ARTICLE pubs.acs.org/IECR
Shortcut Design of Fully Thermally Coupled Distillation Systems with Postfractionator Lorena E. Ruiz-Marín,† Nelly Ramírez-Corona,‡ Angel Castro-Ag€uero,† and Arturo Jimenez-Gutierrez*,§ †
Facultad de Ingeniería, Tecnología y Ciencias Basicas, Universidad Autonoma de Tlaxcala, Apizaco, Tlaxcala, 90008, Mexico Departamento de Ingeniería Química, Alimentos y Ambiental, Universidad de las Americas Puebla, Cholula, Puebla, 72810, Mexico § Departamento de Ingeniería Química, Instituto Tecnologico de Celaya, Celaya, Gto. 38010, Mexico ‡
ABSTRACT: A modification to the fully thermally coupled distillation system, or Petlyuk column, in which a postfractionator is added has recently been considered. The modified structure incorporates the postfractionator aiming for a better match in the composition of the interlinking stages of the Petlyuk column. In this paper we present a design method for the modified thermally coupled system with postfractionator. A shortcut method is used to provide the minimum reflux conditions of the system, and the boundary value method is used to complete the design task. The effectiveness of the design method is shown through the application to several case studies. The effect of the postfractionator on the performance of the Petlyuk system is also analyzed.
1. INTRODUCTION Distillation, the most widely used separation process in the chemical industry, requires high energy consumption levels for its operation. Alternative arrangements aiming to improve the energy efficiency of distillation have been recently explored. One option that has been considered with particular interest is the use of thermally coupled distillation systems (TCDS). Originally developed for the separation of ternary systems, TCDS have gained increasing attention in the field.110 The main TCDS structures that have been considered are the sequence with a side rectifier, the system with a side stripper, and the fully thermally coupled distillation system. In particular, the fully thermally coupled structure, or Petlyuk system has gained increasing interest for industrial applications, since it has been shown to provide significant energy savings with respect to the conventional distillation schemes.1113 The energy savings of the Petlyuk system can be attributed to the reduction of the remixing effects of the middle component of the ternary mixture in the prefractionator. To find minimum internal vapor flows in the Petlyuk system, Fidkowski and Krolikowski3 applied Underwood's equation for ternary mixtures, assuming sharp splits. They showed that the optimal minimum reflux ratio in the prefractionatior was obtained when Underwood’s equation is solved simultaneously for all active roots. Analytical equations for the estimation of minimum reflux ratios of the main column were also reported. A shortcut procedure to evaluate minimum vapor flows in a side-stream stripper configuration was developed by Glinos and Malone.2 The complex column was rearranged into two simple columns, and it was shown that the interconnecting flows could be represented by an equivalent feed stream with a superheated thermal condition. Analytical expressions for sharp splits were reported. This shortcut procedure can be extended to multicomponent mixtures. Carlberg and Westerberg14,15 developed Underwood's equation for the side-stream stripper, side-stream rectifier, and Petlyuk configurations. Underwood’s method was extended for nonsharp r 2011 American Chemical Society
Figure 1. Subsystems of the FTCP column.
columns to cover the entire range of split fractions of the middle component both in the prefractionator and in the main column, and regions of minimum reflux were found as a function of such splits. Petlyuk’s main column was analyzed considering the net feed flow and its thermal quality. Thermally coupled systems and conventional schemes were compared using T-Q diagrams, and they found that the Petlyuk system has a first law advantage (low Received: October 6, 2010 Accepted: April 1, 2011 Revised: March 24, 2011 Published: April 01, 2011 6287
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Table 1. DOF of the FTCP System
utility requirements) but a second law disadvantage (large temperature range of operation). Reflux ratios above the minimum values were not considered. Several authors10,1618 have used Underwood’s equations to compare energy requirements of Petlyuk arrangements with other coupled and noncoupled distillation systems at minimum reflux conditions. Shortcut methods have been proposed for the design of Petlyuk and divided-wall (or Kaibel) columns,6,19,20 which can be used to quickly evaluate the applicability of a Peltyuk system for a given separation problem.10 Alternative structures to the Petlyuk column have been developed by changing or eliminating interconnection flows.18,21 For a Petlyuk column, the mismatch between the feed stream and feed tray composition, and between the interlinking streams and interlinking trays compositions are the main reasons for the reduction of its thermodynamic efficiency.22 The composition differences at the interlinking trays for a Kaibel column have also been studied for quaternary systems.23 A new fully thermally coupled distillation column with postfractionator (FTCP) has been recently proposed by Kim.24 The main purpose of the postfractionator is to solve the mismatch in composition for the interlinking trays of the Petlyuk column, therefore raising its thermodynamic efficiency. From the procedure by Kim,24 Petlyuk and FTCP designs were made using first Fenske’s equation to calculate the minimum number of stages in each section, and then using twice that value to design a practical column. The interlinking trays between the prefractionactor and the main column are selected so that the compositions match as close as possible. The postfractionator is taken from the middle section of the main column, which has a high composition of intermediate component. The objective of this work is to develop a shortcut design method for the FTCP distillation system. The shortcut method uses Underwood's equation to calculate the minimum reflux of each FTCP section, and the number of ideal stages of the main column are estimated with a stage-by-stage procedure. An analysis of degrees of freedom for the system is shown first, followed by the description and application of the design method. Final steps with a validation test and a sensitivity analysis are carried out.
2. ANALYSIS OF DEGREES OF FREEDOM To obtain the degrees of freedom (DOF) for the FTCP system, a similar analysis as the one used by Chavez et al.25 for the Petlyuk system was carried out. The FTCP structure can be divided into three subsystems, the prefractionator, the main column, and the postfrationator, each one constituted by basic elements (stages, condenser and reboiler), as depicted in Figure 1. The degrees of freedom of each subsystem are calculated by adding the DOF for its basic elements, and then subtracting (Cþ2) DOF for each redundant stream. Finally, the DOF for the FTCP system is obtained by adding the DOF for each subsystem and then subtracting the DOF of the corresponding interlinking streams.
Figure 2. Sections of the FTCP system for the design procedure.
Table 1 shows a summary of the DOF for each section of the FTCP. The DOF of section I in Figure 1 (prefractionator) are the same as those obtained by Chavez et al.25 for the Petlyuk's prefractionator, since they have the same structure. Figure 1 section II has 2M þ 4C þ 20 DOF, which represent 2(C þ 3) additional DOF with respect to the original Petlyuk main column. The two additional feeds at the interlinking stages with postfractionator and the flow rates of side streams of the interlinking stages account for such additional DOF. Finally, the overall DOF for the FTCP structure are 2(N þ M þ J) þ C þ 19. DOF were estimated considering that heat transfer can occur in each stage (feed, interlinking sidestream), condenser, condenser splitter and reboiler.
3. DESIGN METHODOLOGY The FTCP system can be divided into seven sections (Figure 2). The prefractionator is identified as section I. The main column is composed of sections II to VI, and includes four interlinking stages, condenser, and reboiler. Section VII corresponds to the postfrationator. 3.1. Design of the Prefractionator (Section I). The first step to design section I is to ensure that 2N þ 3C þ 8 DOF are specified. Pressure and heat transfer of each stage must be known, which accounts for 2N DOF. There are three feed streams that Inf could be specified (F, Lsup 1 , V1 ), which represent 3C þ 6 DOF. sup Inf Feedstreams L1 and V1 are not known when section I is designed because these streams depend on the design of the main column. A virtual condenser and a virtual reboiler can be considered to take 3C þ 4 DOF, so that only the feedstream F must be specified. The recoveries of the light component (rA) and heavy component (rC) in the overhead product are specified to take the remaining DOF. Section I can then be treated as a conventional column with a virtual condenser and a virtual reboiler. The product distillate of the virtual condenser is the difference sup (balance) of D1 = Vsup 1 L1 , and the product of the virtual reboiler inf inf 1 is given by B = L1 V1 . The interlinking flows can be represented 6288
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postfractionator. sup
V7 ¼ S1
V7inf ¼ S2
Figure 3. Postfractionator system: (a) postfractionator, (b) upper section, (c) lower section.
by equivalent feedstreams (D1 and B1) with superheated and subcooled thermal condition, as in Glinos and Malone.2 The design of section I as a conventional column is then straightforward. For a ternary mixture (A,B,C), the recoveries of A and C are specified. The minimum reflux ratio is determined using Underwoods procedure6,19 taking the middle component (B) as a distributed product. 3.2. Design of the Main Column and Postfractionator (Sections IIVII). The main column of the FTCP arrangement is divided into five sections (IIVI, Figure 2), and each of these sections must operate above minimum flow rate conditions. Minimum vapor flow rates for complex column arrangements such as the main column of FTCP can be determined from extensions of Underwood's equation.26,11 Equations 14 estimate the minimum flow rate required for each section of the main column. The section with the highest minimum flow rate will be the controlling section, and will provide the minimum flow rate for the main column. Ri DxDi ¼ II i ¼ 1 Ri φ 3
V2min
V3min ¼
∑
3
∑ i¼1
ð1Þ
Ri ðDxDi D1 x1Di Þ Ri φIII
Ri ðDxDi D1 x1Di þ D7 x7Di Þ ¼ Ri φIV i¼1 3
V4min
V5min ¼
∑
3
∑ i¼1
Ri ðDxDi D1 x1Di
þ D7 x7Di V
Ri φ
þ B7 x7Bi Þ
R x1
3
i Si ∑ VII i ¼ 1 Ri φsup
ð5Þ
R x2
3
∑ i SiVII i ¼ 1 Ri φinf
ð6Þ
At this point, the minimum vapor flow rates for each section of the FTCP system could be determined if all the values of φ were known. However, the interlinking feed stage of sections III and IV is the same as that for the upper section of the postfractionator; these sections therefore must have the same minimum vapor flow rate and therefore the same absorption factor (φIII = φVII sup). A similar analysis can be done with the interlinking feed stage between sections IV and V and the lower section of the postfractionator. Section IV should be a simultaneous rectifying and stripping section; based on this observation, the structure could be rearranged as shown in Figure 4, where section IV is reduced to a cascade of stages. Since it is necessary to specify the flow rate and composition of interconnection streams for this cascade, a total reflux operation can be assumed as a first approximation (L4 = V4) to simplify the design problem. The modified structure (Figure 4b) is more convenient for the estimation of the minimum flow rates of sections IIVII. Notice that section I remains unchanged after the rearrangement. It should also be noticed that the minimum flow rate in section IV is not calculated because the flow rates of sections VII (upper and lower) are set equal to each other, using a feasible value that meets the mass balance and internal flow rates equations. Underwood's equations for the modified structure are given by eqs 712. Each equation estimates the minimum reflux ratio for each individual section. R2min ¼
3
Rx
i Di 1 ∑ R φII i i¼1
where
φII is determined from equation
ð2Þ
R3min
R2min ¼
L2min D sup
Ri x1D L1 ð7Þ II ¼ 1 þ D1 R φ i i¼1 3
∑
" # 3 R ðDx D1 x1 Þ 1 i Di 1 Di ¼ sup þD D ðL1 þ DÞ i ¼ 1 Ri φIII
∑
sup
ð3Þ
where
R3min ¼
L3min sup L1 þ D
φIII is determined from equation
ð4Þ
"
One must analyze the minimum flow rate conditions in section VII, the postfractionator of the system. Figure 3 shows how the postfractionator can be divided into two additional sections; the upper section can be viewed as a stripping section, and the lower section as a rectifying section. The sidestream flow rate, S, is equivalent to the sum of bottoms (S1) and distillate (S2) flow rates. Equations 5 and 6 estimate the minimum flow rates for the upper and lower sections of the
R3min
1 ¼ sup ðL1 þ DÞ where
Rx
sup
Ri ðDxDi D1 x1Di Þ þ D1 D Ri φIII i¼1 3
∑
R3min ¼
sup L3min sup L1 þ D 3
φIII is determined from equation 6289
3
i 4i ¼0 ∑ R φIII i¼1 i
Ry
ð8Þ
#
sup
i 4i ∑ III ¼ 1 i ¼ 1 Ri φ
ð9Þ
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Figure 4. Thermally coupled distillation system with postfractionator: (a) initial structure, (b) modified structure.
R7inf
min
¼
Ri x2Si 1 VIIinf i ¼ 1 Ri φ
sup
3
∑
where R7inf
φVII is determined from equation
R7inf
min
¼
Ri x2Si 1 VIIinf i ¼ 1 Ri φ
R yinf
i 4i ∑ R φVIIinf i¼1 i
∑
Ri x2Si V 1 i ¼ 1 Ri φ 3
∑
L7inf min S2
¼ 1 ð10Þ sup
3
where R7inf
φVII is determined from equation
R5min ¼
3
¼
min
3
R xinf
¼
min
i 4i ∑ VIIinf i ¼ 1 Ri φ
L7inf min S2
¼ 0 ð11Þ
sup
where R5min ¼
φV is determined from equation
3
R x1
L5min S2 Linf
i Bi ¼ 1 11 ∑ B R φV i¼1 i
ð12Þ
The section with the highest minimum reflux flow rate will be the controlling section of the main column. Therefore, the values for minimum reflux obtained with eqs 712 must be compared in the top of the main column, colpost
Rmin ¼ 8 sup > L2min =D > > < ðR ðD þ Lsup Þ þ Lsup þ Lsup Þ=D 3min 1 1 4 max sup sup sup sup sup sup ðR7inf min ðD þ L1 þ L4 þ S V1 V4 Þ þ L1 þ L4 þ SÞ=D > > > sup sup sup sup sup inf : ðR5min ðD þ Lsup þ L þ S V V Þ þ L þ L 1 4 1 4 1 4 þ S L4 Þ=D
ð13Þ It is important to notice that minimum reflux ratios of all sections cannot be found unless the flows and compositions of the side streams as well as the feeds are known. Therefore, flow rates and compositions of interlinking stages to section IV are specified as a first approximation, and then subjected to an optimization procedure. Section IV, which operates at total reflux, becomes unnecessary when the values of interlinking flow
rates tend to zero, in which case the FTCP is reduced to the original Petlyuk system. On the other hand, interlinking stages will change depending on the specified interlinking compositions. It is clear that such values influence the heat duty and the design of the FTCP system. After the minimum reflux is found, the number of trays of the main column can be calculated by using the boundary value design method27 (let us keep in mind that the trays for section I are obtained from FenskeUnderwoodGilliland equations, and Section IV through Fenske’s equation assuming operation at total reflux conditions; all other sections belong to the main column). Product compositions at the extremes of the column are specified. The location of each feed is a dependent variable, and it is found by the intersection of the profiles of the corresponding sections. For ternary mixtures, the boundary value design method can be conveniently developed on a triangular diagram. The number of equilibrium stages and liquid compositions can be obtained from mass balance and equilibrium calculations. A special case of the equilibrium calculation, eq 14, based on constant relative volatilities can be used for ideal mixtures. Ri xi ð14Þ yi ¼ Rj xj
∑
A useful estimation of the composition of interlinking streams can be developed as follows. Liquid composition curves begin in the distillate and bottom compositions of both sections (D-S1 and S2-B) of the main column. For a multicomponent mixture, the feedstream line can be represented by eq 15, and the operating line by eq 16. ! q xDi ð15Þ yi ¼ xi q1 q1 yi ¼ 6290
R xDi xi þ Rþ1 Rþ1
ð16Þ
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Table 4. Product Composition for Each Feed Stream feed component
F1
F2
F3
XAD
0.99
0.98
0.91
XBS
0.92
0.96
0.99
XCB
0.99
0.98
0.91
Table 5. Design Parameters Obtained Using the Shortcut Method M1 design variable
Figure 5. Rectifying and stripping curves and interlinking stages location for the D-S1 section.
F1
F2
M2 F3
F1
F2
M3 F3
F1
F2
F3
Nt
14
14
13
12
12
11
13
12
Nf
7
7
6
6
6
5
6
6
6
Mt MID1
41 7
34 5
39 3
31 3
33 2
35 2
32 13
31 10
30 5
MID4
14
12
9
6
7
5
20
18
11
MS
17
14
14
7
8
7
23
21
20
MIB1
30
25
27
20
23
27
27
26
27
MIB4
24
20
26
12
15
24
25
24
26
Jt
3
6
9
2
3
4
5
6
10
R
2.06 3.22 11.02 1.99 3.23 11.53 1.66 2.32 8.02
12
Llsup V1inf
10.88 11.28 10.88 6.25 6.25 5.90 5.88 5.88 5.54 31.76 30.74 27.26 25.80 23.54 17.74 27.79 27.07 25.55
L4sup
4.53 4.53 4.53 4.53 4.53 4.53 4.53 4.53 4.53
V4inf
4.53 4.53 4.53 4.53 4.53 4.53 4.53 4.53 4.53
Figure 6. Rectifying and stripping curves and interlinking stages location for the S1-B section.
Table 2. Ternary Mixtures Taken for the Case Studies mixture ID
components A/B/C
ESI
pressure (kPa)
M1
n-pentane/n-hexane/n-heptane
=1
202.65
M2 M3
n-butane/n-hexane/n-heptane n-pentane/n-hexane/n-octane
>1
