grasped by a clsed analytical fnctin, an integral mean vale k^^ca1/m2h ^, cnsidered cnstant, is intrdced in its place. The different magnitdes f inflence f k will be discssed in mre detail farther belw. If we nw write: dr,q - kl r ^^`. G^ 1. xdg dxf - xf (llb) Fd (1 -^),^ f F L we btain an integral f the f rm ^d? /( ci'f-?) with the sltin d cq 1 1n (c^^..^. )-f C ^. c^ ^I- cq, The integratin f the left side f the differential eqatin (11b) within the limits f 1= t l^ L ^_^} - - ths gives: F (1-7n) ^^ L F a ^1 7n ) ^ F L (1-9 1) ln (F ^ L `^ ) ^ _ L ^ + F _ F t^ 1 1). ^ h y,1 ^

7 -6- The integral ver the right side f Eqatin (11b) within the limits f x F_ X U at the place f discharge t xf = xf at the place f inflw can be slved by a graphic prcess. We ths btain thrgh integratin f Eqatin (11b) fr height L f the heating cylinder a depen^ence characterized by the fllwing eqatin xf xf 1 dxf ^v1-1 r (12) L- F ln - in " L i`fl' D xdg - xf Starting frm Eqatin (6) we nw determine the dependence f the qantitative relatin m n the inflw and discharge cncentratin. The fllwing relatins apply: F = D 3- F (13a) F D + F (13b) By inserting Eqatin (13b) in Eqatin (6) and by integratin within the limits f xf = xf t xf = xf and D= t D=D we btain an eqatin r frm which the qahtitative relatin m may be determined: x F= xf (14) m= e This reslt i s arrived at in a simpler manner if we take int cnsideratin that the infinitely small change in the amnt f vapr dd is eqal t an infinitely small change in the amnt f liqid df, ths dd = df. Frm eqatin ( 6) ths fllws: 7 ^- x F ')c F df 11_^5 _x fi F _1" ^cfi^xf

8 -7- Fr the graphic sltin f Eqatins (12) and (14) a knwledge f the cnnectins between xdg and xf is reqired; this cnnectin can be btained frm the eqilibrim cnditin setting in dring the evapratin prcess. Accrding t Fig. 1, xdg represents the cntent f lwerbiling sbstance f the vapr dd escaping at any given place 1 n the infinitely small stretch dl frm the liqid with the cncentratin xf. The cnstrctin f the thin-layer vaprizer leads s t assme that the vapr frmed frm the liqid is immediately carried away by same. Nw, the evapratin prcess is characterized by the fact that at a biling temperatre f the liqid, engh heat is spplied t same t enable part f it t evaprate. At their mtal srface f cntact Vapr and liqid are in the phase eqilibrim with ne anther. The graphical sltin f the integrals mentined in Eqatins (12), (14), and (15) can be carried t simply if practically n cncentratin gradient ccrs in the liqid film in a radial directin since in that case the difference (xdg - xf) fr a certain cncentratin f liqid xf is given by the sectin f the rdinate in the xd, xf - diagram 3, lying between the diagnal and the eqilibrim crve. The admissibility f the assmptin that in the liqid film in a radial directin there is n.cncentratin gradient present, can be sbstantiated by the fact that the stirring blades effect an intensive mixing f liqid particles f varis caxial liqid layers f the film. v As is knwn, the eqilibrim crve represents the dependence f the vapr cncentratin xdg [Ml-71 ' n the liqid cncentratin xf EMl-% fr the biling state f a mixtre at an even ttal pressre.

9 -8- Fr a given inflw cncentratin xf and fr a given qantitative relatin m it is pssible, with the aid f Eqatin (14), t determine the cncentratin f the discharge liqid, if Eqatin (14) is written in the frm x F ln.1 _ ( I dx F x_ - x D g F X F X F -- T (16) where J x F ' and J issing liqid. represents the integral vale alltted t the initial cntent the integral vale alltted t the final cntent xof F the In the fllwing pages we shall nw describe the graphic sltin f this integral, which agrees in principle with the well-knwn sltin methd fr the bbble distillatin. The reciprcal vales f the differences x - x which are given by Dg F the sectins f the rdinates between the diagnal and the eqilibrim crve, are pltted ver xf We ths, btain the 1/(x - x ) - crve Dg F in Fig. 2. Fig. 2. Determinatin f the calclatin crves fr the distillatin in a thin-layer vaprizer. (The crse f the eqilibrim crve has been assmed) Fr any desired vale x a nmerical vale J is nw assmed and the F nmerical vale fr the area belw the crve 1/(x - x ) frm x Dg F t any F x calclated and the sm ttal is pltted as integral vale J ver x. F F In this way any desired nmber f J may be calclated fr J assmed at -- the place xf ; this leads t the integral crve. Frm the latter and with the aid f the relatin (16) it is then pssible t determine the

10 -9- ' discharge cncentratin xf fr a given inflw cncentratin xf and fr a given qantitative relatin m. This is illstrated with the aid f the fllwing discssin and is graphically analyzed in Fig. 3. Fig. 3. Dependence f the vapr-exit cencentratin xd and the discharge cncentratin xf n the inflw cncentratin xf fr differ ent qantitative relatins m. (Qalitative representatin) Fr given xf a J--vale can be read ff frm the integral crve f Fig. 2. Eqatin (16) nw permits the calclatin f the integral vale J fr a chsen qantitative relatin m; the desired final cncentratin - - xf fr the integral vale J can be inferred frm the integral crve. Fr a selected qantitative relatin m it is ths pssible t determine fr any xf - vales the xf -vales. In this manner we btain a crve which permits t read ff the cncentratin xf t which the remaining liqid has snk frm an initial cncentratin xf at a qantitative rel atin m. Sch crves can be determined fr varis qantitative relatins. Their qalitative crse is shwn by the slid crves in Fig. 3, which shw the cnnectin between xf and xf with m as parameter. If m= 1, the respective xf -crve cincides with the diagnal, if m it côincides with the abscissa. With the reslts f Fig. 3 and with a relatinship fllwing frm a simple bservatin f the qantitative balance it is als pssible t calclate crves frm which the cncentratin xd f the mixtre vapr leaving the thin-layered vaprizer can be read ff at any desired inflw cncentratin xf b evident frnthe qanti^.tive balance: and at any qantitative relatin m. This is

11 -1- D D + F x F _ F x F (17) D + F = F (13a) This gives: xd _ F x F - F x F F - F (18a) Frm this we get by taking int cnsideratin the qantitative relatin m= F IF -- r : xf --ln xf xd M (18b) and: D _ F (1 --yn) (13c) Fr the sake f cmpleteness the crves xd = f(xf ) are pltted in Fig. 3 in a dtted line; here all changes in cncentratins may nw be simply verlked in the chice f the different qantitative relatins. If, e.g., the qantitative prprtin is changed in a thin-layer vaprizer, the cncentratin change can easily be fllwed in sch a diagram fr the respective mixtre and the qantitative change can be calclated with the aid f Eqatins (13c) and (13a). At the marginal transitin m-i,l, i.e. D-4, the xd - crve cincides with the eqilibrim crve and f r: m-11, i. e. D--1 F it cincides with the diagnal. T determine the dimensins f a thin-layer vaprizer, in which a tw-cmpnent mixtre with an initial cncentratin f xf CM1-%^ f the lwer-biling sbstance is t be vaprized a knwledge f the nmerical vale is reqired, accrding t Eqatin (12), fr the integral mentined belw (Eqatin (19)). This can als be slved by a graphic prcess if the eqilibrim crve and the biling pint crve f the liqid mixtre, that is t be separated, are knwn. If the integral is

12 -11- written in the frm 1 D dxf = J - J (19) xf = xf we mst again nderstand nder J the integral vale alltted t the initial cncentratin xf, and nder J the integral vale alltted t the final cncentratin xf. The reciprcal vales f the prdcts (x^g - xf),. D are pltted in the manner shwn in Fig. 4, abve the liqid cncentratin xf, and we ths receive the crve 1/(xDg - xf) D. The Fig. 4. Graphical determinatin f the integral crve y 1 1 JXDg xf D dxf (Eqilibrim crve and biling-pint crve assmed) integral crve is determined in the already-indicated manner. Fr any desired xf any arbitrary nmerical vale is assmed fr J and fr this the nmerical vale is then calclated fr the area belw the crve xdg - xf 1 1 frm xf t any desired xf. The ttal is pltted as integral vale J ver xf. Different vales J can ths be determined fr the assmed J, which - when pltted ver xf - prdce the integral crve JdXF/(XDg - xf) D. In this manner it is als pssible t determine graphically the respective integral crves fr different temperatre gradients D=^ - tf between heating medim (e.g. water steam) and biling liqid. The crse f the evalatin is shwn in Fig. 4.

13 -12- Fr the prpse f a simple applicatin f Eqatin (12) the differences J - J are nw pltted ver the liqid cncentratin xf with m as parameter. The prcdre is as fllws: frm Fig. 3 the xf -vales fr different assmed xf are read ff at m= cnstant and frm the integral crve in Fig. 4 the nmerical vale crrespnding t the cncentratins xf and xf are taken fr J - J. The qalitative crse f the (J - J)--crves is apparent frm Fig. 5 which shws that the difference (^ - J) is the greater, the smaller the qantitative relatin in, i.e. the smaller the residal liqid with the cntent f xf Fig. 5. Dependence f the difference J - - J. n the inflw cncentratin xf resentatin) fr different qantitative relatins m. (Qalitative rep- By sing Figs. 3 and 5 it is nw pssible with the aid f Eqatin (12), t determine the dimensins f the thin-layer vaprizer at a given inflw cncentratin xf fr any desired qantitative relatin, if the mean heat-transfer nmber 1cL Ckcal/m2h C^ is knwn. Heat-transfer Nmber in a Thin-layer Vap.rizer with Rtating Installatins Accrding t Eqatin (12) it is^hecessary t knw, fr an exact predeterminatin f the dimensins f a thin-layer vaprizer fr the distillatin f a tw-cmpnent mixtre, the nm-^-_rical vale f the integral mean vale kl f the heat-transfer nmber ver the height L f the heating srface, i.e. in the cncentratin range f the t-bedistilled liqid xf at the inlet t xf at the tlet. In literatùre 1) 2) heat-transfer vales in the rder f magnitde f 1 t 2

14 -13- keel/m2h C are reprted, with the aid f which apprximate cnclsins may be drawn fr estimates n the heat-transfer cnditins dring the distillatin f liqids abt which there are n vales, measred in the thin-layer vaprizer, available, especially since the heat-transfer nmber reqired in practice fr the achievement f a definite qantitative relatin m can be reached by reglating the nmber f revltins f the blades. T the magnitdes which inflence the heat-transfer nmber kl belng als, in additin t'the nmber f revltins, the inflw cncentratin xf and the qantitative relatin m- F/F, the temperatre gradient D= td - tf between the heating sbstance and the biling liqid, changeable ver the height, the film thickness s, and as measre fr the qantitative capacity f the vaprizer, the qtient F/ds. In view f the large nmber f factrs inflencing the heat transfer dring the thin-layer distillatin it wld be desirable, with regard t an exact pre-determinatin f the dimensins f a thin-layer vaprizer, t determine with an experimental vaprizer the kl-vale, which depends n the magnitdes kl = f xf s, F/ds), (2) fr the mixtre that is t be separated. Relatinship Between Liqid and Mixtre Vapr in any Desired Crss Sectin f the Vaprizer This relatinship, defined as qtient v F/D, is nt t be cmpared with regard t its cnceivable cntent with the crrespnding relatinship in rectifier clmns where F/D has a cnstant nmerical vale fr the intensifying part and als fr the separating part f the clmn, if n side-prdcts are remved and if the mlar evapratin heats f

15 -14- the tw mixtre cmpnents are eqally large. In the thin-layer vaprizer, hwever, v can assme all nmerical vales that are greater than, r eqal t, 1. In cnnectin with the cnsideratins which led t Eqatin (1), we can write fr the variability f the mixtre-vapr amnt alng the evapratin wall D Dr-t Erivi] (21) The dependence f the relatin v n the qantitative relatin m and n the height 1 then prdces the divisin f Eqatin (1) by Eqatin (12) F. (l -In) F (1-7/1) L -) 4 F ' FL -I' D D D e,q (22a) -7 I c'q Thrgh crrespnding transfrmatin, taking int cnsideratin the rel- atinships (13c) and (9), we find the dependence Y = In (22b) in which the qantitative relatin m can be changed accrding t definitin between 1 and. Eqatin (22h) will be discssed with the aid f Fig. 6 in which v is pltted ver height 1 with different qantlative relatins m as parameter. It shws that v is cnstant nly fr the practically insignificant brder case m e (evapratin witht reside) ver height 1. In general, v decreases hyperblically with an increasing 1 and increases with m. Fig. 6. Relatinship V between liqid and mixtre vapr in any desired crss sectin f a thin-layer vaprizer fr different qalitative relatins m.

16 -15- Crse f the Liqid and the Vapr Cncentratin alng the Wall f the Vaprizer Fr the amnt f liqid F at any desired place 1 the fllwing applies accrding t Eqatin (1) in cmpliance with Eqatin (15): F=F xf = xf dxf xdg - xf - ln F (23a) F= F xf ^7- xf The cmbinatin f Eqatin (1) and Eqatin (23a) prvides the cnnectin between xf and 1: xf ` xf dxf xdg - xf = ln -4- L (23b) F:" xf and by linkage with Eqatin (22b) the depence f the liqid-vapr relatin v n xf xf=xf dxf = ln v xdg - xf v-1 (24) x F=XF After the determinatin f the qantitative relatin m, Eqatin (23) permits, by sing a graphic integratin prcess, t state the dependence f the liqid cncentratin xf, and at the same time its crrespnding biling temperatre, with the aid f the biling-pint crve f the sbstance mixtre that is t be distilled f height 1, if the effect f a pssibly sperimpsed rectificatin is left t f cnsideratin. If there is a

17 -16- mathematical relatinship between xdg and xf, the left sides f Eqatins (23b) and (24) can be integrated directly. If the relative vlatility fr a binary mixtre is knwn, the fllwing applies fr the cnnectin between x and x" : Dg F x - Dg- xf c( 1} (c(-1) xf 1 (25) where C is cnstant in ideal mixtres. Frm a simple cnsideratian f a qantitative balance F= D+F (13b) F- x F- D * x D } F - xf D F x F x F- DT F -D U (26a) and by sing the relatins (1), (13c) and (21) it is then easy t determine mathematically the dependence f th*ixtre- vapr cncentratin XD n height 1: xf x - (1 + In, L ) x, L (26b) D 1--fn d F 1-- h't J r xd ;: xf ^- ^ (xf - xf ) L (26c) a r taking int cnsideratin the relatin v accrding t Eqatin (22b): x D= v xf - (v - 1) ' x FU (27) Fig. 7 shws qalitatively the cnnectin between mixtre-vapr cncentratin xd and liqid cncentratin xf accrding t the relatins (27), (23b) and (22b). It als illstrates the tw brder cases m.=, crres-^, pnding t v - = 1 (ttal evapratin), and m= 1, crrespnding t v- c (n-evapratin).

18 -17- By assming a cnstant relative vlatility4), the integratin f Eqatin (23b) prvides, by taking int cnsideratin the relatin f (25) xf = xf x dxf 1 r ln F xf x_ - x- ^ cc - 1 xf - IX ln 1 - \_ 1 - xf xf = X F _ ln ( l -^, L + 1) (28) Ïr^ by de-lgarithming and slving fr 1 we get: xf ^ 1 1 (1 cc xfcx x F /(! -1) (29) Frm Eqatins (15) and ( 25) we get: 1 a cf-1 C(-1 xf x N 1 ^ 1 - F 1 - x /n xf \ F 1 (3) Fig. 7. Mixtre-vapr cncentratin xd in the vapr ncles in dependence n the liqid cncentratin xf fr different qantitative relatins m. (Qalitative representatin). This expressin is inserted in Eqatin (29): xf JQ -L L 1 - xf ^'1 - x F ^ cc - (31) F -, -1 - xf - 1 F 1 - xf

19 -18- The test fr the extreme vales shws that fr xf = X F 1 becmes eqal t (], and fr xf= xf 1 becmes eqal t L. Eqatin (31) enables s t give fr any desired liqid cncentratin xf the place 1 in the vaprizer where a vapr escapes whse eqilibrim cntent xdg f the lwer-biling sbstance, belnging t the cncentratin xf is given by Eqatin (25) with ct =cnst. In that case it is als pssible t give, with the aid f the bilingliqid alng height 1. By inserting Eqatin (29) in Eqatin (26) we finally btain the vapr cncentratin xd in the vapr ncles crrespnding t the liqid cncentratin prevailing at place 1 xf - xf 1 cc c - 1 x a- 1 xf 1 - F - 1 (32) xf " 1 - xf At the cnclsin f the abve bservatins it mst be pinted t nce again fr the sake f cmpleteness that all relatins mentined s far, t the derivatin f which the Eqatins (1) and (21) were sed, are nly strictly valid if the mlar evapratin heat f the.iqid mixtre in the interested cncentratin range is practically independent f the cncentratin and the lad f the heating srface alng the evaprating wall can be assmed as cnstant. Pressre Distribtin and Vapr Frmatin in the Film Layer T evalate the thin layer with respect t the manner f evapratin it is necessary t get acqainted with the pressre distribtin in the film layer. In the free-film vaprizer it has been bserved that de t the Vapr-bbble frmatin the film ften lifts ff frm the wall; this leads t the frmatin f nn-mistened places. This defect des nt ccr any mre in the.thin-layer vaprizer with mechanically-prdced,

20 -19- rtating film layer, since de t the effect f the centrifgal frce the film is pressed against the wall and the evapratin, therefre, takes place evenly and at a higher nmber f revltins and small temperatre gradients, prbably in the inner cazial layers f the liqid. In this chapter we shall nw carry t an evalatin f the pressre distribtin in the film. If t.à.) represents the anglar velcity,l, the specific gravity f the liqid, s(?) the acceleratin f gravity, and the variable peripheral -.- velcity f the particles f the liqid, the fllwing applies fr the change in pressre in a radial directin: dp 2 1/ 2 d, -IL- d illey. 61e) (33) where, witht restricting the general validity f the bservatin, the height and the width f the film are set eqal t 1, Fig. 8. If a linear Fig. 8. Diagram fr the calclatin f the pressre cnditins in the film. Wand -- wall peripheral velcity gradient is assmed in the film layer = / - r (34) we btain as differential eqatin fr the pressre change in the film 2 dp 1 2. (. r 2 - r 1 1', r (35) 1 represents the peripheral velcity f the innermst caxial layer f liqid adhering t the face f the stirring blades. Assming a practically cnstant film thickness and sbstitting 1-2r n/6, the integratin f Eqatin (35) reslts in

21 -2- p = Sdp é n 2, 2 2.V g? s ^2-92 X?22 In r 1-2r2(? -?^) {- 2 1 (^ar^^^il^ ^11^z1^Ce^ (36a) With the aid f this eqatin it is pssible t calclate the pressre prdced by the centrifgal frce at every place f the thin layer, if the nmber f revltins n is knwn and the flw f the revlving film at this nmber f revltins is characterized by a linear velcity gradient d/dr.- cnstant. The effect f the variability f the thickness f the film, cased by the frmatin f bw waves2) in frnt f the stirring blades, and the changes in velcity f the revlving liqid particles cased thereby, as well as the effect f the evapratin, were disregarded in the rgh bservatin. With the se f the fllwing nmerical example it is being shwn what rder f magnitde the pressre f the rtating thin layer has pn the wall f the cylinder. T simplify matters, (illegible...) take as liqid water with a specific gravity f V= 1 kg/m3. Let the distance f the stirring blades frm the cylinder wall amnt t s= 1 t 2 mm, the inner diameter f the heating cylinder t 2r2 = 3 mm. Fr the maximm pressre, i.e. fr the pressre n the inner wall f' the heating cylinder we can write, accrding t Eqatin (36a): _ r 2 1 r2 Pmax = n2 2 [r,22 In r2-2(r2 - r1) s g 1 r 2 r j (36b) The pressres, calclated with this eqatin, which the rtating film layer exerts n the wall f the heating cylinder are pltted in

22 -21- Fig. 9 ver the nmber f revltins n with s as parameter. We ntice that, e.g., at a nmber f revltins f n = 6 rev./min. half an atmsphere f excess pressre is already reached and at n= 1 rev./min. ne atmsphere f excess pressre is already exceeded. Frm this it may be cnclded that with crrespnding small temperatre gradients between heating medim and the liqid which is t be evaprated a vapr frmatin des nt yet set in directly at the wall, as is illstrated by the fllwing nmerical example. Let s assme that water is evaprated in a thin-layer vaprizer at atmspheric pressre. The temperatre gradient.between heating steam and the water t be evaprated is t amnt t 25 C and the nmber f revltins f the stirring blades t 75 rev./min. These cnditins and a heating-steam temperatre f 125 C reqire an average heat-transfer nmber f 18 kcal/m2h C. Let the heating cylinder be manfactred frm steel with a wall-thickness f 5 mm and an inner diameter f 3 mm. The fllwing expressin then shws the amnt f heat exchanged per nit f srface: O(D (td - t^)` S (t^ - twf)` I^ ( td - tf) where the individal magnitdes have the fllwing meaning! a Dkcal/m2h JC = heat-transfer nmber n the heating steam side,, td M t::-wd [ CI à [kcal/mh a heating steam temperatre, wall temperatre n the heating steam side., thermal cndctivity f the heating jacket twf L C = wall temperatre n the liqid side S 1 CM] thickness f heating cylinder kl fkca1/m2h Ci heat-transfer nmber,

23 -22- tf [ C] = biling temperatre f the liqid in the heating cylinder. Fig. 9. Pressre.11 f the revlving film layer n the cylinder wall in dependence n the nmber f revltins n fr different film thicknesses. Medim: water, inside diameter f heating jacket d.3 m. The small effect f the difference between external and internal diameter f the heating jacket has been left t f cnsideratin here. Inserting the abve nmerical vales we get KL(tD-tF) ' = 45, kcal/m2h. If D is eqal t 5 kcal/m2h C we get: 45, = 5 (125 - twd); twd =.116 C. With 5 kcal/mh C and sl=.5 m we finally get fr the wall temperatre n the side f the liqid: 45, = 5 5 (116 - twf) ; twf = C. The average temperatre n the liqid side ths amnts t C. If n vapr is t be prdced by the layer f liqid adhering directly t the cylinder wall, the pressre f the liqid against the wall mst be greater than the satrated vapr pressre f the biling liqid belnging t the abve-calclated wall temperatre twf. In the case f water the latter amnts, accrding t the water-vapr table, t apprximately.54 atmspheres excess pressre. The pressres (Fig. 9) calclated after Eqatin (36b) lie higher with.56 atm. excess pressre fr s= lmm,.62 atm. excess pressre fr s-:n.1.5 mm, and.73 atm. excess pressre fr

24 -23- s- 2 mm; this shws that fr the abve-mentined cnditins theretically still n vapr develps at the heating wall. An evapratin will start nly at the internal caxial layers f liqid, where the pressre f the liqid prdced by the centrifgal frce is smaller than at the heating wall. A pssibly-ccrring delay in biling in the liqid is then lifted at the latest at the free srface f the revlving liqid film when cming in cntact with the frnts f the stirring blades. These discssins prvide, at the same time, als an explanatin why in the thin-layer vaprizer sltins may be evaprated t very high cncentratins witht any danger f brning tgether with the heating wall. Determinative fr the chice f high nmbers f revltins is the fact that an increase in the nmber f revltin n f the stirring blades cases a cnsiderable increase in the heat-transfer nmber, thereby achieving an increase in the evapratin capacity. Speeds mx p t ver 1 rev./min are seds). Fr reasns f ecnmy, hwever, n cannt be chsen t high since the pwer demand fr the stirrer increases at the same time. On the basis f the abve apprximate calclatin, the assmptin may be expressed that in the thin-layer distillatin in vaprizers with.a mechanically-prdced revlving film layer, at a high speed f the rtating blades and small r medim temperatre gradient between heating medim and biling liqid, n vapr bbbles can frm immediately n the heating wall. Hwever, at lw speeds and high temperatre radients this will definitely be the case.

25 -24- Time f Stay f the Sbstances in the Thin-Layer Vaprizer The average time f stay z f the particles f liqid can be determined frm the relatin z J 36 [s] (37) where J[m^jrepresents the liqid cntent and V Em3/q the hrly thrghpt amnt. Operatinal measrementsl) have shwn that the latter may be varied in the prprtin 1:4. A nmerical example will be sed t give infrmatin n the rder f magnitde f the time f stay: Thin-layer vaprizer: Cnstrctin Lwal), heating srface.8 m2, amnt flwing thrgh p t 4 1/h, width f slit s= 1 mm, (crrespnds t a liqid cntent f m3). The time f stay is ths calclated at z= 7 s. Fr a thrgh-flw amnt f 1 1/h z= 28 s. As can be nticed, in the abve example the time f stay amnts t less than ne-half minte; in this cnnectin it mst als be nticed that the mixtre vapr has a shrter time f stay than the discharge. Fr this reasn temperatre-sensitive sbstances can still be evaprated with care at already relatively high temperatres. In the distillatin f sbstance mixtres the frther advantage is added that at the beginning f the evapratin the film temperatre is relatively lw and nly at the end it assmes higher vales after the main amnt f the sbstances with the lwer biling pint is distilled ff.

26 -25- Cmparisn Between Thin-Layer and Circlatin Vaprizer On the basis f these reslts it is nt difficlt t carry t a cmparisn between a cntining thin-layer distillatin and an evapratin in a circlatin vaprizer. A special advantage f the thinlayer vaprizer with respect t the carefl treatment f a temperatresensitive sbstance mixtre is the fact that the final cncentratin xf, as well as the highest temperatre, is reached nly at the exit frm the vaprizer, while in the circlatin vaprizer the biling dôwn always takes place at the cncentratin xf. Besides, the accm latin f lwer-biling sbstance in the mixtre vapr is hig",r in the case f thin-layer distillatin than in a nrmal distillatin in the circlatin vaprizer; this is why by sing a thin-layer vaprizer as distilling apparats fr a rectifying clmn, a saving may be made in the height f the clmn. Add t this the fact that the time f stay, becase f the spreading f the liqid t & thin film, is cnsiderably less than in the circlatin vaprizer. Cmparative figres with respect t this have already been pblished2). In speeds p t 1 rev./min. and ver, sed in practice, the heat-transfer nmbers kl are relatively high, cmpared t the crrespnding vales in the circlatin vaprizer. Example f Calclatir_ It is intended t decmpse in a thin-layer vaprizer at atmspheric pressre F = 4 Ml/h f a benzene/tlene mixtre with an &nflx cncentratin f xf 2 Ml-% benzene in sch a manner that the discharge F still cntains xf _^: 1 Ml-% benzene. It is assmed that the mixtre flws in at biling temperatre. Of what magnitde mst the effective evapratin height.be if satrated steam

27 -26- f t e 12 C is sed as heating medim and if, at a diameter f the -D vaprizer f d =.3 m the nmber f revltins n f the stirring blades can be chasen s high that an average heat transfer nmber f k = 1 L kcal/m 2 h C is reached? Hw large wld the inflx qantity have t be if the vaprizer reqired fr the abve cnditins is t be sed als fr the distillatin f a benzene-tlene mixtre with an inflw cncentratin f x F = 5 Ml--% benzene at therwise the same cnditins? Hw large is in bth cases the mixtre-vapr cncentratin at the exit frm the vprizer and hw d the cncentratins and temperatres change in the last-named case alng the evapratin wall? Fr the determinatin f the evapratin height L Eqatin (12) can be sed, since the mlar evapratin heats f benzene and tlene d nt differ greatly frm ne anther and the change in the mlar evapratin heat f the mixtre with the cncentratin in the cncentratin range nder cnsideratin can, therefre, be disregarded. First f all, the qantitative relatin m= F /F mst be determined which is given, - - accrding t Eqatin (14), by the inflx and discharge cncentratin. Its graphic analysis is shwn in Fig. 1, where the 1/(x Dg - x F ) crve, calclated with the aid f the eqilibrim crve, and the integral crve fnd frm same by graphic integratin, are pltted. Fr x F ' 2 Ml-% we get in accrdance t Eqatin (14) x F ln -in x F- 1 dx F , frm it7».49; xd3 - xf fr x F 5 Ml-% we find that -1", =.1142.

28 -27- Fig. 1. Graphic determinatin f the calclatin crve fr the determinatin f the qantitative relatin frm the inflx and discharge cncentratin. Benzene-tlene mixtre, pressre f 76 mm mercry, cncentratin '-.anse 1 Ml-%L xf :^ 5 Ml-% benzene. Fig. 11. Graphic determinatin f the integral crve fr ascertaining the dimensins f the vaprizer. Benzene-tlene mixtre, pressre f 76 mm mercry, cncentratin range 1 Ml-%Ç xf :^-5 Ml-% benzene, heating-steam temperatre 12C. Eqatin (18b) nw permits the calclatin f the mixtre-vapr cncentratin xd at the exit. Fr xf = 2 Ml-% we get xd = 2.6, fr xf = 5 Ml-%, n the ther hand xd = 55.2 Ml-%. The 1/(xDg - xf) 1/A crve, ascertained analgsly t Fig. 4 by means f eqilibrim crve, biling-pint crve and heating-steam temperatre, and the integral crve btained frm it by graphical integratin, are pltted in Fig. 11. Frm the integral crve we read f the vale f.417^1 ^ fr C xf = 2 Ml-% A vapr cncentratin f xd = 29.6 Ml-% reqires a mlar evap- ratin heat f r= 781 kcal/ml and a vapr cncentratin f xd Ml-% ne f r z 767 kcal/ml. The difference ths amnts t nly 2%. Accrding t Eqatin (12) we can ths calclate a strctral height f L ln.49 1 '.3 ' -r.417 =.995 m= 1 m

29 -28- Fr an inflx cncentratin f xf =-- 5 Ml=-% we read ff frm Fig. 11 the integral vale.125 ^l/^. By retaining the same evapratin measrements and ther cnditins the inflences f F mst nw amnt, accrding t Eqatin (12), t: F_ ln 'iî 1 = 2.92 Ml/h Reprts in literatrel) cnfirm the fact that fr the thrghpt amnts and evapratin perfrmances chsen in the example, thin-layer vaprizers with the abve-calclated dimensins may be sed. Fig. 12. Mixtre-vapr cncentrai-in xd in dependence n the liqid cncentratin xf, in any desired crss sectin f the vaprizer. Benzene-tlene mixtre, pressre f 769 mm mercry, cncentratin range 1 Ml-% ` xf :^ 5 Ml-%. In Fig. 12 the mixtre-vapr cncentratin xd is pltted ver the liqid cncentratin xf in the interval xf = 1 Ml-% xf xf = 5 Ml-%. Fr this cncentratin range the relative vlatility ( f the mixtre benzene-tlene is almst cnstant (it amnts n an average t 2.4); fr this reasn it was pssible t se fr the calclatin f xd Eqatin (32). At the pint xf :7- xf!),.,xd assmes the eqilibrim vapr cntent belnging t xf in cnfrmance t the als-pltted eqilibrim crve. Fr xf - xf Eqatin (32) prdces the same nmerical vale as Eqatin (18b); lgically, this had t be the case. With the relatins (31) and (32) we btain the change in the liqid cncentratin xf and f the vapr cncentratin xd in the vapr ncles

30 -29- a lng the evapratin wall. These are shwn in Fig. 13, in which is pltted als the crse f the liqid temperatre tf, accrding t the biling-pint crve in the cnsidered cncentratin range. The dependence xf = f(1) can als be determined in part graphically and in part mathematically by sing Eqatin (23b). This is shwn here fr the pint xf = 3 ml-%: Fr this cncentratin the integral vale f 1.24 is read ff frm Fig. 1. With m.1142 we get frm Eqatin (23b): 1.24=1n L , cz t^ d r cq_ =. 316 m The same nmerical vale reslted frm the mathematical evalatin with the aid f Eqatin (31). Fig. 13. Cncentratins and temperatres in the vaprizer. Benzene-tlene mixtre, pressre f 76 mm mercry. xf, xd X Dg tf t`d liqid cncentratin in the film, cncentratin in the vapr ncles, eqilibrim vapr cncentratin with respect t xf biling temperatre f liqid, temperatre f the mixtre vapr in the vapr ncles. Fr the sake f cmpleteness, the phase-eqilibrim cncentratin xdg f the vapr escaping n the srface f the liqid, belnging t X F is als pltted in Fig. 13. Assming that the mixtre-vapr temperatre td is given by the dew temperatre fr the mixtre-vapr cncentratin xd, then the crve td in Fig. 13 shws the change in the mixtre-vapr temperatre in the

31 -3- the vapr ncles alng the evapratin wall. The difference between it and the temperatre f the liqid tf amnts n an average t 3 C. Frm the fact that in mst cases ccrring in practice, the cncentratin difference between liqid-inflx cncentratin and liqid-discharge cncentratin is smaller than in this nmerical example, and ths als the difference ^' - tf? the cnclsin may be drawn that the effect f a pssibly sperimpsed rectificatin may be disregarded in the evalatin. Fig. 14. Dependence f the vapr-exit cncentratin xd arkdl f the discharge cncentratin xf n the inflx cncentratin xf fr varis qantitative relatins m. Benzene-tlene mixtre, pressre f 769 mm mercry. The liqid discharge and liqid exit cncentratins reslting, by maintaining certain qantitative relatins, at varying liqid-inflw cncentratins, are shwn in Fig. 14, which is analgs t Fig. 3, fr the mixtre benzene-tlene in the inflw-cncentratin range ±' xf 1 5 Ml-%. Fr a few qantitative relatins Fig. 15, which ahs been arranged accrding t Fig. 5, prdces the integral vales, reqired fr the evalatin f Eqatin (12), fr the cncentratin interval 18 Ml-% `-^ xf ^= 5 Ml-% f the benzene-tlene mixtre at a distillatin pressre f 76 mm mercry and fr a heating-steam. temperatre f 12 C. Hw the nmber f trays saved by sing a thin-layer vaprizer as distilling apparats fr the separatin f a tw - cmpnent mixtre can be ascertained with the aid f the data which served as the basis fr the abve nmerical example fr the determinatin f the dimensins f a thin-layer vaprizer. In Fig. 12 the cncentratin xd f the

32 -31-- mixtre vapr is pltted fr this example abve the cncentratin x E biling liqid in the interval 1 Ml-% z x E Ë5 Ml-%. The f the cntent f benzene in the vapr is xp 55.2 Ml-% at xf = 5 Ml-% inflw cncentratin and x discharge cncentratin can be reached F als with a separating clmn fr which the slpe tgc f the separating straight line is characterized, accrding t Fig. 16, by the vale x x D - -tgcr F F 1 x F x F D yr.) (38) Fig. 15. Dependence f the difference J - J n the inflw cncentratin x F fr different qantitative relatins le. Benzene-tleine mixtre, pressre 76 mm mercry. Heating-steam temperatre 12 C. Fig. 16. Graphic methd fr cnsidering the separating effect by sing a thin-layer vaprizer as distillatin apparats in the determinatin f the nmber f plates in a separating clmn. Bensene-tlene mixtre, pressre f 76 mm mercry; cncentratin range 1 Ml-% xf 5 Ml-% benzene. In Fig. 16 the end pints 1 and 2 then give the crrelatin f the eqilibrim cncentratins n the theretically-wrking separating plates and the pints 1' and 2' the crrelatin f the cncentratins f liqid and vapr in a hrizntal crss sectin f the clmn nder a tray 6). Fr the chsen example the nmber f the theretical trays saved therefre amnts t n -= 2. The calclated thin-layer vaprizer, cnseq- -t ently, accmplishes as mch as a distillatin installatin and tw

33 -32- theretical trays f a separating clmn in which the Ml relatinship f liqid and vapr is determined by the vale 1/(1 - m). Fr cmparisn the mixtre-vapr cncentratin has als been pltted in Fig. 16 ver the liqid cncentratin in the thin-layer vaprizer; the cncentratin vales f vapr and liqid alltted t ne anther were taken frm Fig. 12. Smmary T begin with, a relatin is derived which makes it pssible t calclate in advance a thin-layer vaprizer fr the distillative separatin f a tw-cmpnent mixtre with almst cncentratin-independent mlar evapratin heat in the interested cncentratin range, if the average heat-transfer nmber fr the evapratin is knwn and if the heating-srface lead alng the evapratin wall may be cnsidered as practically cnstant. A frther relatin serves fr the determinatin f the qantitative relatin between liqid-discharge and liqidinflx amnt by which, at a knwn liqid-inflw cncentratin the exit cncentratins f mixtre-vapr and f the residal liqid are fixed. In additin, eqatins are set p which permit calclatin f the change in the liqid cncentratin and the vapr cncentratin alng the evapratin wall. A rgh calclatin f the pressre cnditins in the revlving liqid film enables s t draw cnclsins n the kind f evapratin. Graphic r mathematical methds f sltin are given fr all relatinships. The advantages f the thin-layer distillatin, as cmpared t the distillatin in the circlatin vaprizer are pinted t. A nmerical example, finally, illstrates the practical applicatin f the derived eqatins.

34 4-33- Bibliôgraphy 1) W. Haschild, this pblicatin, 25, 573/74 (1953). 2) R. Schneider, this pblicatin, 27, 257/51;(1955). 3) E. Kirschbam: Destillier- nd Rektifiziertechnik, 2. Afl. p. 75/77. Berlin-G'*ttingen-Heidelberg ) J.H. Perry: Chemical Engineers' Handbk, 3. Afl. p New Yrk, Trnt, and Lndn ) E.L. Brg, R.L. Prvst and C.V. Bawn, Chem. Engng. Prgr. 51, 273 (1955). 6) E. Kirschbam, Anm. 3, p. 1.