Supplementary Material: ANALYSIS OF THE CONNECTING ZONE...
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Latin American Applied Research an International Journal of Chemical Engineering. 2014, vol. 44, 307-312 (Accepted: March 17, 2014). - S1/S3 - Supplementary Material: ANALYSIS OF THE CONNECTING ZONE BETWEEN CONSECUTIVE SECTIONS IN DISTILLATION COLUMNS COVERING MULTIPLE FEEDS, PRODUCTS AND HEAT TRANSFER STAGES J.A. REYES-LABARTA † , M.D. SERRANO and A. MARCILLA †Chemical Engng Department, University of Alicante, Apdo. 99, Alicante 03080, SPAIN. [email protected] Abstract−− A complementary analysis of particu- lar cases where the compositions of the streams de- veloped in the rectification column coincide with one of the vapor (y GFk ) or liquid (x GFk ) portions gener- ated from the G Fk can be found in this supplemen- tary material. Keywords−− Distillation; Side Stream; Process Design; Heat Stages; Lateral Product. I. Systematic analysis of the changes of sector in the McCabe-Thiele Method. Complementary particular cases: y GFk =y k+1,1 or x GFk =x k,NTk In this section, that is complementary to the general analysis done in section 2 of the main text, we will ana- lyze the general situation of a mass feed stream (M GFk >0) for different thermal conditions of the feed stream (q GFk ), but in specific cases where the composi- tions of the vapor (y GFk ) or the liquid (x GFk ) portion gen- erated from the GF k is coincident with one of both streams defining the stage of the change of sector (i.e. y k+1,1 or x k,NTk ). Though these situations only happen by improbable coincidences, they can be interesting to be analyzed due to the relationships occurring among the streams developed in the column. A. Mixture of a liquid and vapor in equilibrium (0 ≤ q GFk ≤ 1) In case the thermal condition of the feed allows the composition of that liquid stream (x k,NTk ) coincide with the x composition corresponding to IP k , or the composi- tion of the first vapor stream ascending from the next sector coincide with the y composition corresponding to IP k+1 , the composition of the feed stream vapor and liq- uid portions match exactly with that of one of the streams present in the column. If the x composition of IP k coincides with that of the liquid falling from the last stage above the feed, then V GFk , V k,0 and V k+1,1 have the same composition and L k+1,0 is in the intercept of OL k+1 with y k+1,1 = y GFk (Fig- ure S.1a). If the y composition (Figure S.1b) of IP k+1 is that co- inciding with the vapor ascending from the tray below, the three liquids L GFk , L k,NTk and L k+1,0 have the same composition and V k,0 is in the intercept of OL k with x k,NTk = x GFk . The construction is obviously equivalent since the two situations represent both ends of the same equilibrium stage. Figure S1. McCabe-Thiele y/x diagrams for a feed stream (M GFk >0) and 0<q GFk <1: a) y GFk =y k+1,1 ; b) x GFk =x k,NTk B. Superheated vapor (q GFk <0) Again, depending on the composition of the vapor feed, two situations can occur that allow y GFk or x GFk match exactly with one of the streams present in the column. According to Figure S2a, if the feed vapor fraction coincides with the composition of the vapor ascending from the first stage of the subsequent sector, all vapor stream compositions generated in the change of sector coincide: y GFk = y k+1,1 = y k,0 . On the other hand, if we accept that the composition of the liquid streams developed in the change of sector stage where identical (Figure S2b), and then the liquid falling from the last tray of the previous sector had the same x composition as the liquid arriving to the first tray of the next sector (x GFk =x k,NTk = x k+1,0 ), then it must be accomplished that the feed vapor composition frac- tion coincides with the vapor ascending from the last stage of sector k: y GFk = y k,NTk . The V GFk joins the vapor coming from the stage below: V k,0 = V k+1,1 + V GFk and the corresponding diagram (Fig. S2b) shows that y k,0 is located between y k+1,1 and y GFk . Figure S2. McCabe-Thiele y/x diagrams for a superheated vapor feed stream (M GFk >0 and q GFk <0): a) y GFk =y k+1,1 ; b) x GFk =x k,NTk
Transcript of Supplementary Material: ANALYSIS OF THE CONNECTING ZONE...
Latin American Applied Research an International Journal of Chemical Engineering. 2014, vol. 44, 307-312 (Accepted: March 17, 2014).
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Supplementary Material: ANALYSIS OF THE CONNECTING ZONE BETWEEN CONSECUTIVE SECTIONS IN DISTILLATION COLUMNS COVERING MULTIPLE
FEEDS, PRODUCTS AND HEAT TRANSFER STAGES
J.A. REYES-LABARTA†, M.D. SERRANO and A. MARCILLA
†Chemical Engng Department, University of Alicante, Apdo. 99, Alicante 03080, SPAIN. [email protected]
Abstract−− A complementary analysis of particu-
lar cases where the compositions of the streams de-veloped in the rectification column coincide with one of the vapor (yGFk) or liquid (xGFk) portions gener-ated from the GFk can be found in this supplemen-tary material.
Keywords−− Distillation; Side Stream; Process Design; Heat Stages; Lateral Product.
I. Systematic analysis of the changes of sector in the McCabe-Thiele Method. Complementary particular
cases: yGFk=yk+1,1 or xGFk=xk,NTk In this section, that is complementary to the general analysis done in section 2 of the main text, we will ana-lyze the general situation of a mass feed stream (MGFk>0) for different thermal conditions of the feed stream (qGFk), but in specific cases where the composi-tions of the vapor (yGFk) or the liquid (xGFk) portion gen-erated from the GFk is coincident with one of both streams defining the stage of the change of sector (i.e. yk+1,1 or xk,NTk). Though these situations only happen by improbable coincidences, they can be interesting to be analyzed due to the relationships occurring among the streams developed in the column. A. Mixture of a liquid and vapor in equilibrium (0 ≤ qGFk ≤ 1) In case the thermal condition of the feed allows the composition of that liquid stream (xk,NTk) coincide with the x composition corresponding to IPk, or the composi-tion of the first vapor stream ascending from the next sector coincide with the y composition corresponding to IPk+1, the composition of the feed stream vapor and liq-uid portions match exactly with that of one of the streams present in the column.
If the x composition of IPk coincides with that of the liquid falling from the last stage above the feed, then VGFk, Vk,0 and Vk+1,1 have the same composition and Lk+1,0 is in the intercept of OLk+1 with yk+1,1 = yGFk (Fig-ure S.1a).
If the y composition (Figure S.1b) of IPk+1 is that co-inciding with the vapor ascending from the tray below, the three liquids LGFk, Lk,NTk and Lk+1,0 have the same composition and Vk,0 is in the intercept of OLk with xk,NTk = xGFk. The construction is obviously equivalent
since the two situations represent both ends of the same equilibrium stage.
Figure S1. McCabe-Thiele y/x diagrams for a feed stream
(MGFk>0) and 0<qGFk<1: a) yGFk=yk+1,1; b) xGFk=xk,NTk
B. Superheated vapor (qGFk <0) Again, depending on the composition of the vapor feed, two situations can occur that allow yGFk or xGFk match exactly with one of the streams present in the column.
According to Figure S2a, if the feed vapor fraction coincides with the composition of the vapor ascending from the first stage of the subsequent sector, all vapor stream compositions generated in the change of sector coincide: yGFk= yk+1,1= yk,0.
On the other hand, if we accept that the composition of the liquid streams developed in the change of sector stage where identical (Figure S2b), and then the liquid falling from the last tray of the previous sector had the same x composition as the liquid arriving to the first tray of the next sector (xGFk =xk,NTk = xk+1,0), then it must be accomplished that the feed vapor composition frac-tion coincides with the vapor ascending from the last stage of sector k: yGFk = yk,NTk. The VGFk joins the vapor coming from the stage below: Vk,0 = Vk+1,1 + VGFk and the corresponding diagram (Fig. S2b) shows that yk,0 is located between yk+1,1 and yGFk.
Figure S2. McCabe-Thiele y/x diagrams for a superheated vapor feed stream (MGFk>0 and qGFk<0): a) yGFk=yk+1,1; b)
xGFk=xk,NTk
ANALYSIS OF THE CONNECTING ZONE BETWEEN CONSECUTIVE SECTIONS IN DISTILLATION COLUMNS COVERING MULTIPLE FEEDS, PRODUCTS AND HEAT TRANSFER STAGES
J.A. Reyes-Labarta, M.D. Serrano and A. Marcilla
Latin American Applied Research an International Journal of Chemical Engineering. 2014, vol. 44, 307-312. - S2/S3 -
C. Saturated vapor (qGFk =0) In the case represented in Figure S3a, the composition of the feed vapor fraction coincides with the composi-tion of the vapor ascending from the first stage of the subsequent sector (yGFk= yk+1,1= yk,0), the composition of the liquid Lk+1,1 in equilibrium with Vk+1,1 coincides with the liquid composition in equilibrium with the feed (xGFk=xk+1,1) as expected, and the liquid falling from the last tray of sector k has the same x composition as the liquid arriving to the first tray of the next sector (xk,NTk= xk+1,0). In the case where xGFk=xk,NTk (Figure S3b), as for the superheated vapor feed, it can be observed that: yk,0 is aligned between yk+1,1 and yGFk, yGFk=yk,NTk and the liquid composition in equilibrium with yGFk, together with the composition of the liquid streams generated (Lk,NTk, Lk+1,0), coincide: xk,NTk= xGFk= xk+1,0. Both cases, shown in Figures S3a and S3b lead, obviously, to the same number of steps.
Figure S3. McCabe-Thiele y/x diagrams for a saturated vapor
feed stream (MGFk>0 and qGFk=0): a) yGFk=yk+1,1; b) xGFk=xk,NTk
D. Saturated liquid (qGFk =1) In the case where yGFk = yk+1,1 (Figure S4a) the composi-tions of the all the vapor streams generated are the same: yGFk = yk,0 = yk+1,1, xGFk=xk+1,1 and the relationship between the liquid streams is fulfilled (Lk+1,0 = LGFk + Lk,NTk). For the case represented in Figure S4b when the feed liquid composition xGFk coincides with the liquid composition descending from sector k (xk,NTk), the com-position of the vapor Vk,NTk in equilibrium with Lk,NTk coincides with the vapor composition in equilibrium with the feed (yGFk= yk,NTk) and, analogously to Figure S4a, yk,0= yk+1,1 despite the yGFk being different.
Figure S4. McCabe-Thiele y/x diagrams for a saturated liquid
feed stream (MGFk>0 and qGFk=1): a) yGFk=yk+1,1; b) xGFk=xk,NTk
E. Undercooled liquid (qGFk >1) According to Figure S5a, if we accept that the composi-tion of the vapor streams in the change of sector does not vary (yGFk= yk,0= yk+1,1), then the feed liquid compo-sition (xGFk) must coincide with xk+1,1. The LGFk joins the liquid coming from the stage above: Lk+1,0 = Lk,NTk + LGFk, so xk+1,0 is aligned between xk,NTk and xGFk.
If the composition of the liquid feed coincides with the composition of the liquid descending from the last stage of sector k (xGFk= xk,NTk= xk+1,0), the y composition of IPk+1 coincides with that of the vapor coming up from the first stage below the feed (Figure S5b). In this case yk,0 is aligned with yk+1,1 and yGFk but not in between because yk+1,1 is higher than yk,0 since the undercooled liquid stream addition yields a poorer separation.
Figure S5. McCabe-Thiele y/x diagrams for a undercooled liquid feed stream (MGFk>0 and qGFk>1): a) yGFk=yk+1,1; b)
xGFk=xk,NTk
REMARK A review and extension of the McCabe Thiele method and the completed deduction of the generalized equa-tions can also be found in the Open Academic Reposi-tory of the University of Alicante (RUA) (http://hdl.handle.net/10045/23195). Additionally, a website of self-learning about the McCabe-Thiele method for the design of distillation columns can be consulted: http://iq.ua.es/McCabe-V2/ (http://hdl.handle.net/10045/2283). In the same sense, a website of self-learning about the Ponchon-Savarit method for the design of distillation columns can be consulted at http://iq.ua.es/Ponchon/, as well as a resume of the Extension of the Ponchon and Savarit Method for Designing Ternary Rectification Columns:
- http://hdl.handle.net/10045/14600 - http://hdl.handle.net/10045/14601 - http://hdl.handle.net/10045/10023 - http://hdl.handle.net/10045/42101
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Marcilla, A., Gómez, A., Reyes, J.A. and Olaya, M.M., “New method for quaternary systems liquid-liquid extraction tray to tray design”, Ind. Eng. Chem. Res. 38(8), 3083-3095 (1999).
Reyes, J.A., Gómez, A. and Marcilla, A., “Graphical concepts to orient the Minimum Reflux Ratio Cal-culation on Ternary Mixtures Distillation”, Ind. Eng. Chem. Res., 39, 3912-3919 (2000).
Reyes-Labarta, J.A., Caballero, J.A. and Marcilla, A. “A novel hybrid simulation-optimization approach for
ANALYSIS OF THE CONNECTING ZONE BETWEEN CONSECUTIVE SECTIONS IN DISTILLATION COLUMNS COVERING MULTIPLE FEEDS, PRODUCTS AND HEAT TRANSFER STAGES
J.A. Reyes-Labarta, M.D. Serrano and A. Marcilla
Latin American Applied Research an International Journal of Chemical Engineering. 2014, vol. 44, 307-312. - S3/S3 -
the optimal design of multicomponent distillation columns”. Computer Aided Chemical Engineering, 30, 1257-1261 (2012).
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Reyes-Labarta J.A., Serrano MD, Marcilla A., “Graphi-cal Representation of the Changes of Sector for Particular Cases in the Ponchon Savarit Method”. Open Acad. Repository of the University of Ali-cante, http://hdl.handle.net/10045/42101 (2014b)
