Analysis of the zone connecting consecutive sectors indistillation columns by the Ponchon-Savarit method
Analysis of the zone connecting consecutive sectors indistillation columns by the Ponchon-Savarit method
University of Alicante Department of Chemical Engineering
A. Marcilla*, M.D. Serrano and J.A. Reyes-Labarta.Dpto. Ingeniería Química, Universidad de Alicante, Apdo. 99, Alicante 03080, Spain.
Telf. (34) 965 903867 Fax (34) 965 903826. e-mail: [email protected]
References
McCabe-Thiele [1] and Ponchon-Savarit [2] methods are two classical graphical methods for the design of binary distillation columns very useful for didactical purposes and forpreliminary calculations. Nevertheless, their description in the literature is not complete and not all the cases are analysed.Aprevious paper [4] dealt with McCabe-Thiele and thiswork focuses on the Ponchon-Savarit method.Aconsistent analysis of what may happen when in the zone connecting consecutive sectors in the column (ZCCS) is presented forany feed condition, together with the different possibilities to extract products or to add or remove heat.
Systematic analysis of the changes of sector
[1] McCabe, W.L, Thiele, W.E. Ind. Eng. Chem. 1925, 17, 605.[2 Ponchon, M. Tech. Modern, 1921, 13, 20. Savarit, R. Artset Métiers, 1922, 3, 65.
]
[3] Ledanois, J.M.; Olivera-Fuentes, C. Ind. Eng. Chem.Process Des. Dev. 1984, 23, 1-6.[4] Marcilla, A.; Serrano, M.D.; Reyes-Labarta, J.A. Ind. Eng.Chem. Res. 2011. (Under review)
Figure 1. Ponchon-Savarit H,h-y,x diagram and streamsat the side stream stage for a generalized feed: a) FPapproach; b) considering the sector of change.
IPk
�k+1
Vk,0
Vk+1,1
Lk,NTk
LGFk
Lk+1,0
IPk+1
Vk,NTk
VGFk
�k
c
�k
Lk+1,1
GFk
GFk
Lk+1,0
Vk,0
Vk+1,1
Lk,NTk
b)
VGFk
LGFk
GFk
V =Vk+1,1 k,0Lk,NTk
a)
Vk+1,2 Lk+1,1=Lk+1,0
k,NTk
k+1,1
k+1,1
k,NTk
k+1,2
�k+1
Vk,0, Vk+1,1
FP
Lk,NTk
LGFk
, Lk+1,0
Vk,NTk
VGFk
�k
Lk+1,1
GFk
Vk+1,2
Lk+1,2
LGFk
Lk,NTk
Lk+1,0
Vk,0
VGFk
Vk+1,1
MFk
Lk+1,0
Vk,0
Vk+1,1
Lk,NTk
Vk,NTkLk,NTk-1
Lk+1,1Vk+1,2
MF = Vk GFk
Vk,0
Vk+1,1
Lk,NTk
Vk,NTk Lk,NTk-1
Lk+1,1Vk+1,2
L =GFk
Lk+1,0V =Vk+1,1 k,0
Lk,NTk
Vk,NTk Lk,NTk-1
Lk+1,1Vk+1,2
= Lk+1,0
L =GFk MFk
Lk+1,0
Lk,NTk
Vk,NTk Lk,NTk-1
Lk+1,1Vk+1,2
V =Vk+1,1 k,0
V =GFk MFk
Vk,0
Vk+1,1
Vk,NTkLk,NTk-1
Lk+1,1Vk+1,2
Lk,NTk= Lk+1,0
Vk,0
Vk+1,1
Lk,NTk
Lk+1,0
EFk
Vk,0
Vk+1,1
Lk,NTk
Lk+1,0
EFk
a)
b)
c)
d)
e)
f)
g)
h)
i) Not applicable
Not applicableNot applicable
Not applicableNot applicable
Not applicable
Not applicable
Not applicable
LGFk
VGFk
LGFk
VGFk
1. Scheme of the ZCCS 2. V = VGFk k+1,1 3. L = LGFk k,NTk 4. V = V and L = LGFk k+1,1 GFk k,NTk
MFk
Lk+1,0
Vk,0
Vk+1,1
Lk,NTk>MFk
Vk,NTkLk,NTk-1
Lk+1,1Vk+1,2
GFkLMFk
Lk+1,0
Vk,0
Vk+1,1
Lk,NTk>MFk
GFkV
VGFk
LGFk
VGFk
LGFk
�k
c
�k+1
�k
FP IPk
IPk+1
V ,VGFk k,NTk
Vk,NTk-1
Vk,0
L , L , LGFk k+1,0 k,NTk
Vk+1,1
�k+1
Lk+1,1
LGFk
FP
IPk+1
Vk+1,2
Lk+1,2
Lk,NTkLk+1,0
�k
c
�k+1
�k
IPk
V , V , VGFk k,0 k+1,1
Vk,NTkGFk
Vk,0
Vk+1,1
FP
Lk,NTk
LGFk
Lk+1,0
IPk+1
Vk,NTk
VGFk
�k
c
�k
Lk+1,1
IPk
�k+1
�k
�k
cFP
IPk
IPk+1
�k+1
�k
�k
c
FPIPk
IPk+1
�k+1
�k
�k
c
FP
IPk
IPk+1
Vk,NTk
Lk,NTk
V , V , VGFk k,0 k+1,1
Lk+1,0
LGFk
Vk,NTk-1
V , VGFk k,NTk
Vk,0Vk+1,1
Vk,NTk
LGFk
Lk+1,0
Lk,NTk
k+1,1V
VGFk
Lk+1,1
�k+1
�k
�k
c
IPk+1
IPk
FP
VGFk
GF ,Lk GFk
Vk,NTk
Lk+1,0
Lk,NTk
V , Vk,0 k+1,1
Lk+1,1
�k+1
�k
�k
c
IPk+1
IPk
FP
GF , L , Lk GFk k+1,1
Vk,NTk
Lk+1,0
Lk,NTk
V , V , VGFk k,0 k+1,1
�k+1
�k
�k
c
IPk+1IPk
FP
Vk,NTk-1
Lk,NTk-1
Lk+1,1
V , VGFk k,NTk
GF , L , L , Lk GFk k,NTk k+1,0
V , Vk,0 k+1,1
�k+1
�k
�k
c
IPk
IPk+1
FP
�k
�k
c
IPk
IPk+1
FP
�k
�k
c
IPk
IPk+1
FP
Vk,NTk
V , V , VGFk k,0 k+1,1
Lk,NTk
VGFk
L , LGFk k+1,1
Lk+1,0
Vk,NTk-1
L , L , LGFk k,NTk k+1,0�k+1 �
k+1
Vk+1,1
Lk+1,1
VGFk
LGFk
zGFk
Vk,NTk
Lk,NTk
Vk,0
Vk+1,1
Lk+1,0
�k+1
�k
�k
c
IPk+1
IPk
FP
VGFk
GF , L , L , Lk GFk k,NTk k+1,0
Vk,NTk-1
Lk,NTk-1
Vk,NTk
V , Vk,0 k+1,1
Lk+1,1
Lk+1,0
IPk+1
IPk
Vk,0Vk+1,1
Vk,NTk
Lk+1,1
Vk+1,2
Lk+1,2
�k+1
�k
�k
c
�k
�k+1
�k
c
IPk+1IPk
Lk+1,1
VGFk
Vk,0
MFk
�k+1
�k
�k
c
FPIPk
IPk+1
�k+1
�k
�k
c
FPIP
k
IPk+1
�k+1
�k
�k
c
FP
IPk
IPk+1
Vk,NTk
L , Lk,NTk k+1,0
V , V , VGFk k,0 k+1,1
LGFk
Vk,NTk-1
GF , V , Vk GFk k,NTk
Vk,0
Vk+1,1
L , L , LGFk k,NTk k+1,0
Vk,NTk
LGFk
k+1,1V
Lk+1,1
Vk,0
Lk,NTk-1
GF ,Vk GFk
L , Lk,NTk k+1,0
Vk,0
xk+1,1
�k+1
�k
�k
c
IPk+1
IPk
FP
Vk,NTk
LGFk
GF , V , V , Vk GFk k,0 k+1,1
L , Lk,NTk k+1,0
FPLGFk
LGFk
Lk,NTk
Lk+1,0
Vk,0
VGFk
Vk+1,1
Lk+1,1
V , V , VGFk k,0 k+1,1
L , L , LGFk k,NTk k+1,0
FP
Lk,NTk Lk+1,0
LGFk
VGFk
Vk+1,1
Vk,0
Lk+1,0 LGFk
Vk,0Vk+1,1
Vk,NTk
VGFk
�k
�k
c
�k+1
�k
�k
c
�k+1
�k
�k
c
�k+1
�k
�k+1
�k
c
�k
�k+1
�k
c
�k
�k+1
�k
c
�k
�k+1
�k
c
�k
�k
c
�k+1
�k
�k
c
�k+1
Lk,NTk-1
Vk,NTk-1
Lk,NTk-1
Vk,NTk
Lk,NTk
Lk,NTk
GFk
GFk
GFkGFk
GFk
GFk
GFk
GFk
L , L , LGFk k+1,0 k,NTk
Vk,NTkLk,NTk-1
Lk+1,1Vk+1,2
Vk,NTk Lk,NTk-1
Vk,NTk Lk,NTk-1
Lk+1,1Vk+1,2
Lk+1,1Vk+1,2
When a feed stream is considered (GF ), whatever its physical condition, it is commonly assumed to be introduced to a single tray
(k+1,1 in Fig. 1a) where it mixes with the vapour of the tray below (k+1,2) and with the liquid of the tray above (k,NTk). The streamsleaving this feeding stage (L and V ) are considered to be in equilibrium and the separation between the liquid (L ) and
vapour (V ) portions is considered to have a small influence in the calculations (V =V , L =L ). The feed Gf is aligned with
difference points (DP) and and this line crosses the dew curve in a unique point FP used as the reference for the calculation.
Nevertheless, some authors consider the change of sector DP when the side stream is a partly vaporized feed [3]. To complete
the academic literature dealing with this subject we have generalized equations for the operating lines or DP that define the
change between two consecutive sectors for any feed condition, together with the different possibilities to extract products or
to add or remove heat.According to nomenclature of Figure 2:
k
k+1,1 k+1,1 GFk
GFk k+1,1 k,0 k+1,1 k+1,0, k
k k+1
k
k
� ��
�
C
C
In this work all the streams involved in the connecting sector zones, as well as the corresponding DP, and their characteristics IP
and IP , which define the optimum position for the side stream, are located in the diagrams. The example in Fig. 1b shows the case
where the vapour and liquid portions of the feed stream differ with the streams developed in the column: V joins the vapour
coming from the stage below (V = V + V ), which implies that V is aligned between V and V ; whereas L joins the liquid
coming from the plate immediately above (L = L + L ) so L is aligned between L and L . In this case, neither V nor
L are in equilibrium, so they are located outside the H,h/x curves, as shown in the magnifications presented in Fig.1b specified
ones, since relationships among streams occurring in the changing sector zone are not fulfilled
k
k+1
GFk
k,0 k+1,1 GFk k,0 k+1,1 GFk GFk
k+1,0 k,NTk GFk k+1,0 k,NTk GFk k,0
k+1,0
This detailed analysis shows that, whensolving a case of a design calculationproducts can only be extracted from liquidor vapour streams that actually exist in thecolumn, and heat extractions or additionscan also be done to existing streams, if not
. Any other consideration leads toincoherent design predictions sincerelationships among streams occurring inthe ZCCS are not fulfilled.
the specifications of the column must beupdated
From the study of different examples wecan state that the result obtained by usingthe ZCCS Ponchon-Savarit methodand the FP approach may be nearly thesame, though depending on theequilibrium of the particular systemanalysed and other variables. However thepresented procedure provides a clearanalysis of what is happening at thecolumn, and allows being aware of the typeof approximation normally carried out, thusfacilitating the comprehension of themethod, that otherwise could bemisunderstood or difficult to be explained.
strict
Differences between the classical and ZCCS analysis
A systematic analysis of the different possible situations is presented in Figure 3. This analysis does not only show the relationshipsoccurring among the ZCCS but also between them and the rest of streams at the previous or subsequent stages.The streamsdeveloped in the rectification column can coincide with one of the vapour (V ) or liquid (L ) portions generated from the
generalized feed and then be coincident with one of both streams defining the ZCCS (i.e. V or L ), as shown in column 2 and 3
of the figure. Otherwise, the equilibrium streams developed can differ from those originated from the side stream and lie inside theZCCS, which should only be used once during the tray calculations (column 4).
GFk GFk
k+1,1 k,NTk
1. Scheme of the ZCCS 2. V = VGFk k+1,1 3. L = LGFk k,NTk 4. V = V and L = LGFk k+1,1 GFk k,NTk
Figure 3. . Ponchon-Savarit y-x diagrams for a GF : a) MF >0, 0<q <1; b) MF >0, q <0; c) MF >0, q =0; d) MF >0, q =1; e) MF >0, q >1; f) MF <0, q =0; g) MF <0, q =1; h)
EF <0; i) EF >0. For each one of these GF , different cases are analysed: 1. Scheme of the ZCCS; 2. V =V ; 3. L =L ; 4. V ?V and L ?L .k k GFk k GFk k GFk k GFk k GFk k GFk k GFk
k k k GFk k+1,1 GFk k,NTk GFk k+1,1 GFk k,NTk
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k
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D
LD+ D
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k
s 1
��
k
s 1
(x ,h )D D
(z , )GFS SHF
(x ,h )k+1,i k+1,i
(y ,H )k+1,i k+1,i
(x ,h )D D
(x ,H )D D
R (x ,h )R R
(z )GFS
Figure 2.Generalizedscheme of arectificationcolumn. Enthalpyand compositionof streams havebeen included.
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