ANALYSIS OF THE ZONE CONNECTING CONSECUTIVE SECTORS IN GENERALIZED DISTILLATION COLUMNS BY USING THE PONCHON-SAVARIT METHOD

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1 Latn Amercan Appled Research 46: (2016) ANALYSIS OF THE ZONE ONNETING ONSEUTIVE SETORS IN GENERALIZED DISTILLATION OLUMNS BY USING THE PONHON-SAVARIT METHOD A. MARILLA, M.D. SERRANO and J.A. REYES-LABARTA hemcal Engng. Department, Unversty of Alcante, Apdo. 99, Alcante 03080, SPAIN. Abstract Ponchon-Savart s a classcal graphcal method for the desgn of bnary dstllaton columns. Ths method s stll wdely used, manly wth ddactcal purposes, though t s also vald for prelmnary calculatons. Nevertheless, no complete descrpton has been found n boos and stuatons such as dfferent thermal feed condtons, multple feeds, possbltes to extract by-products or to add or remove heat, are not always consdered. In ths wor we provde, a systematc analyss of the Ponchon-Savart method by developng generalzed equatons for the operatng lnes or dfference ponts, as well as a consstent analyss of what may happen n the zone between two consecutve trays of the correspondng sectors separated by a lateral stream of feed, product, or a heat removal or addton. The graphcal nterpretaton of all stuatons shown allows a clarfyng vew of the dfferent possbltes n the rectfyng column and completes the exstng lterature about ths method. Keywords Dstllaton; Sde Stream; Process Desgn; Heat Stages; Lateral Product. I. INTRODUTION Many references dealng wth the desgn of bnary dstllaton columns, descrbe the Ponchon-Savart and the Mcabe-Thele methods. Equatons for the operatng lnes (OL) and dfference ponts (DP) are always developed for columns wth sngle or multple feed addtons but product extractons and heat addtons or wthdrawals are not always consdered. Furthermore, when a feed stream s consdered, whatever ts physcal condton, t s commonly assumed to be ntroduced to a sngle tray where t perfectly mxes wth the vapor of the tray below and wth the lqud of the tray above. The streams leavng ths feedng stage are consdered to be n equlbrum, as n any other theoretcal stage. Ths separaton between the lqud and vapor portons s consdered to have a small nfluence n the calculatons of the number of trays. onsequently, the equaton that defnes the change between two consecutve sectors n a column s not usually developed and the zone of such change of sector s not represented. Nevertheless, some authors have ponted out the necessty of ncorporatng the consderatons of those partly vapor feeds to the graphcal methods to develop generalzed equatons. Although t s not the general trend, some references consder the zone between consecutve sectors for a two phase feed ntroducton to a dstllaton column (Ledanos and Olvera Fuentes, 1984; Wanat, 2012). Addtonally some references can be found n the lterature dealng wth the advantages of usng the Ponchon-Savart method and ts geometrcal concepts n partcular cases, where molar latent heat depends on composton and heat of mxng s consderable, such as: multcomponent dstllaton, reactve dstllaton, quaternary lqud-lqud extracton, mnmum reflux calculatons and nternal heat ntegrated dstllaton columns (HID) (Reyes-Labarta et al., 2012; Lee et al., 2000; Marclla et al., 1997; 1999; Reyes et al., 2000; Ho et al., 2010, Waabayash and Hasebe, 2013). In prevous wors (Reyes-Labarta et al., 2014a), generalzed equatons for OL were systematcally developed and analyzed for sectors and zones connectng consecutve sectors due to feeds, products or heat removals or addtons on the Mcabe-Thele method, usng a Generalzed Feed Operatng Lne (GFOL) approach. In ths paper, equatons for OL and DP are systematcally developed for the Ponchon-Savart method wth dfferent sde streams (feeds, products and/or heat removals or addtons). Ths wor wdens the academc lterature dealng wth ths subject. All the streams nvolved n the stages correspondng to the zones connectng consecutve sectors, as well as the correspondng DP, are unambguously located n the enthalpycomposton dagrams. II. GENERALISED EQUATIONS A generalsed dstllaton column has a total condenser and several sectors, whch are adabatc zones wthout lateral feed or products streams. Two consecutve sectors and +1, are separated by a generalsed feed (GF ) and we consder that only a sngle GF can be added or removed between two consecutve steps. The GF can be ether a mass stream or an enthalpy stream. In the frst case, we consder M GF the mass flow rate, z GF the molar fracton, and H GF the specfc enthalpy of such stream. In the case where there s not a net mass flow n or out the column, we consder that E GF s the heat flow added or removed to the column by an ntermedate heat exchanger. onsderng all the possbltes, as a summary the generalzed n or out feed consdered and ther character- 127

2 Latn Amercan Appled Research 46: (2016) stcs are shown n Table 1. In the Ponchon-Savart method varaton of GF wth composton s consdered: GF=H F-h F where H=f(y) and h=f(x). On the other hand, V +1,+1 s the vapour flow of composton y +1,+1 that leaves tray +l of secton +1, n equlbrum wth L +1,+1. L +1, s the lqud flow of composton x +1, that leaves tray of secton +1, D s the dstllate flow of composton x D, R s the resdue flow of composton x R, and L D s the lqud reflux to the column. A sector has NT trays and the streams have the subscrpt correspondng to the tray they leave. In each sector we use the subscrpt 0 for the stream enterng ts frst and last trays. A. Operatve lne (OL) and Dfference Pont (DP) n a sector of a generalzed column As n the Mcabe-Thele method, the equatons correspondng to the OL of a general rectfcaton column are deduced n order to establsh a relatonshp between the composton of a vapour stream ascendng from a stage and that of the lqud descendng from the upper stage. A total mass balance between tray of secton +1 and the condenser s done: V L D M (1) 1, 1 1, 1 s1 where +1 represents the dfference between the vapour and lqud mass flows crossng between two consecutve trays n sector +1 beng a fcttous net flow, so called dfference pont (DP) n the Ponchon-Savart method, that s used for solvng the calculaton of the number of stages. For each adabatc sector of a column these net mass and enthalpy flows are constant. A mass balance over the more volatle component results n: V 1, 1 y 1, 1 D x D L 1, s1 M x 1, z z 1 1 (2) The composton z +1 of the fcttous stream +1 s gven by the followng expresson, whch allows obtanng the abscse of +1 n the enthalpy-composton dagram: Table 1. omplaton of the dfferent cases presented for a generalzed feed stream (GF) and ts characterstcs. Name and flow rates Thermal condton Molar fracton V GF [molar fracton] L GF [molar fracton] q GF > 1 z GF Feed q GF = 1 x GF (1-qGF) M GF q GF M GF M GF>0 0<q GF<1 z GF [y MGF HGF GF] equlbrum [x GF] equlbrum q GF = 0 y GF q GF < 0 z GF Product (1-qGF) M M GF<0 q GF = 0 y GF GF [y GF] equlbrum 0 MGF HGF Product M GF<0 MGF hgf Heat add. M GF=0 E GF>0 Heat rem. M GF=0 E GF<0 q GF = 1 x GF 0 -- x GF -- y GF E GF/ GF [y GF=x GF] E GF/ GF [y GF] q GF M GF [x GF] equlbrum -E GF/ GF [x GF] -E GF/ GF [x GF=y GF] z 1 D xd M z s1 1 (3) An enthalpy balance provdes: V1, 1 H 1, 1 L 1, h 1, (4) D h Q M H E M D D s1 s1 1 1 where QD s the heat removed n the condenser. The net enthalpy flow n sector +1 s represented by +1M +1. Obvously, M +1 (ordnate of +1 n the enthalpycomposton dagram) s gven by: M 1 DhD QD M H E (5) 1 S1 S1 Ths DP (z +1, M +1) s the common pont of all the operatve lnes of sector +1. Usng Eq. (1) and (2): L / 1, V 1, 1 y 1, 1 z 1 x 1, z 1. (6) And wth Eq. (1) and (4): L 1, / V 1, 1 H 1, 1 M 1 h 1, M 1 (7) Equaton (7) corresponds to the operatve lne (OL) of sector +1 of a rectfcaton column that allows the calculaton of the subsequent stages belongng to that sector. In the specfc enthalpy-composton dagram they are straght lnes that pass through the ponts (x +1,, h +1,) representng saturated lqud streams that leave stage of sector +1, (y +1,+1, H +1,+1) representng saturated vapour streams that leave next stage +l of sector +l; and (z +1, M +1) representng the fcttous stream +1, net mass flow of sector +1 of the column. The above defntons have been deduced generally and they can be appled to any stage n any sector of the column. Locaton of +1 n the enthalpy-concentraton plot s defned by M +1 and z +1 (Eq. 3 and 5). In sector +1, the calculaton algorthm for the stages alternates the use of the OL wth the equlbrum calculatons. Nevertheless, consecutve sectors must be connected n the column and t must be specfed where to use each one of the correspondng DP and how to calculate the vapour stream leavng the frst stage of each new sector when that of the lqud leavng the last stage of the upper sector s nown, n order to obtan the mnmum number of stages for the specfed separaton. III. DIFFERENE POINT (DP) OF A GENERALISED FEED GFK FOR ONNETING TWO ONSEUTIVE SETORS IN A OLUMN The analyss of the change of sector n most references of the Ponchon-Savart method s lmted to the locaton of the pont that we have named as FP (Fg. 1). Nevertheless, such analyss though approxmate s unrealstc and does not allow clear understandng of the dfferent operatons and processes that may be nvolved whenever a generalsed feed s ntroduced nto a dstllaton column. The analyss we wll present could be vewed as unnecessarly complex for applcatons and the results expected from the Ponchon-Savart method. We beleve however, that t has a fundamental ddactcal value and defntely helps the understandng of the processes that may be nvolved n any gven generalzed 128

3 A. MARILLA, M. D. SERRANO, J. A. REYES-LABARTA feed operaton, and the awareness of the type of approxmaton normally carred out. In other way, the method could be msunderstood or dffcult to be explaned. The locaton of such an FP pont s not suffcent as a reference for all the possble feed condtons and operatons. Instead, the value must be calculated of the dfference between the vapour stream ascendng from the frst stage of the sector below the feed and the lqud stream descendng from the last stage of the sector above the feed. The zone connectng consecutve sectors (that we wll name ZS herenafter) must be consdered. Lqud and vapour portons L GF and V GF generated by the GF ntroducton are equlbrum streams for mass feed (as shown, for example, n Fg. 1a where GF =MF ) or products, or streams wth the same compostons for heat addtons or extractons. In the enthalpy-composton dagram (e.g. Fg. 1a), two sectors and +1 (wth ther correspondng and +1 DPs) are connected by the ZS whch doman s defned by the ordnate and abscse (z, M ) of ts characterstc DP ( ) and two compostons over the saturated lqud curve IP and IP +1 that are determned by the sde stream (.e. the GF ) that separates both consecutve sectors. The ZS, for any sde stream, has a DP defned as: V L NT V VGF L NT V (8) 1,1,,0, GF V 1,1 L, NT V 1,1 L 1,1 LGF LGF (9) 1 where L,NT corresponds the lqud flow that leaves tray NT (the last one) of secton. Accordng to Eq. 8 and 9, s the graphcal ntersecton pont of two straght lnes: V and GF 1 L. GF The abscse and ordnate of are gven by the correspondng enthalpy and mass balances: M M VGF HGF / LGF hgf M / (10) 1 1 z z VGF ygf / LGF xgf z / (11) 1 1 The must be used only once n the step-by-step calculaton, wth the meanng that the feed has entered the column n just one stage, and the new lqud and vapour streams must be correspondngly updated, as n the case of the Mcabe-Thele constructon, to obtan the mnmum number of stages. The ntersectons of the two lnes V and GF 1 L, whch have been used to defne and to lmt the ZS, wth the saturated lqud GF curve also determne the characterstc ponts IP and IP +1 of ths ZS (Fg. 1). For a mass feed stream V GF s the vapour generated from the generalzed feed (GF ) n equlbrum wth L GF. In the case of a heat sde stream, the dfference s that the vapour and lqud (V GF, L GF) have the same composton x GF =y GF and are not n equlbrum. wth the satu- The ntersecton of the OL rated lqud curve provdes IP : ygf zgf xip zgf H GF equvalent to : V GF M h M IP Fgure 1. Ponchon-Savart y-x dagrams for a GF: a) MGF>0, 0<qGF<1; b) MGF>0, qgf<0; c) MGF>0, qgf=0. d) MGF>0, qgf=1; e) MGF>0, qgf>1; f) MGF<0, qgf=0. g) MF<0, qgf=1; h) EF<0; ) EF>0. y z x z H M h M GF (12) GF IP GF GF IP and the ntersecton of L wth the saturated GF 1 lqud curve gves IP +1: z z x z M M h M (13) GF 1 IP IP1 1 In the followng sectons we wll analyse n detal the dfferent possbltes of mass feeds, consderng ther thermal condtons or ther lqud fractons, the removal of a lqud or vapour product as well as the heat addton to a lqud stream or heat removal from a vapour stream n a rectfyng sector,.e.: a sector above the man mass feed. wll be represented for all cases of generalzed feeds and the optmum poston for the sde stream, gven by IP or IP +1, wll be analysed. 129

4 Latn Amercan Appled Research 46: (2016) IV. SYSTEMATI ANALYSIS OF THE HANGES OF SETOR A systematc analyss of the dfferent possble stuatons, accordng to the prevous generalsed equatons, s presented n Fg. 1. The frst column shows the scheme of the ZS together wth all the exstng ntermedate streams. For the case of generalzed mass feed streams (GF), the compostons of the streams developed n the rectfcaton column do not generally match wth any of the vapour (V GF) or lqud (L GF) portons generated from GF (partcular cases when there exts any concdence can be consulted n Reyes-Labarta et al., 2014b). For other types of nput streams, dfferent from mass feeds, t must be consdered that the stream to be removed (when the GF s a mass product) or to be heated or cooled (for the case of heat addton or removal) must actually exst n the column. onsequently, when solvng a partcular case of a desgn calculaton, the specfcatons of the column must be adapted to the already exstng streams. The analyss of all cases presented n ths secton not only shows the relatonshps occurrng among the streams nvolved at the ZS, but also between them and the rest of streams at the prevous or subsequent stages. A. Mass feed Ths s the case most frequently consdered n the lterature. In order to connect two consecutve sectors +1 and separated by a feed, s obtaned. The abscse and ordnate of are gven by the correspondng enthalpy and mass balances (Eq. 10 and 11). Frst column of Fg. 1a-e shows all streams developed n the change of sector n the column for mass feed streams at dfferent thermal condtons. Accordng to Fg. 1a-e, the te-lne y x represents the equlbrum separaton tang place at the feed stream: x GF s the GF GF composton of L GF whch s the lqud n equlbrum wth a vapour V GF of composton y GF The ntersectons of V and GF L wth the bubble-pont curve h=f(x) GF provde IP and IP +1, respectvely, that are the characterstc ponts of the. It can be observed that the covers the ampltude of a te-lne n the equlbrum dagram. Ths must be used only once n the step-bystep calculaton, wth the meanng that the feed has entered the column and the new lqud and vapour streams must be correspondngly updated. Dependng on the feed thermal condton or the lqud fracton of the feed (q GF), fve subcases may be found. Lqud and vapour mxture n equlbrum (0<q GF <1) We wll start wth the case of a feed, that when enterng the column generates a mxture of a lqud L GF and vapour V GF n equlbrum, where the lqud fracton generated (q GF) s comprsed between 0 and 1. Fgure 1a represents the stuaton of such a feed. They show the DPs of sectors and +1 (.e.: and +1) and the. The operatng lne for the change of sector s used to locate of streams coherently: the vapour fracton V GF jons the vapour comng from the stage below (V,0 = V +1,1+V GF), whch mples that V,0 (of composton y,0) s algned between V +1,1 (of composton y +1,1) and V GF (of composton y GF); whereas the feed lqud fracton L GF jons the lqud comng from the plate mmedately above (L +1,0 = L,NT + L GF) whch mples that L +1,0 (x +1,0) s algned between L,NT (x,nt) and L GF (x GF). In ths case, nether of the ntermedate streams V,0 nor L +1,0 (of compostons y,0 and x +1,0) are equlbrum streams, so they are located on the correspondng straght lnes defned outsde the H/y and h/x curves, as shown n magnfcaton of dagram n Fg. 1a, unless such equlbrum enthalpy lnes were straght lnes. Ths analyss of the change of sector s somewhat dfferent from what s presented n some text boos that use the pont FP as reference. Superheated vapour (q GF <0). In the dagram of Fg. 1b, GF s located n the regon over the dew pont curve H=f(y) and consequently, the vapour y GF composton s lower than the composton of the feed (z GF). Snce V GF>M GF, and accordng to Eq. (10), s nearer the equlbrum lne than and +1, whch s unfavourable for the separaton. Note that FP s now out of the nterval defned by IP and IP +1 In ths case, y +1,1<y GF<y,NT. The stuaton of the ntermedate streams s represented analogously to the prevous case of the mxture of lqud and vapour n equlbrum. Nevertheless, as stated before, for the superheated vapour feed t can be observed that V,0 (y,0) s algned between V +1,1 (y +1,1) and V GF (y GF) but L +1,0 (x +1,0) s algned but not between L,NT (x,nt) and L GF (x GF) snce L GF s a negatve stream. Saturated vapour (q GF=0) In ths case M GF=V GF and the vapour composton of the feed z GF s the same as y GF (Fg. 1c). The dagrams of Fg. 1c shows that concdes wth +1, accordng to Eq. (9), because L GF=0. Ths s the only thermal condton for the feed where IP concdes wth the FP pont so any of both approaches gves the same results. The lqud fallng from the last tray of sector has the same composton as the lqud arrvng to the frst tray of the next sector (x,nt= x +1,0). The locaton of the ntermedate streams s represented analogously to the prevous case. It can be observed that the relatonshps among the ntermedate streams are fulflled. Saturated lqud (q GF=1) In Fg. 1d M GF=L GF s a saturated lqud located n the h=f(y) curve, the matches up wth because V GF=0. In ths case the FP pont does not concde wth IP but wth IP +1. The composton of vapour streams V,0 and V +1,1 are the same: y,0=y +1,1. Undercooled lqud (q GF >1) In the dagram of Fg. 1e M GF s an undercooled lqud, thus located under the h=f(y) curve. Snce L GF>M GF and accordng to Eq. (10), s nearer the H/y and h/x curves than and +1, whch s unfavourable for the separaton at the specfc stage of the change of sector. As expected, L +1,0 (x +1,0) s algned between L,NT 130

5 A. MARILLA, M. D. SERRANO, J. A. REYES-LABARTA (x,nt) and L GF (x GF) but the composton of V,0 (y,0) s lower than both of V +1,1 (y +1,1) and of V GF (y GF). B. Mass product hanges of sectors due to saturated vapour and saturated lqud products are analysed n ths secton (Fg. 1f,g). The extracton of a product n the rectfyng secton provoes +1 to be nearer the H/y and h/x curves than, consequently more stages are needed, as compared to the case of a mass feed addton. For mass feeds, t was consdered that the stream to be added could concde or dffer from one of the streams n equlbrum wth the feed (L GF or V GF). In the case of mass products, the sde stream specfcatons must concde wth one of the streams present n the column. Saturated vapour (q GF =0) In Fg. 1f, matches up wth +1 because q GF = 0 and L GF =0. As n the case of a saturated vapour stream feed, IP concdes wth the FP pont. Fgure 1f shows that when a vapour product V GF s extracted from V +1,1 of a column (y GF = y +1,1), the lqud stream compostons of L,NT (x,nt) and L +1,0 (x +1,0) are the same. Any other stuaton s nonsense snce a non-exstng stream can never be extracted. Saturated lqud (q GF =1) In Fg. 1g, concdes wth because q GF=1 and V GF =0. As n the case of a feed, for a saturated lqud feed stream IP +1 and the FP pont are concdent. Fgure 1g shows that the relatonshps among compostons of ntermedate streams are analogously fulflled: x GF= x,nt and y,0=y +1,1 for the only possble case of the extracton of a lqud stream n the ZS where the vapour stream compostons reman nvarable.. Heat removal or addton n an enrchment sector When a heat flow s removed from a vapour V GF of composton y GF causng the correspondng condensaton, the flow enterng the stage above decreases by V GF = EF /, and consequently the lqud flow enterng the stage below ncreases by L GF = -EF / (EF <0 accordng to Table 1), both streams L GF and V GF havng the same composton x GF = y GF. When heat s added to the lqud L GF of composton x GF causes a vaporzaton that mples a lqud flow decrease and the consequent vapour flow ncrease (EF >0 accordng to Table 1). Heat removal from a vapour stream n an enrchment sector Because of the lqud flow ncrease, s nearer the H/y and h/x curves than and +1 s more separated than, as shown n Fg. 1h. The effect of the heat removal n the enrchment secton of a column favours the separaton. The coherent constructon shown n the dagram allows the fulflment of the relatonshp among the streams flowng at the ZS: L +1,0 (x +1,0) s algned between L,NT (x,nt) and L GF (x GF), as shown n the correspondng magnfcaton, and the composton of all vapour streams (V GF, V,0, V +1,1) concde: y GF = y,0 = y +1,1. Fgure 2. Effect of dfferent EGF. Heat addton to a lqud stream n an enrchment sector All the features related to ths case are shown n Fg. 1. The global effect of the heat addton n the rectfyng secton of a column s unfavourable snce the mxture of vapours at the ZS yelds a vapour V,0 rcher n the less volatle component (the composton of V +1,1 (y +1,1) s greater than the composton of V,0 (y,0)). The coherent constructon shown n the dagram allows the fulflment of the relatonshp among the streams: V,0 (y,0) s algned between V +1,1 (y +1,1) and V GF (y GF), as shown n the correspondng magnfcaton, and the composton of all lqud streams (L GF, L +1,0, L,NT) concde. D. zones and use of IP and IP+1 as references for the change of sector. Heat removals or addtons are dfferent to mass streams where the lqud and vapour orgnated from the feed are n equlbrum, whch defnes a doman that always comprses a te-lne (Fg. 1a-g). However, n case of heat streams, the doman can be greater or smaller than the zone correspondng to a te-lne, dependng on the E GF value. Fgure 2 shows an example where, for the case of a heat extracton and a gven te-lne separaton, dfferent E GF are consdered and thus, dfferent szes of the zone are obtaned: smaller as the extracted heat ncreases (E GF> E GF > E GF). Note that for any sde stream, sector domans are contnuous over the saturated lqud curve. For mass extractons or addtons sector zones are also contnuous over the saturated vapour curve. In these cases IP +1 s located at a smaller composton than IP. For heat streams, however, t can be noted that z +1 = z accordng to Eqs. 4, 6, 9-11 and IP +1 s located to the rght of IP +1 zones are overlapped on the saturated vapour curve (Fg. 1h,). Note the dfference between mass feed, on one hand, and mass product and heat streams, on the other, regardng the use of n calculatons. s used n all cases once n the step by step constructon but, contrary to a feed mass streams, where t can be used at any ntermedate pont of ts doman, for mass extracton or for heat extractons or addtons only the OLs of that concde wth one of the correspondng lmts of the doman belongng to sector or +1 can be used. 131

6 Latn Amercan Appled Research 46: (2016) Though n ths wor the graphcal method has been analysed, the generalzed equatons have been mplemented analytcally wth Excel and Vsual Basc for Applcaton macros n a tool that allows the desgn of a bnary column wth ten possble generalzed feed streams, whch has been used to study dfferent examples. From that study we can state that the result obtaned (.e. number of stages) by usng the Ponchon-Savart method wth ths strct analyss may be nearly the same, though dependng on the equlbrum of the partcular system analysed and other varables. However, t provdes a clear analyss of what s happenng at the column, thus facltatng the comprehenson of the method. V. ONLUSIONS In ths wor a closer to realty analyss of what may happen when changng sector n the column, s carred out. We present generalsed equatons for the correspondng OL and DP for the dfferent sectors n a column as well as those for the ZS due to feeds, products or heat removals or addtons. All the streams nvolved n the ZS, as well as the OL, are located n the Ponchon-Savart dagrams. The presented procedure has a fundamental ddactcal value snce t provdes a clear analyss of what s happenng at the column, and allows beng aware of the type of approxmaton normally carred out, thus facltatng the comprehenson of the method, that otherwse could be msunderstood or dffcult to be explaned. OMPPLEMENTARY INFORMATION A webste of self-learnng about the Ponchon-Savart method for the desgn of dstllaton columns can be consulted at as well as a resume of the Extenson of the Ponchon and Savart Method for Desgnng Ternary Rectfcaton olumns ( REFERENES Ho, T.J.,.T. Huang, L.S. Lee and.t. xtended Ponchon-Savart method for graphcally analyzng and desgnng nternally heat-ntegrated dstllaton columns, Ind. Eng. hem. Res., 49, (2010). Ledanos, J.M. and. Olvera-nchon-Savart and Mcabe-Thele methods for dstllaton of Two-Phase Feeds Ind. Eng. hem. Process Des. Dev., 23, 1-6 (1984). Lee, J.W., S. Hauan, K.M. Len and A.W. Westerberg, A graphcal method for desgnng reactve dstllaton columns: I. the Ponchon-Savart method Proc. of the Royal Socety A: Mathematcal, Physcal & Eng. Scences, 456, (2000). Marclla, A., Gómez, A. and Reyes, New method for desgnng dstllaton columns of multcompo- Lat. Am. Appl. Res. 27, (1997). Marclla, A., A. Gómez, J.A. Reyes and M.M. Olaya, New method for quaternary systems lqud-lqud extracton tray to tray desgn Ind. Eng. hem. Res., 38, (1999). Reyes, J.A., A. Gómez and A. Graphcal concepts to orent the Mnmum Reflux Rato alculaton on Ternary Mxtures Dstllaton Ind. Eng. hem. Res., 39, (2000). Reyes-Labarta, J.A., J.A. aballero and A. A novel hybrd smulaton-optmzaton approach for the optmal desgn of multcomponent dstllaton columns,omputer Aded hemcal Engneerng, 30, (2012). Reyes-Labarta, J.A., M.D. Serrano and A. Marclla, Analyss of the onnectng Zone between onsecutve Sectons n Dstllaton olumns overng Multple Feeds, Products and Heat Transfer Stages, Lat. Am. Appl. Res., 44, (2014a). (Sup.materal: and.../10045/23195). Reyes-Labarta, J.A., M.D. Serrano and A. Marclla, Graphcal Representaton of the hanges of Sector for Partcular ases n the Ponchon Savart Method, Open Acad. Repostory of the Unversty of Alcante, (2014b). Waabayash, T. and S. Hasebe, Desgn of heat ntegrated dstllaton column by usng H-xy and T-xy dagrams omp. and hem. Eng., 56, (2013). Wanat, P.., Separaton Process Engneerng. Includes Mass Transfer Analyss, (3 rd ed.), Prentce Hall, Massachusetts (2012). Receved: February 25, Accepted: July 13, Recommended by Subject Edtor: Marcelo Secler. 132